Emerging Technology Report (ETR)
The Structural Design of Ultra-High Performance Concrete
Chair
Benjamin Graybeal*
Secretary
Charles Kennan Crane
Voting Members ACI 239
Sriram R. Aaleti
Mohammed G. Alnaggar
Matthew J. Bandelt
Jean-Philippe Charron
David Conciatori
Rafic El-Helou
Liberato Ferrara
Bradley W. Foust
Philipp Hadl
Heidi Helmink
Commented [vp1]: Membership will be updated on day of first
ballot
James Milligan
John J. Myers
Vic Perry*
Carin L. Roberts-Wollman
Surendra P. Shah
Kay Wille
Theresa M. Ahlborn*
Claus Brix
Eckart R. Buhler
Dominique Corvez
Nicolas Ginouse
Brian H. Green
Katrin Habel
Sub-Committee ACI 239C Members
Mo Li
Luis Felipe Maya Duque
Fatmir Menkulasi
Barzin Mobasher
Cristopher D. Moen
Mohamed Moustafa
Gregory Nault
Ali Semendary
Luca Sorelli
Paul White
*Members, Subcommittee 239-C

SChair, Subcommittee 239-C
Consulting Members
James K. Hicks
Antoine E. Naaman
Larry Rowland
This emerging technology report gives an overview on the Structural Design of Ultra-High
Performance Concrete. It briefly introduces these concretes, their properties and design
principles for their use. It is not intended to provide mandatory design rules, but rather to serve
as a starting point for the structural engineer on understanding design methodologies for this
class of materials.
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Content
1.0 Introduction and Scope
1.1 Introduction
1.2 Scope
1.3 Global UHPC Codes, Standards and Guides
2.0 Notation and Definitions
2.1 Notation
2.2 Definitions
3.0 Material Properties
3.1 Mechanical Properties
3.1.1 Compressive behavior
3.1.2 Tensile behavior
3.1.3 Flexural behvior
3.1.4 Shear behavior
3.1.5 Bond behavior
3.2 Durability Properties
3.2.1 Absorption
3.2.2 Salt-scaling and Freeze/Thaw
3.2.3 Permeability
3.2.4 Acid and Sulphate Resistance
3.2.5 Delayed Ettringite Formation
3.2.6 Leaching and Efflorescence
3.2.7 Abrasion
3.2.8 Alkali-Silica Reaction
3.3 Time Dependent Properties
3.3.1 Creep Coefficient
3.3.2 Shrinkage
3.3.3 Thermal Coefficient of Expansion
3.4 Fire Properties
3.5 Other Properties
3.5.1 Fibre-Matrix interaction
3.5.2 Cyclic Strength and Stiffness Degradation
3.5.3 Dynamic Strength
3.5.4 Fatigue Behavior
3.5.5 Property Gradients
4.0 Strength Design Considerations
4.1 Compression and Tension
4.1.1 Compression
4.1.2 Tension
4.2 Flexure
4.3 Combined Axial and Bending
4.4 Shear and Torsion
4.4.1 Shear
4.4.2 Torsion
5.0 Serviceability and Durability Design Considerations
5.1 Serviceability
5.2 Durability
5.2.1 Durability requirements for Exposure Classes and crack width limitations
in Reinforced Structures
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5.2.2 Crack width control
5.2.3 Durability under Mechanical load
5.2.4 Durability of cracked elements under Chemical load
5.2.5 Durability of cracked elements in a marine environment
5.2.6 Life Cycle Assessment
5.3 Serviceability
5.3.1 Deflection and camber
5.3.2 Crack control
5.3.3 Vibrations
5.3.4 Stress
5.3.5 Fatigue
5.3.6 Time Dependent Effects
5.3.7 Temperature Effects
6.0 Future Research Needs
7.0 References
8.0 Appendices
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ACI 239C – Structural Design of UHPC
1.0
Introduction and Scope – Vic Perry
1.1
Introduction
Ultra-high performance concrete (UHPC) was first introduced into the global construction market
in the 1990s, and has seen steady growth since. This relatively new family of concretes has
improved strength, ductility and durability when compared to normal and high-performance
concretes. In 2015, ACI Committee 239 defined UHPC as concrete that has a specified
compressive strength of at least 150 MPa (22,000 psi) with specified durability, tensile ductility
and toughness requirements; fibers are generally included to achieve specified requirements.
Based on an extensive review of the literature on UHPC globally, this document is a synthesis
of this information by a group of UHPC experts, as listed on the title page. This document is not
a design standard or guide, but does provide a discussion on design methodologies for the
designer. The document also does not provide test methods for the characterization of UHPC
but it does discuss options for obtaining the mechanical properties based on test methods
available. The characterization of the mechanical properties of UHPC is covered in a separate
ETR on the Methods and Materials for UHPC.
This Emerging Technology Report on the structural design of UHPC is organized as a designer
might use it - by first covering material properties and then showing the use of these properties
to design for strength (shear, flexure, and compression), and finally to check for durability and
serviceability. The structural design of UHPC discusses the structural limit state predictions that
apply to members and systems including multiple materials are discussed. The document also
identifies research needs for the development of future documents on UHPC.
1.2
Scope
This document covers UHPC with discrete fibers and elements with and without primary
reinforcing (rebar or prestressing tendons).This document discusses the use of UHPC that is a
cementitious material having a minimum specified strength of 120 MPa, containing discrite
fibers for tensile post-cracking ductility with a minimum specified direct tensile strength of 4.0
MPa. Material constitutive properties and design stresses are discussed as design inputs in
Section 3. The intended outputs are strength and serviceability predictions at structural scale
limit states as presented in Sections 4 and 5, respectively. This ETR integrates national and
international experiences with UHPC and utilizes recent experimental and computational
research to describe a design basis that advances UHPC design and construction.
Structural design considerations for cast-in-place concrete and precast construction methods
are noted. But the document does not cover or develop new test methods or construction
methods. Information on test methods applicable to UHPC has been developed by ASTM and
construction methods applicable to UHPC will be developed by new ACI 239D Sub-Committee
(Materials and Methods of Construction for UHPC). However, this ETR references these
documents and other international standards, guides and research papers.
The ETR references and compares the information from current global codes, standards or
guides published by the following agencies and jurisdictions:
- American Society of Testing and Materials (ASTM, USA)
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- Swiss Institute of Engineers and Architects (SIA, Switzerland)
- French Society of Civil Engineers (AFGC, France)
- Japanese Society of Civil Engineers (JSCE, Japan)
- Standards Australia (SA, Australia)
- Canadian Standards Association (CSA, Canada)
- German Committee on Structural Concrete (GCSC, Germany)
- Spanish Association of Concrete, Scientific-Technical Committee No. 1 (ACHE, Spain)
- Federal Highway Administration (FHWA, USA)
Section 6 of this ETR provides research needs to advance UHPC to full codes and standards
level. Section 7 provides references.
1.3
Global UHPC Codes, Standards and Guides
Since the beginning of the year 2000, global standards organizations, code bodies and
professional user groups have developed guidelines, standards and codes for the materials,
methods of construction and the structural design of UHPC. The following section covers each
of these global documents by briefly highlighting the scope of the document.
1.3.1
American Society of Testing and Materials
In July of 2017, the American Society of Testing and Materials published it first document
specifically for UHPC. The new publication, ASTM C1856/1856M – 17 “Standard Practice for
Fabricating and Testing Specimens of Ultra-High Performance Concrete”, provides procedures
for fabricating and testing specimens in the laboratory and the field, using a representative
sample of UHPC, for the purpose of determining the properties of the material.
The standard practice provides procedures for obtaining compressive strength, flexural strength,
static modulus of elasticity, Poisson’s ratio, creep in compression, length change, resistance to
abrasion, resistance to freezing and thawing and penetration of chloride ions.
This standard practice does not provide direct tensile material properties, which are required to
use the tensile properties of UHPC in structural design. In order to determine direct tensile
properties an inverse analysis would be required to be used in conjunction with the test
procedure for flexural strength.
Prior to the publication of this new ASTM C1865/C1856M, owners and users of UHPC had no
standard method to confirm if the material properties of the supplied material met the specified
properties.
1.3.2
French Standards
In the late 1990’s, the French Society of Civil Engineers (Association Française de Génie Civil
[AFGC]) began the development of a guide on UHPC. The initial guidelines document published
in 2003, was revised and re-issued in 2013. Subsequently in 2016 and 2017, the French
Standards Institute (Association Française de Normalisation [AFNOR]) published 2 French
standards on UHPC, as follows:
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-
NF P 18-710: National addition to Eurocode 2 – Design of concrete structures: specific rules
for Ultra-High Performance Fibre-Reinforced Concrete (UHPFRC) – April 16, 2016.
NF P 18-470: Ultra-High Performance Fibre-Reinforced Concrete (UHPFRC):
specifications, performance, production and conformity – 2017.
The French standard NF P 18-470 provides the rules for the selection of raw materials, testing
methods and QA/QC requirements to determine the fresh and hardened properties of UHPC. It
also provides classifications for different categories of UHPC based on the hardened durability
and strength (compression and direct tensile) properties. The standard specifies 5 categories for
compression ranging from 130 MPa to 250 MPa and 3 categories for direct tension, covering
strain hardening through to strain softening. Additionally, it covers the production (batching,
transporting, casting, consolidation and curing) and methods to validate in-situ hardened
properties.
The French standard NF P 18-710 provides the rules for the structural design of buildings and
civil engineering structures in unreinforced, reinforced and pre-stressed UHPC containing
discrete fibers (UHPFRC). This standard provides the rules and models for compression,
tension and shear analysis and design. The standard provides reliability management, limit
states design and durability design. Also included are methodologies to determine the direct
tensile properties based on flexural prism or plate testing with a detailed inverse analysis.
One of the strengths of the French standard is the extensive work that has been completed in
the area of understanding of fiber orientation due to the handling and placing of UHPC and its
impact on the reliability of the hardened material properties. The standard provides rules for
tensile strength reduction factors based on casting methods, element shape and size.
Additionally, the two French UHPC standards are written to provide continuity between the
constitutive material property behavior and the structural design models.
1.3.3
Swiss Standards
In December 2014, the Swiss Society of Engineers and Architects (SIA) published prSIA 2052:
“UHPC: Material, Design and Construction (Béton fibré ultra-performant [BFUP]: Matériaux,
dimensionnement et exécution)”. The document provides rules for the design of non-reinforced,
reinforced and prestressed structures with UHPC. In addition it provides design methodology
for composite structures of conventional reinforced concrete with UHPC thin bonded overlays.
PrSIA 2015 maybe used for UHPC with a compressive strength of 120 MPa or greater and
containing discrete fibers that provide a minimum of 7.0 MPa in direct tension. Three tensile
strength categories from strain-softening through strain-hardening are permitted. Tensile
material properties are determined using a dog-bone direct tension test or by the use of flexural
tests and an inverse analysis.
Strength design models and rules are provided for compression, flexure and shear. As well
reliability factors are included. A short commentary is provided on fire and fatigue. Also,
annexes are provided that cover material property characterization, QA/QC and test methods.
1.3.4
Australian Standards
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In January 2000 the University of New South Wales under contract by VSL (Australia) published
“Design Guidelines for RPC Prestressed Concrete Beams”. This document is similar in
methodology to guides written in France by the industry and the AFGC in the late 1990’s. The
guidance and recommended design principles followed very closely the French Guidelines
published in 2003. This guideline also included design examples of UHPC prestressed beams.
In 2018, Standards Australia Limited published DR AS 3600 “Concrete Structures” including
Section 16 which covers “Steel Fibre Reinforced Concrete”. The standard provides the
methodology (test methods and reliability factors) for determining the compressive and tensile
properties of FRC, which may be applied to UHPC. Rules are provided to determine the tensile
properties from flexural (prisms with inverse analysis) or direct tension tests from dog-bone
specimens. The standard covers both strain-hardening and strain-softening FRC with and
without reinforcement or prestressing tendons. Design models are provided for compression,
flexure and shear (strut & tie)..
The standard also provides rules for durability (including fire), serviceability and pre-construction
quality testing.
1.3.5 Canadian Standards
The Canadian Standards Association, (CSA), similar to the French standards provides two
separate standards for UHPC - CSA A23.1 Annex U “Materials and Methods of Construction”
and CSA S6 Annex 8 “Structural Design of Bridges with FRC”. Both of the CSA Standards on
UHPC have been approved by the technical committees and will be published in 2019, as nonmandatory Annexes but written in mandatory language.
The standard CSA A23.1, Annex U “Materials and Methods of Construction” covers UHPC
materials as follows:
- 2 categories of compressive strength (120 – 150 MPa & >150MPa),
- 3 categories of tensile strength (strain hardening, strain softening and non-fibre)
- 3 categories for durability
The standard provides rules for pre-blended, partial pre-blended and non-preblended supply
and batching of UHPC. Also, provided are all of the requirements testing to characterize the
material properties, QA/QC, batching, transporting, placing, curing and demoulding.
The standard CSA S6, Annex 8 “Structural Design of Bridges with FRC” covers the following:
- FRC and UHPC for all categories of compressive strength,
- Design models for compression, flexure and shear,
- Reliability and strength reduction factors,
- Methods to determine the direct tensile properties from prism with inverse analysis or direct
tension tests,
- Specific rules for the design of thin bonded bridge deck overlays, waffle deck panels and
UHPC Field Cast Connections.
1.3.6 Japanese Guides
In the late 1990’s VSL (Japan), Taisei Construction and Teiheyo Cement Company commenced
developing UHPC for the Japanese market. In 2006 the Japanese Society of Civil Engineers
(JSCE) published “Recommendations for Design and Construction of Ultra High Strength Fiber
Reinforced Concrete Structures (Draft). JSCE Guidelines for Concrete No. 9”. This document is
similar in methodology to guides in France by the industry and the AFGC in the late 1990’s. The
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guidance and recommended design principles followed very closely the French Guidelines
published in 2003.
1.3.7
German Guides
The German Committee for Structural Concrete, in 2017, has prepared draft guidelines for
UHPC which applies to structures exclusively reinforced with steel fibres, both precast and castin-place, with passive reinforcing bars or prestressing. This new guidelines in based on
European Normes (EN) and the years of UHPC research conducted in Germany under the
German Research Foundation priority funding program “Sustainable Building with UHPC”
[Schmidt et al, 2014 & 2017]. The guide covers raw materials, mix proportioning, quality control,
methods for characterizing the fresh and hardened properties, production, structural design
(tensile strength characterization by 3- point bending notched prism) and design examples. The
guideline includes 3 categories of compressive strength (C130, C150 and C175) and follows EN
requirements for durability. The new German Guidelines for UHPC are expected to be published
by the end of 2018.
1.3.8
Spanish Guide
On November 2015, the Spanish Association of Concrete, Scientific-Technical (ACHE)
Committee No. 1, created a Task Group to develop the first Spanish Guidelines on UHPFRC
[Lopez et al., 2017]. The guideline includes 6 categories of compressive strength (120, 135,
150, 175, 200 and 225 MPa), two categories for tensile strength (strain-hardening and strainsoftening, similar to French Guidelines) and follows EN requirements for durability. The
guidelines will also cover raw material requirements (including maximum size aggregate and
fibre size), workability properties, environmental exposure conditions, placing methods and
geometric considerations. It is anticipated that the Spanish Guidelines for UHPC will be
published by early 2019.
1.3.9
Federal Highway Administration
In 1999, the FHWA became interested in the use of UHPC as a resilient material for building the
highway infrastructure. Early research work led to the publication of 2 important US documents FHWA-HRT-06-103 “Material Property Characterization of Ultra-High Performance Concrete”
and FHWA-HRT-06-115: Structural Behavior of Ultra-High Performance Concrete Prestressed IGirders”.
While the FHWA does not publish codes or standards, it does prepare guidelines (known as
TechNotes) which the industry does rely on for guidance. Additionally, the FHWA staff experts
prepare draft standards of guides for other agencies to adopt.
The FHWA publications are based on a UHPC defined as a cementitious composite material
composed of an optimized gradation of granular constituents, a water-to-cementitious materials
ratio of less than 0.25, and a high percentage of discontinuous internal fiber reinforcement. The
mechanical properties of UHPC include 21.7 ksi (150 MPa) and sustained post-cracking tensile
strength greater than 0.72 ksi (5 MPa).
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In 2013, the FHWA (under the Highways for Life Program) published FHWA-HRT-13-032
“Design Guide for Precast UHPC Waffle Deck Panel Systems including Connections”. The
Guide provides information on general arrangements, Waffle Deck Panel design, UHPC
connections between adjacent panels and the panel to beam.
In 2014, the FHWA published FHWA-HRT-14-084 “Design and Construction of Field-Cast
UHPC Connections”. This 36 page guide provides an overview of UHPC and the utilization of
the material for precast connections, examples of projects completed, examples of typical
connection details, structural design rules for UHPC connections, construction (batching,
casting and curing) methodology suggestions and recommended testing requirements.
Currently the FHWA is drafting a UHPC specification for T1 Committee of AASHTO on the
Structural design of bridges utilizing UHPC. It is anticipated that this document will be available
in 2019.
Over the period since 1999, the FHWA has published numerous documents on UHPC, including
a State-of-the-Art Report, FHWA-HRT-13-060 in 2013. All of the FHWA documents can
downloaded at https://www.fhwa.dot.gov/.
2.0 Notation and Definitions - Vic Perry
The following section covers the notations and definitions used in this ETR for the structural
design of UHPC.
2.1 Notation
To be completed as sections are finalized.
A – Absorption
C – Corrosion rate
Deff – Diffussion Effective
Ec – Young’s Modulus of Elasticity
f’c – compressive strength
Kair – Permeability in Air
KG - a factor calculated by comparing their flexural strength to that of a molded specimen with
cast specimen to determine the global impact of random fiber orientation
KL – a factor calculated by comparing their flexural strength to that of a molded specimen with
cast specimen to determine the local impact of random fiber orientation
Kwater – Permeability in Water
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leff – Effective fiber length
St -Shrinkage at a given time
ν – Poisson’s Ratio
vf – Volume fraction of fibers contained in the mixture
ε’c – Strain at peak stress
σ – Axial stress (MPa)
φ – Porosity in water
2.2 Definitions
For the purpose of the ETR on the structural design of UHPC the following definitions apply:
Batch — a volume of materials placed into a mixer and uniformly blended, then discharged.
Characteristic property — the value obtained from tests, which corresponds to a statistical 95%
probability of meeting or exceeding.
Creep coefficient – the ratio of the load-induced strain per unit of stress at any time difference
after the immediate loading compared to the instantaneous load-induced strain.
Ductility — the ability to deform without failure after cracking or yielding.
Commented [vp2]: ACI Terminology: batch — (1) quantity of
material mixed at one time or in one continuous process; (2) to
weigh or volumetrically measure and introduce into the mixer the
ingredients for a quantity of material.
Commented [vp3]: ACI Terminology: creep — time-dependent
deformation due to sustained load.
Commented [vp4]: ACI Terminology: ductility — the ability of a
material to undergo large permanent deformation without rupture.
Failure — a state in which rupture, severe distortion or displacement, or loss of strength has
occurred as a result of load-carrying capacity of a component or connection having been
exceeded.
Fiber — a discrete, elongated element that imparts tensile and crack resistant properties.
Commented [vp5]: If already in ACI Terminology, then delete
Commented [vp6]: The ACI Terminology definition is “fiber — a
slender and elongated solid material, generally with a length at
least 100 times its diameter”. This definition doesn’t work for
UHPC. For example UHPC typically uses a fiber of 0.2 x 12 mm
which has an aspect ratio of 60, which is less than the minimum in
the ACI definition.
Material identity card — a document that provides the details of the components, mixing
instructions, curing instructions and properties of a specified UHPC mixture.
Matrix — that portion of the UHPC not including fibers or reinforcing elements.
Particle packing — the process where the voids between larger sized constituent materials are
filled with smaller sized constituent materials to the maximum, providing the minimum void
space in the matrix.
Modified particle packing — adjusting the particle packing to improve one or more fresh
or hardened properties of the matrix by over filling the voids between the larger sized
materials.
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Commented [vp7]: ACI Terminology: matrix — (1) the cement
paste in which the fine aggregate particles in mortar are embedded;
(2) the mortar in which the coarse aggregate particles in concrete
are embedded; (3) the resin or binders that hold the fibers in
fiberreinforced polymer together, transfer load to the fibers, and
protect them against environmental attack and damage due to
handling
Post setting – the time following setting when an element has sufficient strength to be self
supporting.
Pre-blend — a mixed combination of the powder mineral components, to which water,
admixtures and fibers are added at the concrete mixer.
Partial pre-blend — a pre-blend where not all of the powder mineral components are
pre-blended.
Specified property — the value required in the contract specifications.
Strain — deformation.
Commented [vp8]: ACI Terminology: strain — the change in
length per unit of length, in a linear dimension of a body
Tension hardening – the ability to carry increasing load beyond the first crack.
Tension softening - the ability to carry a reduced load which is less than the first cracking load.
Thermal treatment — a process of heating the UHPC to an elevated temperature, above normal
heat of hydration, in the presence of high relative humidity, holding the elevated temperature for
a period of time to complete the hydration process, and then slowly cooling to ambient
temperature.
Ultra-high performance concrete (UHPC) — a cementitious composite material, normally
containing fibers, with enhanced strength, durability, and ductility compared to high performance
concretes.
Note: UHPC normally contains fibers for post-cracking ductility, have a specified compressive
strength of at least 120 MPa by 28 days, and are formulated with a modified multi-scale particle
packing of inorganic materials of normally less than 0.6 mm diameter (larger sizes may be
used).
Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) – sometimes used to denote
UHPC containing fibers.
Working Time — the period of time which the mixture maintains a flow within the specified flow
limits and without negative impact on the in-situ hardened properties.
To be completed as sections are finalized.
3.0 Material Properties
The mechanical properties of UHPC are required as inputs for the structural design of elements
produced from UHPC. Due to the low permeability and ultra-high performance of UHPC, many
of the standard test methods currently used to characterize the mechanical properties of
conventional or high performance concrete do not provide accurate results for UHPC, unless
there are test modifications.
In July 2017, ASTM published a new standard “ASTM C1856/C1856M-2017 Standard Practice
for Fabricating and Testing Specimens of UHPC” to address the need for standardized
characterization of UHPC. This new standard practice references current ASTM Standard test
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methods and states the required exceptions or changes applicable to UHPC so that the results
are representative of the mechanical properties of UHPC.
A comparison of a range of thetypical values of several mechanical properties of undamaged
state (unloaded) UHPC, high performance concrete (HPC) and normal concrete (NC) shown in
Table 3.1.
Table 3.1: Typical range of property values for undamaged state UHPC, HPC and NC
Property
UHPC
HPC
Young’s Modulus, Ecm (GPa)
Characteristic Compressive Strength, f ck (MPa)
Mean Compressive Strength, fck (MPa)
Characteristic tensile limit of elasticity, f ctk (MPa)
Mean tensile limit of elasticity, fctk (MPa)
Characteristic post-cracking strength, fctfk (MPa)
Mean post-cracking strength, fctfk
Linear coefficient of thermal expansion (µm/m/oC)
Poisson’s ratio
Freeze/thaw (ASTM C666) RDM (%)
Permeability (Coulombs Passing)
Permeability in air, Kair (m2)
Permeability in water Kwater (m/s)
Diffusion effective Deff (m2/s)
Absorption, A (kg/m2/s1/2)
Corrosion rate, C (µm/yr)
Porosity in water, φ (%)
[[Charron & Desmettre]
45 – 65
120 – 200
130 – 230
4.0 -10.0
5.0 – 12.0
5.0 – 10.0
6.0 – 12.0 MPa
11
0.21
100
18-500
< 10-15
< 5 x 10-14
10-14
0.0003
< 0.01
1-6
50 – 100
60 – 120
0.5 – 3.0
1.0 – 5.0
0
0
11
Y
90
500 -1500
10-17
10-13
10-12 - 10-13
0.003 – 0.01
0.25
8 - 12
NC
15 – 50
20 – 60
0 – 1.0
0.5 – 2.0
0
0
11
Z
70
1000+
10-15 – 10-16
10-11 – 10-12
10-11 – 10-12
0.01 – 0.03
1.20
12 - 16
3.1 Mechanical Properties
3.1.1 Compressive behavior - Rafic
The compression constitutive behavior of UHPC materials vary from conventional and
high performance concretes. The material is assumed to have discrete steel fiber reinforcement
capable of bridging splitting cracks that develop during compression loading and provide a postpeak ductile behavior. Section 3.1.1.1 describes the typical stress-strain behavior of UHPC and
Section 3.1.1.2 covers the existing test methods to obtain different key properties of
compression behavior, including strength, f’c, modulus of elasticity, Ec, Poisson’s ratio, ν.
3.1.1.1 Uniaxial Stress-Strain Trends in Compression - Rafic
Sample uniaxial compressive stress-strain behavior of thermally-treated UHPC
containing 2% fibers by volume (vf = 2%) with typical post-peak crack pattern of the
compression cylinder are shown in Figure 3.1.1.1. The average trend is plotted as a thicker solid
line and a thin line for the individual results, calculated from ranges of axial stresses at one
value of axial strain. Tests performed by El-Helou (2016) on a commercially available UHPC
consisted of loading UHPC cylinders, having 3 in (76 mm) diameter and a height of 6 in (152
mm), at a constant circumferential expansion rate. The results show an initial linearly elastic
behavior with stiffness equal to modulus of elasticity, Ec. The stiffness begins to degrade as
splitting cracks start to form resulting in a non-linear behavior (Note: In a narrow region close to
the peak strength) reaching the ultimate compressive strength of the material f’c. As the material
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Commented [vp9]: LF: Can we specify if any method was used
to reduce friction between specimen and platens?
is strained beyond the strain at peak stress, ε’c, the fibers provide confinement and improve the
ductility of the compression response. For instance, the results of Figure 3.1.1.1 show an
average stress equal to 50% of the material ultimate capacity at post-peak axial strain of 0.006
(El-Helou, 2016). The full compressive stress-strain behavior of a commercially available UHPC
with 0%, 2%, and 4% can be found El-Helou (2016). The stress-strain trends, obtained for
strains up to the strain at peak loading, for 5 commercially available UHPCs are available in
Haber et al. (2018).
Figure 3.1.1.1 Sample uniaxial compressive stress-strain response of a commercially available
UHPC with 2% fibers (d is the cylinder diameter, h is the height, and θ is the out of plane angle
at cylinder top end) [El-Helou 2016, Ref XX].
Compression tests were conducted using a 220 kip (55 Ton) testing machine operated under
closed-loop control. The 2"x 4" cylinders tested were ground to a flatness level of 1/1000” by
using grinding equipment. This is an important factor in uniformly distributing the load over the
whole specimen. Although the top platen swivels to enable a uniaxial load application, it is
preferable to have parallel ends for each specimen to minimize the eccentricity of the applied
load.
A special fixture was developed to attach the two LVDTs (Linear Variable Differential
Transformer) to measure the axial strain in the specimen. A constant gage length of 2.5 inches
was used for all specimens. This apparatus is shown in Figure 3.1.1.2. The instrumentation
includes a LVDT to measure change in length of the specimen, a radial strain gage to measure
radial deformation, and an ultrasonic pulse velocity transducers. The fixture permits the axial
and circumferential deformations to be measured as the specimen undergoes the post peak
response and cracking results in significant dilatation of the sample. A chain type fixture is used
to measure the circumferential strain in the specimen. The test was controlled by LVDTs which
measures the axial strain, and the extensometer which measures the circumferential strain.
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Using a combination of these two control parameters in sequence, it was possible to capture the
post peak response. By achieving a well-controlled post peak behavior, the specimens do not
experience an explosive type of failure mechanism, and the true stress-strain response is
measured.
Figure 3.1.1.2 set up of the compression stress strain test to measure axial and circumferential
strain in UHPC specimens
Figure 3.1.1.3, compares the compressive response of the control UHPC with a fiber reinforced
UHPC mixture. The composition of the UHPC is based on a quaternary OPC-fly ash-micro
silica-limestone binder mixture and designated as (F17.5M7.5L5) representing a 30%
replacement of Portland cement. The control mixtures reached an axial strain of 0.0032 at an
ultimate load of 22.2 ksi, while with the addition of 1% steel fibers, the strain at peak load
increased to 0.0041. Fiber addition is best demonstrated in the response under the transverse
direction which shows a significantly higher dilatation and a higher strength and ductility as
compared to the control samples. [ ADOT Report]
Examination of the strain softening region indicates that the plain UHPC specimens behave in a
brittle manner while much ductility is observed in the fiber reinforced samples. This is typical of
high strength materials when the strength of the interface increases to the level of aggregates
and mortar, therefore the cracks have a lower likelihood of following along the tortuous path of
interfaces. This behavior is negated in the presence of fibers which provide a tortuous path for
the growth of cracks and increase the toughness by the bridging mechanisms. A larger area
under the stress-strain diagram indicates a more ductile failure mode. It has also been
observed that stiffness as measured by the slope of the stress strain response in the initial
linear range is higher for the fiber reinforced samples.
Note, that even when the sample is loaded to strain levels as much as 0.006, the average stress
carrying capacity in the post peak region is a minimum of 6 ksi and an average value of 12.5 ksi.
This level of ductility must be addressed in design equations as compressive strength is
maintained for a large range of applied strain.
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Figure 3.1.1.3 set up of the compression stress strain test to measure axial and circumferential
strain in UHPC specimens
Compressive strength gain with age was measured by Ahlborn et. al (2012) for non-thermally
treated specimens and specimens thermally-treated at various ages. Thermally-treated
specimens gained strength at the same rate as a non-thermally treated until the thermal
treatment was applied at which the compressive strength “locked-in” at 30 ksi. Non-thermally
treated specimens continued to gain strength beyond 28 days, eventually reaching 25 to 27 ksi.
Graybeal (2005) conducted similar tests and found that non-thermally treated specimens
approached a strength of 22 ksi. The primary difference was observed to be due to the time at
at which specimens were demolded. Graybeal demolded specimens at 24 hours while Ahlborn
et. al demolded specimens at 3 days.
3.1.1.2 Tests to Obtain Compression Properties - Vic
3.1.1.2.1 Strength - Vic
The common standard test method for the compressive strength of concrete is ASTM C39;
however due to the high strength of UHPC this method requires modifications to provide
consistent reliable results and facilitate being conducted at most concreting test laboratories
[Perry, 2015]. ASTM C39 can be used to determine the compressive strength of UHPC made
from 75 mm x 150 mm cylinders with modifications to the end preparation of the specimen and
the load rate increased to reduce the required time to complete the test [Graybeal, 2015]. Refer
to the ASTM C1856/C1856M-2017, “Standard Practice for Fabricating and Testing Specimens
of Ultra-High Performance Concrete” to determine the compressive strength of UHPC.
In certain countries such as Denmark and the Czech Republic, cubes have also been used to
obtain the compressive strength of UHPC. Research conducted by Ahlborn et. al, (TRB paper),
and Graybeal & Davis (Ref 7.3.1.1.3) has shown that cubes or cylinders maybe used as long as
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Commented [MOU10]: Dual units will be needed throughout
Commented [vp11]: This will be done once the text is close to
final
the contact surfaces of the test specimen are flat and parallel and the compression machine has
sufficient capacity to conduct the test.
Other jurisdictions using a standard test method similar to the ASTM C1856/C1856M Standard
Practice for Fabricating and Testing Specimens of Ultra-High Performance Concrete are France
[AFNOR NF P 18-470], Canada [CSA A23.1 Annex U - UHPC], Switzerland [SIA Design
Guideline 2052:2016] and Australia [AS5100.5:2017, Section 16]
It is common practice for the characteristic compressive strength property be determined based
on a statistically significant number of consecutive strength tests of specimens coming from a
minimum number of separate batches of a single mixture design [France AFNOR NF P 18-470
and Canada CSA A23.1 Annex U - UHPC]. The provided values of each parameter should be
equal to the average minus X times the standard deviation of the tests, where X is a function of
the number of tests
The rate of gain in compressive strength vs time is impacted by curing temperatures, similar to
normal or high performance concretes; however the rate and magnitude of early strength is
significantly higher. Figure 3.1.1.2.1 shows the rate of gain in compressive strength vs time for
curing temperatures of 41C(105F), 23C(73F) and 10C(50F). Note, during the first 12 hours of
curing at 41C (105F) the hourly increase in compressive strength can be more than 2
MPa/hour(300 psi/hr).
Figure 3.1.1.2.1 Compressive strength gain vs time for various curing temperatures[FHWA
HRT-12-064]
.
3.1.1.2.2 Modulus of Elasticity and Poisson’s Ratio - Vic
Procedures for direct measurement of Young’s modulus and Poisson’s ratio are presented in
The Documet [ADOT Report, Mobasher et al.]. Refer to Table 3.1 for typical values of young’s
modulus and Poisson ratio. Also there is a significant post peak ductility in compression due to
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Commented [vp12]: Need this reference!!!
the confining effect of the steel fibers. Post peak strain softening range can have a significant
impact in load redistribution and ductile performance of structures utilizing UHPC mixtures.
Ahlborn et. al (2011) found that regardless of curing regime or specimen age, UHPC
consistently achieved an ultimate modulus of elasticity of approximately 8,000 ksi (55 GPa) and
a Poisson’s Ratio of 0.21. Graybeal (FHWA-HRT-06-103) reported modulus of elasticity values
between 6200 ksi (42.8 GPa) for untreated specimens and 7650 ksi (52.8 GPa) for steam
treated values. Furthermore, the following is recommended by FHWA for determining the
modulus of elasticity, Ec, in lieu of test results (FHWA-HRT-14-084).
𝐸𝑐 = 1500 √𝑓𝑐′
for f’c in ksi
In Graybea’sl work, full compression stress-strain response was collected for each set of
cylinders under various curing regimes and at various ages (Figure 3.1.1.2.2.1). This data
clearly shows the change in the relationship between compressive strength and modulus of
elasticity as curing time proceeds.
Figure 3.1.1.2.2.1 Selected stress- strain responses for UHPC cured at various ages [Graybeal
2007]
As discussed above empirical relationship exist to relate compressive strength with modulus of
elasticity. However, according to Graybeal [2007], these equations are not accurate predictors
for modulus of elasticity for compressive strengths of less than 25 MPa (3.6 ksi), due to the non
linearity in the gain of the strength vs modulus of elasticity (see Figure 3.1.1.2.2.2).
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Figure 3.1.1.2.2.2 Modulus of Elasticity as a function of compressive strength [Graybeal, 2007]
The static modulus of elasticity and Poisson’s ratio can be determined in accordance with ASTM
C469/C469M on specimens prepared in accordance with ASTM C1856/C1856M Standard
Practice for Fabricating and Testing Specimens of UHPC with a modified Compressometer and
Extensometer using displacement transducers for measuring displacement. Also, CSA A23.1
Annex U on UHPC and AFNOR NF P 18-470 provide guidance on obtaining the modulus of
elasticity and Poisson’s ratio.
3.1.2 Tensile behavior - Rafic
The tension behavior and constitutive properties are unique features of UHPC. Section
3.1.2.1 describes the typical stress-strain behavior of UHPC in uniaxial tension and Section
3.1.2.2 covers the existing test methods to obtain different key properties of tensile behavior.
3.1.2.1 Uniaxial Stress-Strain Trends in Tension - Rafic
Sample tensile uniaxial stress-strain behavior of UHPC in tension for UHPC containing
2% fibers by volume are shown in Figure 3.1.2.1. The average trend is plotted as a thicker solid
line and a thin line for the individual results, calculated from ranges of axial stresses at one
value of axial strain. These tests were performed at the Federal Highway Administration
(FHWA) Turner-Fairbank Highway Research Center (TFHRC) on a commercially available
UHPC and results can be found in Haber et al. (2018). The tests consisted of UHPC prisms,
having a square cross section of 2 in (51 mm) and a length of 17 in (432 mm), loaded in tension
at a constant displacement rate as described in Graybeal and Baby (2013). The results show an
initial linearly elastic behavior, with stiffness equal to the modulus of elasticity, Ec. As the tensile
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2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Average
Individual Specimens
Material: U-D
Fiber Volume: 2 %
fc = 18.6 ksi
Age: 7 Days
Samples Included: 4
12
10
8
6
4
Axial Stress (MPa)
Axial Stress (ksi)
strain increases, the behavior becomes non-linear until the first discrete crack at which the
material enters the multiple cracking phase. Discrete cracks start to consecutively form and the
strength is equal to or greater than the first cracking strength. The multi-cracking phase ends
with the localization of strains into a single crack at which the material loses strength as strains
increase. For information on the idealized behavior of five commercially available UHPCs, refer
to Haber et al. (2018).
2
0
0.002
0.004
0.006
Average Axial Strain
0.008
0
0.01
Figure 3.1.2.1 Sample uniaxial tensile stress-strain response of a commercially available UHPC
with 2% fibers [FHWA, HRT-18-036].
3.1.2.2 Test methods to obtain Tension Properties- Vic
Tensile strain-hardening or strain-softening (Figure 3.1.2.2), or the capacity to retain a nonnegligible and reliable tensile strength resistance in the post-cracking regime is a distinct feature
of UHPC. Therefore, the experimental identification of post-cracking tensile behavior and
defining parameters to suitably characterize the material from a design perspective is of the
utmost importance. Many experimental tensile tests, direct or indirect, have been used;
however, no widely-acceptable direct tensile test standard has been established to date.
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Figure 3.1.2.2 Tensile Strain Hardening and Strain Softening Behavior of UHPC.
Direct tensile test methods provide the most “direct” way to obtain the tensile properties of
UHPC, as shown in Figure 3.1.2.1; however, the end attachments conditions in the testing
apparatus can lead to induced bending moments and increased variability of test results;
therefore, some jurisdictions specify flexural prism tests in a strain controlled system, then apply
an inverse analysis to obtain the tensile properties of the UHPC. The flexural prism test with
inverse analysis also has limitations depending on whether the UHPC exhibits tensile strainhardening or strain-softening properties. In some cases of strain-softening materials, the prism
test with inverse analysis can show strain-hardening behavior when it is actually strainsoftening.
The tensile strength can be determined on prismatic specimens molded or cut from full-sized
structures and tested in accordance with ASTM C1856/C1856M Standard Practice for
Fabricating and Testing Specimens of UHPC, and calculated in accordance with an inverse
analysis of AFNOR NF P 18-470, Appendix D, or SIA Design Guideline 2052:2016 Appendix E.
Alternatively, the tensile properties can be determined with direct tensile tests for strainhardening UHPC only. Direct tensile test methods may be found in the Australian guidelines [AS
5100.5:2017, Section 16], the Swiss Standard [SIA Design Guideline 2052:2016] or from FHWA
[Graybeal & Baby ‘Development of Direct Tension Test Method for UHPFRC, ACI Materials
Journal March-April 2013].
It is common practice that the characteristic tensile strength property be determined based on a
statistically significant number of consecutive strength tests of specimens coming from a
minimum number of separate batches of a single mix design (France AFNOR NF P 18-470 and
Canada CSA A23.1 Annex U - UHPC). The provided values of each parameter should be equal
to the average minus X times the standard deviation of the tests, where X is a function of the
number of tests.
3.1.3 Flexural Behavior
There are numerous test methods used to determine the flexural strength of concretes based on
testing various geometric sized prismatic specimens in 3 or 4 point bending. All of these
methods provide different results due to size effects, fiber orientation, casting techniques and
other variables. Flexural strength is not a mechanical property commonly used in the design of
structures with UHPC. Only the tensile behavior as explained in section 3.1.2 above is
applicable. Refer to Section 4.3 for flexural strength design considerations.
In the flexural test, due to the disparity between the tensile and compressive response of the
UHPC mixtures, the behavior is dominated by the relatively weak tension response. Cracking in
tensile zone leads to loss of stiffness, however the fibers that intersect the cracks pullout and
stabilize the crack growth.
Therefore in a flexural test the contribution of fibers to the resistance to crack propagation is
balanced against the superior performance of UHPC in compression. The net effect is that the
fibers intersecting the crack growth path provide bridging by forming a closing pressure that
resists crack opening and increase the material’s fracture toughness. Correlation between the
strengthening of the matrix phase by means of a critical volume fraction of fibers has been
studied by many researchers (Yang et al., 2010; Yang and Ye, 2002, Mobasher, Ouyang and
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Shah, 1991). Flexural testing is the key experimental procedure to showcase the interaction
between the tensile and compressive behavior.
Figure 3.1.3. shows the flexural response of a UHPC plain specimen with a UHPC sample
containing 1% steel fibers by volume (Vf = 1% - red line). The unreinforced UHPC beam (Vf =
0% - blue line) behaves as a brittle material and the load-deflection response increases linearly
up to a load of about 4 kN (800 lbs), corresponding to an elastic equivalent flexural stress of ****
at a mid-span deflection of 0.1 mm (0.004 in). At this point, the failure is imminent as a crack
forms in a sample which propagates to the full depth of the specimen. Due to the brittle
response, the load carrying capacity is exhausted as a single crack propagates without any
resistance from the matrix. The flexural response of the beam containing 1% fiber volume
shows the significant ductility obtained with the fibers. This ductility enhancement can be
studied at various stages of load-deformation response, as follows:
1) The crack initiation point in the fiber reinforced specimen is identified by the nonlinearity
in the ascending response and shown to be at higher loads as compared to the plain
unreinforced UHPC. This nonlinearity that takes place prior to reaching the maximum
load is quite distinct and corresponds to the stable growth of microcracks, which leads to
the accumulation of damage at the peak load.
2) The peak load for the fiber reinforced specimen (red line) is as high as 22% as
compared to the unreinforced control specimen (blue line).
3) The post-peak response is dominant in the fiber reinforced specimen and the sample is
able to carry a significant portion of the maximum load beyond the ultimate strength
point.
Figure 3.1.3 Comparison of the load-deflection response of control sample with a
composite containing 1% fiber volume mix series F17.5M7.5L5.
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Commented [vp13]: Need the value
Commented [vp14]: This sentence is not clear??? Clarify or
delete.
It is noted that the incorporation of 1% steel fibers has a beneficial effect on the flexural
behavior and the post-peak response. While there is no post-peak response for the unreinforced
specimen as shown by the brittle behavior (blue line in Figure 3.1.3), the fiber-reinforced
specimens demonstrate a considerable non-linear response after the occurrence of the first
crack.
The flexure testing was terminated at an ultimate mid-span deflection of 4 mm for the fiber
reinforced specimens. This value is nearly 40 times greater than the mid-span deflection at the
first cracking point in the unreinforced UHPC beams. Additionally, the load carrying capacity at
this level is as high as 60% of the peak load. This indicates that after reaching the peak load,
the sample is capable to maintain a large percentage of load carrying capacity for a significant
range of deformation. The peak load sustained by the UHPC beams containing 1% fiber
volume is about 22% , 177 lb. (0.8 kN) higher than the peak load in the unreinforced UHPC
beams 799 lb. (3.55 kN). (which corresponds to elastic equivalent flexural stresses of ******)
[ADOT report]
Commented [vp15]: This sentence does not agree with Figure
3.1.3
3.1.4 Shear Behavior
Shear strength is not a mechanical property that can be characterized by a test method. Direct
tensile strength across the crack is used in the design model. Refer to section 4.3 on Shear
Design Considerations for more information.
Explain that the engineering community of shear is not the direct shear but the final failure of
when the flexural crack becomes critical. Multiple mechanisms should be looked at like direct
shear etc.
Commented [vp16]: Mohammed Comment. Email to
Mohammed Aug 24 for info
3.1.5 Bond Behavior
The bond strength of UHPC is considered for three categories; the bond of UHPC to other
concretes and surfaces, the bond developed under fiber pullout, and the development length of
discrete reinforcement in UHPC.
Bond of UHPC to other concrete has been studied by Harris et. al (2011) and Graybeal & Haber
(FHWA-HRT-17-097 & HRT-18-036). Harris et al conducted an experimental study to evaluate
the bond strength between UHPC overlays and normal strength concrete substrates with
variable surface textures. Slant shear and splitting prism tests demonstrated that under
compression testing, the bond strength of all roughened surface speimens was greater than the
standard smooth finish. Bond strength of indirect tension tests were not as sensitive to surface
roughness, but were still within ACI’s Guide for the Selection of Materials for the Repair of
Concrete. Graybeal and Haber prepared two different concrete substrates with two different
surface preparations (Scarification & hydro demolition) and cast an UHPC overlay. Pull-off
testing was conducted in accordance with ASTM C1583. Testing showed that the UHPC bond
strength ranged from 0.8 MPa (114 psi) to 4.5 MPa (651 psi). Additionally, Graybeal & Haber
conducted ASTM C78 flexural beam tests to determine the bond between normal concrete and
UHPC. Results of this testing ranged from 3.0 MPa (430 psi) to 4.3 MPa (620 psi) for UHPC
cured for 7 days. The failure of the beam tests was in the constant bending moment region of
the beam and predominantly in the normal concrete substrate.
Subsequent to those studies , ASTM C1583/C1853M was accepted and can be used to
determine the tensile bond strength of UHPC to concrete surfaces. ASTM C1853/C1853M
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Standard Test Method for the Tensile Strength of Concrete Surfaces and the Bond Strength or
Tensile Strength of Concrete Repair and Overlay Material by Direct Tension (Pull-off Method)” is
a method that can provide bond property values for UHPC.
The development length of discrete reinforcement in UHPC was studied by Graybeal [FHWAHRT-14-084 & HRT-14-090], Emmerson and Hale, [Emerson , 2011], and Fehling,[Fehling,
2014]. In general, the bond strength of discrete reinforcement is higher in UHPC than normal
strength concrete or HPC. The higher bond strength will shorten bar development lengths and
impact the horizontal shear connections (ie Nelson Stud length, spacing and arrangement)
between conventional concrete or HPC and UHPC. FHWA-HRT-14-084 provides guidance for
basic development lengths with adjustments for cover and spacing considerations. Due to the
very short bond development length of pre-stressing strands or other tension reinforcing, the
end anchorage zones should be checked for higher concentrations of tension, particularly in
prestressed I-Shaped girders in the region of the web to bulb interface.
Test methods for the measurement of bond of steel fibers have been addressed in detail in
ACI544-9R-17. The characteristics and behavior of fiber-matrix interface plays an important
role in controlling the mechanical performance of UHPC. The bond characteristics of fibercementitious matrix is normally measured by means of pullout tests which determine the
interfacial fiber-matrix behavior. Parameters that influence the pullout behavior of fibers are
affected by fiber and mixture types, embedded fiber lengths, and processing methods. Four
main factors influence the bond between fiber and matrix: 1) physical and chemical adhesion; 2)
mechanical component of bond, such as deformed, crimped and hooked end fibers; 3) friction
and shrinkage clamping effects; and 4) fiber-to-fiber interlock.
Fiber pullout has be studied in the context of fiber-matrix interaction and is discussed in more
detail in section 3.5.1 Fiber-Matrix Interaction.
3.2 Durability Properties
Durability can be addressed in both the uncracked (unloaded( condition and the cracked
(loaded) condition. The deterioration mechanisms are different for each condition. This section
covers the uncracked condition. The cracked condition is covered in section 5.0.
Deterioration of concrete in the uncracked condition is mostly caused by the transport of fluids
and gases through the capillary pore structure of the internal matrix. UHPC has a lower porosity
than conventional concrete due to its higher packing density which forms a discontinuous pore
structure in the matrix. The hydrated matrix of UHPC, therefore, has a low permeability,
discontinuous pore structure and the high fiber dosages create a tight cracking pattern resulting
in a high durability level; hence more aggressive test methods are required to obtain results
that are meaningful and valuable in comparing the relative properties. The durability properties
of uncracked UHPC is typically an order of magnitude superior to HPC[FHWA]. Refer to Table
3.1 for typical values.
3.2.1 Absorption
The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a low
level of absorption. As shown in Table 3.1 from work conducted by Charron et al, the absorption
of UHPC is in the range of 0.003 kg/m2/s1/2.
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The absorption of UHPC can be determined on specimens following a 28-day moist curing, in
accordance with ASTM C642. [ASTM C1856/C1856M Standard Practice on Fabricating and
Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC].
3.2.2 Salt-scaling and Freeze/Thaw Resistance
The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high
level of resistance to salt-scaling and freeze/thaw. Thomas et al. (2012) report on a set of three
specimens of UHPC that have been placed at the mid-tide level of the marine exposure site at
Treat Island, Maine, over the past 15 years. The exposure conditions at Treat Island were very
severe with 6-metre tides and more than 100 freeze-thaw cycles per year. Extensive
experimental investigations have been carried out on the specimens, such as measurement of
strength and stiffness, electrical properties, chloride profiling, corrosion activity of reinforcing
steel and microstructural evaluation. No visible deterioration was evident after exposure periods
of 5 to 15 years and there was no evidence of any degradation of mechanical properties after
more than 1500 freeze-thaw cycles. Further, no corrosion of rebars has been observed,
although the concrete cover was only 25, 19 or 10 mm. The depth of chloride penetration was
extremely low, approximately 1/3 of that of typical HPC with 8.5% silica fume and w/c-ratio =
0.33 under same conditions. Consequently, a much longer service life of UHPC structures
compared to HPC – elements can be expected.
Ahlborn et. al (2011) reported an increase in RDM (<2%) and mass (<1%), and negligible
changes in length (<0.01%), for UHPC specimens after 300 cycles following ASTM C666
(Procedure B), independent of curing regime. Companion wet-dry specimens demonstrated
similar increases in RDM and mass, suggesting specimens did not deteriorate but rather
continued to hydrate during testing. The resistance of UHPC to freezing and thawing
degradation was also quantified by FHWA (2006). In total, 690 cycles according to ASTM C666
(Procedure A) of freezing and thawing were conducted. The results showed only minor changes
in mass.
The salt-scaling of UHPC specimens in accordance with ASTM C672 by Graybeal found that
independent of curing regime or age, UHPC showed no signs of scaling, spalling, or other
deterioration. Extended cyclic testing again showed no deterioration of the UHPC under these
conditions. (FHWA-HRT-06-103). Refer to Table 3.1 for typical values.
The freezing and thawing performance of UHPC can be determined on specimens following a
28-day moist curing, in accordance with ASTM C666. The testing should be continued on each
specimen until it has been subjected to at least 300 cycles or until its relative dynamic modulus
(RDM) of elasticity, as defined in Test Method C666/C666M, reaches 60%, whichever occurs
first, unless other limits are specified. [ASTM C1856/C1856M Standard Practice on Fabricating
and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC].
3.2.3 Permeability
3.2.3.1 Chloride ion Penetration
The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high
level of resistance to chloride ion penetration [Thomas et al]. Ahlborn et. al (2011) reported
chloride ion penetration in the negligible range (<100 Coulombs passing) for thermally-treated
and air-cured UHPC specimens. Initially, the creation of an electric short circuit from the steel
fiber reinforcement was a concern, but because of the random fiber distribution and short fiber
length at a rate of 2% by volume, no such electric short occurred [Thomas et al.,2016]. It should
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be noted that while curing regime does not appear to affect the chloride penetration on the
documented scale, air-cured specimens showed higher ranges. Graybeal (FHWA-HRT-06-103)
found similar results; thermally treated specimens had negligible penetration and ambient cured
specimens bordered on negligible and very low.
The rapid chloride ion penetration of UHPC is often determined on molded or cut specimens in
accordance with ASTM C1202/C1202M. The test specimen can be fabricated from the matrix
with or without fibers. This test approximates the resistance to chloride ion penetration by
measuring an electrical current passing through a sample of UHPC. After 28 to 56 days of moist
curing, the penetration potential is typically measured as very low to negligible. [ASTM
C1856/C1856M Standard Practice on Fabricating and Testing Specimens of UHPC and CSA
A23.1 Annex U on UHPC]. Other test methods that may be used include ASTM C1202, ASTM
C666, and AASHTO T259.
3.2.3.2 Carbonation
The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high
level of resistance to carbonation. Classical test methods to determine the carbonation
properties provides extremely low test results, typically within testing error for the test method
[Graybeal]. Carbonation testing is normally not conducted nor a concern with UHPC. If
carbonation test results are required, then tests may be conducted using standard test methods
and increasing the CO2 concentration levels and the test duration to provide meaningful results
for comparing various UHPC’s for carbonation performance.
3.2.4 Acid and Sulphate Resistance
3.2.4.1 Sulphate Resistance
The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high
level of resistance to Sulphate attack. Typically UHPC’s perform better than high sulphate
resistant concrete performs. Research by Piérard, [Piérard, 2012] showed that UHPC prisms
exposed Na2SO4 (at a rate of 16 g of SO4/L) for 500 days did not exhibit any expansion.
The sulphate resistance of UHPC can be determined, on specimens without fibers, in
accordance with CSA A3004-C8, Procedure A at 23oC for 12 months. [Canadian CSA A23.1,
Annex U on UHPC]. The limited studies that are available report little-to-no deterioration of the
UHPC when immersed in a sodium sulfate solution for 500 days. There have not been any
incidents documented of deterioration of UHPC due to Sulphate attack.
3.2.4.2 Acid Resistance
The low permeability of UHPC provides performance under specific acid attack superior to
normal or high-performance concretes [Schmidt et al.]. Whereas with conventional concretes
acids may permeate throughout the matrix and cause deterioration from within as well as on the
exterior, with UHPC the deterioration mechanism is mostly from the surface. The matrix of
UHPC has a low permeability, discontinuous pore structure and a tight cracking pattern,
resulting in an improved level of resistance to acid attack.
Classical test methods to determine the performance of UHPC under specific acid environments
provides low test results [Schmidt et al & Koneig and Dehn]. Testing UHPC’s for acid resistance
can be conducted using standard test methods and increasing the concentration levels and the
test duration to provide results for comparing various UHPC’s for acidic performance. Schmidt
et al subjected UHPC specimens (heat treated and non heat treated) to sulphuric, lactic and
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ammonium containing waters using a proton consumption method to characterize the UHPC’s
performance. Results for the range of tests conducted in accordance with EN standards are
presented in their paper.
Metallic fibers contained in the UHPC may be subject to corrosion in highly acid environments;
however due to UHPC’s low permeability, discontinuous pore structure and tight crack spacing
the performance is superior to normal or high performance concrete.
3.2.5 Delayed Ettringite Formation
The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high
level of resistance to delayed ettringite formation. According to Canadian CSA A23.1, Annex U,
UHPC receiving a thermal treatment with an internal material temperature greater than 70 ºC
should contain supplementary cementitious material. There have not been any incidents of
delayed ettringite formation problems documented with UHPC.
For more information on UHPC subjected to a thermal treatment of more than 70 ºC and
measures to control potential for delayed ettringite formation refer to ACI 201.2R-16 and ACI
308R, Clause 3.10.
3.2.6 Leaching and Efflorescence
UHPC has a high resistance to through-leaching due to its densely compacted matrix resulting
in very low permeability. However, surface efflorescence can appear on new UHPC elements
prior to sealing. This type of efflorescence is generally a one-time occurrence and can easily be
sand-blasted or pressure washed away for a cleaner finish. UHPC’s resistance to leaching is a
factor of crack control which prevents moisture from impregnating the interior of the matrix to
draw out the soluble minerals.
3.2.7 Abrasion
The abrasion resistance of UHPC is superior to that of high performance concrete. Research by
Graybeal [FHWA-HRT-06-103] using a modified (doubling wheel load) ASTM C944 “Test
Method for Abrasion Resistance of Concrete or Mortar Surfaces by the Rotating-Cutter Method”
showed improved abrasion performance for UHPC. UHPC specimens with various curing
regimes gave results of 0.07 to 2.56 grams.
The abrasion loss of UHPC can be determined on specimens following a 28 day moist curing, in
accordance with ASTM C944/C944M, using a double load of 197 +/- 2 Newtons on the test
specimen. [ASTM Standard Practice on Fabricating and Testing Specimens of UHPC and CSA
A23.1 Annex U on UHPC].
3.2.8 Alkali-Silica Reaction
UHPC has a high resistance to alkali aggregate reactions such as ASR due to its lack of internal
free water (low w/c ratio) and its very low permeability which prohibits free water from infiltrating
the matrix to initiate the reaction. Additionally, high quality fine aggregates are frequently used in
UHPC and are often non-reactive in nature. The use of these material constituents generates a
very low permeability and discontinuous pore structure, thereby reducing the possibility of alkalisilica reaction from occurring. Various tests can be used to measure alkali-silica reactivity of
UHPC, whereby ASTM C1260 is the most commonly used. The level of expansion measured
using this test is typically well below the threshold value considered for innocuous behavior.
There have not been any incidents of alkali-silica problems documented with UHPC.
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3.3 Time Dependent Properties
Mohammad & Andy- Add Early Age Behavior and effect of age on material properties and
curing effect. Young modulus (Rafic will update Mohammad on this based on FHWA work) add
this section.
3.3.1 Creep Coefficient
UHPC exhibits very low creep coefficients in the range of 0.3 to 0.8 if thermally treated. Fleitstra
(2011) studied early age creep and shrinkage behavior under conditions to mimic a prestressing
operation. While previous studies considered creep tests on specimens after thermal treatment
was applied, Fleitstra studied the creep behavior for specimen thermally treated while under
load. Specimens were subjected to creep loads of 20% and 60% of initial strength in an attempt
to bound the induced stresses caused during prestressing applications. The average creep
coefficient was found to be 0.76 and 1.12 for the 20% and 60% load levels, respectively. These
coefficients are much higher than Graybeal at 0.29 (FHWA report) and higher than the
conservative values of SETRA (0.20), JSCE (0.40) and UNSW (0.30). However, no other
research has incorporated the application of a compressive load (such as prestressing) before,
during and after thermal curing. Mullen (2013) represented Fleitstra’s creep strain data, cr, as a
function of time t in days after loading until thermally treated at which point the creep strain is
“locked in”.
𝜀𝑐𝑟 =
𝑡 0.6
∗ 1713 < 1713
4.069 + 𝑡 0.6
Refer to FHWA HRT-06-103 and HRT-18-036 for more information on creep.
The creep coefficient in compression can be measured on 75 mm x 150 mm cylindrical
specimens prepared in accordance with ASTM Standard Practice for Fabricating and Testing
Specimens of UHPC and in accordance with ASTM C512/C512M. Creep testing can be
conducted at a sustained load of specified strength of the UHPC. Creep testing can be
conducted on specimens following a 28 day moist curing. [ASTM C1856/C1856M Standard
Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC,
FHWA-].
3.3.2 Shrinkage
Graybeal et al conducted shrinkage tests on UHPC specimens in accordance with ASTM C157
and ASTM C1581 (early age) to characterize the early age and long-term shrinkage of UHPC
materials. The results of this testing show that UHPC can have an unrestrained shrinkage
comparable to well designed conventional concretes. Graybeal presented the following
modified ACI equation for determining the shrinkage as a function of time after casting:
St = S ult x t/(A + t)
Where, A = 35; St is the shrinkage at a given time, t and Sult is the ultimate shrinkage the
concrete will undergo.
Graybeal showed the ultimate autogenous (sealed) shrinkage can be as high as 850
microstrain. Drying shrinkage (in air) can be as high as 1400 microstrain.
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Commented [MOU17]: Reported test results? Ahlborn ICI
2015, others? Tess can summarize if others provide some more
references
Long-term Shrinkage testing can be conducted on prisms of 75 mm x 75 mm x 280 mm,
prepared in accordance with ASTM C1856/C1856M Standard Practice for Fabricating and
Testing Specimens of UHPC. The change in length of the UHPC specimens can be measured
in accordance with ASTM Test Method C157/C157M or C341/C341M, at 1d, 4d, 7d, 14d, 28d,
56d and 90d. [ASTM C1856/C1856M Standard Practice on Fabricating and Testing Specimens
of UHPC and CSA A23.1 Annex U on UHPC]. Early age shrinkage can be determined using
ASTM C 1581. Graybeal suggests that this test is difficult to conduct on heavily fibered UHPC
and that it may be necessary to run the test without the fiber to obtain results for early
autogenous shrinkage [Graybeal, FHWA HRT-18-036, 2018]
3.3.3 Thermal Coefficient of Expansion
The coefficient of thermal expansion was measured by Graybeal (FHWA-HRT-06-103) and
Ahlborn et. al (2011) for thermally treated and air-cured UHPC specimens using the provisional
AASHTO test specification TP60-00. Based on test results, a coefficient of thermal expansion of
8.2 x 10-6/°F was recommended by Ahlborn et. al (2011) for thermally treated specimens
independent of age. Ahlborn et. al (2011) also found the coefficient of thermal expansion
increased from 7.53 to 7.74 x 10-6/°F as non-thermally treated specimens increased in age from
3 to 28 days. As such, a value of 7.7 x 10-6/°F was recommended for air-cured specimens, a
value that lends well to field applications such as concrete bridge deck overlays. These
recommendations fell within range of the Japanese recommendations of 7.5 x 10 -6/°F for steamtreated UHPC samples and Graybeal’s thermally treated specimens with a coefficient of thermal
expansion of 8.3 x 10-6/°F. (FHWA-HRT-06-103). These values are somewhat higher than
thermal expansion coefficients of 7.74 x 10-6/°F for normal strength concretes.
The thermal expansion coefficient for UHPC has been specified by Ahlborn et al. (2008), JSCE
(2010), AFNOR NF P 18-470 (2016), Graybeal (2014), SIA 2052 (2016) and Hussein et al.
(2016) as 13.9 x 10-6°C, 13.5 x 10-6°C, 11 x 10-6°C, 14.7 x 10-6°C, 10 x 10-6°C and 16.9 x 10-6°C
for temperatures between -60 to 60°C, respectively. Habel (2004) describes that the initial
thermal expansion coefficient is between 40 and 60 x 10-6°C and decreases to its final value
during the first 36 hours of hydration.
The thermal coefficient of expansion can be measured on 75 mm x 150 mm cylindrical
specimens prepared in accordance with ASTM C1856/C1856M Standard Practice for
Fabricating and Testing Specimens of UHPC. The Thermal Coefficient of Expansion can be
determined in accordance with AASHTO T 336. [ASTM C1856/C1856M Standard Practice on
Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC].
3.4 Fire Properties
There is limited research material available on the fire performance of UHPC. However, there
have been no reported incidents of failure of UHPC structures due to fire [Behloul et al,
AFGC/SETRA and Ye et al ].
The following categories can be applied to UHPC:
a) FN – Non-fire-exposed UHPC: Conventional UHPC may be used in non-fire exposure
applications without the use of accelerated curing or the inclusion of polypropylene fibers.
b) F1 – Fire Exposed UHPC: UHPC that could be exposed to fire shall contain as a minimum
0.2% by volume of polypropylene fibers.
c) F2 – Hydrocarbon fire exposure: UHPC that could be exposed to a hydrocarbon fire shall
contain as a minimum 0.3% by volume of polypropylene fibers with an aspect ratio ≥ 65.
[Canadian CSA A23.1 Annex U on UHPC].
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Code specified fire resistance ratings are typically assigned to an assembly based on the
performance of that assembly in a standard fire test such as the ULC S101 Fire Test and are
not assigned on a material basis. UHPC has very low permeability and as a result could be
susceptible to explosive spalling when exposed to fire unless mitigating measures are taken.
While UHPC has been found to perform better than conventional HPC when exposed to
[Behloul et al] fire, the curing status (internal moisture content) and mix design of UHPC can
influence the performance of UHPC under fire exposure conditions.
The fire resistance of UHPC that has been thermally treated at 90°C for 48 hrs is generally
superior to UHPC that has not received accelerated curing. Thermal treatment serves to remove
any free water in the concrete matrix, reducing the potential for spalling. The use of at least
0.1% by volume of polypropylene fibers has also been shown to significantly reduce spalling in
UHPC by reducing the buildup of hydrostatic pore pressure at elevated temperatures. The use
of steel fibres has not been found to reduce spalling but does serve to retain the spalled
sections of concrete once the hydrostatic pressure exceeds the tensile strength of the
UHPC[Behloul et al and Hosser et al] .
Residual strength studies at elevated temperatures have shown that a variety of UHPC mixes
will perform similarly to European Code2 Class 1 and Class 2 concrete. Other UHPC mixes
however have fallen outside this range and as a result, no prescriptive residual strength values
for UHPC are offered at this time.
3.5 Other Properties
3.5.1 Fiber-Matrix Interaction – Luca Sorelli
3.5.1.1 Fiber dispersion, orientation and content
The fiber dispersion, orientation and content strongly affect the mechanical response for tensile
tests (Bayard 2003) and flexural tests (Bernier et Behloul 1996).
The fiber dispersion and orientation depend on the followability of the fresh concrete, the casting
procedure, the geometry of the molds and any embedments (Barnett et al. 2010; Ferrara,
Ozyurt, et Di Prisco 2011; Folgar et Tucker 1984; Kooiman 2000; Martinie et Roussel 2011).
The effective distribution (dispersion and orientation) of fibers can be quite complex due to wall
effects and rheology of the mix design. For instance, fibers tend to be locally aligned in the
proximity of the molds surface and when flowing around embedded reinforcing. Furthermore,
the fiber efficiency (defined as the average fiber length projection along the principal tensile
stress direction) increases approximately 25% passing from a tridimensional random distribution
to a bidirectional one [Guenet 2012; Kooiman 2000].
The placing method can strongly affect the orientation and dispersion of the fibers (Martinie et
Roussel 2011). The orientation normally does not affect the first cracking load but has an effect
of up to 50% on the post-cracking ultimate tensile strength in bending [Bernier et Behloul 1996;
Maya Duque, De la Varga, et Graybeal 2016] as shown in Figure 3.5.1.1. The highest UHPFC
flexural strengths have been achieved when placement is made in the direction of the measured
tensile strength. As for thin elements, the fiber orientation is rather bidirectional due to the wall
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effect, which favors the flexural response [Guenet, 2016, 2012]. Theoretically, for a randomly
distributed fiber orientation, the fiber orientation coefficient increases from 0.5 to 0.637 (increase
of 27%) passing from a three-dimensional configuration to a bi-dimensional one [Kooiman,
2000].
(a)
(b)
Figure 3.5.1.1. Effect of the fiber orientation on the (a) tensile response (Bayard 2003) and on
(b) the flexural response (Bernier et Behloul 1996).
3.5.1.2 Fiber pull-out
ACI document 544-9R and ACI 544 -10R discuss the history and methodology for fiber pullout
testing in detail and the impact of fiber dispersion and orientation.
.
Although there are no ASTM or EN standards for testing procedures for fiber pullout in cement
matrices to determine bond strength, there is literature that describes the test setup and how
loading conditions can strongly affect test results. Single-sided test profiles have been carried
out with by Grünewald 2004; Markovic 2006, Naaman and Najm 1991; Groth 2000, Cunha et al.
2007, Silva et al. ,2009. Banthia et al. have extensively studied the effect of fiber geometry and
orientation on the pull-out behavior of a single macro-fiber [Banthia 1990].
In UHPC, the fiber-matrix pull-out behavior has been optimized with respect the matrix strength
to favor the strain-hardening behavior and dissipation mechanisms (Lee et al. 2010; Wille, Kim,
et Naaman 2011; Wille et Naaman 2012). For instance, it was observed that the equivalent
bond strength of deformed fibers embedded in UHPC reaches up to 47 MPa (6.8 ksi), which is
almost five times the equivalent bond strength of straight fibers (10 MPa [1.4 ksi]) embedded in
the same matrix (Wille et Naaman 2012). Furthermore, the equivalent bond strength of straight
steel fibers, which are commonly used in UHPC can be doubled to a value exceeding 20 MPa
(2.9 ksi) by optimizing the UHPC matrix through composition and particle size distribution,
leading to an atypical (preferential fiber orientation) pullout load-slip-hardening behavior.
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3.5.1.3 Fiber dispersion validation
There exists practical methods to assess the fiber orientation, which varies from simple fiber
counting on cracked surface to image analysis based technique which statistically estimates the
average orientation of the fiber from the elliptical shape of the fibers observed on the cut surface
(Krenchel 1975; Delsol et Charron 2017). The image analysis can be based from 2D image
analysis taken from cut and polished surface or from 3D images reconstructed by X-ray
technique (Guenet 2016) as shown in Figure 3.5.1.2. More recently, Magnetic Inductance
Methods (MIM) (Ferrara, Faifer, et Toscani 2012) have been applied to reasonable spatial
distribution of the fibers (Baril, Sorelli, Réthoré, Baby, et al. 2016). Figure 3.5.1.3 shows the fiber
orientation assessed by MIM which well correlate the theoretical prediction of fibers by
computational fluid-dynamics and the distribution of micro-cracks detected by stereovision 3D
image analysis. (Baril, Sorelli, Guenet, et al. 2016).
(a)
(b)
(c)
(d)
Figure 3.5.1.2. Assessment of steel fiber distribution of a UHPFRC beam by micro-tomography
(Guenet 2016) for : (a) 1% of steel fiber; (b) 2% of steel fiber; (c) 1% of steel fiber with a steel
reinforcement; (d) 2% of steel fiber with a steel reinforcement.
(a)
(b)
(c)
Figure 3.5.1.3 (a) Non-destructive tests (Magnetic Inductance Measurement, MIM) to measure
the fiber orientation in thin panels (Ferrara, Faifer, et Toscani 2012); (b) Example of fiber
direction measured in each cell; (c) fiber direction predicted by computational fluid-dynamics
(Baril, Sorelli, Guenet, et al. 2016).
3.5.1.4 Fiber factor and impact on tensile properties
The fiber orientation may or may not be isotropic depending on the casting techniques,
consolidation methodologies, form shape, wall effects and other reasons as has been explained
in the sections above. The final orientation of the fibers may or may not be beneficial to the
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tensile properties of the hardened UHPC. It is important for the designer to validate if the in-situ
fiber orientation is as assumed in the design
In plate elements, fiber orientation can affect the full development of the micro-cracks, which is
key to guarantee the structural ductility of a bidirectional UHPCs. For instance, the effect of the
fiber orientation on the flexural response of thin UHPCs plates elements has been investigated
by considering the presence of a casting flow defect (Baril, Sorelli, Réthoré, Baby, et al.
2016)(see figure 3.5.1.4). The discontinuity in the fiber orientation could reduce the microcracking growth with a decrease of the load bearing capacity and the structural ductility.
(a)
(b)
Figure 3.5.1.4. (a) Load-deflection curve for a UHPFRCs slab without (a) and with fiber
orientation defect (red line in the square on the right high corner of each figure) with view of the
microcracks at different loading stages (b) (Baril, Sorelli, Réthoré, Ferrara, et al. 2016).
More practically, in order to account for the effect of the fiber orientation, French national
recommendations (AFGC/SETRA 2013) and national code (AFNOR 2016) proposes a suitability
test which consist of extracting UHPC samples according to different directions from the fullscale structure (see example of suitability test for a I-gider beam in Figure 3..5.1.5). Then, the
sawn samples are tested in bending and an average K-factor is calculated by comparing their
flexural strength to that of a sample molded specimen with random fiber orientation. A local and
a global K-factor have been defined to account for local (minimum) and global (average) effects.
The K-factor is finally employed to reduce the design tensile law of UHPCs. Based on several
experiences the K-factor ranges from 0.6 (favorable) to 2.5 (unfavorable).
The French recommendations proposes two coefficients Local and Global, a KL=1.7 and KG=1.3
in the case of lack of a sustainability test. The tensile law employed in design is further reduced
by the K-factor to account for the effect of the fiber orientation. The model code 2010 also
recognizes the K-factor. The CSA S6, Annex 8, Australian Guidelines, German Guidelines,
Swiss Specification and Spanish Guidelines all provide guidance for factors to account for fiber
orientation and dispersion.
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Figure 3.5.1.5. Example of sample extraction for the sustainability test as proposed by
AFGC(2013).
.
3.5.2 Cyclic Strength and Stiffness Degradation – Vic Perry
The type of cyclic loading (amplitude, frequency, magnitude and duration) in which a structure is
subjected is a function of the location and type of application (wind for wind turbine shafts, traffic
for bridges or seismic). To date, simulated traffic cyclic loadings have been tested for bridge
structures more than either wind or seismic loadings. Research by Graybeal and
Hartmann;,Parsekian et al; Scmmidt and others has shown good performance for UHPC under
equivalent highway cyclic loadings when the tensile stress level is maintained below 40% of the
UHPC’s elastic tensile modulus of rupture, in tests conducted on more than 2 million cycles of
loading.
Research by Loraux and Sritharan et al provides examples and research on the use of UHPC
for tall wind turbine shafts. Constant amplitudes uniaxial compressive fatigue tests were
conducted on thin UHPC plates. The fatigue endurance limit of UHPC under compressive
stresses at 10 million cycles was determined to be around 65% of the ultimate limit state. UHPC
was found to be particularly well suited for offshore turbine support structures [Loraux, 2018].
The seismic performance of UHPC connections for precast bridge super structure elements was
undertaken at the SUNY, Buffalo and determined that even in severe earthquakes (mid-spans
subjected up to 0.61 g in acceleration) the bridge deck resilience was excellent with no signs of
damage [Lee, 2014].
3.5.3 Dynamic Strength – Tess Ahlborn, Bradley Foust & Barzin Mobasher
It is generally accepted that concrete materials experience an increase in compressive
strengths under dynamic loading scenarios (Bischoff and Perry 1991). Structural loading can
encompass a broad range of strain rates, from creep on the order of 10-8 s-1 to ultra-high
dynamic rates at a fraction of a millisecond (Figure 3.5.3.1). A number of experimental
techniques exist to investigate high strain rate material properties under uniaxial loads: split
Hopkinson pressure bar (SHPB), falling weight devices, flywheel facilities, hydraulic machine,
etc. [Meyers, Nicholas & Hoge]. On the other hand, flexural impact behavior of cement
composites has also been studied by means of low- and high-velocity impact using Charpy,
Izod, drop-weight, and ballistic tests. These tests can be either instrumented or heuristically
based and the resistance is measured based on fracture energy, damage accumulation, and
measurement of the number of drops to achieve a desired damage or stress level
[Bindiganaville et al and Mobasher]. Due to the various test methods, it has been well
established that the mechanical response of cement-based materials is affected by the strain
rate [Mobasher].
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Earthquake/Induced Shock
Creep
Quasi-Static
Vehicle Impact
Hard Impact (Missiles,
Rock Falls)
Blast
Ultra High
Rate
Strain Rate (1/sec)
Figure 3.5.3.1 Strain rates vs type of loading
Both normal-strength concrete (Bischoff and Perry 1991) and UHPC (Cavill et al. 2006; Rong et
al. 2010; Clark 2013) show strength increases at high strain rates. This strength increase is
customarily quantified using the dynamic increase factor (DIF), the ratio of dynamic failure
strength to quasi-static failure strength. Normal strength concrete, ambient cured UHC, and
thermally treated UHPC specimens were tested in compression at 2:1, 1:1, and 0.5:1 aspect
ratios using the SHPB method (Clark 2013). Based on results of specimens meeting
recommended tolerances, DIFs were found to be between 3.65 and 4 for NSC, 1.73 and 2.95
for ambient cured UHPC, and 1.21 and 2.45 for thermally treated UHPC for strain rates between
102 and 103 s-1. While UHPC experiences a relative increase in dynamic compressive strength,
it is less strain rate sensitive than NSC.
Dynamic tensile data on fiber reinforced concrete that characterize the full displacement-load
history are, however, limited because a standard test methodology does not exist for various
strain ranges which can be achieved with different equipment. Characterization
of dynamic tensile properties of materials is also challenging as the failure process is affected
by the mode and manner of testing. Problems appear at high rate loading due to inertial effect,
non-uniform loading, and difficulties in measuring reliable mechanical properties. Lack of
general agreement about the standards and methodology used to conduct dynamic tests further
complicates the merging of the databases [Xiao].
Xu and Wille investigated the fracture energy of UHPFRC under direct tensile loads with
varying strain rate (10-4 s-1 to 10-1 s-1), where the dynamic impact factor (DIF) was as high as
1.53. Meng et al. conducted flexural tests of UHPC beam specimens with displacement ranging
from 0.05 to 5.00 mm/min. For the notch-to-depth ratio of 1/6, the flexural strength increased
from 23.59 to 38.36 MPa, while pronounced increases in residual strengths were also observed.
Rong and Sun conducted spalling tests to determine the dynamic tensile behavior of UHPC
using a SHPB test machine. Some important findings were reported including the significant
rate sensitivity of spalling strength, crack pattern and successful implementation of numerical
modelling using Johnson-Holmquist-Concrete material model. Cadoni and Forni tested notched
UHPC specimens using a Split Hopkinson Tensile Bar at stress rates ranging from 400 to 1000
GPa/s. Tran et al. investigated the direct tensile responses of UHPC at quasi-static and dynamic
strain rates of 5-24 s-1 using SEFIM and found that the tensile resistance was much higher
compared to static loads.
Stone and Krauthammer investigated the input energies necessary to fail UHPC and UHPFRC
cylinders via a drop hammer. Static and dynamic impact experiments were carried out on 150
mm x 300 mm (6” x 12”) NSC and UHPC (with and without fibers) cylinders using a drop
hammer. Mix design for the UHPC (with and without fibers) were the same except for the
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inclusion of 30 mm hooked steel fibers. Test data was analyzed to investigate total input energy
and energy distribution at specimen failure. Impact velocities for the UHPC (with and without
fibers) specimens were approximately 2.0 and 3.7 m/s, respectively. Static testing indicated
similar energy capacities for the UHPC, with and without fiber specimens. Under impact testing,
the UHPC specimens with fibers required 477-700% higher input energy to ensure failure
compared to the UHPC without fiber specimens. This enhanced energy capacity was primarily
attributed to the steel fibers which minimized brittle failure and restricted crack propagation.
Larger scale testing of structures is underway. Using a high-capacity shock-tube that can
simulate a blast wave generated by the hemispherical free air surface bursts of high explosives,
testing was conducted on a series of UHPC columns with variable detailing [Aoude et al.].
Results showed that UHPC in columns significantly improved performance under extreme
loading, and seismic detailing further enhance performance. Field tests of columns also
showed superior performance to high-strength concrete columns under blast loading conditions
[Xu et al.]. Additional research is on-going to study the effect of accumulated damage on the
blast response of UHPC columns.
Furthermore, the effect of fiber alignment on the dynamic compressive strength and ductility of
an ultra-high performance concrete was investigated by Groeneveld, et. al. Flow-induced steel
fiber alignment was nondestructively characterized using x-ray computed tomography. While
dynamic compression strength was independent of fiber orientation, the ductility, as measured
at peak stress, increased with the proportion of fibers oriented perpendicular to the applied load.
UHPFRC exhibits excellent performance under high-strain rates and has been successfully
employed in military applications and safe barriers. Based on several tests, UHPC
demonstrated superior performances under extreme dynamic loading when compared to
conventional concrete [(Habel and Gauvreau ; Millard et al. Parant et al.]. UHPC have a high
energy-dissipation capacity combined with the transfer of tensile stress after cracking, which
could be of interest when intense dynamic loads are involved and the overall strength is an
issue. Figure 3.5.3.2 shows the relative tensile strength (normalized to the static tensile
strength) of a UHPCs in fiction of the deformation rate [(Millon et al.]. With strain rate greater
than 1/s the tensile strength increases up to 16 times. As for applications, the impact strength of
UHPCs was also studied in connection with radioactive-waste container applications
[(Toutlemonde et al.] and protective structures [(Rebentrost and Wight]. Note that the fiber
distribution can lead to considerable anisotropy of both the static and dynamic properties
[Adeline].
The effect of possible anisotropy damage due fiber distribution due to blast impact may
require further study for specific marine applications
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Figure 3.5.3.2 Relative tensile strength of UHPCs at different strain rate showing multiplicative
factor of 16 at high strain rate [Millon et al.].
Figure 3.5.3.3 shows the effect of the fiber type on UHPC and HSC dynamics behavior. While
the steel fibers are the most effective to increase the dynamics tensile strength, the High
Density Polyethylene fibers are the most effective to increase the dynamics fracture energy
[(Curosu and Mechtcherine].
(a)
(b)
Figure 3.5.3.3 (a) Dynamic tensile strength and (b) dynamics fracture energy material
properties of ordinary concrete (OC) and UHPC with steel, PVA and HDPE fiber [Curosu and
Mechtcherine 2016].
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While the dynamic strength and ductility of UHPC continues to be investigated, documented
design standards are not available for this material under high strain rate loadings.
3.5.4 Fatigue Behavior – Luca Sorelli
The main aim of the fatigue tests is to establish relations between the upper stress level S and
corresponding number of cycles to failure N, the so-called S-N or Wöhler curves. Figure 3.5.4.1
shows a typical fatigue behavior of UHPC under bending in terms of deflection vs. cycles for
a beam tested at a load level of 50% of the static flexural strength [Lappa, Braam, and
Walraven]. After the initial stage, where the deformations increase rapidly, the process is
stabilized and the deformations increase slowly at a constant rate. These first two stages
normally correspond to 80% of the total fatigue life of the test specimen. Before failure at about
30500 cycles, the deformations then again increase rapidly.
Figure 3.5.4.1 Example of deflection increase at increasing number of load cycles during a
fatigue test of a UHPC beam under bending [Lappa, Braam, and Walraven 2004].
The tensile fatigue behavior (Figure 3.5.4.2)of UHPC under constant amplitude fatigue cycles
was studied up to a maximum of 10 million cycles with the objective to determine the
endurance limit([Makita and Brühwiler].
An endurance limit1 EL was obtained in all three domains of UHPC tensile behavior and at a
stress levels of (1) EL = 0.7 in the elastic domain, (2) EL = 0.6 in the strain hardening domain
and (3) EL = 0.45 in the strain softening domain. UHPC specimens subjected to a given tensile
stress showed rather large differences in local deformations, which confer significant stress and
deformation redistribution capacity to the bulk material enhancing thus the fatigue behavior.
UHPC fatigue fracture surface showed clear signs of matrix spalling and pulverization, which is
the result of snubbing as well as abrasion of fibers.
1
EL is defined as the ratio between the maximum fatigue stress and the elastic limit strength of UHPFRC
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(a)
(b)
Figure 3.5.4.22 (a) test set-up for tensile fatigue test; (b) Fatigue S-N curve under tension
[Makita and Brühwiler 2014].
For fatigue loading under compression, S-N-curves for UHPCs and NSC are compared in
Figure 3.5.4.3 (a), showing a rather good-natured behavior. Fibers are essential to reduce the
scatter of those results. The (relative) stress range of UHPFRC for a large number of load
reversals (> 2 million) is similar high as for NSC, while the absolute stress level is much higher
than for NC.
Fatigue testing on UHPCs (Ductal FM ®) was stopped after about 1 million cycles where only
little damage was observed on all specimens. After fatigue testing, the specimens were
subjected to quasi-static flexural force again and there was no influence of preceding bending
fatigue loading on the ultimate resistance of the specimens [(Behloul et al. 2005]. Other
researchers found similar results Flexural fatigue test on UHPCs were carried out by [Lappa,
René Braam, and Walraven 2006].
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(a)
(b)
Figure 3.5.4.3. (a) Comparison of NC and UHPCs in terms of S-N-curves under tension [Fehling
et al.2014]; (b) Triaxial and uniaxial S-N curves for UHPCs [Grünberg and Ertel, 2012].
In general, the test results on UHPC fatigue resistance showed a large scatter due to variation
in material strength, applied stress level, distribution of fibers, number of fibers at critical crosssections and test specimen type [Abbas, Nehdi, and Saleem, 2016].
The fatigue behavior of UHPC structures has also been tested. For instance, the thin slab of
UHPC waffle deck was tested under cyclical flexural loading according to the Eurocode loading
conditions without any sign of damage [Gomes et al., 2011].
When submerged, conventional concrete (not pre-stressed) shows a reduction of fatigue
endurance, apparently due to high pore pressures generated within the microcracks.
Interestingly, UHPC the addition of microsilica in UHPC did not shown such reduction [Gerwick,
2002].

The effect of the underwater condition on the UHPC may be further experimentally
verified for marine applications due to the limited data in open literature, although the
results of Gerwick seems to indicate that this is not critical for UHPC [Gerwick].
3.5.6 Property Gradients
Thermal and moisture gradients exist in UHPC structures just as they do in other concrete
systems. Thermal gradients can be handled with the same design considerations as normal
strength concrete. However, due to the low porosity of UHPC, moisture gradients are more
severe compared to conventional concretes or HPC.
4.0 Strength Design Considerations
This section on strength design considerations reviews the strength of UHPC members at the
ultimate limit state at the cross-sectional level for a variety of structural actions. The failure
modes addressed in this chapter are based on material failure. The structural actions
considered are flexure, shear, torsion, axial load, and combinations of axial loads and bending
moments. Structural limit state predictions are covered so that they apply to members and
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systems including multiple materials or hybrid solutions (for example: UHPC Filled Steel tubes
or UHPC Filled FRP Tubes). The required inputs are uniaxial material behavior in compression
and tension for UHPC and reinforcing materials. Guidelines for how to obtain these inputs are
provided in Chapter 2 – Mechanical Properties.
4.1 Compression and Tension Design Considerations
4.1.1 Compression – Mohamed Moustafa
Compression members or struts can be part of different architectural or structural systems such
as trusses. However, the most common application is columns under pure axial load, which is
the focus of this section.
While the ultra-high compressive strength of UHPC makes it an obvious solution for columns
and struts, the use of fibers within the matrix provide an additional benefit of being able to
reduce the quantity of ties in columns. The tensile capacity of the fiber matrix provides additional
resisting to busting forces of column reinforcement in compression.
Several studies investigated the behavior of UHPC columns. Kimura et. al. (2007) investigated
the effect of (1) volumetric ratio of steel fibers, (2) lateral reinforcement ratio, and (3) axial
loading type of reinforced UHPC columns with varying axial load under cyclic loading. They
used NSK (Nagashima et al. 1995) model for stress-strain relationship of concrete, developed
for HSC, in which the effect of steel fibers is not taken into account. Furthermore, they
considered NZS equations for assessment of maximum flexural strength of RC columns, which
is suitable for concrete with the maximum strength of 200 MPa and without steel fibers. The
results of their tests can be summarized as follows: (1) UHPC columns exhibited very good
flexural strength and load carrying capacity up to drift angel of 3% even under varying high axial
loading condition; (2) For UHPC with strength of 200 MPa, the maximum flexural strength under
varying axial load was about 1.47 times of Ultra High Performance Columns without steel fibers;
(3) The NSK and NZS equations are appropriate for calculation of maximum flexural strength of
UHPC with maximum strength of 200 MPa, while ACI and AIJ equations overestimate the
strength by 4 to 28% (Table 4.1); (4) Addition of steel fibers results in reduction of column
damage, crack dispersion, and decreasing crack width. In Table 1, unit 600 is 198 MPa plain
concrete without any steel fibers, and unit 601, 602, and 603 are 207 MPa UHPC with 1% steel
fibers. Moreover, Illich et. al. (2014) studied the load-carrying behavior of full-scale pretensioned columns of UHPC under the same eccentric compression loads at the both ends.
They used their special method of loading control to be able to record post-peak behavior of
columns.
Table 4.1 Comparison of measured to calculated maximum strength [Kimura et al. 2007].
Hosinieh et al. (2015) examined the influence of UHPC and transverse reinforcement detailing
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Commented [vp18]: Define
Commented [vp19]: Define
on strength, ductility, and failure mechanisms of six large-scale specimens, designed based on
Canadian CSA A23.3-14 code, under pure axial load. They observed that for a particular
transverse reinforcement configuration, reduction of space of transverse reinforcements results
in enhancement of columns post-peak ductility with a moderate increase in the column capacity
under axial loads. For a particular spacing of transverse reinforcement, their configurations did
not have a significant effect on column strength whereas toughness (area under the load-strain
curve) was enhanced. Compared to the same experiments, carried out on HSC columns, UHPC
columns have higher load carrying capacity (Fig. 4.1.1a). The influence of UHPC on post-peak
ductility was more apparent in low confined and less important in highly confined columns. This
means UHPC and transverse reinforcement have hybrid role in enhancement of post peak
behavior. The authors also used two literature proposed confinement models for HSC; however,
they need to be modified for UHPC. They observed good agreement between the experimental
and numerical results from Aoude’s FRP confinement model (2008), and their own proposed
model for unconfined UHPC (Fig. 4.1.1b). In Fig. 4.1.1a, CRC stands for Compact Reinforced
Composite, a UHPC mixed developed in Denmark. C3-80 column has the reinforcement
configuration type of C3 with 80 mm hoop spacing, and CS8 is a HSC column with similar size
and configuration to C3-80. In Fig. 1b, HSC1 and HSC2 are confinement models proposed
respectively by Razvi and Saatcioglu (1999) and Légeron and Paultre (2003), and FRC1 is
fiber-reinforced concrete confinement model proposed by Aoude (2008).
Fig. 4.1.1 Comparison of: (a) normalized load-strain response for UHPC vs. HSC columns; and (b)
experimental and analytical load-strain curves predicted using HSC models (HSC1 and HSC2) and fiber
reinforced concrete confinement model (FRC1) after Hosinieh et al. (2015).
Shin et. al. (2017) investigated the axial load response of UHPC columns with compressive
strengths of 163 and 181 MPa. They used UHPC of 1.5 % steel fibers. They tested nine UHPC
columns with ratios of 0.9-9.9% transverse reinforcement and two different configurations to
study the applicability of the existing equations in predicting behavior of UHPC columns.
In addition to studying axial capacity of UHPC columns, few studies considered buckling of
UHPC columns associated with the likely UHPC smaller sections compared to conventional
concrete. Schmidt and Heimann (2011) and Heiman et. al. (2013) investigated the reliability of
slender UHPC structural members to assess the likelihood of their buckling and decrease in
safety level, and compared the results of probabilistic analysis of HSC columns of high rise
buildings with the conservative design provisions of Eurocode 1 and 2. The study documented a
considerable safety deficit in Eurocode 2, Part 1-1 (buildings). The safety elements become
ineffective when buckling occurs prior to steel yield or concrete strength. The reliability of UHPC
members must be considered and the effects of shrinkage have to be taken into account in a
probabilistic model of UHPC.
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Commented [vp20]: LF: What does it means “prior to concrete
strength”?
If it is buckling for sure it will occur before the concrete achieves its
strength (and considering compatibility this may also mean before
steel yields)
Please elaborate better this sentence
Also: what do you mean with “safety deficit of EC2?”
And “the safety elements become ineffective when …”
Commented [vp21]: LF: The first part of this statement is
rather obvious (when we design we consider in some way the
“reliability”) …
Please explain why shrinkage has to be taken into account
(because it induces deformations which in a structural assembly
which is redundant may results in stresses e.gf. due to moments
and this increases the buckling “proneness?)
4.1.1.1 Modeling of UHPC Columns
Davila (2007) discussed analytical modeling for UHPC and the evolution in design codes and
their philosophical bases. Caldwell (2011) used the stress-strain relationship shown Fig. 4.2.1.1
for UHPC modeling to numerically study the incurrence of plastic hinges and inspect the
resultant behavior of NSC and UHPC columns under severe and short duration dynamic loads.
Using a similar constitutive model (Fig. 4.1.1.1), Astarlioglu and Krauthammer (2014)
numerically compared the response of a reinforced UHPC column with the same size and same
reinforced NSC column under four levels of idealized loads. They analyzed 16 columns (four
axial load cases for each blast load level and four blast load configurations). They observed that
the difference of UHPC and NSC in peak displacement, when the load is small enough that
does not lead to failure, was relatively small. On average, displacement in UHPC columns was
respectively 27% and 30% smaller than NSC columns for simply supported and fixed boundary
conditions.
Commented [vp22]: LF: A plastic hinge is likely to occur when
some moment is present
So if we are speaking about columns under compression this
reference is not appropriate here
Commented [vp23]: LF: Displacements: what do you exactly
mean?
Axial shortening?
Or is the investigation of the column under axial load and lateral
deflection?
Fig. 4.1.1.1 Stress-strain curve used for UHPC modeling (Caldwell 2011 and Astarlioglu and
Krauthammer 2014).
4.1.1.2 – applicable code discussion?
Commented [vp24]: To be Completed by Mohammed
Moustafa
4.1.2 Tension – Vic Perry
There have been very few examples of the use of UHPC for structural elements solely in
uniaxial tension. One such example is the canopy shell struts for the Shawnessy LRT Station
roof (See Fig 4.1.2) constructed in Calgary, Canada in 2004 [Perry et al, 2005]. The struts
designed for axial compression and tension used redundant stainless-steel reinforcing bars in
addition to designing the UHPC cross-section to carry the full compression and tension loads.
Not only did the redundant reinforcing bars have the capacity to carry the full axial loads in the
event of a post-cracking failure, but they also assist in distributing the tensile strains during the
strain hardening and strain softening phases.
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Fig 4.1.2 UHPC Canopy shells supported on UHPC Struts. Photo Credit: Perry
4.1.2.1 – applicable code discussion?
Commented [vp25]: To be Completed by VP
4.2 Flexure – Fatmir Menkulasi
Flexural behavior of reinforced concrete members is understood better than shear behavior,
which is typically estimated using semi-empirical approaches. Because of the differences in
constitutive relationships between normal strength concrete (NSC) and ultra-high performance
concrete (UHPC) the estimation of flexural strength of members constructed with UHPC has
resulted in a different yet similar approach to that used for NSC. In essence, the parabolic
stress-strain relationship typically used for NSC is replaced with an idealized curve for UHPC.
The main difference on the compression side is that often the relationship between stress and
strain in UHPC is almost linear with some softening taking place as the peak stress is achieved.
Post-peak behavior varies depending on the amount of fibers. Accordingly, the familiar
Whitney’s stress block used for traditional reinforced concrete members is typically replaced
with either a linear or bilinear curve for UHPC members.
On the tension side of the stress-strain curve there is a fundamental difference compared to
NSC beam behavior. In NSC members the tensile strength of concrete is typically ignored
because tensile strength is typically 1/10 of the compressive strength, tensile failure is brittle
and tensile strength cannot be relied upon when ductile member behavior is desired. Depending
on the amount of fibers used, UHPC offers a much improved behavior in tension. In several
mixes, the peak tensile strength is greater than the first cracking strength exhibiting a strain
hardening property. Additionally, tensile strengths in excess of 15 MPa (2 ksi) are possible,
which is a significant contribution considering that many concrete structures are built with
concrete that has a compressive strength in the range of 20 to 35 MPa (3-5 ksi). The
idealization of the tension curve in UHPC members continues to be a subject of research with
some researchers proposing a bilinear curve (trapezoid) and others suggesting a rectangular
approximation.
This section provides a summary of the literature review on the flexural design of UHPC
members and it references studies that provide a flexural design approach for the ultimate limit
state of reinforced and prestressed concrete sections. All presented approaches are based on
the assumption that plane sections before bending remain plane after bending. Studies that deal
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with the subjects of cracking, stiffness, and deflections are discussed under the serviceability
section.
One of most comprehensive design guidelines and standards for UHPC to date has been
developed by the Association Française de Génie Civil (AFGC), i.e. French Association for Civil
Engineering (2016a, 2016b). Flexural design is based on specified stress-strain relationships in
compression and tension. For compression, two stress-strain curves are provided depending on
whether the goal is to conduct nonlinear analysis or to design for the ultimate limit state (Fig.
4.2.1). A parabolic curve is specified for conducting nonlinear analysis as shown in Fig. 4.2.1a
and equations 1 through 7 can be used to develop the curve. In these expressions, fctfm is the
mean value of the post-cracking strength (which can be determined based on section 5.5.4 of
standard NF P18-470 (2016a)), and Kglobal is the orientation factor associated with global effect.
(a)
(b)
Fig. 4.2.1 Stress-strain relation of UHPC in compression for: (a) non-linear structural analysis; (b) design
at ULS according to French-Standard (2016a).
𝜀
𝜀𝑐1,𝑓
𝜎 = 𝑓𝑐𝑚
𝜀 𝜑.𝜂
𝜂−1+(
)
𝜀𝑐1,𝑓
𝜂.
𝜀𝑐1,𝑓 = [1 + 4
𝑘0 =
𝐸𝑐𝑚
⁄
1 3
𝑓𝑐𝑚
𝑘
𝜂=
𝑘−1
𝜀𝑐1,𝑓
𝑘 = 𝐸𝑐𝑚
𝑓𝑐𝑚
𝜑=
{
(1)
2⁄
𝑓𝑐𝑡𝑓𝑚
𝑘0
𝑓 3
] [1 + 0.16 2
] 𝑐𝑚
(𝑓𝑐𝑚 + 800) 𝑘0
𝐾𝑔𝑙𝑜𝑏𝑎𝑙 . 𝑓𝑐𝑚
(3)
(4)
(5)
1
𝑙𝑛 (1 − 𝜂 +
𝜂 𝜀𝑐𝑢1,𝑓
)
0.7 𝜀𝑐1,𝑓
𝜀𝑐𝑢1,𝑓
)
𝜂. 𝑙𝑛 (
𝜀𝑐1,𝑓
𝜀𝑐𝑢1,𝑓 = [1 + 15
(2)
𝑠𝑖
𝑠𝑖
𝜀 ≤ 𝜀𝑐1,𝑓
𝜀 > 𝜀𝑐1,𝑓
(6)
2⁄
𝑓𝑐𝑡𝑓𝑚
20
𝑘0
𝑓 3
] [1 +
] [1 + 0.16 2
] 𝑐𝑚
(𝑓
𝐾𝑔𝑙𝑜𝑏𝑎𝑙 . 𝑓𝑐𝑚
𝑓𝑐𝑚
𝑐𝑚 + 800) 𝑘0
(7)
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For estimating flexural strength at the ultimate limit state a bilinear compression curve is
specified as shown in Fig. 4.2.1b. Equations 8 through 10 can be used to generate the curve
where, fctfm is the mean value of the post-cracking strength (which can be determined based on
section 5.5.4 of standard NF P18-470) , Kglobal is the orientation factor associated with global
effect ( section 4.4.3 of standard NF P18-470), and fcm is the mean value of compressive
strength (section 5.5.2 of standard NF P18-470). Physical testing is required to either develop
the full stress-strain relationship of UHPC in tension or to obtain key parameters such as those
shown in Fig. 4.2.2. For additional information on the French recommendations the reader
should refer to references 2016a and 2016b. Once the stress-strain relationship for UHPC in
compression and tension is defined, the calculation of nominal moment capacity is based on
principles of equilibrium and strain compatibility.
𝑓𝑐𝑑 = 𝛼𝑐𝑐 𝑓𝑐𝑘 ⁄𝛾𝑐
ɛ𝑐0𝑑 = 𝑓𝑐𝑑 ⁄𝐸𝑐𝑚
𝜀𝑐𝑢𝑑
𝑓𝑐𝑡𝑚
= (1 + 14
) . 𝜀𝑐0𝑑
𝐾𝑔𝑙𝑜𝑏𝑎𝑙 . 𝑓𝑐𝑚
(8)
(9)
(10)
Fig. 4.2.2 Definition of fctf (a) in case of a local maximum, (b) where there is no local maximum
(French-Standard 2016a).
In 2006, the Japan Society of Civil Engineers (JSCE) published Recommendations for Design
and Construction of Ultra High Strength Fiber Reinforced Concrete Structures (Draft) that builds
on the JSCE Standard Specifications for Concrete Structures. Similar to French
Recommendations the use of stress-strain curves rather than an equivalent stress block is
recommended for flexural design. No minimum amount of steel reinforcement is required
because the bridging action of the steel fibers provides the strength after cracking. Physical
testing os required to characterize the stress-strain relationship of concrete in tension. Uchida
et. al. (2006) provides a discussion of the JSCE UHPC design and construction
recommendations.
Gowripalan and Gilbert (2000) developed design guidelines for Ductal prestressed concrete
beams. The idealized stress-strain relationship for uniaxial compression and tension is defined
as shown in Figs. 4.2.3 and 4.2.4, respectively, assuming that there is at least 2% steel fibers by
volume. Lf indicates the length of fibers and D indicates the depth of the beam. The compressive
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stress-strain relationship features a trilinear curve. The maximum compressive stress is limited
to 85% of that obtained from cylinder/cube compressive strength tests and the modulus of
elasticity is taken equal to 50,000 MPa. The maximum compressive stress remains constant up
to a strain of 0.004 then reduces linearly to zero stress and a maximum compressive strain of
0.007. In tension, the stress-strain relationship also features a trilinear curve with the maximum
tensile stress equal to 5.0 MPa. The tensile strain at the end of the yield plateau and the
maximum tensile strain are defined in Fig. 4.2.4. However, when estimating the nominal
moment capacity of a prestressed concrete beam it is recommended that the strain and stress
distributions shown in Fig. 4.2.5a and 4.2.5b be used for cross-section with bonded and no
bonded reinforcement, respectively. For cross-sections with bonded reinforcement, the
maximum compressive strain is limited to 0.0035. For sections containing no bonded
reinforcement the ultimate strength in bending may be assumed to occur when the extreme fiber
tensile strain equals εt,p as defined in Fig. 4.2.4. The design flexural strength is obtained by
multiplying the theoretical moment by the strength reduction factor ϕ. The strength reduction
factor of 0.8 is used for sections containing bonded reinforcement or tendons and 0.7 for
sections containing no bonded reinforcement or tendons.
Fig. 4.2.3 Design stress-strain relationship in
compression (Gowripalan and Gilbert 2000).
Fig. 4.2.4 Design stress-strain relationship in
tension (Gowripalan and Gilbert 2000).
a)
b)
Fig. 4.2.5 Stress and strain distribution at ultimate bending limit state (Gowripalan and Gilbert 2000): a)
cross-section with bonded reinforcement, b) cross-section with no bonded reinforcement
Graybeal (2008) states that “until a significant number of full-scale flexure tests are completed, it
will not be possible to present a calibrated set of conservative parameters for use in the flexural
design of UHPC prestressed girders.” However, in absence of such data Graybeal (2008)
suggests the utilization of the uniaxial stress-strain response depicted in Fig. 4.2.6 and the
following criteria for the flexural design of prestressed UHPC beams maybe used:
1. A maximum compressive strength of 24 ksi (165 MPa) corresponding to 0.85 times the
observed steam-treated compressive strength;
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2. A tensile capacity of 1.5 ksi (10.3 MPa), corresponding to 0.5 times the pre- and
postcracking uniaxial tensile capacity;
3. A modulus of elasticity of 7,600 ksi (52.4 GPa), and
4. A limiting tensile strain of 0.007 corresponding to 70% of the tensile strain observed in
the extreme tensile fiber of the girder just prior to gross cracking, strain localization, and
girder failure.
A division of the suggested maximum design compressive strength with the modulus of
elasticity results in a maximum compressive strain of 0.00316. The design philosophy detailed
by Graybeal (2008) is similar to portions of some UHPC structural design procedures detailed
elsewhere (Association Française de Génie Civil 2002; Casanova and Rossi 1996; Gowripalan
and Gilbert 2000; Uchida et al. 2005).
Fig. 4.2.6. Simplified uniaxial stress-strain behavior for I-girder flexural design (Graybeal 2008)
Almansour and Lounis (2010) used a bilinear curve on the compression side and ignored tensile
contribution when estimating the flexural strength of pretensioned UHPC elements. The bilinear
approximation of the stress-strain curve was based on the French Code (AFGC 2002), is shown
in Fig. 4.2.7, and includes: i) a first line from zero stress and zero strain up to a strength of (f cu)
and a strain of (fcu/Euhpc); and ii) a second line that is horizontal up to the ultimate strain of ε cu =
0.003, (εcu = 0.0035 in the Japanese recommendations (JSCE 2006)). The ultimate strength (f cu)
is given by AFGC (2002) and adapting to CHBDC (CSA 2006) yields:
0.85𝜑 𝑓
𝑐 𝑐𝑗
(1)
𝑓𝑐𝑢 =
𝜃
Where fcj is the cylinder compressive strength at age j, which is taken in present study
equal to 28 days; θ is a factor related to the probability of the load application period or rate of
loading where θ = 1.0 for loads with application period equal to or greater than 24 hours, θ = 0.9
for loads applied over a period between 1 hour and 24 hours, and θ = 0.85 for loads with an
application period of less than 1 hour; φc is a coefficient that takes into account the uncertainty
and variability of UHPC resistance, as well as localized effects. Fig. 4.2.8 illustrates the
distribution of strain and stress in a composite bridge I-beam and deck section.
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Fig. 4.2.7. Mechanical properties of an ultra-high performance concrete (UHPC) and high
performance concrete (HPC) (Almansour and Lounis 2010)
Fig. 4.2.8. Stress and strain distribution at the ultimate limit state for UHPC girders
(Almansour and Lounis 2010)
Aaleti et al. (2013) proposed a linear curve on the compression side and a bilinear one on the
tension side for the estimation of flexural strength in UHPC waffle decks (Fig. 4.2.9). This
approach is similar to that proposed by Graybeal (2008) for prestressed I-girders and includes
the following criteria:
 UHPC exhibits tensile capacity well past its initial tensile cracking strength, until fiber
pullout occurs at a tensile strain (εtu) of 0.007. This strain value is a conservative
estimate for fiber pullout and is recommended for design. The corresponding limiting
tensile strength (ftu) of UHPC is taken as 1.2 ksi.
 UHPC exhibits a linear compressive stress-strain response up to the compression failure
beginning at a compressive strain of 0.0032. Thus, the compressive strain at the ultimate
limit state (εcu) is taken as 0.0032 and the corresponding compressive strength (f cu) is
taken as 24 ksi.
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Fig.4.2.9. Strain and stress distribution along the cross-section at cracking and ultimate limit
states (Aaleti et al. 2013)
The flexural design approaches presented so far include a maximum compressive strain that is
either equal to or slightly higher than 0.003. This maximum compressive strain directly limits the
amount of longitudinal reinforcement that could be used in flexural members, which in turn limits
the flexural capacity of the members (Kaka et al. 2016). Kaka et al. (2016) concluded that the
maximum usable compressive strain that could be safely used in the design of UHPC flexural
members is εcu = 0.015 (Fig. 4.2.10). This leads to load carrying capacities that were 4.5 to 5
times higher than those of equivalent reinforced concrete beams designed with tension
controlled behavior as recommended by ACI 318 (2014) and AASHTO LFRD Specifications
(2017). Such a high load carrying capacity was made possible by using five times more flexural
reinforcement than what would be allowed based on the current tension controlled limit for
reinforced concrete members, which is based on a maximum concrete compressive strain at
failure equal to 0.003 and a minimum tensile strain in reinforcement equal to 0.005. In terms of
behavior, it was concluded that the UHPFRC beam exhibited very large deflections with a few
small flexural cracks. For design purposes it was concluded that the depth of the compression
block could be determined using the same β 1 parameter that is used for conventional concrete.
Finally, it was concluded that the contribution of the tensile stress from UHPFRC to the moment
capacity warrants further study.
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Fig. 4.2.10. (a) ACI 318 and AASHTO design criteria; (b) strain profile of RC beam; (c) strain
profile UH-FRC beam (Kaka et al. 2016)
Yao et al. (2016) and Soranakom and Mobasher (2008) used a bilinear stress-strain relationship
on the compression side and a trilinear one on the tension side to propose a bilinear momentcurvature relationship for predicting the load deformation response of statically determinate
UHPC beams (Fig. 4.2.11). Analytical solutions that characterize the full range distribution of
curvature, angle of rotation and deflection at any point along the beam were proposed.
Fig. 4.2.11. Material models for homogenized UHPC: (a) compression model and (b) tension
model
Naaman (2018) investigated the influence of various stress-strain relationships on the nominal
moment capacity of a fiber reinforced concrete section. Fig. 4.2.12 shows possible distributions
at nominal bending resistance and Fig. 4.2.13 shows typical stress block models for simplified
analysis. The following observations were made:
1) In all cases the numerical value of nominal bending moment Mn, shows very little
sensitivity to the shape of the concrete stress block in compression (rectangular,
parabolic, or triangular) and is mainly influenced by the tensile response of the
composite.
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2) Changing the shape of the tensile stress block from rectangular with average postcracking stress 𝜎̅𝑝𝑐 to triangular but with the same 𝜎̅𝑝𝑐 reduces the modulus of rupture
(MOR) by about 28%. Naaman (2018) defines the MOR as the maximum value of
equivalent elastic bending stress corresponding to the nominal bending resistance of a
beam (that is, moment at maximum load). The MOR can be calculated by dividing the
nominal moment capacity, Mn, by the elastic section modulus with respect to the extreme
tensile fiber, St.
3) If a stress-elongation response or a stress versus crack opening response is available,
estimating the average post-cracking stress 𝜎̅𝑝𝑐 for and estimated crack opening at
nominal bending resistance allows for a rational reasonably accurate prediction of
nominal bending moment Mn.
In general, it was determined that the stress-strain relationship for UHPC in tension has a much
greater influence on the nominal moment capacity of the section than the stress-strain
relationship in compression. This emphasizes the importance of either characterizing the tensile
response of UHPC using reliable test methods or developing simplified relationships that are
based on reliable test results.
Fig. 4.2.12. Typical examples of strain and stress distributions at nominal bending resistance
(Naaman 2018)
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Fig. 4.2.13 Typical stress block models for simplified analysis: (a) Assumed linear strain
diagram, (b) Parabolic compression stress block, uniform tensile stress block, c) ACI
rectangular compression stress block, uniform tensile stress block, d) ACI rectangular
compression stress block, triangular tensile stress block, e) Triangular compression stress
block, uniform tensile stress block (Naaman 2018)
This section provided a summary of various flexural design approaches for UHPC members. In
general, all approaches were based on the incorporation of the uniaxial stress-strain relationship
for UHPC in sectional analysis to estimate the flexural strength at any given section. There is
currently no consensus as to: 1) what the maximum usable concrete compressive strain is, 2)
what the maximum usable tensile strain is, 3) what is the minimum amount of fibers needed to
achieve a certain maximum usable compressive or tensile strain, 4) what are the definitions for
tension-controlled, compression-controlled and transition zone behavior, and 5) how to best
represent the compressive and tensile behavior of UHPC at a material level when conducting a
sectional analysis at the ultimate limit state. Additionally, the type of reinforcement that UHPC
interacts with plays an important role in overall member behavior. The use of UHPC in common
and repetitive applications will perhaps provide the impetus for arriving at a unified approach for
the flexural design of UHPC members.
4.3.x.x – applicable code discussion?
Commented [vp26]: To be completed by Fatmir Menkulasi
4.3 Combined Axial and Bending – Mohamed Moustafa
In many design cases, columns are designed to carry combined axial loads and bending
moments. Only the behavior of UHPC columns under pure axial is briefly discussed in Section
4.2. However, more insight into the general design of UHPC columns under combined axial and
bending forces, which can build on flexure design principles, is presented here. The effects of
axial loads (mainly compression) can further increase the flexure capacity, which is important to
properly quantify when columns are considered as part of lateral load resisting systems, e.g.
moment frames in buildings or bridge columns. Limited testing under flexural or axial loads
indicates that the flexural and axial strengths of UHPC members can be calculated with
reasonable accuracy if the stress-strain relationships of UHPC are included in the analyses. The
calculations are more complex than using the simplified approach of a rectangular compressive
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Commented [vp27]: In the References for this section is listed
53 references but none of them are refered to here in the section.
Many of these references are already referred to in other parts of
this document, so they are duplicated.
My suggestion is delete them all unless any specific ones are
relevant to this section.
stress block and zero tensile strength. Brief survey of how combined axial and flexure UHPC
design is tackled in standards and guidelines along with the different experimental and
analytical efforts that aimed at response characterization of UHPC is presented here. Moreover,
novel UHPC and hybrid column designs, behavior of UHPC columns under different types of
hazards, and modeling efforts for UHPC columns are briefly discussed.
4.3.1 UHPC Column Behavior under Lateral Loading and Different Hazards
Some studies also considered the behavior of UHPC columns under different types of lateral
static or dynamic loads subject to hazards such as earthquakes, fire, or blast and are briefly
summarized below.
4.3.1.1 Earthquakes
Sugano et al. (2007) studied a series of tests on columns and frames of UHPC buildings under
seismic loading to provide guidelines for design and construction. Based on their investigation,
UHPC is basically a brittle material which can be confined using high or ultra high strength
lateral reinforcements. In this case, the UHPC columns can tolerate very high axial compression
forces. The flexural behavior of UHPC columns also can be well assessed when taking the
tensile resistance of UFC and confinement by lateral reinforcements into considerations. Steelfibers in UHPC mixture significantly enhanced the shear resistance of columns and frames. On
the other hand, Joe and Moustafa (2016) conducted a preliminary analytical study to investigate
the design implications of using UHPC for seismic bridge piers in lieu of conventional concrete.
They showed that up to 40% reduction in the columns cross-section can be obtained if UHPC is
used to achieve same plastic moment capacity and ductility as conventional concrete piers
under seismic loading.
Chao et. al. (2016) studied seismic response of UHPC beams and columns with relatively
higher amount of longitudinal reinforcement (> 2.5%) used for moment frame beams compared
to what is acceptable for conventional RC beams. Based on their research, UHPC columns
have higher strength and drift capacity before significant damages, compared to RC columns. In
UHPC columns failure phenomena such as: concrete spalling and crushing, bar buckling and
hoop failure are reduced. At moderate drift of 1.0 to 2.0 %, minor damages happens. UHPC
column had no strength degradation until 2.5 % drift and could maintain its peak strength at
approximately close to a 4 % drift. The researchers also showed that the ACI 318 requirements
can be relaxed if UHPC columns and beams are used. Particularly, the confinement
requirements and amount of transverse reinforcement can be reduced for high strength
concrete (>10 ksi) columns.
Commented [vp28]: LF: It is important to clearly report here if
the study of the behavior under seismic loadings was done through
(quasi static) cyclic loading tests or through truly dynamic behavior
I assume in most cases it is the former
Commented [vp29]: clarify
Commented [vp30]: Define UFC
Commented [vp31]: LF: We should define better what is minor
damage, significant damage etc
Information on cross sections, height, reinforcement details should
be provided both for UHPC specimens and for reference NSC ones
Wang et. al. (2016) established a finite element model, using Kent-Park model, to study the
seismic performance of a pier of UHPC and high-strength steel. Concrete 02 by OpenSees
platform is used as the constitutive model while the modified Kent-Park model is used for the
skeleton curve. Comment: Specify what kind of constitutive relationship is Concrete 02 by
open sees (Please avoid software jargon) and also what does minor axial load and medium
amount of transverse reinforcement mean Based on their parametric studies, the following
requirements were suggested to be considered for desirable seismic performance of UHPC: (1)
Axial load ratio to be less than 0.4; (2) To have a drift ratio less than 1%, for a UHPC pier under
minor axial load ratio and medium amount of transverse reinforcement, less than 2%
longitudinal reinforcement to be used; (3) For small axial load ratio, the increase of transverse
reinforcement can reduce residual drift ratio while it does not have any effect on ductility and
energy dissipation of UHPC columns; (4) For short piers with high axial load ratio, the maximum
ground acceleration capacity is a little insecure using inelastic response spectra, based on the
nonlinear dynamic time history analysis.
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Commented [vp32]: Ratio of what?
Commented [vp33]: This paragraph is not clear
4.3.1.2 Blast
Aoude et. al. (2015) presented the results of a study examining the blast load performance of
UHPC columns. Li et. al (2015) carried out field blast tests on the four columns of their own
developed UHPC, and compared the results with the numerical model. They noted that UHPC
has superior blast resistant features. In the later study, the authors used the material model type
10 in LS-DYNA, which can be defined by user based on the uniaxial compression test on
UHPC, to model the UHPC behavior in compression. Similarly, Zhang et. al. (2017) also used
LS-DYNA to study the behavior of UHPC filled double skin steel tube columns under blast
loading. They derived pressure-impulse diagrams for UHPC filled double skin steel tube
columns in terms of residual axial load-carrying capacity after blast load, and examined the
effect of axial load ratio, steel tube thickness, column dimension and concrete strength on
pressure-impulse diagrams.
Zhang et. al. (2015) evaluated the residual behavior of UHPC infilled double-skin steel tubular
columns after close-in blast loading. They carried out eight blast tests on three square and five
circular columns with two different axial load levels. Then, they applied static axial compressive
loads on the specimens until failure to investigate their residual capacity. Based on their
observations, the axial load capacity of both undamaged circular and square columns were the
same with negligible difference, which was probably due to better confinement status for circular
ones. However, the flexural capacity of square columns was larger than circular ones. The
columns with applied axial load of about 25% of their axial capacity, had larger flexural capacity
while less ductility, compared to the load free columns. The UHPC infilled double-skin steel
tubular columns could retain 60% of their axial load capacity after blast load. Localized buckling
of outer steel tubes at mid span/ or column ends were observed. The columns with smaller
permanent displacement had larger peak residual axial capacity. Besides, columns with no axial
load, were more ductile than those with axial load during blast tests.
Xu et. al. (2016) tested four 0.2m×0.2m×2.5m reinforced UHPC columns under different
designed explosions with same standoff distance of 1.5m, and compared their efficiency with
four same sized and same reinforced HSC columns. Based on their investigations, use of
UHPC rather than HSC can reduce the maximum and residual displacements and enhance the
blast resistance of columns. Moreover, the axially loaded specimens have smaller deflections
because of the influence of boundary conditions, which outweighs the P-delta effect.
4.3.1.3 Fire
Unlike all the outstanding mechanical features of UHPC, its particular material properties and
slenderness of structural elements leads to its sensitivity against fire. High packing density
causes the high pore pressure, which results in concrete spalling when the remained water is
evaporated. Zehfuss and Siemon (2015) showed that it is possible to prevent explosive spalling
using polypropylene fibers. They evaluated the load bearing capacity of UHPC columns in
expose of fire, and simulated it using finite element method.
4.3.2 Novel Hybrid Beam-Column designs using UHPC
The previously mentioned studies considered mainly columns entirely constructed using UHPC.
However, numerous other studies considered UHPC as one component of novel and innovative
new columns designs (e.g. Xiangguo et al. 2013; Markowski and Lohaus 2017). Two popular
hybrid columns are UHPC-filled steel tubes and Fiber Reinforced polymer (FRP) tubes. Other
designs include UHPC cores in conventional concrete and segmental UHPC columns.
4.3.2.1 UHPC-filled Steel Tubes
Liew and Xiong (2012) tested 18 steel tubes infilled with ultra-high strength concrete, 4 steel
tubes infilled with normal strength concrete, and 5 hollow steel tubes. Although tubes filled with
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Commented [vp34]: LF: I understand that blast and also fire
tests were mdae on columns
But there is a conceptual difference between the quasi static cyclic
loading tests on columns, which can be interpretated on e.g. M-N
diagrams etc and blast and fire tests which resulted in most cases in
qualitative comparison observations
Also please since there is a section devoted to hybrid design this
should also contain the cases of steel columns filled with uhpc
Please try to rearrange the section coeherently
Commented [vp35]: Explain what is LS-DYNA
Commented [vp36]: LF: I do not like to include jargon from
commercial codes
Please say that a finite element modelling was performed (you may
cite the code but please detail the model: e.g bilinear compression,
trilinear tension etc)
Commented [vp37]: Any conclusions? Relative to HPC or NC?
Commented [vp38]: Same as what? Each other or original
columns?
UHPC had higher load-carrying capacity, they were brittle after the peak load. Their ductility,
however, could be improved by applying the load only on the concrete core, adding steel fibers
into the concrete core or increasing the steel contribution ratio. Based on their study, on
average, Eurocode 4 underestimate the strength of UHPC filled composite stub columns by
14.6%, ignoring confinement effect of fibers, and by 3.5% considering confinement effect of
fibers. They recommended use of at least 0.3-1.0% steel fibers. Dexin (2012) examined the
structural behavior of Concrete filled steel tubes (CFSTs) with ultra-high strength concrete
(UHSC) and high strength steel (HSS) under static loading, to assess the preload effect on the
overall buckling resistance of CFST columns under concentric compression, and extend current
design codes to UHSC, HSS and preload effect. N.V. Tue et al. (2014) studied load bearing
behavior of three different stub columns of confined NSC, HSC, and UHPC in steel tubes.
Based on their observations, UHPC, compared to the two other groups of concrete, has higher
stiffness, upper level of service load, and a rather intense shrinkage, which leads to closing of
the gap between concrete core and steel tube only beyond the service level. Besides, smaller
section area can be chosen if UHPC is used as concrete core in the stub columns. Guler et. al.
(2013) conducted some experiments on circular UHPC-filled steel tube columns under
monotonic axial compression. They investigated the concrete contribution ratio, strength
enhancement index and ductility index, in relation to the diameter-to-thickness ratio of the
columns. Liew et. al. (2014) investigated the behavior of tubular columns in-filled with UHPC at
ambient and elevated temperature. Empelmann et. al. (2016) investigated the behavior of
compact thin-walled reinforced UHPC columns with circular hollow sections under centric and
eccentric normal force.
Recently, Hoang and Fehling (2017a) presented a review of past experimental studies on
UHPC-filled steel tubes under axial loading on entire section and on concrete core. They
investigated the behavior of circular UHPC filled steel tube columns under concentric loading on
concrete core using a finite element model in ATENA-3D (Hoang and Fehling 2017b). They
carried out a parametric study to assess the effect of concrete compressive strength, steel tube
thickness, and steel yield strength on compressive behavior. Hoang and Fehling (2017c) also
studied the effect of confinement factor and the diameter to thickness ratio on strength and
ductility in circular steel tube confined concrete columns infilled with UHPC.
4.3.2.2 FRP-filled Steel Tubes
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Commented [vp39]: LF: Is this something comparable to what
we are “defining” as UHPC here?
Commented [vp40]: Can we add any conclusions here?
Commented [vp41]: Can we add any conclusion here?
Zohrevand (2012) developed a hybrid system of
UHPC-filled fiber reinforced polymer (FRP)
tubes
and
provided
a
comprehensive
experimental investigation using different fiber
types and thickness under uniaxial compression.
Zohrevand and Mirmiran (2012, 2013a, 2013b)
studied he confinement behavior of UHPC due
to FRP tubes and experimentally evaluated its
cyclic behavior within twice length of the plastic
hinge in columns under a constant axial load
and reverse cyclic lateral load. Based on their
observations, such a system has significantly
higher flexural strength and initial stiffness,
lower residual drift, and relatively similar energy
dissipation compared to the reinforced concrete.
Guler et. al. (2013) and Guler (2014)
investigated the behavior of axially loaded UHPC short circular columns wrapped with CFRP,
GFRP, and AFRP sheets. They developed a three dimensional finite element model to predict
the axial stress-strain relationship and ultimate strength of FRP-wrapped UHPC columns. They
evaluated the validity of four confinement models and three codes (ACI-440, CSA-S806-02, and
ISIS CANADA) in comparison with the experimental results from six unconfined and 36 different
types of the FRP-wrapped UHPC columns under monotonic axial compression. Girgin et. al.
(2015) pursued a design oriented combined model to predict the ultimate strength and strain for
axially loaded 7 to 190 MPa FRP-confined circular short columns. Ridha (2017) numerically and
experimentally investigated the performance of square FRP tubular columns in filled with UHPC
under axial-flexural (P-M) loading. They tested eight specimens: four with FRP tubes under
initial load eccentricity 0, 10, 85 and 95 mm, three reference columns without FRP tube under
initial load eccentricities 0, 10, 85 mm, and one with FRP tube under pure bending. The
obtained P-M interaction diagram of UHPC infilled FRP tubular columns are shown in Fig. 5 and
compared against theoretical P-M interaction diagrams that are based on ACI principles.
4.3.2.3 Other Hybrid Designs
Hudoba and Mikus (2013) compared load carrying capacity of a column of conventional
reinforced concrete with four different groups of hybrid columns: solid steel core, smooth 70-mm
diameter UHPC core, corrugated 72-mm diameter UHPC core, and 78-mm diameter UHPC
core in corrugated steel tube, which all had same steel reinforcement. Zhang et al. (2016)
examined behavior of UHPC infilled double-skin tube columns under close-in blast loading.
Popa et. al. (2016) investigated the differences in economy and section between design of a 40
story building by two types of columns: simple section (regular columns made of regular
concrete class C35/45) and compound section (columns with the core made of UHPC class
C130 and an outer shell of RC also class C34/45). They used an equivalent strength and
modulus of elasticity to calculate the pre-dimensions for compound sections in Ultimate Limit
State (ULS). They analyzed the 40-story building in SAP2000 and processed the data for each
column independently. As a conclusion, the reduction of the transversal section was between
32.18% and 62.13% for the columns belonging to the first 30 stories. Ichikawa et al. (2016)
tested two different details of UHPC segments, they proposed for plastic hinge region in
conventional reinforced concrete columns, under orbital bilateral cyclic loading. They
investigated the failure modes, dissipated energy, and equivalent viscous damping.
Using UHPC for column repairs and retrofits can also be considered a hybrid column design.
Massicotte et. al. (2013) presented a seismic strengthening technique using UHPC jackets to
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Commented [vp42]: Where is this Figure referenced in text?
Commented [vp43]: Can we add that ACI is conservative or
more research is required?
Commented [vp44]: LF: Shouldn’t it be 37/45?
prevent splitting failure mode (lap-splice failure, concrete cover spalling, and longitudinal
buckling) in splice regions which does not have adequate reinforcement details. They tested
their proposed technique on four large-scale rectangular bridge piers with the 2:1 cross
sectional ratio. For unconfined 24db long lap splices, they captured drift ductility ratio up to 8
without any strength reduction for bars up to 45mm in diameter. The longitudinal bar buckling
was also eliminated for 300 mm stirrup spacing. Based on their claim, UHPC with 3% fiber
content is sufficient for elimination of failure when using reinforcement diameter up to 45 mm. Li
et. al. (2017) developed a technique to repair conventional reinforced concrete columns
damaged in earthquake, using HPC. They evaluated the efficiency of their proposed technique
by comparing load-carrying capacities, displacement ductility, stiffness, and energy dissipation.
They recommended 1.5 times of the width or height as the repair height of HPC for damaged
columns.
4.4 Shear and Torsion – Ali Semendary
Commented [vp46]: LF: You may also cite works by Beschi et
al. (eslevier journals)
Commented [vp47]: Please provide the full reference
4.4.1 Shear
4.4.1.1 One-way shear – Mohamed
UHPC shear behavior is characterized by complex load transfer mechanisms due to the
presence of fibers that gap the cracks and provide additional strength and ductility. Available
literature includes studying of the factors contributing to UHPC shear strength, applicable code
provisions, and modeling. Regular and Prestressed UHPC I beams with and without stirrups
were tested by (Voo et al.(2010), Florent Baby(2013), Zheng et al.(2016), and Randl et
al.(2018)). Tests investigated shear span to depth ratio (a/d), different fiber contents, fiber
orientation, fiber shape, prestressing level and stirrup content. Results generally show higher
shear capacities and much more ductility that are functions of fiber content and distribution.
Researchers also studied shear strength UHPC of beams reinforced with high strength steel
(Xia et al.(2010) and Qi et al.(2016). Their results also have shown ductile failures and multiple
crack bridging by fibers. Additional investigations included UHPC applications to I beams with
web openinings (Zagon et al.(2015)) and shear reinforcement spacing upper limit (Lim et
al.(2016)).
On the modeling side, (Ngo et al.(2016)) proposed a theoritical model for UHPC beams shear
strnegth based on their experiments considering variable a/d ratios. Chen et al.(2011) used a
concrete-damaged plasticity (CDP) model to investigate both shear and bending behavior of
UHPC beams with good agreement with experimental data.
4.4.1.2 Punching Shear
Research on the punching shear capacity of UHPC was carried out at Virginia Tech [Harris].
Twelve small slabs 1140 mm x 1140 mm (45 in x 45 in) were tested to failure to characterize the
punching shear strength of UHPC. The variables considered were the slab thickness 50, 60, 7
75 mm (2, 2.5, and 3 in) and loading plate dimensions from 25 x 25 mm to 75 x 75 mm (1 in x 1
in to 3 in x 3 in). The results of the testing were compared to several existing models for
punching shear. The two equations that predicted strengths most reliably were the current ACI
punching shear equation and a modified bolt pullout equation. After evaluation of the test
results, the minimum slab thickness required to prevent a punching shear failure in the top
flange due to an 200 mm x 500 mm (8 in x 20 in) wheel patch was determined to be 25 mm (1
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Commented [vp45]: This solution has been used on a bridge in
BC, Canada. Reference Paper Perry & Doiron, CSCE SMSBC, Calgary
2014.
August 28, 2018
in). Except in the case of very thin slabs (ie waffle deck slabs for highway bridges), punching
shear is normally not a critical design factor.
Attempts were made to assure fully restrained supports in order to increase the flexural strength
thereby increasing the likelihood of a punching shear failure. Both flexural and punching failure
modes were observed and it was concluded that the type of failure depends on the area of
loading plate and the slab thickness. The two types of failure are shown in Figure 4.541.2.1(a
and b).
(a)
(b)
Figure 4.4.1.2.1. Typical crack pattern: (a) Punching shear failure;(b) Flexure failure (Harris
2004)
The results demonstrated that the punching shear capacity of the slab was significantly
improved due to the tensile capacity of UHPC, which caused a 60 mm (2.5 in.) slab thickness
to provide sufficient punching shear capacity for bridge applications. The punching shear
capacity of UHPC slab could be estimated using the modified ACI equation for concrete
breakout strength. This conclusion was conducted based on the failure mode that was observed
in the tested specimens. The observed conical failure was similar in appearance to the breakout
cone for concrete as shown in ACI 318-02 (ACI 2002) for a surface with an embedded bolt in
tension. The size of the bolt head was found to have no impact on the failure cone. However,
some modification was made to the equation to be applicable to the commercial UHPC product
with tensile strength up to 11 MPa. The tensile load was assumed equivalent to the applied
punching load. Similar to the bolt head applying load to the slab through the head (Figure
4.4.1.2.2a), the load applied to the Ductal® slabs results from the loading plate (Figure
4.4.1.2.2b).
(a)
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(b)
Figure 4.4.1.2.2: (a) Concrete breakout failure surface; (b) UHPC (Ductal®) breakout (punching
shear) failure surface (Harris 2004)
The modified ACI equation for concrete breakout strength was found to provide a best
measurement of the punching strength of UHPC slabs.
(3. ℎ + 𝑐)2 − 𝑐 2
𝑉𝑐 = 𝑁𝑏 = 𝑘1 . 𝑓𝑡 .
(1)
√ℎ
Where:
𝑓𝑡 = split cylinder tensile strength (ksi)
𝐾1 = empirical constant derived using NLREG software = 0.38
ℎ = slab thickness (in.)
𝑐 = loading plate dimension (in.)
Joh eta al. (2008) investigated the punching shear capacity of 1600 x 1600 mm (63 in. by 63 in.)
unreinforced UHPC slabs. A fixed edge was used to force the punching shear failure. All tested
slabs failed in punching shear mode. The results from the test were compared with the values
predicted using Harris (2004) and ACI 318-05 (ACI 2005) punching formula. The ACI punching
formula gives 73% of actual punching strength, which was considered a good prediction. The
modified equation by Harris (2004) gives similar accuracy as the ACI 318-05 (ACI 2005).
Zohrevand et al (2015) examined the optimal use of UHPC within the critical punching shear
area by conducted an experimental and analytical studies. The tested variables were
reinforcement ratios and depth/area of UHPC. For each reinforcement ratio, slabs were made
from normal concrete, UHPC or hybrid. The hybrid slabs were made in order to examine
different distances from the face of the column using full or partial depth UHPC. The results
demonstrated the punching shear capacity of a flat slab, which was made fully from UHPC, is 3
times more than made of NC. Furthermore, the punching shear capacity of the slab enhanced
by 70% if a full-depth of UHPC was applied within the area enclosed by a perimeter located at a
distance equal to the slab thickness from the column face. However, the punching shear
capacity does not significantly improve when the half-depth of UHPC was implemented. The
punching shear capacity was examined using ACI 318-11 (ACI 2011) and Harris models. The
results showed that both models significantly underestimate the punching shear capacities of
flat slabs with partial or full UHPC. Furthermore, the proposed mode by Harris (2004) is not
applicable to reinforced UHPC slab. The authors recommend more studies to be done in order
to develop analytical models to predict the punching capacity of reinforced UHPC slabs.
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4.4.1.3 Horizontal Shear
Also, at Virginia Tech twenty-four push-off tests were performed to determine if the current
horizontal shear design equations could accurately predict the horizontal shear strength of
composite UHPC (Ductal®) and Lightweight concrete sections. Effects from various surface
treatments, reinforcement ratios, and aspect ratios, were determined. The results predicted by
the current design equations were compared to the actual results found during testing. The
current design equations were all found to be conservative. For its ability to incorporate various
cohesion and friction factors, it is recommended that the equation from AASHTO LRFD
Specification (2004) be used for design [Banta & Roberts-Wolmann]
4.4.2 Torsion
The torsional behavior of members made of UHPC were investigated by many researchers.
Fehling and Ismail (2012) conducted an experimental study on twelve UHPC beams with/out
steel fibers and with/out traditional reinforcement. The studied parameters were steel fiber type
(different bond properties with UHPC), steel fiber volume, longitudinal reinforcement ratio, and
web reinforcement ratio. The varied steel fiber volumetric ratios were (0.0, 0.5, and 0.9 %) and
varied longitudinal and web reinforcement volumetric ratios were (0.0, 1.4 and 2.48 %) and (0.0,
1.68 and 2.53 %), respectively. The results show that cracking and torsion capacities were
enhanced by adding steel fibers to the plain UHPC beams. When the steel fibers volumetric
ratio increased, the number of the cracks per meter also increased. When the longitudinal
reinforcement was added to the beam along with steel fibers, the ductility of the beam improved
but not the ultimate strength. The ultimate torsion capacity and ductility were improved only by
adding the web reinforcement along with the longitudinal reinforcement to the UHPC beams
with steel fibers.
Ismail et al (2016) investigate the capability of three analytical models to predict the ultimate
torsional capacity of UHPC beams with/out traditional (longitudinal and transverse)
reinforcement. The validated models were based on the well-known thin-walled tube and space
truss analogies for reinforced concrete under torsion. The three models also utilize the common
additive approach for determining the torsional capacity. The first model was proposed by
Empelmann and Oettel (2012) who conducted an experimental study on box girders constructed
with UHPC under pure torsional loading and combined loading of torsion moments and normal
forces. The experimental study showed that total torsional capacity can be calculated by the
sum of the contribution of the traditional (longitudinal or transverse) reinforcement and the steel
fiber. The second model was proposed by Joh et al. (2012) who conducted an experimental
program to investigate the torsional capacity of UHPC square members having the same cross
section but different reinforcement details. The author reported that the models proposed by
Empelmann and Oettel (2012) and Joh et al. (2012) consider only the contribution of the steel
fibers through tensile force perpendicular to the crack direction. However, the model proposed
by the authors was based on experimental observations and literature review considered the
contribution of the steel fibers through tensile and shear force along the cracking surface.
Furthermore, the authors believe that the model proposed by Empelmann and Oettel (2012)
provides no values for the thickness of the thin walled tube for the case of UHPC beams without
traditional reinforcement. It instead uses the available wall thickness of the hollow UHPC girder
which in some cases may not necessarily be reasonable. The authors reported that the
contribution of the steel fibers along the cracking surface was considered not only in normal
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direction to the crack but also in tangential direction. This indicates that the steel fibers
contributes to the torsional capacity through both tensile and shear forces. The nominal
torsional capacity of fiber-reinforced UHPC member under torsion can be expressed as fellow: .
𝜎𝑐𝑓0 ×𝐴𝑤
× 2𝐴𝑘
(2)
𝑇𝑛 =
𝑐𝑜𝑠𝜃 × (ℎ − 𝑡𝑒𝑓𝑓 )
Where: 𝐴𝐾 = (𝑏 − 𝑡𝑒𝑓𝑓 ) × (ℎ − 𝑡𝑒𝑓𝑓 ); 𝐴𝑤 = 𝑡𝑒𝑓𝑓 ×
tensile strength of UHPFRC
(ℎ−𝑡𝑒𝑓𝑓 )
𝑠𝑖𝑛𝜃
; 𝜎𝑐𝑓0 represents the post cracking
5.0 Serviceability and Durability Design Considerations
Section 3.0 Material Properties covers the mechanical (including durability) properties and
characterization of UHPC in the uncracked (unloaded) condition. This section 5.0 Serviceability
and Durability covers UHPC in the loaded (elastic or cracked) condition.
5.1 Serviceability – Barzin Mobasher & Yao
A sustainability based approach is based on defining the design parameters based on a limit of
allowable stress, deflection, crack width, or strain measure. Such an approach cannot be
obtained from the limit state, or ultimate strength analysis. Mobasher and co-workers
[Soranakom (2009), Mobasher (2011), Mobasher & Yao (2012) & Yao et al (2017)] presented a
simplified parametric model based on serviceability limit state (SLS) and ultimate limit state
(ULS) criteria for the design of general FRC and hybrid reinforced concrete flexural members.
This model can be implemented both for strain softening and strain hardening FRC such as
SFRC, TRC and UHPC. A general strain hardening tensile, and an elastic perfectly plastic
compression model as derived by Soranakom and Mobasher [2009] and shown in Fig. 5.1.1 is
used. Tensile response is defined by tensile stiffness, E, first crack tensile strain cr, ultimate
tensile capacity, peak, and post crack modulus Ecr. In order to simplify material characteristics of
strain-hardening FRC, and yet obtain closed form design equation generation several
assumptions are made. Equations can be simplified to idealized bilinear tension and elastic
compression models as shown ignoring the post-peak ranges in both tension and compression.
Fig. 5.1.1 Material models and simplified portions for serviceability limits for strain-hardening
FRC: (a) compression model; and (b) tension model
Moment capacity of a beam section according to the imposed tensile strain at the bottom fiber
(t = cr) can be derived by the following steps: (1) determine linear strain and stress
distributions, (2) force components by integration of stresses, (3) solve for the depth of neutral
axis location, k, by force equilibrium, and obtain the strain-curvature relationship. The internal
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moment is obtained from the force and strain distribution and expressed as follows:
M n  (C2
k 2  2k  1
2

2 k 3
) M cr ;
1 k
where C2  C1  2C1   2 ,M cr 
 cr bh 2
6
(1)
General derivation of all potential combinations for the interaction of tensile and compressive
response are presented in [Soranakom & Mobasher (2008 & 2009)]. The nominal moment
capacity of a flexural member Mn must be decreased by a reduction factor to account for
variability in materials and workmanships according to ACI-318 Sec. 9.2 [Soranakom &
Mobasher (2009)] where r is the reduction factor for strain-hardening FRC:
r M n  M u
(2)
Using this approach, one can simulate the flexural response of any member by starting from a
known or back-calculated tensile and compressive constitutive response. For example, Meng et
al. [Soranakom & Mobasher (2009)] tested UHPC beams with dimension of 400x75x75 mm
(16x3x3 inch) in accordance with JCI method. Effect of notch-to-depth ratio were evaluated at
three levels of N/D= 1/6 corresponding to notch depth of 12.5 mm (1/2 inch). Using a constant
rate of the mid-span deflection as the control parameter, loading rates ranging from 0.05
mm/min (0.002 inch/min) to 5.00 mm/min (0.2 inch/min) were used in accordance with available
test methods. Figures 5.1.2(a) and (b) compare the simulated and experimental flexural stressdeflection responses of the UHPC beams with different notch depths and loading rates.
(a)
(b)
Figure. 5.1.2. (a) Tension Models, Comparisons Between Experimental and Simulated Flexural
Stress-Deflection Responses for Different N/D of (b) 1/6, (c) 1/3, (d) 1/2.
The tensile material properties illustrated as multi-linear stress-strain diagrams were backcalculated by fitting the experimental flexural responses for N/D of 1/6, as shown in Figure 2(a).
The results show that in order to fit the experimental loading rate effect, the tensile and residual
strength of have to increase from 9.5 to 15.9 MPa (67%) and 3.1 to 5.2 MPa (67%),
respectively. The loading rate effects revealed by the increasing strength in tensile stress-strain
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laws agree with the experimental investigations on tensile properties of UHPC under varying
strain rates [Meng et al (2017), Zhang et al (2014) & Pyo et al (2015)]. The percentages of
improvement are consistent with those of flexural strength measured from experiment.
General procedures for analysis of beams, panels and 2-D slabs have been developed based
on this approach in recent publications and calibrated against a wide range of published work
[ACI 318]. Appendix I shows a sample set of calculation for a standard UHPC beam.
5.2
Durability – Mo Li
The dense microstructure of UHPC provides a low permeability and reduces transport of
corrosives to steel reinforcements, leading to improved durability of structures. This concept
relies upon the UHPC to remain uncracked within a structure to resist the transport of water,
chloride ions, oxygen, etc. In field conditions, cracking can result from various mechanical and
environmental factors. For example, the relatively high autogenous shrinkage of UHPC due to a
low water-to-cement ratio and lack of coarse aggregates, when restrained, can lead to cracking
in UHPC. Cracks provide pathways for the penetration of aggressive ions to cause reinforced
concrete deterioration. Designing for more durable reinforced concrete structures with UHPC
thus requires the understanding of the crack width control capacity of UHPC under various
loading and environmental conditions, and the effects of cracking on the durability and
serviceability of UHPC and reinforced UHPC.
The following section covers on the design of UHPC for improved durability through crack
control, and the characterization of the durability of UHPC that can provide commentary for
UHPC structural design with improved durability.
5.2.1 Durability requirements for Exposure Classes and crack width limitations in
Reinforced Concrete structures
Design standards and codes for concrete structures suggest crack width limitations for different
environmental exposure conditions, to ensure structural durability in these environments.
Permissible crack widths at the tensile face of reinforced concrete structures for service loads
under different environmental conditions, according to ACI 224R-01 and JSCE Standard
Specifications for Concrete Structures-2007 are summarized in Table 5.2.1.
Table 5.2.1 Permissble Crack Width vs Exposure Condition
Exposure condition
Permissible crack width (mm)
ACI 224R-01
Dry air or protective membrane
0.41
Humidity, moist air, soil
0.30
Deicing chemicals
0.18
Seawater and seawater spray; wetting and drying 0.15
Water retaining structures
0.10
JSCE-07
Deformed bars and Prestressing steel
plain bars
Normal
0.005c
0.004c
Corrosive
0.004c
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Commented [vp48]: For what service life?
Commented [vp49]: Can we add a column to the table for HPC
& NC
Severely corrosive
* c – concrete cover, not exceeding 100 mm
0.0035c
-----
The most stringent crack width limit is placed on water-retaining structures, with maximum
allowable crack width of 100 µm (0.004 in.). For exposure conditions of seawater and seawater
spray, wetting and drying, the maximum allowable crack width is 150 µm (0.006 in.). For deicing
chemical exposure, a maximum crack width of 180 µm (0.007 in.) is specified. Within the current
ACI code (ACI 318-14), a maximum crack width is no longer explicitly specified, although
previous versions of the design code, such as ACI 318-95, suggested 300 µm (0.012 in.) as an
upper limit. The AASHTO (1998) design code relies on the calculation of a “Z” factor, for which
maximum crack width limits are set depending on the type of environmental exposure. In JSCE
Standard Specifications for Concrete Structures (2007), crack width limit for corrosion of
reinforcement is also determined depending on the environmental exposure conditions of the
structure, which are classified into “normal environment”, “corrosive environment” and “severely
corrosive environment”. Normal environment refers to normal outdoor environment with ordinary
conditions without any airborne salt, underground, etc. Corrosive environment refers to
environment with more frequent cyclic drying and wetting, and underground environment below
the level of underground water containing especially corrosive (or detrimental) substances that
may cause harmful corrosion of reinforcement. Normal environment also includes the
environment of marine structures submerged in seawater, or structures not exposed to severe
marine environment. Severely corrosive environment includes: (a) environment in which
reinforcement is subjected to detrimental influences considerably, and (b) environment of
marine structures subjected to tides, splash, or exposed to severe ocean winds (JSCE 2007).
For the severely corrosive environment, the crack width limit is 0.35% of concrete cover
thickness which shall not exceed 100 mm (4 in).
5.2.2 Crack width control – Philipp Hadl
Crack width limitation of UHPC with different amounts of steel fibers including or not including
conventional steel reinforcement has been investigated by different researchers such as Habel
et al. (2007), Leutbecher & Fehling (2008) or Jungwirth (2006). Leutbecher & Fehling (2008)
developed an analytical model to predict the crack width and pattern for steel fiber reinforced
UHPC combined with conventional steel rebars. Initially the model describes single crack
formation of unreinforced UHPC considering shrinkage, followed by crack pattern and spacing
at stabilized cracking. The principles of crack formation are similar to normal strength concrete,
as can be seen in Figure 5.2.2.2. Subsequently it describes crack width limitation for fiber
reinforced UHPC with or without conventional steel rebars including effects of shrinkage. Figure
5.2.2.1 shows the strain distribution at stabilized cracking for fiber reinforced UHPC combined
with conventional rebars for the case, that crack spacing is smaller than the load transmission
length lef of the fibers (sr,max ≤ 2∙lef). This behavior is usually achieved by high fiber contents
(strain-hardening UHPC).
Leutbechers & Fehlings (2008) approach can be used for UHPC reinforced with steel rebars
(without fibers), fiber reinforced UHPC with tension softening behavior as well as strain
hardening behavior. Further, the approach has been verified by experimental investigations with
different amounts of steel fibers (0.9, 1.45, 2.0 Vol.-%). The experimental and theoretical studies
showed, that the tension stiffening effect increases strongly with increasing fiber content, but
crack spacing and crack widths do not decrease in the same manner. The results obtained with
different amounts of steel fibers showed that in combination with steel reinforcing bars, the
UHPC does not need to show strain hardening behavior to achieve progressive crack formation
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with very small crack spacings and crack widths, which improves the durability of structures.
This means, that by combining steel reinforcing bars and fibers, the crack width does not
decrease proportionally with increasing fiber content. In addition, the distance of the transverse
reinforcing bars strongly affects the crack pattern.
Fig. 5.2.2.1. Strain distribution at stabilized cracking for UHPC without fibers for the case sr,max =
2∙les (left) and with fibers and conventional rebars for crack distance sr,max ≤ 2∙lef (right)
In contrast to the described results of Leutbecher & Fehling (2008), Jungwirth (2006) research
showed a direct superposition of reinforcing bars and fiber content. Jungwirth used a strainhardening UHPC and the crack spacing observed in direct tension tests was lower than 15 mm
(0.6 in). This research distinguishes between extremely fine so called meso-cracks due to fibers
formed before activating the conventional reinforcement and macro-cracks caused due to the
bond with conventional reinforcing bars.
Habel et al. (2007) investigated numerically and experimentally the behavior of a composite
consisting of a normal-strength reinforced concrete beam and an UHPC-topping layer applied in
the tensile zone. The fiber-reinforced UHPC showed a fiber content of 6 Vol.-% (fiber length 10
mm [0.4 in]; diameter 0.2 mm [0.008 in]). Additional steel reinforcing bars were used in the
UHPC-layer. The maximum crack spacing with combined reinforcement was only 30 mm (1.25
in) and very small crack widths have been observed similar to the results of Jungwirth (2006).
Fig. 5.2.2.2. Crack pattern of UHPC reinforced with steel fibers combined with rebars Habel et
al. (2007)
According to the Swiss Recommendations SIA 2052 (2007) Strain-Hardening UHPC is
waterproof until a tensile strain of 1‰. For concrete types UA(mild strain-hardening) and UB
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(strain-hardening UHPC) no exact crack-width calculation is required. Further, the French
guideline AFNOR NF P 18-470 (2016) requires no crack width limitation for high strain
hardening UHPC (strain hardening tensile law also in the ULS), since the crack width is
expected to be extremely small. For other types of UHPC (low strain hardening und strain
softening UHPC), methods for calculating the exact crack width and spacing are given in
AFNOR NF P 18-470 (2016). Further, the Australian guideline provides a simplified calculation
method for crack width limitation if the tensile stress exceeds 6.0 MPa (870 psi) in the design.
Research by Charron 2008 and Moreira XXXX has shown that small cracks (< 50 µm [ 0.002
in]) that are no longer active and have been subjected to moisture ingress, in the crack open
condition, can reseal due to the autogeneous self-healing properties of UHPC. This resealing
effect can provide additional protection and improved durability to UHPC structures. More
information on the self-healing can be found in section 5.1.3.2, below.
5.2.3 Durability under mechanical load (focusing on crack formation) – Jean-Philippe
Charron
5.2.3.1 Crack pattern and crack width
Table 5.2.2 summarizes information on crack opening and crack spacing measured in UHPC
under various load levels, with or without rebar in addition to the fiber content. For material
characterization specimens, crack opening varies between 5 to 11 µm at peak load with a crack
spacing ranging between 3 to 6 mm. For structural members without rebar under service load,
crack opening varies between 10 to 55 µm with a crack spacing ranging between 20 to 55 mm.
Larger values are obtained with a lower fiber content both for crack opening and crack spacing.
Under ultimate load, the crack opening increases between 27 to 80 µm, again larger values are
related to a lower fiber content. For structural members with rebar under service load, crack
opening is approximately 30 mm with a crack spacing around 29 mm. Under ultimate load,
crack opening can reach approximately 90 mm.
As general trends, crack opening and crack spacing under loads seem smaller in material
characterization specimens than in structural members for equivalent fiber content. Structural
members with and without rebar present similar crack opening and crack spacing in service
condition, however crack opening reaches at ultimate load is higher in presence of rebar since
they control partly the failure and increase the maximal load. Besides, all results of Table 5.2.2
were measured in UHPC submitted to a static loading, however Lachance et al. () showed that
the application of cyclic loading representing a truck circulation on UHPC bridge slabs increases
progressively the crack opening. Research by Graybeal [2010] showed that cyclic loading, in the
cracked condtion, of reinforced UHPC beams had an increase in load displacement for the first
2 million cycles then appeared to reach a plateau for the next 3 million cycles, at which time the
test was stopped. More information on this research can be found in section 5.1.5.
Table 5.2.2 - Crack opening and crack spacing measured in UHPFRC under load
Reference
Wille et al.
(2014)
Application Reinfor- Vf (%)
cement Lf(mm)
Dog-bone Without
2
specimens rebar
13-30
s (MPa) or
UHPC (%)
0.39 - 0.48
%
Load
condition
Peak load
(1st crack)
w (µm)
s (mm)
9 - 11
4-6
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Commented [vp50]: Reference?
Wille et al.
Dog-bone
(2014)
specimens
Nehdi et al. Tunnel
(2015)
segments
Nehdi et al. Tunnel
(2015)
segments
Hubert et
Tieal. (2015)
specimens
Lachance
Bridge
et al.
slabs
(2016)
Vf and VL: fiber content &
crack spacing
Without
rebar
Without
rebar
Without
rebar
With
rebar
With
rebar
3
13-30
1
8-16
3
8-16
2
10
4
13
0.41 - 0.45
%
250 MPa
450 MPa
250 MPa
438 MPa
Peak load
(1st crack)
1st crack
Ultimate load
1st crack
Ultimate load
Service load
Ultimate load
Service load
Ultimate load
5-9
3-5
27 - 55
55 - 80
10 - 20
27 - 40
29
87
30
90
40 - 55
20 - 35
29
12
-
Length, s : rebar stress, UHPC : UHPC strain, w : crack opening, s :
5.2.3.2 Effect of crack pattern and width on transport properties
Water absorption and water permeability were measured on undamaged and damaged UHPC
(without rebar) having residual crack opening of about 50 µm (Charron et al., 2008). Sorptivity
coefficient measured after 3 days increases from 3.5E -4 to 6.6E-4 L/m2s0.5 in presence of
microcracks, while permeability coefficient obtained after 35 days of exposition rises from an
undetected value (≤1E−12 m/s) to 2.80E−12 m/s with microcracks. As expected the transport
properties increase in presence of microcracks, but they remained lower than those of an
undamaged concrete with a water/binder ratio equal to 0.45.
Water penetration under load was also evaluated in UHPC with rebar in addition to the fiber
content (Hubert et al. 2015). In service condition (rebar stress around 250 MPa), the UHPC
showed crack openings of 29 µm with an instantaneous water permeability of 2.8E -8 m/s, while
reinforced concrete presented crack widths of 148 µm with an instantaneous water permeability
of 3.6E-6 m/s. Very low permeability coefficient of UHPC under load is related to its thin crack
openings, but also to their very high surface roughness and multi-branching pattern.
Difference between immediate and 35-day measurements of permeability coefficients described
above is linked to the strong chemical interactions of water with UHPC, which initiate gradually
with time calcium carbonate precipitation in cracks and hydration of residual clinker at crack
surface. This provides a high capability of self-healing to the material than can reduce by few
orders of magnitude water permeability (Charron et al., 2008). As a matter of fact, Moreira et al
() showed recently that crack opening ranging from 42 to 88 µm in UHPC were totally sealed
after 3 months of exposition to wet and dry cycles. This explain how UHPC specimens
subjected to fatigue tests and then immersed in water with chlorides can exhibit a greater
flexural resistance in comparison to control specimens (Parant 2003).
The crack openings in UHPC members in service condition are generally inferior to 50 µm
(Table 5.2) in comparison to crack width between 200 and 300 µm expected in reinforced
concrete. The very thin crack openings, crack roughness and high self-healing capability of
UHPC limit significantly transport properties and thus deterioration mechanisms.
5.2.4 Durability of cracked elements under chemical loads – Greg Nault
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Commented [vp51]: Reference?
The durability of UHPC under chemical loads, such as de-icing chemicals, alkali reactivity, and
sulphate attack, is largely dependent on the material’s chemical composition, internal pore
structure, and susceptibility to penetration. The UHPC’s mix design (which falls outside the
scope of this document) determines the compactness and imperviousness of the matrix to
chemical ingress. Improvements in durability performance can often be attained by utilizing
advanced curing techniques, such as thermal treatment (i.e. accelerated curing), to more
thoroughly hydrate the cementitious materials in the UHPC. This, ultimately, decreases the
internal porosity of the matrix and reduces the permeability of the material to ingress.
With regard to the structural design of UHPC for durability under chemical loads, appropriate
concrete cover and crack width control are the key parameters to ensuring the long-term
durability and performance of the material. According to the Eurocode 2 specification, minimum
cover thickness to reinforcing/prestressing steel should range from 5 mm to 25/30mm
depending on the structural class of the element and the exposure class of the UHPC. For
highly aggressive environments, such as areas subjected to cyclic wet/dry cycles, frequent
freeze/thaw cycles, and salt/salt-water exposure, the cover thickness should be on the higher
end of the acceptable range (i.e. 20-30 mm).
Likewise, crack widths should be controlled to minimize infiltration by water and other chemical
aggressors. Eurocode 2 specifications recommend an allowable crack width of 0.05 mm to 0.3
mm depending on the exposure class, internal reinforcement characteristics, and load
combination. In general, an allowable crack width of 0.1 mm is typically sufficient for elements in
highly aggressive exposure conditions. For more information on crack width allowances and
designing for crack control, refer to sections 5.1.1 and 5.1.2.
5.2.5 Durability of cracked elements in a marine environment – Rafic El-Helou
Limited research has been conducted to assess the structural performance of a UHPC section
subjected to simultaneous mechanical in an marine environment. Given the exceptional
durability characteristics of uncracked UHPC, particularly its low permeability, it is necessary to
determine that the cracks in UHPC components (i.e. bridge girder subjected transient loads and
deicing chemicals) would not cause significant ingress of liquid into the material resulting in
corrosion of steel fiber reinforcement and loss of UHPC’s tensile capacity (Graybeal, 2010).
Graybeal (2010) tested a mild steel reinforced UHPC beam having a rectangular cross section,
152 mm wide and 381 mm deep, and a span of 4.88 m. The beam was reinforced with two #4
bars positioned at the bottom of the specimen with 35 mm cover. The beam was subjected to
500,000 loading-unloading cycles over 154 days in a four-point bending configuration during
which the tensile face of the beam was continuously wetted using an open-cell sponge soaked
in a 15% NaCl solution. The applied load surpassed the first flexural tensile cracking capacity by
14% creating a series of flexural crack near midspan. The simultaneous application of structural
and environmental loadings to the cracked UHPC beam during this test did not result in any
apparent degradation of the member’s flexural capacity or degradation of the crack bridging
fibers. The NaCl was reported to penetrate to a depth of 3 mm on the side faces of the beam
and 5 mm on the tensile face.
5.2.6 Life Cycle Assessment – Vic Perry
5.2.6.1 End of Life Treatment
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To date, there are no examples of disposing or decommissioning of a UHPC structure. It is
suggested that at the end of the service life, the element should be considered for reuse.
Although there are no significant safety or environmental considerations for UHPC that are
different from regular concrete, end of life reuse, recycling, or disposal options do have special
considerations. Due to the nature of UHPC, it is extremely challenging to demolish UHPC
elements as it is designed to be highly resistant to such intentional destructive treatment.
Primary consideration should be given to reuse of structural elements if the element meets the
required mechanical performance characteristics and this can be achieved with minor physical
modifications. If UHPC does need to be disposed of, diamond cutting large elements into
smaller, more manageable sizes should be undertaken [7.5.1.7.1].
5.2.6.2 Service life prediction
Currently there is a limited amount of research that has been under taken on developing a life
prediction models for UHPC. Research undertaken in France in the late 90’s covered tests
methods typically used by the Nuclear Authority of France to predict life performance. This
testing indicated that a life rating of 300 years could be achievable. Research was undertaken
and sponsored by the US Army Corp of Engineers in the early to mid-90’s by installing test
prisms on the long-term exposure site in Treat Island Maine. The test site is a wharf at mean
tide, where the test specimens are subjected to wet/dry on each tide cycle and freezing/thawing
during winter months ( see section 5.1.5.2 above). Thomas et al has used Fick’s Law to predict
it would take 1000 years for a chloride ion to penetrate through 50 mm of UHPC.
6.0 Future Research Needs
6.1 Test methods to characterize the tensile properties of UHPC
6.2 Tension Response Cracking Pattern
6.3 Compressive stress-strain: There is currently no consensus as to: 1) what the maximum
usable concrete compressive strain is, 2) what the maximum usable tensile strain is, 3) what is
the minimum amount of fibers that need to be included to achieve a certain maximum usable
compressive or tensile strain, 4) what are the definitions for tension controlled, compression
controlled and members in the transition zone, and 5) how to best represent the compressive
and tensile behavior of UHPC at a material level when conducting a sectional analysis at the
ultimate limit state. Additionally, the type of reinforcement that UHPC interacts with plays an
important role in overall member behavior. The use of UHPC in common and repetitive
applications will perhaps provide the impetus for arriving at a unified approach for the flexural
design of UHPC members.
6.4 The performance of horizontal Shear-stud interaction confined in UHPC (Deck to beam
connections)
6.5 Punching Shear in reinforced UHPC slabs.
6.6 Beam-column Inter-action design methods
6.7 Torsion design equations
6.8
7.0 References
7.1.2 Scope:
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American Society of Testing and Materials (ASTM), Annual Book of Standards, Section 4
Construction, Volume 04.01 Cement and Volume 04.02 Concrete and Aggregates, 2017, USA
Swiss Institute of Engineers and Architects (SIA), “Béton fibré ultra-performant (BFUP);
Matériaux, dimensionnement et exécution” prSIA 2052- 2014, Switzerland
Association Française de Normalisation (AFNOR – French standard institute), “National addition
to Eurocode 2 – Design of concrete structures: specific rules for Ultra-High Performance
Concrete Fibre-Reinforced Concrete (UHPFRC)”, NF P 18-710 2016, France
Japanese Society of Civil Engineers (JSCE) “Recommendations for Design and Construction of
Ultra High Strength Fiber Reinforced Concrete Structures” (Draft), 2006, Japan.
Standards Australia (SA, Australia) DR AS 3600:2017 Concrete Structures, Section 16 “Steel
Fibre Reinforced Concrete”, 2017, Australia.
Canadian Standards Association (CSA), CSA A23.1/2 Annex S on Ultra-High Performance
Concrete, 2019, Canada
Canadian Standards Association (CSA), CSA S6 Annex 8.1 on Fibre Reinforced Concrete,
2019, Canada
Federal HighWay Administration (FHWA), “Ultra-High Performance Concrete: A State-of-the-Art
Report for the Bridge Community”, Publication No. FHWA-HRT-13-060, 2013, USA
Schmidt, M. et al, “Sustainable Building with Ultra-High Performance Concrete”, Press
University of Kassel 2014, ISBN: 978-3-86219-480-3, Germany.
Schmidt, M., Leutbecher, T., Piotrowski, S. and Weins, U. “The German Guideline For UHPC”,
Proceedings of the AFGC-ACI-fib-RILEM Int. Symposium on UHPFRC, October 2017,
Montpellier, France, pp 545-554.
Lopez, J.A., Serna, P. & Navarro-Gregori, J. “Advances in the Development of the First
UHPFRC Recommendations in Spain: Material Classifications, design and Characteristics”,
Proceedings of the AFGC-ACI-fib-RILEM Int. Symposium on UHPFRC, October 2017,
Montpellier, France, pp 565-574.
Material Properties
Charron, J.-P., Desmettre, C., (2013) Potential use of fiber reinforced concretes for
constructions of durable civil engineering infrastructures, Technical report ST13-01
Polytechnique of Montréal, Canada, 45 pages. In French.
7.3.1 Mechanical Properties
7.3.1.1
Compression
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El-Helou, R. G. (2016). “Multiscale Computational Framework for Analysis and Design of UltraHigh Performance Concrete Structural Components and Systems.” Doctoral Dissertation,
Virginia Polytechnic Institute and State University, Blacksburg, VA. Retrieved from:
http://hdl.handle.net/10919/73381.
Haber, Z.B., De La Varga, I., Graybeal, B. A., Nakashoji, B., and El-Helou, R. (2018).
“Proporties and behavior of UHPC-class Materials.” FHWA-HRT-18-036. Federal Highway
Administration, Washington, DC.
Ahlborn, T. M., Harris, D. K., Misson, D. L., Peuse, E. J. (2012) Strength and Durability
Characterization of Ultra-High Performance Concrete Under Variable Curing Conditions.
Structures 2011 - Transportation Research Record (TRR No. 2251), 68-75. Washington, D.C.:
Transportation Research Record (TRR), Journal of the Transportation Research Board.
Graybeal. B.A. (2005) “Characterization of the Behavior of Ultra-High Performance Concrete,”
PhD Dissertation, University of Maryland, College Park, Maryland.
7.3.1.1.2 Test Methods to Obtain Compressive Properties
Perry, V. H., “Ultra-High Performance Concrete Advancements and Industrialization 0 The
Need for Standard Testing”, Advances in Civil Engineering Materials, ASTM Volume 4, Issue 2,
W. Conshohocken, PA, USA 2015.
Graybeal, B. “Compressive Testing of Ultra-High Performance Concrete”, Advances in Civil
Engineering Materials, ASTM Volume 4, Issue 2, W. Conshohocken, PA, USA 2015.
Graybeal, B. and Davis, M. “Cylinder or Cube: Strength Testing of 80 to 200 MPa (11.6 to 29
KSI) Ultra-High Performance Fiber-Reinforced Concrete", ACI Materials Journal, NovemberDecember 2008, pp. 603-9, USA, 2008.
FHWA-HRT-06-103 “Material Property Characterization of Ultra-High Performance Concrete”,
FHWA, McLean, VA, USA, 2006.
FHWA-HRT-12-064 “Compression Response of a Rapid-Strengthening Ultra-High Performance
Concrete Formulation”, FHWA, McLean, VA, USA, 2006
Graybeal, B., “Compressive Behavior of Ultra-High Performance Concrete”, ACI Materials
Journal, Vol. 104, No. 2, March – April, 2007.
7.3.1.2
Tension
Haber, Z.B., De La Varga, I., Graybeal, B. A., Nakashoji, B., and El-Helou, R. (2018).
“Proporties and behavior of UHPC-class Materials.” FHWA-HRT-18-036. Federal Highway
Administration, Washington, DC.
Graybeal, B. A., and baby, F. (2013). “Development of direct tension test method for ultra-high
performance fiber-reinforced concrete.” ACI Mater. J., 110(2), 177-186.
7.3.1.3 Flexural
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7.3.1.4 Shear
7.3.1.5 Bond Strength
7.3.1.5.1 FHWA-HRT-14-084 “Design and Construction of Field-Cast UHPC Connections.
Harris, D. K., Sarkar, J., Ahlborn, T. M. (2011) Interface Bond Characterization of Ultra-High
Performance Concrete Overlays. Concrete Materials 2011 - Transportation Research
Record(TRR No. 2240), 40-49. Washington, D.C.: Transportation Research Board; Journal of
the Transportation Research Board.
FHWA-HRT-14-090 - Bond Behavior of Reinforcing Steel in Ultra-High Performance Concrete
Graybeal, B. and Haber, Z., “Ultra-High Performance Concrete for Bridge Deck Overlays”
FHWA-HRT-17-097, McLean VA, USA, 2017.
Emerson E. J., Edmundo D. R., Royce W. F., and Hale, W. M., “Transfer and Development
Lengths and Prestress Losses in Ultra-HighPerformance Concrete Beams”,
transportationResearch Record: journal of the Transporation Research Board, No. 2251, pp. 7681, Washington, DC, 2011.
Fehling, E. and Lorenz, P., “Anchorage and Overlapping of Non-Prestressed Reinforcement in
UHPC”, Sustainable Building with UHPC, University of Kassel Press, Volume No.22, 2014.
7.3.2 Durability Properties
FHWA-HRT-06-103 – Material Property Characterization of Ultra-High Performance Concrete
7.3.2.1 Absorption
FHWA-HRT-06-103 – Material Property Characterization of Ultra-High Performance Concrete
7.3.2.2 Salt-scaling and Freeze/Thaw
FHWA-HRT-06-103 – Material Property Characterization of Ultra-High Performance Concrete
7.3.2.3 Permeability
7.3.2.3.1 Chloride ion Penetration
Thomas, M. et al, “Marine performance of UHPC at Treat Island”,3rdInternation Symposiumon
UHPC, HiPerMat2016, Kassel, Germany, 2016.
7.3.2.3.2.1 Carbonation
Graybeal, B.,–“ Material Property Characterization of Ultra-High Performance Concrete”,
FHWA-HRT-06-103, McLean, Va, USA 2006.
7.3.2.4 Acid and sulphate resistance
Schmidt, H., Schmidt-Dohl, F., Franke, L. and Deckeimann, G., “Resistance of UHPC to
Chemical Attack”, Sustainable Building with UHPC, University of Kassel Press, Volume No.22,
2014.
Koenig A., Dehn F. “Acid Resistance of Ultra High-Performance Concrete (UHPC)”, In:
Sobolev K., Shah S. (eds) Nanotechnology in Construction. Springer, Cham , 2015.
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Piérard, J., Dooms, B. and Cauberg, N., “Evaluation of Durabillity Properties of UHPC using
Accelerated Lab Tests”, Proceedings of UHPC & Nano-Technology in Construction, Kassel,
Germany, 2012.
7.3.2.5 Delayed Ettringite Formation
7.3.2.6 Abrasion
7.3.2.7 Alkali-Silica Reaction
7.3.3 Time Dependent Properties
7.3.3.1 Creep coefficient
Flietstra, J.C. (2011) Creep and Shrinkage Behavior of Ultra High Performance Concrete under
Compressive Loading with Varying Curing Conditions,” MS Thesis, MIchigan Tech University.
Mullen, C.H.(2013) Determining the effect of Thermal Treatment Timing on deflections of UltraHigh Performance Concrete Beams”, MS Thesis, MIchigan Tech University.
7.3.3.2 Shrinkage
Graybeal, B., Zachary B. Haber, Igor De la Varga, Brian Nakashoji, and Rafic El-Helou,
“Properties and Behavior of UHPC- Class Materials” , FHWA-HRT-18-036, McLean, Va., USA,
2018.
De la Varga et al., “ Enhancing Shrinkage Properties and Bond Performance of Prefabricated
Bridge Deck Coneection Grouts: Material and component Testing”, Journal of Materials in civil
Engineering, ASCE, ISSN 0899-1561, USA, 2018
7.3.3.3 Thermal Coefficient of Expansion
7.3.4 Fire Properties
Behloul et al., “Fire Resistance of Ductal -Ultra-High Performance Concrete”,
Proceedings of the First fib Congress, Osaka, Japan, 2002, pp. 421–430.
AFGC/SETRA, “Ultra-high performance fibre-reinforced concretes –
Recommendations”, Interim Recommendations, AFGC publication, France, 2013.
Hosser, D., et al “Theoritical and Experimental Determiniation of the High Temperature
Behaviour of UHPC”, Sustainable Building with UHPC, University of Kassel Press, Volume
No.22, 2014.
Hao-wen Ye, Nai-qian Feng, Yan Ling-hu, Zhi-wei Ran, Li-xun Lin, Shi-kun Qi, and Yi Dong,
“Research on Fire Resistance of Ultra-High-Performance Concrete”, Hindawi Publishing
Corporation, Advances in Materials Science and Engineering, Volume 2012, Article ID 530948,
China, 2012.
7.3.5 Other Properties
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7.3.5.1 Fibre Matrix Interaction & Fibre Orientation
AFGC/SETRA. 2013. « Ultra-high performance fibre-reinforced concretes Recommendations ». Interim Recommendations, AFGC publication, France.
http://www.afgc.asso.fr/index.php/publications/41-publications/documents-scientifiques-ettechniques/37-documents-scientifiques-et-techniques-edition-afgc.
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Armelin, Hugo S., et Nemkumar Banthia. 1997. « Predicting the flexural postcracking
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Banthia, Nemkumar. 1990. « A study of some factors affecting the fiber-matrix bond in steel
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Banthia, Nemkumar, et Jean-Fancois Trottier. 1994. « Concrete reinforced with deformed steel
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Baril, M. A., L. Sorelli, J. Réthoré, F. Baby, F. Toutlemonde, L. Ferrara, S. Bernardi, et M.
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Baril, M.A., Luca Sorelli, Thomas Guenet, Florent Baby, Liberato Ferrara, Marco Faifer, et
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Baril, M.A., Luca Sorelli, Réthoré, Liberato Ferrara, François Toutlemonde, Florent Baby,
Sébastien Bernardi, et Mario Fafard. 2016. « The Effect of Casting Flow Defects on the Crack
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Delsol, S., Charron, J.-P., (2013) Numerical modeling of UHPFRC mechanical behavior based
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Ferrara, Liberato, Nilufer Ozyurt, et Marco Di Prisco. 2011. « High mechanical performance of
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Fu, Shao-Yun, et Bernd Lauke. 1996. « Effects of fiber length and fiber orientation distributions
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Maya Duque, L.F., I. De la Varga, et B. Graybeal. 2016. « Fiber Reinforcement Influence on the
Tensile Response of UHPFRC ». In First International Symposium on UHPC. Des Moines,
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Naaman, Antoine E., et Surendra P. Shah. 1976. « Pull-out mechanism in steel fiber-reinforced
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Shah, Surendra P., et B. Vijaya Rangan. 1971. « Fiber reinforced concrete properties ». In
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Sorelli, Luca, Nemkumar Banthia, Vivek Bindiganavile, Giovanni Plizzari, Ying-shu Yuan,
Surendra P. Shah, et Heng-lin Lü. 2003. « Static and dynamic responses of hybrid fiber
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Wille, Kay, et Antoine E. Naaman. 2012. « Pullout Behavior of High-Strength Steel Fibers
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7.3.5.2 Cyclic Strength and Stiffness Degradation
Graybeal, B., and Hartmann, J., “Ultra-High Performance Concrete Material Properties”,
Transportation Research Board Annual Meeting, 2003, Washington, DC, USA.
Parsekian, G. A., Shrive, N. & Perry, V., “Static and Fatigue Tests on Ductal® UHPFRC
Footbridge Sections”, Proceedings of the Fifth ACI/CANMET/IBRACON International
Conference on high-Performance Concrete Structures and Materials, 18-20 June 2008,
Manaus, Amazon State, Brazil, Publication No. SP-253, Ed., Figueiredo, E.P.et al., American
concrete Institute, Farmington hills, MI, 2008, pp273-290.
Schmidt, M, et al., “Durability of Ultra-High Performance Concrete”, Proceedings of the 6th
International Symposium on High Strength/High Performance Concrete”, Leipzig, Germany,
June 2002, Ed., Konig, G., Dehn, F., and Faust, T.,, Vol. 2, pp 1,367-1.376.
Loraux, C.T. “Long-term monitoring of existing wind turbine towers and fatigue performance of
UHPFRC under compressive stresses”, Thesis, University of Lausanne, Switzerland, 2018.
Sritharan, S. and Schmitz, G., “Design of Tall Wind Turbines utilizing UHPC”, Proceedings of
Int. Symposium on UHPFRC, Rilem-fib- AFGC, Marseille, France, 2013
Lee, G. C., Huang, C., Song, J. and O’Connor, J. S., “Seismic Performance of Precast Girders
with Field-Cast UHPC Connections, MCEER, SUNY, Buffalo, USA, ISSN 1520-295X, 2014.
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M.A. Meyers, Dynamic Behavior of Materials, 1 edition, Wiley-Interscience, New York,
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T. Nicholas, Tensile testing of materials at high rates of strain, Exp. Mech. 21 (1981)
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K.G. Hoge, Influence of strain rate on mechanical properties of 6061-T6 aluminum under
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V. Bindiganavile, N. Banthia, Polymer and Steel Fiber-Reinforced Cementitious
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V. Bindiganavile, N. Banthia, Polymer and Steel Fiber-Reinforced Cementitious
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B. Mobasher, Chapter 5 - Textile fiber composites: Testing and mechanical behavior, in:
T. Triantafillou (Ed.), Text. Fibre Compos. Civ. Eng., Woodhead Publishing, 2016: pp. 101–150.
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X. Xiao, Dynamic tensile testing of plastic materials, Polym. Test. 27 (2008) 164–178.
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M. Xu, K. Wille, Fracture energy of UHP-FRC under direct tensile loading applied at low
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W. Meng, Y. Yao, B. Mobasher, H.K. Khayat, Effects of Loading Rate and Notch-toDepth Ratio of Notched Beams on Flexural Performance of Ultra-High-Performance Concrete
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Z. Rong, W. Sun, Experimental and numerical investigation on the dynamic tensile
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E. Cadoni, D. Forni, Experimental analysis of the UHPFRCs behavior under tension at
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Groeneveld, A.B., T. M. Ahlborn, C. K. Crane, C. A. Burchfield, E. N. Landis, Dynamic strength
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7.3.5.4
Abbas, S., M. L. Nehdi, and M. A. Saleem. 2016. “Ultra-High Performance Concrete: Mechanical
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Behloul, M., G. Chanvillard, P. Pimienta, A. Pineaud, and P. Rivillon. 2005. “Fatigue Flexural
Behavior of Pre-Cracked Specimens of Special UHPFRC.” Special Publication 228: 1253–68.
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Curosu, Iurie, and Viktor Mechtcherine. 2016. “Tensile Behavior of Strain-Hardening CementBased Composites (SHCC) Subjected to Impact Loading.” In Ultra-High Performance Concrete
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7.4.2 Compression and Tension
7.4.2.1 Compression
7.4.2.2 Tension
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Almansour, H., Lounis, Z. (2010). “Innovative design approach of precast–prestressed girder
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7.4.4 Combined Axial and Bending
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Caldwell, Tricia. 2011. “Plastic Hinge Behavior of Reinforced Concrete and Ultra High
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Chao, Shih-Ho et al. 2016. “Seismic Behavior of Ultra-High-Performance Fiber- Reinforced
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Davila, Ricardo S. 2007. “Recommendations for the Design of Ultra-High Performance
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Dexin, Xiong. 2012. “Structural Behaviour of Concrete Filled Steel Tubes With High Strength
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Empelmann, Martin, Corinna Mueller, and Daniel Busse. 2016. “Compact Reinforced UHPC
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Feng, J.W., and P.Y. Yan. 2008. “Mechanical Behaviour of UHPC and UHPC Filled Steel
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Girgin, Zehra Canan, and Konuralp Girgin. 2015. “A Design-Oriented Combined Model (7
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Guler, Soner. 2014. “Axial Behavior of FRP-Wrapped Circular Ultra-High Performance
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Guler, Soner, Alperen Copur, and Metin Aydogan. 2013. “Nonlinear Finite Element Modeling
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Hosinieh, Milad Mohammadi, Hassan Aoude, William D Cook, and Denis Mitchell. 2015.
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Kimura, Hideki, Yuji Ishikawa, Atsushi Kambayashi, and Hiroto Takatsu. 2007. “Seismic
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Li, Jun, Chengqing Wu, Hong Hao, and Yu Su. 2015. “Investigation of Ultra-High
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Li, Xiuling, Juan Wang, Yi Bao, and Genda Chen. 2017. “Cyclic Behavior of Damaged
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Liew, J.Y.R., M.X. Xiong, and D.X. Xiong. 2014. “Design of High Strength Concrete Filled
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Liew, J Y Richard, and D X Xiong. 2012. “Ultra-High Strength Concrete Filled Composite
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Massicotte, Bruno, Marc-André. Dagenais, and Fabien. Lagier. 2013. “Performance of
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Maten, R.N. ter. 2011. “Ultra High Performance Concrete in Large Span Shell Structures.”
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MS, Ridha. 2017. “Axial-Flexural Interaction of Square FRP Tube Columns In-Filled with
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Popa, Mircea, Zoltan Kiss, Horia Constantinescu, and Geanina Bolca. 2016. “Case Study:
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Russell P. Burrell, Hassan Aoude and Murat Saatcioglu. “Blast Behaviour of Ultra High
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Schmidt, Holger, and Martin Heimann. 2011. “Probabilistic Modelling of HSC and UHPC
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Sugano, Shunsuke, Hideki Kimura, and Kazuyoshi Shirai. 2007. “Study of New RC
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Tue, Ngyen Viet, Holger Schneider, Gert Simsch, and Detlef Schmidt. 2004. “Bearing
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Uchida, Yuichi, Junichiro Niwa, Yoshihiro Tanaka, and and Makoto Katagiri. 2006. “Outlines
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Zhang, Fangrui et al. 2016. “Experimental Study of CFDST Columns Infilled with UHPC
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7.4.5 Shear and Torsion
7.4.5.1 Shear
7.4.5.1.1 Punching Shear
Harris, D. K. (2004). “Characterization of punching shear capacity of thin UHPC plates.” M.S.
thesis, Virginia Polytechnic Institute and State Univ., Blacksburg, VA.
Harris, D, and Roberts-Wollmann C., “Characterization of the Punching Shear Capacity of Thin
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Zohrevand, P., Yang, X., Jiao, X., & Mirmiran, A. (2014). Punching Shear Enhancement of Flat
Slabs with Partial Use of Ultrahigh-Performance Concrete. Journal of Materials in Civil
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7.4.5.1.2 Horizontal Shear
Banta, T. and Roberts-Wolmann, C., “Horizontal Shear Transfer between UHPC and
Lightweight Concrete”, Virginia Polytechnic Institute, Blacksburg, Virginia, February 2005.
7.4.5.1.3 One-Way Shear
Baby, Florent, Pierre Marchand, and François Toutlemonde. "Shear behavior of ultrahigh
performance fiber-reinforced concrete beams. I: Experimental investigation." Journal of
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Baby, Florent, Pierre Marchand, and François Toutlemonde. "Shear behavior of ultrahigh
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Chen, Linfeng, and Benjamin A. Graybeal. "Modeling structural performance of secondgeneration ultrahigh-performance concrete pi-girders." Journal of Bridge Engineering 17.4
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Lim, Woo-Young, and Sung-Gul Hong. "Shear tests for ultra-high performance fiber reinforced
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Ngo, Tri Thuong, et al. "Shear resistance of ultra-high-performance fiber-reinforced concrete."
Construction and Building Materials 151 (2017): 246-257.
Qi, Jia-Nan, et al. "Post-cracking shear strength and deformability of HSS-UHPFRC beams."
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Randl, Norbert, Tamás Mészöly, and Peter Harsányi. "Shear Behaviour of UHPC Beams with
Varying Degrees of Fibre and Shear Reinforcement." High Tech Concrete: Where Technology
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Voo, Yen Lei, Wai Keat Poon, and Stephen J. Foster. "Shear strength of steel fiber-reinforced
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Xia, Jun, et al. "Shear failure analysis on ultra-high performance concrete beams reinforced with
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Zagon, Raul, Stijn Matthys, and Zoltan Kiss. "Shear tests on SFR-UHPC I-shaped beams with
or without web openings." Ultra-High Performance Concrete and High Performance
Construction Materials (HIPERMAT). Vol. 27. 2016.
Zheng, Hui, and Zhi Fang. "Experimental Study on Shear Behavior of Prestressed Ultra-High
Performance Concrete I-girders." IABSE Symposium Report. Vol. 106. No. 5. International
Association for Bridge and Structural Engineering, 2016.
7.4.5.2 Torsion:
Fehling, E. and Ismail, M., “Experimental Investigations on UHPC Structural Elements Subject
to Pure Torsion,” Proceedings of Hipermat 2012 3rd International Symposium on UHPC and
Nanotechnology for High Performance Construction Materials, Ed., Schmidt, M., Fehling, E.,
Glotzbach, C., Fröhlich, S., and Piotrowski, S., Kassel University Press, Kassel, Germany,
2012, pp. 501–508. 91 191.
Joh, C. et al., “Torsional Test of Ultra High Performance Fiber-Reinforced Concrete Square
Members,” Proceedings of Hipermat 2012 3rd International Symposium on UHPC and
Nanotechnology for High Performance Construction Materials, Ed., Schmidt, M., Fehling, E.,
Glotzbach, C., Fröhlich, S., and Piotrowski, S., Kassel University Press, Kassel, Germany,
2012, pp. 509–516. 192.
Empelmann, M. and Oettel, V., “UHPFRC Box Girders Under Torsion,” Proceedings of Hipermat
2012 3rd International Symposium on UHPC and Nanotechnology for High Performance
Construction Materials, Ed., Schmidt, M., Fehling, E., Glotzbach, C., Fröhlich, S., and
Piotrowski, S., Kassel University Press, Kassel, Germany, 2012, pp. 517–524.
Fehling, E. and Ismail, M., “Experimental Investigations on UHPC Structural Elements Subject
to Pure Torsion,” Proceedings of Hipermat 2012 3rd International Symposium on UHPC and
Nanotechnology for High Performance Construction Materials, Ed., Schmidt, M., Fehling, E.,
Glotzbach, C., Fröhlich, S., and Piotrowski, S., Kassel University Press, Kassel, Germany,
2012, pp. 501–508. 91 191.
Ismail, M, Fehling, E. and Hoang An L. “Comparative analytical Modelling of reinforced
UHPFRC under pure Torsion” Conference: 4th International Symposium on Ultra-High
Performance Concrete and High Performance Construction Materials, Kassel, March 9-11,
2016, At Kassel, Germany, Volume: No.27.
7.5 Serviceability and Durability Design considerations
7.5.1 Serviceability
C. Soranakom, B. Mobasher, Flexural Design of Fiber-Reinforced Concrete, Mater. J. 106
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B. Mobasher, Mechanics of Fiber and Textile Reinforced Cement Composites, CRC Press,
2011.
B. Mobasher, Y. Yao, C Soranakom, Analytical solutions for flexural design of hybrid steel fiber
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Y. Yao, X. Wang, K. Aswani, B. Mobasher, Analytical procedures for design of strain softening
and hardening cement composites, International Journal of Advances in Engineering Sciences
and Applied Mathematics, 1-14, 2017
Soranakom C, Mobasher B. Correlation of tensile and flexural response of strain softening and
strain hardening cement composites. Cem Concr Compos, 2008;30:465-477.
ACI Committee 318. Building Code Requirements for Structural Concrete. ACI Manual of
Concrete Practice, American Institute, Detroit, USA, 2005.
W. Meng, Y. Yao, B. Mobasher, H.K. Khayat, Effects of Loading Rate and Notch-to-Depth Ratio
of Notched Beams on Flexural Performance of Ultra-High-Performance Concrete, Cem. Concr.
Compos. (2017).
Standard JC, Method of test for fracture energy of concrete by use of notched beam, Japan
Concr. Inst. JCI-S-001-2003 (2003).
X.X. Zhang, A.M. Abd Elazim, G. Ruiz, R.C. Yu, Fracture behaviour of steel fibre-reinforced
concrete at a wide range of loading rates, Int. J. Impact Eng. 71 (2014) 89–96.
doi:10.1016/j.ijimpeng.2014.04.009.
S. Pyo, K. Wille, S. El-Tawil, A.E. Naaman, Strain rate dependent properties of ultra high
performance fiber reinforced concrete (UHP-FRC) under tension, Cem. Concr. Compos. 56
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7.5.2 Durability
Durability requirements for Exposure Classes and crack width limitations in Reinforced
Concrete Structures
7.5.2.2 Crack width control
Leutbecher, T., Fehling, E.: 2008. Crack Width Control for Combined Reinforcement of Rebars
and Fibers exemplified by Ultra-High-Performance Concrete. In fib Task Group 8.6 Ultra High
Performance Fibre Reinforced Concrete – UHPFRC. Varenna, September 5th 2008.
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Leutbecher, T., Fehling, E.: 2012. Tensile Behavior of Ultra-High-Performance Concrete
Reinforced with Reinforcing Bars and Fibers: Minimizing Fiber Content. ACI Materials Journal
109 (2).
Jungwirth, J.: 2006. Zum Tragverhalten von zugbeanspruchten Bauteilen aus UltraHochleistungs-Faserbeton. PhD-Thesis. EPFL Lausanne.
Habel, K., Denarie, E., Brühwiler, E.: 2007. Experimental Investigation of Composite Ultra-HighPerformance Fiber-Reinforced Concrete and Conventional Concrete Members. ACI Structural
Journal. 104 (1).
Swiss Institute of Engineers and Architects (SIA). 2016. SIA 2052. Béton fibré ultra-performant
(BFUP) : Matériaux, dimensionnement et exécution. Switzerland.
Association Française de Normalisation. 2016. NF P 18-710. National addition to Eurocode 2 –
Design of concrete structures: specific rules for Ultra-High-Performance Concrete FibreReinforced Concrete (UHPFRC). France.
Gowripalan, N., and Gilbert, R. I. (2000). Design guidelines for RPC prestressed concrete
beams. Australia.
7.5.2.3 Durability under Mechanical load
K. Wille a, S. El-Tawil, A.E. Naaman (2014) Properties of strain hardening ultra high
performance fiber reinforced concrete (UHP-FRC) under direct tensile loading, Cement &
Concrete Composites, 48, pp. 53–66.
Charron, J.-P., Denarié, E., Brühwiler, E., (2008) Transport properties of a UHPFRC in cracking
state, Cement and Concrete Research, Vol. 38, pp. 689-698.
Moncef L. Nehdi, Safeer Abbas, Ahmed M. Soliman (2015) Exploratory study of ultra-high
performance fiber reinforced concrete tunnel lining segments with varying steel fiber lengths and
dosages, Engineering Structures, 101, pp. 733–742.
C.W. Aldea, S.P. Shah, A.F. Karr, (1999) Permeability of cracked concrete, Materials and
Structures, 32 (219) pp. 370–376.
N. Hearn, (1998) Self-sealing, autogenous healing and continued hydration: what is the
difference? Materials and Structures 31, pp. 563–567.
Lachance F, Charron J-P, Massicotte B. (2016). Development of Precast Bridge Slabs in High
and Ultra-High Performance Fiber Reinforced Concretes. ACI Structural Journal, V. 113, No. 5,
September-October 2016. Pp. 929-939.
Hubert, M., Desmettre, C. Charron, J.-P., (2015) Influence of fiber content and reinforcement
ratio on the water permeability of reinforced concrete, Materials and Structures., September
2015, Volume 48, Issue 9, pp 2795-2807.
Charron et al, BEFIB2016.
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E. Parant, Damage mechanisms and mechanical behaviors of a multi-scale
under harsh conditions: fatigue, impact, corrosion, Ph.D. thesis of Ecole
Nationale des Ponts et Chaussées, France, 2003.
Charron, J.-P., Denarié, E., Brühwiler, E., (2008) Transport properties of a UHPFRC in cracking state,
Cement and Concrete Research, Vol. 38, pp. 689-698.
Lachance F, Charron J-P, Massicotte B. (2016). Development of Precast Bridge Slabs in High and UltraHigh Performance Fiber Reinforced Concretes. ACI Structural Journal, V. 113, No. 5, September-October
2016. Pp. 929-939.
Hubert, M., Desmettre, C. Charron, J.-P., (2015) Influence of fiber content and reinforcement ratio on the
water permeability of reinforced concrete, Materials and Structures., September 2015, Volume 48, Issue
9, pp 2795-2807.
Graybeal, B., “Simultaneous Structural and Environmental Loading of a UHPC Component”,
FHWA HER-10-055, McLean, Va., 2010.
7.5.2.4 Durability under Chemical load
“Material Property Characterization of Ultra-High Performance Concrete”, FHWA-HRT-06-103,
Federal Highway Administration, August 2006.
“Ultra-High Performance Concrete: A State-of-the-Art Report for the Bridge Community”,
FHWA-HRT-13-060, Federal Highway Administration, June 2013.
Acker, P. and Behloul, M., “Ductal® Technology: a Large Spectrum of Properties, a Wide Range
of Applications”, Proceedings of the International Symposium on Ultra High Performance
Concrete, Kassel, Germany, September 2004.
Franke, L et al., “Behaviour of ultra high-performance concrete with respect to chemical attack”,
Proceedings of the Second International Symposium on Ultra High Performance Concrete,
Kassel, Germany, March 2008.
Pierard, J. et al., “Durability Evaluation of Different Types of UHPC”, Proceedings of the RILEMfib-AFGC International Symposium on Ultra-High Performance Fibre-Reinforced Concrete,
Marseille, France, October 2013.
Rehacek, S. et al., “UHPC and FRC in Severe Environmental Conditions, Resistance Against
Freeze-thaw Cycles, Aggressive Chemical Agents and Dynamic Loading”, Proceedings of the
First International Interactive Symposium on UHPC, Des Moines, Iowa, June 2016.
7.5.2.5 Durability Under Temperature Effects
Ahlborn, T., Peuse, E., Li Misson, D.: 2008. Ultra-high-Performance-Concrete for Michigan
Bridges Material Performance–Phase I. Research Report No. MDOT RC-1525.
Behloul, M, Chanvillard, G., Casanova, P., Orange, G.: 2012. Fire Resistance of Ductal Ultra
High Performance Concrete. In Proceedings of fib symposium 2012. Osaka, Japan.
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Felicetti R., Gambarova P.G., Natali Sora M.P. and Khoury G. A: 2000. Mechanical behaviour of
HPC and UHPC in direct tension at high temperature and after cooling. In Proc. 5th Symposium
on Fibre-Reinforced Concrete BEFIB 2000. Lyon (France), September 13-15, p. 749-758.
FHWA: 2006. Material Property Characterization of Ultra-High Performance Concrete.
Graybeal, B.: 2014. Design and Construction of Field-Cast UHPC Connections. In Report No.
FHWA-HRT-14-084.
Habel, K.: 2004. Structural Behaviour of Elements Combining Ultra-High Performance Fibre
Reinforced Concretes (UHPFRC) and Reinforced Concrete. PhD-Thesis. EPFL Lausanne,
Switzerland.
Hussein, H., Walsh, K., Sargand, S., Steinberg, E.: 2016. Effect of extreme temperatures on the
coefficient of thermal expansion for ultra-high performance concrete. In First Interactive
Symposium on UHPC. Des Moines, IA.
Japan Society of Civil Engineers Guide (JSCE). 2010. Recommendations for Design and
Construction of Ultra High Strength Fiber Reinforced Concrete Structures.
Schneider, U., Diederichs, U., Horvath, J.: 2003. Verhalten von Ultrahochfesten Betonen
(UHPC) unter Brandbeanspruchung. Beton- und Stahlbetonbau. 98 (7).
Swiss Institute of Engineers and Architects (SIA). 2016. SIA 2052. Béton fibré ultra-performant
(BFUP) : Matériaux, dimensionnement et exécution. Switzerland.
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Performance of UHPC at Treat Island. In Proceedings of Hipermat 2012. Kassel, Germany.
Ye, H.-W., Feng, N., Ling-hu, Y., Ran, Z., Lin, L., Qi, S., Dong, Y. : 2012. Research of Fire
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7.5.2.6 Durability Under Combined Mechanical and Environmental Load
Graybeal, B., “Simultaneous Structural and Enviromental Loading of an Ultra-High Performance
Concrete Component” Federal Highway Administration, Report No. FHWA-HRT-10-054, July
2010
7.5.2.7 Life Cycle Assessment
7.5.2.7.1 End of Life Treatment
Canadian Standards Association (CSA), CSA A23.1/2 Annex S on Ultra-High Performance
Concrete, 2019, Canada
7.5.2.7.2 Service Life Prediction
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Thomas, M., Green, B., O`Neal, E, Perry, V., Hayman, S., Hossack, A.: 2012. Marine
Performance of UHPC at Treat Island. In Proceedings of Hipermat 2012. Kassel, Germany.
8.0 APPENDICES:
Commented [vp52]: All of these Appendices should be deleted
and put into the future Guide.
The following Appendices may be included into the ETR, depending on the state of
complimentary documents published at the time of balloting this ETR on the Structural Design of
UHPC.
Appendix A: Material Characterization Methods
Appendix B: Simulation-Based Design
Appendix C: Examples of UHPC Construction
Appendix D: Research Gaps
Appendix E: Demand Forces and Stresses
Appendix F: Design Examples
Solved Example Problems for – Parametric Based Design for UHPC:
The sample problem can be constructed under three different cases:
Case A - The sizes of the beam and the residual strength of the material are known, the maximum
allowable load is required for a given geometry.
Case B - Size of the beam and the loading condition (moment demand) are known, the level of residual
strength is required.
Case C - The residual strength of the material and the loading condition (moment demand) are known,
the size of the section is required.
Case A- Calculation of the moment capacity of a given section
The aim of this section is to use the simplified ultimate strength approach and compare the parametric
design of FRC with the solutions obtained from ACI 544.8R-16 in order to illustrate the process of
obtaining moment capacity for a section and compute the allowable service load.
Problem Statement- Compute the maximum allowable load on a simply supported beam with a span of
L  10 ft  3.04 m  and a rectangular Section 6” by 2” (152mm by 305mm) is used. UHPC concrete
has fc'  22 ksi (151.6 MPa), ft  1.2 ksi (8.27 MPa) .
Design
for
a
material
with
feq,3  580 psi  4 MPa  . Assume a concrete density as c  150 lb/ft (2402.7 kg/m ) and
3
3
compute unfactored moment by assuming   1 (  is strength reduction factor which is less than 1 in
accordance to ACI 318-14 Section 10.5.1 (ACI 318-14).
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Commented [MOU53]: I think example problems should be
reserved for the guide. This document is intended to review the
information that would support development of a guide.
For illustration of the calculation and comparison, Case A is addressed in this example. Fig. A.1. aFig. A.1.
a shows a schematic side view of simply supported beam under a center loading is used.
F
Fig. A.1. a. Sample problem, simply supported beam with center point loading.
Step 1: Define geometric and material parameters
L  10 ft (3.3 m), b  12" (0.3 m), h  6" (0.15 m),   1, fc '  22 ksi (151.6 MPa)
Assume   1 , thus: Ec  E ; also ft '  6.7 fc '
E  57000 fc '  8.454(10)6 psi  58.2 GPa 
 cr  6.7 f 'c  6.7 22000 =993.77 psi  6.85 MPa 

993.77
 cr  cr 
 1.17(10)-4
E
8454466
βtu is the normalized ultimate tensile strain in the section and since it is assumed that the section will
maintain its residual tensile strength. This value is expected to be imposed as a large number. In this
example, it is considered to be equal to 50, i.e. tu   tu /  cr  50 . Therefore, maximum tensile strain
allowed is  tu  0.0055 or 0.55% .
ω is the ratio of compressive strength to tensile strength and obtained as (according to Eq. 5)
ω
f c'
ft
'

f c'
22000

 22.24
εcr γE 0.000117 1 8454466
Step 2: Calculate demand moment
M u  M DL  M F
Where, 𝑀𝐷𝐿 is moment due to dead weight & MF is the moment due to point load.
72
w
150=75 lb/ft 1.09 kN/m 
144
M DL 
wL2 75 102

 937.5lb-ft 1.27 kN-m 
8
8
For a simply supported beam the maximum moment is at the center of the beam:
F  10
lb-ft  kN-m 
 M n  M u  937.5 
4
Step 3: Calculate Cracking moment
Cracking moment is given by:
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1
1
1
M cr   cr bh 2  (993 psi) 12" (6") 2   5.95 kips-ft (8.33 kN-m)
6
6
12
Step 4: Determine post crack tensile strength (ACI 544.8R-16)
Use the formula for plain FRC, in to consideration (according to Eq. 7)
 6f

eq ,3 f c
Mn  
  ( f + 3f  )
eq ,3
c


M ,
 cr

ξ = 15.8 for inch-lb; ξ = 1.32 for SI
 6  580  22000 

  5.958  2.923 kips-ft (4.2 kN-m)
15.8(580  3  22000) 
F 10 

M u  M n   937.5 
  2923.4 lb-ft
4 

F  794.36lb(3.53kN )
In the case of a normal strength beam with same dimensions ( fc '  22000 psi (151.6 MPa) ,
fc '  6000 psi (41.4 MPa) ), the computed allowable load would be F  323lb(1.4kN ) .
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