See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/339090045
Out-of-plane response of ECC-strengthened masonry walls
Article in Journal of Structural Integrity and Maintenance · February 2020
DOI: 10.1080/24705314.2019.1692165
CITATIONS
READS
25
1,633
2 authors:
Pankaj Munjal
Shamsher Bahadur Singh
National Institute of Technology Kurukshetra
Birla Institute of Technology and Science, Pilani
31 PUBLICATIONS 579 CITATIONS
278 PUBLICATIONS 2,086 CITATIONS
SEE PROFILE
All content following this page was uploaded by Pankaj Munjal on 07 February 2020.
The user has requested enhancement of the downloaded file.
SEE PROFILE
Journal of Structural Integrity and Maintenance
ISSN: 2470-5314 (Print) 2470-5322 (Online) Journal homepage: https://www.tandfonline.com/loi/tstr20
Out-of-plane response of ECC-strengthened
masonry walls
Pankaj Munjal & S. B. Singh
To cite this article: Pankaj Munjal & S. B. Singh (2020) Out-of-plane response of ECCstrengthened masonry walls, Journal of Structural Integrity and Maintenance, 5:1, 18-30, DOI:
10.1080/24705314.2019.1692165
To link to this article: https://doi.org/10.1080/24705314.2019.1692165
Published online: 06 Feb 2020.
Submit your article to this journal
View related articles
View Crossmark data
Full Terms & Conditions of access and use can be found at
https://www.tandfonline.com/action/journalInformation?journalCode=tstr20
JOURNAL OF STRUCTURAL INTEGRITY AND MAINTENANCE
2020, VOL. 5, NO. 1, 18–30
https://doi.org/10.1080/24705314.2019.1692165
Out-of-plane response of ECC-strengthened masonry walls
Pankaj Munjal and S. B. Singh
Civil Engineering Department, Birla Institute of Technology and Science, Pilani, India
ABSTRACT
This paper focuses on the flexural behavior of masonry walls strengthened with precast engineered
cementitious composite (ECC) sheet. The walls were subjected to out-of-plane static loading and
analyzed using ABAQUS. For the validation of numerical results, four masonry walls of size 762 × 480
× 230 mm were cast using burnt clay bricks and cement mortar. Out of four, two masonry walls were
strengthened with precast ECC sheet using epoxy as adhesive, and the remaining two acted as control
specimens. The validation of numerical results with the experimental results shows that the model can
effectively capture the nonlinear behavior of masonry and ECC to predict the strength and failure
mechanism. The influence of mesh size on the numerical results is also reported. Further, a parametric
study has been carried out to observe the effect of several parameters such as percentage of ECC
reinforcement ratio, span/depth (L/d) ratio and width/thickness (b/h) ratio of the strengthened masonry
walls. This study reveals that the precast ECC sheet increases the load-carrying capacity and ductility of
brick masonry walls and hence demonstrates its performance as a strengthening element for brick
masonry structures.
Introduction
Masonry walls are primarily designed to withstand vertical
loads as masonry is strong in compression (Singh, Chauhan, &
Munjal, 2018). Since masonry is weak in tension, the walls are
most vulnerable to the seismic lateral loads. The development
of affordable and effective strengthening techniques for
masonry walls is an urgent need. Numerous strengthening
materials such as metallic or polymeric grid, fiber-reinforced
polymer, engineered cementitious composite (ECC) and textilereinforced mortars may be used for strengthening purposes.
Among these materials available today for strengthening, the
use of ECC has been designated as an attractive strengthening
material (Billington et al., 2009; Kyriakides & Billington, 2008;
Kyriakides, Hendriks, & Billington, 2012).
Recent investigations have demonstrated the great advantages of ECC for strengthening and retrofitting purpose. The
use of ECC for the strengthening of masonry structures has
attracted great attention due to its ductile behavior. Kyriakides
and Billington (2008), Billington et al. (2009), Maalej, Lin,
Nguyen and Quek (2010), Lin, Biggs, Wotherspoon and
Ingham (2014) and Maalej et al. (2010) show that the ECC is
very effective for strengthening of masonry structures.
Kyriakides and Billington (2008) studied the flexural response
of masonry walls strengthened with 13-mm-thick ECC sheet
and reported that the flexural strength of strengthened
masonry walls has increased by 160–280% of that of control
specimens. Billington et al. (2009) carried out an experimental
study on masonry-infilled non-ductile concrete frame retrofitted with an ECC layer of thickness 13 mm. The infill frames
were tested for in-plane cyclic loading, and it was demonstrated that the use of ECC for retrofitting has significantly
enhanced the performance of infill masonry walls. Maalej
et al. (2010) investigated the out-of-plane resistance of unreinforced masonry walls of size 1000 × 1000 × 100 mm strengthened with ECC. The strengthened masonry walls have shown
CONTACT S. B. Singh
Concrete damage plasticity
(CDP); engineered
cementitious composite
(ECC); macro modelling;
masonry walls; out-of-plane
response
the increase in the load-carrying and deflection capacity ranging from 197% to 2135% of that of control specimens. Lin
et al. (2014) carried out the experimental investigation on the
in-plane behavior of concrete masonry wallets strengthened
with the ECC shotcrete mix. Twenty-six concrete masonry wallets of dimension 1180 × 1200 × 140 mm were constructed and
strengthened with ECC shotcrete of thickness 10–15 mm. Lin
et al. (2014) concluded that the in-plane shear strength of the
strengthened masonry wallettes has significantly improved. In
another study by Lin, Lawley, Wotherspoon and Ingham (2016),
the flexural response of clay brick masonry walls of size 4100 ×
1150 × 230 mm strengthened with 30-mm-thick ECC was
investigated. Lin et al. (2016) observed that the flexural
strength of strengthened masonry walls has increased in
between 646% and 1267% of that of control walls.
In the last two decades, considerable numerical research
has been performed to predict the performance of masonry
walls subjected to different loading conditions (Lourenço,
Rots, & Blaauwendraad, 1998; Tarque et al., 2010). For smallscale structures where a more accurate response of masonry
components is required, the micro-modelling is the most
appropriate method to predict the actual behavior of
masonry (Bolhassani, Hamid, Lau, & Moon, 2015; Felix,
1999). Although micro-modelling approach is more realistic
for masonry behavior, modelling becomes complicated due
to high computational cost. Kyriakides et al. (2012) proposed
the nonlinear micro-modelling method to simulate the small
masonry beams strengthened with ECC. Kyriakides et al.
(2012) concluded that micro-modelling method is capable
to observe the experimental performance of ECCstrengthened masonry beams. The macro-modelling methods with homogenization-based technique neglecting brick–
mortar interaction have been successfully used for predicting
the behavior of masonry walls (Daniel & Dubey, 2015;
ElGawady, Lestuzzi, & Badoux, 2006; Kang, Yoon, Ryu, &
sbsinghbits@gmail.com; sbsingh@pilani.bits-pilani.ac.in
© 2020 Korea Institute for Structural Maintenance and Inspection
KEYWORDS
JOURNAL OF STRUCTURAL INTEGRITY AND MAINTENANCE
Shin, 2019; Laurenco, Rots, & Blaauwendraad, 1995; Stavridis
& Shing, 2010).
The advantages of macro-modelling approach over micromodelling are the following: (a) Macro-modelling approach
required less computational effort and time, whereas micromodelling approach required high computation effort and
takes more time (Blasi, De Luca, & Aiello, 2018); (b) Macromodelling approach is generally adopted for finding the
global overall response, whereas micro-modelling approach
is suitable for local behavior (Kunnath, 2018); (c) Macromodelling approach can be used for large scale (e.g. masonry
walls made of more than one layer of stack-bonded bricks),
whereas micro-modelling approach is suitable for small scale
like masonry prism with one layer of stack-bonded bricks; (d)
Macro-modelling approach is reliable for its great approximation results with the comparison to micro-modelling
approach for the case of masonry walls (Abbas & Saeed,
2017). Abbas and Saeed (2017) reported that the difference
between the results obtained from macro-modelling
approach and micro-modelling approach is less than 2%.
However, little research has focused on numerical simulation based on macro-modelling approach on strengthening
of masonry structures with ECC. Recently, Singh, Patil and
Munjal (2017) investigated the ECC-strengthened masonry
beams based on the macro-mechanics approach, and the
presented macro-modelling approach has shown good
agreement with the experimental results. The above study
on retrofitting and strengthening of masonry walls with ECC
shows that more research work on burnt clay brick masonry
walls subjected to out-of-plane loading is required to be
carried out. In this study, a macro-modelling approach is
used for predicting the out-of-plane response of masonry
walls strengthened with ECC sheet. A commercial finiteelement program (ABAQUS) is used for numerical modelling,
and results are validated with the experimental results.
Moreover, different parameters such as thickness of ECC
sheet, effect of width to thickness ratios and span to depth
ratios of the specimens are also considered for the present
study.
Experimental program
The experimental program was planned to examine the effectiveness of precast ECC sheet for the flexural strengthening of
masonry walls. The experimental investigations were carried
out on unstrengthened and strengthened masonry walls
along with the ECC sheets against the out-of-plane loading.
A total of four brick masonry walls (Figure 1) of dimensions
762 × 480 × 230 mm (span × width × thickness) were constructed by an experienced mason. The thickness of the
mortar was maintained 10–12 mm. Out of four specimens,
two were strengthened on tension face with 25-mm-thick
ECC sheet, and the remaining two specimens acted as control
walls. Masonry walls were cured by wet jute bags for 28 days
before strengthening and testing. In addition to the brick
masonry walls, two ECC sheets of size 762 × 480 × 25 mm
(length × width × thickness) were also cast and tested under
four-point loading to examine the out-of-plane response of
ECC sheets.
The detailed description of masonry walls used in this
study has been presented in Table 1. To discriminate between
numerically modeled and experimental specimens, the
designations “X-A” and “X-E” are used, where “X” indicates
19
Figure 1. Schematic diagram of control masonry wall.
the specimens defined in Table 1; “A” stands for the numerically modeled specimen; and “E” refers to the experimental
specimen. For the casting of brick masonry walls, the Portland
pozzolana cement (PPC) and river sand locally available in
Rajasthan, India, were used. The cement mortar of mix proportion of 1:3 (cement:sand) was used in this study. The same
material properties of river sand and PPC were used as
described by Singh, Munjal and Thammishetti (2015). The
locally available (Rajasthan, India) burnt clay bricks of dimension 230 × 110 × 75 mm (length × width × thickness) were
used in this investigation. Burnt clay bricks were immersed in
water for 24 h before the manufacturing of walls to avoid the
absorption of water from the fresh mortars.
Details of the properties of the materials used for this
study are described by Singh and Munjal (2017) and briefly
summarized in Table 2. The stack-bonded five-brick unit with
cement mortar of mix proportion of 1:3 (cement:sand) was
cast as masonry prisms. The compressive strength and water
absorption tests were conducted as per standard IS
1905:1987 (1987) and IS 3495:1992 (1992), respectively. The
five specimens were tested for each property reported in
Table 2 along with coefficient of variation in percentage.
Material and mix design of ECC
ECC generally consists of mixtures of cement, fly-ash, silicasand, superplasticizer, water and polymeric fibers to reinforce
the mix. The mix proportion of ECC used in this study has
been taken from literature (Madappa, 2011) and presented in
Table 3. In this study, PPC as binder, micro silica-sand with an
20
P. MUNJAL AND S. B. SINGH
Table 1. Details of masonry wall specimens.
Sr. no. Wall designation
1
MW-A,
MW-E
2
ECC-A,
ECC-E
3
FW-A,
FW-E
4
FWT-A-10,
FWT-A-25,
FWT-A-50,
FWT-A-75,
FWT-A-100,
FWT-A-150
5
FWL-A-762,
FWL-A-1000,
FWL-A-1250,
FWL-A-1500
6
FWW-A-480,
FWW-A-750,
FWW-A-1000
Wall descriptiona
Control/unstrengthened masonry wall
Control ECC sheet of depth 25 mm
Flexural strengthened masonry wall with ECC sheet of thickness 25 mm
Flexural strengthened masonry wall with ECC sheet of thickness 10, 25, 50, 75, 100
and 150 mm, respectively
Flexural strengthened masonry wall of length 762, 1000, 1250 and 1500 mm,
respectively
Flexural strengthened masonry wall of width 480, 750 and 1000 mm, respectively
In specimen designated as X-A or X-E, “X” refers to specimens described; “E” stands for the experimentally tested
specimen; and “A” refers to the numerically modelled specimen.
a
Table 2. Experimental material properties.
Material
Burnt clay brick
Size (mm)
230 × 110 × 75
Cement mortar
Masonry prism
(5 brick units)
ECC (cube)
ECC (coupon)
70.7 × 70.7 × 70.7
230 × 110 × 423
70.7 × 70.7 × 70.7
310 × 75 × 13
Parameter
Water absorption (%)
Compressive strength (MPa)
Compressive strength (MPa)
Compressive strength (MPa)
Properties
13.65 (13.98)a
8.24 (18.26)
20.85 (1.98)
3.61 (22.98)
Compressive strength (MPa)
Tensile strength (MPa)
Modulus of elasticity (GPa)
Rupture strain (%)
51.10 (2.65)
2.70 (3.85)
8.2 (3.85)
0.40 (3.85)
Five specimens were tested for each property.
Value in parentheses represents coefficient of variation in percentage.
a
Table 3. Mix proportion of engineered cementitious composite (ECC).
Cement (kg/m3) Micro silica-sand (kg/m3) Class-F fly-ash (kg/m3) Water (kg/m3) Superplasticizer (kg/m3) Polyester fiber (kg/m3)
620
620
620
290
8.5
26
average grain size of 100 µm and class F fly-ash were used to
prepare the ECC. The superplasticizer used in the study is
based on second-generation polycarboxylic ether polymers,
developed using nano-technology and compatible with all
types of cement. The polyester fibers of size 12 mm × 25–35
µm (length and diameter) with a unique triangular shape
were used in this study. The triangular cross-section of the
fiber provides 40% more surface area which helps for more
bonding compared to other shapes. The specific gravity,
tensile strength, melting point and elongation of polyester
fiber are 1.31, 480 MPa, 250–265ºC and 30%, respectively.
Five specimens of ECC cubes and coupons of size
70.7 mm and 310 × 75 × 13 mm, respectively, were tested
after the age of 28 days to examine the material properties (i.e. compressive and tensile strength) of ECC. The
compressive strength of ECC cubes was tested as per IS
516:1959 (2006). The tensile test of ECC coupons was
performed in Universal Testing Machine (UTM) of capacity
100 kN, and the load was applied at a displacement control rate of 0.5 mm/min. The average results of ECC cubes
and coupons along with the coefficient of variation are
presented in Table 2.
Installation of ECC sheet on masonry walls
The ECC sheet was bonded on the face of brick masonry walls
using epoxy adhesive (Sikadur 330). The ECC sheet was as
wide as the masonry wall. The surface of walls and ECC sheet
was cleaned and leveled of all extraneous material using
grinder. The remaining gaps were filled with gypsum plaster.
First, epoxy was applied on the walls at the position of the
sheet and spread evenly. Then, ECC sheet was pasted on the
surface of masonry walls. The thickness of epoxy was maintained approximately 1 mm. The walls were covered and the
uniform pressure was applied to allow the sheet to fix to the
wall without the formation of any air gaps. The ECCstrengthened walls were left for air curing for 15 days.
Test set-up
A servo-hydraulic actuator of capacity 300 kN was used to
apply the four-point loading on the masonry walls as shown
in Figure 2. Load and deflection of the walls were measured
through the control system and linear variable displacement
transducer, respectively. The walls were tested with a ramp
JOURNAL OF STRUCTURAL INTEGRITY AND MAINTENANCE
21
Figure 2. Four-point bending test set-up of masonry wall for flexure failure.
loading in the displacement control mode at the rate of
0.05 mm/s until failure.
Experimental results
The load–displacement response of control masonry walls
(MW-E) and ECC-strengthened masonry walls (FW-E) is shown
in Figure 3. The unstrengthened/control masonry walls (MW-E)
failed at the ultimate average load of 15.48 kN, and the corresponding mid-span deflection of approximately 1.02 mm was
observed. In the unstrengthened/control masonry walls, the
flexural cracks started at the tension face and propagated
towards the compression face, leading to sudden failure.
A joint bond failure took place near the center of the wall as
shown in Figure 4. As shown in Figure 3, the tensionstrengthened masonry walls with ECC sheet show higher flexural strength in comparison to control walls. It is observed that
the load-carrying capacity of flexural strengthened masonry
walls with precast ECC sheet has increased to 440% of that of
control/unstrengthened masonry walls. In the ECCstrengthened masonry walls, flexural vertical cracks appeared
near to constant bending moment zone. Later, some inclined
cracks developed in the shear zone. Then, one inclined dominant crack due to stress concentration started close to the left
side of the loading point and leading to flexural failure of the
masonry wall as presented in Figure 5. The average experimental load versus deflection responses has been discussed in
detail along with numerical results later in the section entitled
“Validation of numerical modelling”.
Numerical modelling
The finite-element-based numerical modelling was carried
out using commercial software, ABAQUS. There are mainly
three approaches to simulate the nonlinear behavior of
masonry structures depending on the degree of accuracy
and simplicity desired as follows (Lourenço, 1994):
(i) Detailed micro-modelling: In this approach, masonry
units and mortar are expressed by continuum elements, whereas brick–mortar interface is expressed
by discontinuous elements.
90
80
70
Load (kN)
60
MW-E (First Specimen)
MW-E (Second Specimen)
FW-E (First Specimen)
FW-E (Second Specimen)
50
40
30
20
10
0
0
1
2
3
4
5
6
Mid-span deflection (mm)
Figure 3. Load–deflection response of experimentally tested masonry wall.
7
8
9
10
22
P. MUNJAL AND S. B. SINGH
Figure 4. Failure pattern of unstrengthened/control masonry wall (MW-E).
ECC Sheet
Figure 5. Failure pattern of ECC-strengthened masonry wall (FW-E).
(ii) Simplified micro-modelling: In this method, masonry
units are expressed by continuum elements, whereas
the behavior of the mortar joints and brick–mortar
interface is lumped in discontinuous elements.
(iii) Macro-modelling: The macro-modelling method does
not make a discrimination between individual
masonry units and mortar joints but treats brick
masonry as a homogeneous model.
The first two approaches are the most accurate model for
describing masonry behavior, but these require a large computation memory and huge time for the analysis of masonry
structures. The last approach (i.e. macro-modelling) provides
a superior understanding of the global behavior of masonry
structure. The interaction between brick and mortar is usually
negligible in the macro-modelling approach (Daniel & Dubey,
2015). This approach is best to examine the behavior of large
masonry walls, where little experimental data are adequate
for calibrating the material properties.
In this study, macro-modelling was done by considering the
masonry as a composite homogeneous model. The basic feature of the homogeneous model is that weak brick unit, strong
mortar and unit–mortar interfaces are smeared so that the
whole brick masonry is characterized by the homogeneous
isotropic material. For the numerical modelling, the graphical
user interface of ABAQUS CAE was used to make all the parts,
assemble, define boundary conditions, mesh, apply loads, submit jobs and examine the results. For modelling of masonry
and ECC, the solid elements C3D8R (8-nodes isoparametric
three-dimensional brick elements with reduced integration)
were used. The 8-nodes three-dimensional cohesive elements
of element type COH3D8 were used for epoxy. The Pin and Pinsupported boundary conditions were applied at both ends by
restraining the translation in the in-plane direction.
Material model
The concrete-damaged plasticity (CDP) model is a continuum
plasticity-based damage model for simulation of the constitutive behavior of concrete. This model was theoretically
described by Lubliner, Oliver, Oller and Oñate (1989) and
developed by Lee and Fenves (1998). It gives a general capability for modelling concrete, masonry and other brittle materials in all types of structures. ABAQUS uses the concept of
isotropic damage in combination with isotropic tensile and
compression plasticity in order to represent the inelastic behavior of material (Dassault Systèmes Simulia Corporation, 2017).
The key aspects of the CDP model in ABAQUS include yield
criterion, softening rule, hardening rule, flow rule and the
compressive and tensile behavior along with damage
JOURNAL OF STRUCTURAL INTEGRITY AND MAINTENANCE
variables. Based on previous studies (Khalil, Etman, Atta, &
Essam, 2016; Kupfer, Hilsdorf, & Rusch, 1969; Pereira, Campos,
& Lourenço, 2015), CDP parameters were used to model the
masonry and ECC sheet as they precisely account the nonlinear material behavior. It assumes that the failure of masonry
and ECC can be modeled using the plasticity characteristics
and response to uniaxial compression and uniaxial tension.
Plasticity parameter
The details of the plasticity parameter for this study are
described by Singh et al. (2017) and briefly summarized here.
The plasticity parameters of masonry and ECC used for this
study are reported in Table 4. The dilation angle (ѱ) measured
in the p-q plane at high confining pressure and is determined
using sensitivity analysis. The default value of flow potential
eccentricity (ε) is taken as 0.1 which describes the rate at which
the hyperbolic flow potential approaches its asymptote.
Another parameter defining the condition of materials is
the point when the concrete experiences failure under biaxial
compression. The fbo/fco is the ratio of initial biaxial compressive yield stress to the initial uniaxial compressive yield stress.
Kupfer et al. (1969) have performed the experimental studies
to calculate the factor fbo/fco. The default value of fbo/fco is
taken as 1.16 as per ABAQUS user’s manual. The other parameter Kc is defined as the ratio of second stress invariant of
the tensile meridian to the compressive meridian. In this
study, the default value of Kc is taken as 0.667 as per
ABAQUS user’s manual. The viscoplastic regularization is
used to overcome the convergence difficulties which may
develop due to material softening behavior and stiffness
degradation. The viscoplastic regularization method will
allow stresses beyond outside of the yield surface. The small
value of viscoplastic regularization generally helps improve
the rate of convergence in the softening regime, without
compromising the results. The viscosity parameter is taken
as 1 × 10−5 after many sensitivity analyses were performed.
Compressive behavior
The compressive stress–strain relationship along with the
damage properties when it is subjected to uniaxial compressive loading is shown in Figure 6. The response is
linear until the initial value of yield stress is reached
(Point A). In the plastic regime, the response is typically
considered by stress hardening followed by strain softening. The value of compressive yield stress (σc) versus
inelastic or crushing strain (~εin
c ) is provided in ABAQUS in
the tabular form. The inelastic strain (~εin
c ) is calculated as
the difference between the total compressive strain and
the elastic strain which corresponds to undamaged
material as shown below in Equation (1).
el
~εin
c ¼ εc εoc
Dilation
angle (ψ)
30°
37°
Eccentricity fbo
fco
Kc
(ε)
0.1
1.16 0.667
0.1
1.16 0.667
Viscosity parameters
(μ)
1 × 10−5
1 × 10−5
(1)
where εeloc ¼ σEoc , εc = total compressive strain and εeloc = elastic
strain with respect to the undamaged material. For example,
in Figure 6, at point C, if total stress = σcc , the corresponding
strain = εcc , and from Equation (1), inelastic strain at point
strain at point C (εcc ) minus the
C (~εin
c ) is equal to the total
el
elastic strain at point C εoc ¼ σEcco . Similarly, inelastic strain
corresponding to respective yield stress is calculated on different intervals of compressive stress–strain response.
Further, plastic compressive strains are neither negative nor
decreasing with increased stresses and can be calculated
using Equation (2) (Lourenço, 1994).
~εpl
εin
c ¼~
c Table 4. Plasticity parameters used for CDP model for masonry and ECC.
Type
of
material
Masonry
ECC
23
dc σ c
ð1 dc Þ Eo
(2)
where dc is uniaxial compressive damage variables. The compressive damage variable (dc) is the rate of degradation of the
material stiffness which holds true for the region beyond
Figure 6. Uniaxial compressive stress–strain relationship (Dassault Systèmes Simulia Corporation, 2017).
24
P. MUNJAL AND S. B. SINGH
peak compressive stress (Point B in Figure 6) and calculated
using Equation (3).
dc ¼ 1 σc
σcu
(3)
where σcu is peak compressive yield stress.
Tensile behavior
The tensile post-failure stress–strain relationship is presented
in Figure 7 in order to simulate the complete tensile behavior
of the material in ABAQUS. The uniaxial stress–strain response
is assumed linear elastic up to its tensile stress (Point A). After
cracking, the descending trend is modeled by a softening
process in terms of cracking strain. The cracking strain ~εck
t
is the difference between total strain and elastic strain that
refers to undamaged material and is shown in Equation (4).
el
~εck
t ¼ εt εot
(4)
where εelot ¼ Eσot , εt = total tensile strain and εelot = elastic strain
respective to the undamaged material. Further, plastic tensile
strains that are neither negative nor decreasing with
increased stresses can be calculated using Equation (5)
(Dassault Systèmes Simulia Corporation, 2017).
~εpl
εin
t ¼~
t dt
σt
ð1 dt Þ Eo
(5)
where dt is uniaxial tensile damage variables. The tensile
damage variable (dt) is the rate of degradation of the material
stiffness which holds true for the region beyond peak tensile
stress (Point A in Figure 7) and calculated using Equation (6).
dt ¼ 1 σt
σto
(6)
where σto is peak tensile yield stress.
The compressive and tensile material properties used in
numerical modelling were obtained from the experimental
tests performed by Singh and Munjal (2017) and are presented in Tables 5 and 6 in the form of yield stress versus
inelastic/cracking strain with the omission of subsequent
assumptions: (i) the tensile strength of masonry has taken as
Table 5. Yield stress and the corresponding strain values of masonry.
Compression stiffening properties
Yield stress
(MPa)
Inelastic strain × 10−2
1.51
0.00
2.24
0.06
3.24
0.10
3.61
0.12
3.07
0.40
2.50
0.75
Tension stiffening properties
Yield stress
(MPa)
0.36
0.05
-
Cracking strain × 10−2
0.00
0.68
-
Table 6. Yield stress and the corresponding strain values of ECC.
Compression stiffening properties
Yield stress
(MPa)
31.20
42.31
51.10
39.53
30.12
20.52
Inelastic strain × 10−2
0.00
0.05
0.17
1.46
2.78
5.02
Tension stiffening properties
Yield stress (MPa)
2.65
2.70
1.64
0.69
0.65
-
Cracking
strain × 10−2
0.00
0.17
0.25
0.36
0.37
-
10% of its compressive strength (Daniel & Dubey, 2015;
Kyriakides et al., 2012) and (ii) the Poisson’s ratio of masonry
is taken as 0.2 (Ghiassi, Oliveira, Lourenço, & Marcari, 2013).
The material properties of masonry and ECC used in numerical modelling were obtained experimentally and are presented in Table 2. The modulus of elasticity of ECC and
masonry used for numerical modelling is 8200 and 1216
MPa, respectively, based on experimental results.
Cohesive behavior
ECC sheet was bonded to masonry surface using epoxy which
is considered to be a thin viscous film that produces the
surface-to-surface contact between the masonry surface and
ECC sheet. In this study, epoxy is defined as cohesive elements (COH3D8), and bi-linear traction–separation law is
used. In ABAQUS, the traction–separation model assumes
initially linear elastic behavior, followed by the initiation and
evolution of damage. The failure of the developed cohesive
Figure 7. Uniaxial tensile stress–strain relationship (Dassault Systèmes Simulia Corporation, 2017).
JOURNAL OF STRUCTURAL INTEGRITY AND MAINTENANCE
bond is characterized by progressive degradation of the
cohesive stiffness, derived from the damage process.
ABAQUS imposes this contact behavior only for node-tosurface interactions, which means that each contact interaction needs to be assigning a slave surface to a master surface
while a master surface can interact with several slave surfaces.
The elastic constitutive matrix that tells the normal and shear
stresses to the normal and shear separations across the interface defines the model as in Equation (7) (Dassault Systèmes
Simulia Corporation, 2017).
8 9 2
38 9
Knn Kns Knt < δn =
< tn =
t ¼ ts ¼ 4 Kns Kss Kst 5 δs ¼ Kδ
(7)
: ;
: ;
tt
Knt Kst Ktt
δt
where t is the nominal traction stress vector, δ is the corresponding separations, and n stands for the normal direction, while
s and t stand for in-plane principal directions. In this study, the
stiffness components were treated as uncoupled cohesive behavior in the normal, shear and tangential directions. Hence, the
off-diagonal terms in Equation (7) would be zero for uncoupled
behavior. The value of the stiffness (K) should be adequate to
avoid the interpenetration of crack faces and numerical problems such as spurious traction oscillation (Song, Dávila, &
Rose, 2008; Turon, Camanho, Costa, & Dávila, 2006). The stiffness
used for numerical modelling is calculated based on Equation (8)
(Dassault Systèmes Simulia Corporation, 2017).
Ki α:
Ei
ta
(8)
where Ki and Ei are stiffness and modulus in normal, shear and
tangential directions, ta is thickness of adhesive layer and α is
a parameter defined by Turon et al. (2006) and its value must
be larger than 1 (Song et al., 2008; Turon et al., 2006). In this
study, the stiffness of normal (Knn), shear (Kss) and tangential
(Ktt) directions is assumed to be the same (Knn = Kss = Ktt). The
stiffness of the cohesive element is calculated as 28,000 MPa
based on Equation (8).
Mesh sensitivity
The mesh sensitivity analysis is a very important aspect of the
numerical modelling, especially for damage plasticity model, in
the sense that analysis does not converge to a unique solution
as the mesh refinement leads to narrower crack bands. The
influence of the mesh refinement with element size equal to 5,
10, 15, 20 and 50 mm on the behavior of the masonry walls and
ECC sheets was examined. In addition, the computation time
required for different mesh sizes is also considered.
Consequently, the system used for sensitivity analysis had the
configuration of Intel(R) Core (TM) i7-4790 CPU @ 3.60 GHz, 4
Core(s), 8 Logical Processor(s) with 32 GB of RAM (Randomaccess memory) working with Windows-7 64 bits.
Figures 8 and 9 show, respectively, the normalized load (ratio
of numerical load (Pnum)/experimental load (Pexp)) versus midspan deflection curves for masonry and ECC. In the graph legend,
“M-5“ stands for element size of 5 mm, and value in parentheses
represents the computational time taken for that element size.
The predicted normalized load increases slightly as the mesh size
reduces up to certain limit. Considering the normalized load
(numerical value/experimental value), the element sizes of 20
and 10 mm have shown the better compromise (value nearest
to 1) in the case of masonry walls (Figure 8) and ECC sheet (Figure
9), respectively. All subsequent analyses of ECC-strengthened
masonry walls were conducted using these mesh sizes, i.e.
20 mm for masonry and 10 mm for ECC sheet. It is observed
that ECC sheet modelling requires a smaller mesh size (10 mm) to
achieve convergence due to its requirement of more nodal
points than masonry. The epoxy was modeled as a cohesive
element in between the masonry wall and the ECC sheet. The
fine-meshed cohesive elements compared to solid elements
have a better convergence rate of solution as found from the
sensitivity analysis. The meshing size of 5 mm for cohesive elements (epoxy) was found most suitable for this study in terms of
convergence. A typical meshed masonry wall strengthened with
ECC is shown in Figure 10.
Validation of numerical modelling
The average experimental results of all the specimens in
terms of peak load and mid-span deflection were compared
with the results obtained from ABAQUS and are reported in
Table 7. The average load–deflection response of numerically
modelled and experimentally tested specimens of
unstrengthened and strengthened masonry walls is presented in Figures 11–13. Figure 11 illustrates the comparison
of the out-of-plane response of unstrengthened masonry wall
1.05
1.04
Normalized Load (Pnum/Pexp)
M5 (170 Hrs)
1.03
M10 (5 Hrs)
1.02
M15 (3.5 Hrs)
M20 (1.5 Hrs)
1.01
M50 (20 Min)
1
0.99
0.98
0.97
0.96
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mid-span deflection (mm)
Figure 8. Mesh sensitivity analysis of control masonry wall (MW-A).
25
1
1.1
1.2
1.3
26
P. MUNJAL AND S. B. SINGH
1.2
1.1
Normalized Load (Pnum/Pexp)
1
0.9
0.8
0.7
0.6
M5 (2.5 Hrs)
0.5
M10 (25 Min)
0.4
M15 (3.5 Min)
0.3
M20 (3 Min)
0.2
M50 (1 Min)
0.1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Mid-span deflection (mm)
Figure 9. Mesh sensitivity analysis of ECC sheet (ECC-A).
Figure 10. Model of meshed ECC-strengthened masonry wall (FW-A).
Table 7. Validation of experimental results with numerical study.
Experimental
Numerical
Peak Mid-span Peak Mid-span
Wall desig- load deflection load deflection
nation
(kN)
(mm)
(kN)
(mm)
MW
15.48
1.02
15.71
1.01
ECC
2.62
15.87
2.85
15.25
FW
83.80
9.45
87.42
8.80
% Age
error in % Age error
peak in mid-span
load
deflection
1.48
0.21
8.80
3.91
4.32
6.88
obtained using ABAQUS (using M20 mesh size) and experimental four-point bending tests. It is observed that the out-of
-plane response of unstrengthened walls is in close proximity
to the respective experimental response with a maximum
deviation of 0.21% in the deflection and 1.48% in the
corresponding peak load. Similarly, it is shown in Figure 12
that numerically (using M10 mesh size) and experimentally
obtained out-of-plane response of 25-mm-thick ECC sheet is
in close agreement with a maximum deviation of 3.91% and
8.80% in the corresponding deflection and peak load, respectively. Hence, it is validated that the numerical modelling of
unstrengthened masonry walls and ECC sheets for out-ofplane loading provides satisfactory results as they are close
to respective experimental results.
The results attained by ABAQUS for ECC-strengthened
masonry walls are validated with the respective experimental
results as presented in Figure 13. It observed that the experimental and numerical out-of-plane responses are in close
proximity with a maximum deviation of 4.32% in peak load.
However, the stiffness of numerically modelled walls is slightly
JOURNAL OF STRUCTURAL INTEGRITY AND MAINTENANCE
27
16
14
Load (kN)
12
10
8
MW-E
6
MW-A
4
2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Mid-span deflection (mm)
0.8
0.9
1
1.1
Figure 11. Load–deflection response of control masonry wall (MW).
3
2.5
Load (kN)
2
1.5
ECC-E
1
ECC-A
0.5
0
0
1
2
3
4
5
6
7
8
9 10 11
Mid-span deflection (mm)
12
13
14
15
16
Figure 12. Load–deflection response of ECC sheet (ECC).
90
80
70
Load (kN)
60
50
40
FW-E
FW-A
30
20
10
0
0
1
2
3
4
5
6
7
Mid-span deflection (mm)
8
9
10
Figure 13. Load–deflection response of ECC-strengthened masonry wall (FW).
more and may be attributed to pre-cracking flexural behavior
that has not considered in the numerical modelling. The nature of the load–deflection response is observed to be similar.
Parametric study
The parametric study has been conducted by changing the
various parameters such as thickness of ECC sheet, length and
width of the strengthened masonry walls to observe the effect
of ECC reinforcement ratio, span to depth ratio (i.e. L/d) and
width to thickness ratio (i.e. b/h) of strengthened wall. Serial
numbers 4–6 in Table 1 provide a detailed nomenclature of the
walls analyzed in ABAQUS as a part of the parametric study. It
may be noted that all the specimens for the parametric study
were tested for a four-point loading test, and loading points
are kept fixed.
28
P. MUNJAL AND S. B. SINGH
Results and discussions
and consequently the decreased value of wmax/h. It may be
attributed to an increase in stiffness of the ECC-strengthened
walls. Thus, it could be noted that a small percentage of ECC
reinforcement ratio could be beneficial in terms of ductility. In
order to examine the effect of L/d ratio while keeping the width
and thickness of the specimens and ECC reinforcement ratio
constant, the length of the specimens was changed from 762
to 1500 mm.
It is observed from Figure 15 that the increase in L/d ratio
(i.e. 2.72 to 5.75) while keeping the ECC reinforcement ratio
constant has significantly decreased the normalized flexural
strength (M/fmbd2). The wmax/h value has increased with
increases of L/d ratio for a fixed value of flexural load. It is
worth noting that for the lowest value of L/d ratio, i.e. (L/d=
2.72), the flexural stiffness is higher initially and then drops to
that for L/d = 5.75. The shear deformation becomes predominant in the FWL-762 specimen (L/d= 2.72) and reduces the
flexural strength. It is also clear that increasing the length of
the wall will cause the decrease in flexural strength and
increases the ductility of ECC-strengthened wall. Figure 16
shows the effect of width to thickness ratio (b/h) on the
The effect of the ECC reinforcement ratio for a fixed value of
span and depth of masonry on the out-of-plane response of
strengthened masonry walls is shown in Figure 14. In the
graph legend, “FWT-10 (4.15%)”, the FWT-10 stands for flexural strengthened masonry wall with a 10-mm-thick ECC
sheet; value in parentheses represents the ECC reinforcement
ratio which is calculated by the cross-sectional area of ECC
over the total cross-sectional area of the strengthened
masonry wall.
It may be noted that the graph is plotted between normalized flexural strength (M/fmbd2) and wmax/h to propose the
design chart of ECC-strengthened masonry walls. Here, M is
the maximum bending moment at the mid-span of the wall; fm
is the masonry compressive strength; b is the width of specimen; d is the distance between the extreme compression fiber
of masonry to the centroid of ECC sheet; wmax is the maximum
mid-span deflection of the specimen; and h is the total depth of
the strengthened specimens. It is observed from Figure 14 that
the value of M/fmbd2 of strengthened masonry walls increases
with an increase in ECC reinforcement ratio (i.e. 4.15–39.37%)
Normalized flexural strength (M/fmbd2)
0.1
0.09
0.08
0.07
0.06
FWT-10 (4.15%)
FWT-25 (9.77%)
FWT-50 (17.79%)
FWT-75 (24.51%)
FWT-100 (30.21%)
FWT-150 (39.37%)
0.05
0.04
0.03
0.02
0.01
0
0
0.01
0.02
0.03
0.04
0.05
0.06
wmax/h
Figure 14. Effect of ECC reinforcement ratio on flexural response of strengthened masonry wall.
Normalized flexural strength (M/fmbd2)
0.1
0.09
0.08
0.07
0.06
0.05
0.04
FWL-762 (L/d=2.72)
FWL-1000 (L/d=3.70)
FWL-1250 (L/d=4.72)
FWL-1500 (L/d=5.75)
0.03
0.02
0.01
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
wmax/h
Figure 15. Effect of L/d ratio on flexural response of strengthened masonry wall for ECC reinforcement ratio of 9.77%.
0.045
JOURNAL OF STRUCTURAL INTEGRITY AND MAINTENANCE
29
Normalized flexural strength (M/fmbd2)
0.16
0.14
0.12
0.1
0.08
0.06
FWW-480 (b/h=1.88)
FWW-750 (b/h=2.93)
0.04
FWW-1000 (b/h=3.91)
0.02
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
wmax/h
Figure 16. Effect of b/h ratio on flexural response of strengthened masonry wall for ECC reinforcement ratio of 9.77%.
flexural response of the wall. It is observed that for the lowest
value of b/h (i.e. b/h = 1.88), the normalized flexural strength
(M/fmbd2) is the lowest for a particular deflection (i.e. wmax/h),
while it is highest for b/h = 2.93 but with reduced deflection.
However, it may be noted that for b/h = 3.91, there is
a remarkable increase in load capacity as well as deformation
capacity. Thus, it could be recommended that b/h = 3.91 is
beneficial for the flexural strength of the wall for a limited
range of geometrical dimensions. It is observed that increasing the width of the wall will increase the flexural strength as
well as ductility of the ECC-strengthened wall. However, a fullscale analysis is required for a large-scale masonry wall to
verify this recommendation.
Conclusion
The study presents an investigation into the numerical analysis of masonry walls strengthened with ECC sheet in flexure
and subjected to out-of-plane loading. The numerical results
are validated with the corresponding experimental results.
A parametric study is also presented to observe the influence
of numerous parameters using finite-element-based software
(ABAQUS). The following conclusions are made regarding the
strengthening of masonry wall with ECC sheet and subjected
to out-of-plane loading.
(i) Load-carrying capacity of flexural strengthened
masonry walls with precast ECC sheet has increased
440% of that of control/unstrengthened masonry
walls.
(ii) The numerical results are sensitive to the mesh element size of the concrete damage plasticity model.
Accurate element mesh size of the CDP model is
essential for the finite-element analysis.
(iii) This study will help the researcher and designer to
determine the necessary ECC reinforcement ratio as
per the required strength in the strengthened
masonry walls for a limited range of geometrical sizes.
(iv) It is recommended that for a given span to depth
ratio, width to thickness ratio of 3.91 is beneficial,
while the span to depth ratio should be equal or
greater than 3.70 to avoid the negative effect of
shear deformations.
Article highlights
● The out-of-plane response of masonry walls strengthened with ECC
sheets was investigated.
● A nonlinear finite-element macro-modelling approach has been
developed.
● The mesh sensitivity analysis was performed.
● A design chart for ECC-strengthened masonry walls was developed.
● The developed design charts will be helpful for strengthening of
masonry walls using ECC sheets.
Acknowledgments
This project is a part of a research project (SR/S3/MERC/0051/2012)
funded by the Department of Science and Technology (DST), New
Delhi. Financial support by DST, New Delhi, to effectively execute the
project is highly appreciated.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
This work was supported by the Science and Engineering Research Board
[SR/S3/MERC/0051/2012].
References
Abbas, A., & Saeed, M. (2017). Representation of the masonry walls
techniques by using FEM. Australian Journal of Basic and Applied
Sciences, 11(13), 39–48.
Billington, S. L., Kyriakides, M. A., Blackard, B., Willam, K., Stavridis, A., &
Shing, P. B. (2009). Evaluation of a sprayable, ductile cement-based
composite for the seismic retrofit of unreinforced masonry infills.
Proceeding of ATC & SEI conference on improving the seismic performance of existing buildings and other structures, San Francisco
California, United States: Applied Technology Council and Structural
Engineering Institute.
Blasi, G., De Luca, F., & Aiello, M. A. (2018). Hybrid micro-modelling
approach for the analysis of the cyclic behaviour of RC frames.
Frontiers in Built Environment, 4(75), 1–12.
Bolhassani, M., Hamid, A. A., Lau, A. C. W., & Moon, F. (2015). Simplified
micro modeling of partially grouted masonry assemblages.
Construction and Building Materials, 83, 159–173.
Daniel, A. J., & Dubey, R. N. (2015). Finite element simulation of brick
masonry building under shock loading. Coupled System and
Mechanics, 4(1), 19–36.
30
P. MUNJAL AND S. B. SINGH
Dassault Systèmes Simulia Corporation. (2017). ABAQUS analysis user’s
manual. Providence (RI): ABAQUS Inc.
ElGawady, M. A., Lestuzzi, P., & Badoux, M. (2006). Shear strength of URM
walls upgraded with FRP. Engineering Structures, 28(12), 1658–1670.
Felix, I. (1999). Compressive strength and modulus of elasticity of masonry
prisms (Master’s thesis). Carleton University Ottawa, Ontario.
Ghiassi, B., Oliveira, D. V., Lourenço, P. B., & Marcari, G. (2013). Numerical
study of the role of mortar joints in the bond behavior of
FRP-strengthened masonry. Composite Part B: Engineering, 46, 21–30.
IS 1905-1987. (1987). Indian standard code of practice for structural use of
unreinforced masonry. New Delhi: Bureau of Indian Standards.
IS 3495-1992. (1992). Indian standard methods of tests of burnt clay building bricks. New Delhi: Bureau of Indian Standards.
IS 516-1959. (2006). Indian standard methods of tests for strength of
concrete. New Delhi, India: Bureau of Indian Standards.
Kang, J., Yoon, H. A., Ryu, E. M., & Shin, Y. S. (2019). Analytical studies for
the effect of thickness and axial load on load bearing capacity of fire
damaged concrete walls with different sizes. Journal of Structural
Integrity and Maintenance, 4(2), 58–64.
Khalil, A. E. H., Etman, E., Atta, A., & Essam, M. (2016). Nonlinear behavior
of RC beams strengthened with strain hardening cementitious composites subjected to monotonic and cyclic loads. Alexandria
Engineering Journal, 55(2), 1483–1496.
Kunnath, S. K. (2018). Modeling of reinforced concrete structures for
nonlinear seismic simulation. Journal of Structural Integrity and
Maintenance, 3(3), 137–149.
Kupfer, H., Hilsdorf, H. K., & Rusch, H. (1969). Behavior of concrete under
biaxial stresses”. ACI Journal, 66(52), 656–666.
Kyriakides, M. A., & Billington, S. L. (2008). Seismic retrofit of
masonry-infilled non-ductile reinforced concrete frames using
spray-able ductile fiber-reinforced cementitious composites. Proceeding
of 14th world conference on earthquake engineering (pp.1–7). Beijing.
Kyriakides, M. A., Hendriks, M. A. N., & Billington, S. L. (2012). Simulation of
unreinforced masonry beams retrofitted with engineered cementitious composites in flexure. Journal of Materials in Civil Engineering,
24(5), 506–515.
Laurenco, P. B., Rots, J. G., & Blaauwendraad, J. (1995). Two approaches for
the analysis of masonry structures: Micro and macro-modeling.
HERON, 40(4), 313–340.
Lee, J., & Fenves, G. L. (1998). Plastic-damage model for cyclic loading of
concrete structures. Journal of Engineering Mechanics, 124, 892–900.
Lin, Y., Lawley, D., Wotherspoon, L., & Ingham, J. M. (2016). Out-of-plane
testing of unreinforced masonry walls strengthened using ECC
shotcrete. Structures, 7, 33–42.
View publication stats
Lin, Y. W., Biggs, D., Wotherspoon, L., & Ingham, J. M. (2014). In-plane
strengthening of unreinforced concrete masonry wallettes using ECC
shotcrete. Journal of Structural Engineering, 1401(11), 04014081.
Lourenço, P. B. (1994). Analysis of masonry structures with interface elements: Theory and applications (Report 03-21-22-0-01). Delft: Delft
University of Technology.
Lourenço, P. B., Rots, G., & Blaauwendraad, J. (1998). Continum model for
masonry: Parameter estimation and validation. Journal of Structural
Engineering, 124(6), 642–652.
Lubliner, J., Oliver, J., Oller, S., & Oñate, E. (1989). A plastic-damage model
for concrete. International Journal of Solids and Structures, 25, 229–326.
Maalej, M., Lin, V. W. J., Nguyen, M. P., & Quek, S. T. (2010). Engineered
cementitious composites for effective strengthening of unreinforced
masonry walls. Engineering Structure, 32(8), 2432–2439.
Madappa, S. V. R. (2011). Response and micromechanics based design of
engineered cementitious composite structure (Doctoral dissertation).
BITS Pilani, Rajasthan.
Pereira, J. M., Campos, J., & Lourenço, P. B. (2015). Masonry infill walls
under blast loading using confined underwater blast wave generators
(WBWG). Engineering Structures, 92, 69–83.
Singh, S. B., Chauhan, A., & Munjal, P. (2018). Composite mechanics-based
design approach for FRP-strengthened walls. Journal of Structural
Integrity and Maintenance, 3(3), 160–170.
Singh, S. B., & Munjal, P. (2017). Bond strength and compressive
stress-strain characteristics of brick masonry. Journal of Building
Engineering, 9, 10–16.
Singh, S. B., Munjal, P., & Thammishetti, N. (2015). Role of water/cement
ratio on strength development of cement mortar. Journal of Building
Engineering, 4, 94–100.
Singh, S. B., Patil, R., & Munjal, P. (2017). Study of flexural response of
engineered cementitious composite faced masonry structures.
Engineering Structures, 150, 786–802.
Song, K., Dávila, C. G., & Rose, C. A. (2008). Guidelines and parameter
selection for the simulation of progressive delamination. Proceedings of
Abaqus users’ conference, Rhode Island, RI.
Stavridis, A., & Shing, P. B. (2010). Finite-element modeling of nonlinear
behavior of masonry-infilled RC frames. Journal of Structural
Engineering, 136(3), 285–296.
Tarque, N., Espacone, E., School-iuss, R., Varum, H., Camata, G.,
Spacone, E., & Blondet, M. (2010). Numerical modelling of in-plane
behaviour of adobe walls. Proceeding of 8th conference on seismology
and earthquake engineering (pp. 1–12), Lisbon.
Turon, A., Camanho, P. P., Costa, J., & Dávila, C. G. (2006). A damage model
for the simulation of delamination in advanced composites under
variable-mode loading. Mechanics of Materials, 38(11), 1072–1089.