Seismic Response of Wharf Structures Supported in
Liquefiable Soil
Andriani Ioanna Panagiotidou
Diploma in Civil Engineering (2009), National Technical University of Athens,
Department of Civil Engineering
Submitted to the Department of Civil and Environmental Engineering in Partial
Fulfillment of the Requirements for the Degree of
Master of Science in Civil and Environmental Engineering at the
MASSACHUSETTS INS fIE
OF TECHNOLOGY
Massachusetts Institute of Technology
JUL 0 8 2013
June 2013
LIBRARIES
© 2013 Massachusetts Institute of Technology. All rights reserved.
Signature of Author
Department of ti)vil and Environmental Engineering
May 13, 2013
Certified by
Andrew
J. Whittle
Professor of Civil and Environme tal Engine ring
I
T
sispupe
isor
Accepted by
Heidi M. Nepf
Chair, Departmental Committee for Graduate Students
Seismic Response of Wharf Structures Supported in
Liquefiable Soil
Andriani loanna Panagiotidou
Submitted to the Department of Civil and Environmental Engineering on May 13, 2013, in
Partial Fulfillment of the Requirements for the Degree of Master of Science in Civil and
Environmental Engineering
Abstract
This research analyzes the vulnerability of wharf structures supported on loose granular
waterfront fills that are susceptible to liquefaction during seismic events and considers the
effectiveness of pre-fabricated Vertical (PV) drain systems in mitigating potential damage. The
analyses are based on non-linear finite element simulations using the OpenSees open-source
software framework. The analyses make extensive use of an advance macroelement
formulation by Varun (PhD, 2010), which captures efficiently the fundamental mechanisms of
saturated granular soil behavior. The thesis explains in detail the mechanical components of the
macroelement as well as the necessary calibration steps.
Numerical simulations of a typical berth of port facilities on the US West coast have been
carried out using as earthquake loading the time histories of free field displacements and of
excess pore pressures predicted by Vytiniotis (PhD, 2011) at specific locations along the
embedded length of piles (for a suite of 56 ground motions). The results show that the primary
cause of the structural damage is indeed the lateral spreading of the soil and therefore
retrofitting efforts should be targeted in limiting the development of pore pressures that cause
the lateral spreading. This argument is then tested by comparing the performance in numerical
simulations for the case where full-depth PV drains are installed at locations behind the crest of
the slope (i.e. minimally-intrusive mitigation system) and for the case of a fully densified slope
for the same suite of ground motions. These results indicate that soil improvement methods
assist in reducing structural damage to pile-deck connection locations. The results also show
that the densification of the slope is only marginally superior to the less intrusive improvement
with PV-drains.
Thesis Supervisor:
Andrew J. Whittle
Title:
Professor of Civil and Environmental Engineering
Acknowledgements
First and foremost I would like to thank my advisor Prof. Andrew J. Whittle for transforming me from a
student to a researcher and for so patiently editing this thesis. I would like also to thank Linde
Foundation for the fellowship that I was awarded the first year of my studies as well as Alexandros S.
Onassis Foundation for its support during my SM years. Special thanks to Dr. Vytiniotis for being always
a "deus ex machina" and to Gonzalo, Despina, Yixing and Davoud for all their valuable help and support.
I would also like to thank Dr. Varun and Dr. Shafieezadeh for providing useful code.
Finally I would like to express my gratitude to my family and my friends who have stood by me despite
my many faults.
5
6
Contents
3
Abstract...................................................................................................................................................
1
Introduction.........................................................................................................................................15
Thesis Overview ...........................................................................................................................
17
Literature Review ................................................................................................................................
22
1.1
2
3
2.1
Soil-Structure Interaction............................................................................................................22
2.2
Soil-Structure Interaction for Pile Foundations......................................................................
23
2.3
State of the art methods of analyses .....................................................................................
25
M odel of Soil-Structure Interaction ................................................................................................
31
Overview of M acro-elem ent Form ulation of the M acroelem ent ...........................................
31
3.1.1
Drained Behavior of M acroelem ent...............................................................................
32
3.1.2
Undrained Behavior of the Macroelem ent .....................................................................
35
3.1.3
Partially Drained Behavior of the M acroelem ent ..........................................................
40
3.1
3.2
4
5
44
Calibration of the Varun (2010) Macroelem ent for Toyoura Sand ........................................
62
Seism ic Response of Pole-supported W harf Structures.................................................................
4.1
Problem Description....................................................................................................................62
4.2
Ground M otions and Free Field Analyses ..............................................................................
65
4.3
Results of Untreated Scenario.................................................................................................
66
4.4
Effectiveness of Ground Improvement System s ...................................................................
71
4.5
M odeling of Pile-Deck Connection..........................................................................................
73
4.6
Conclusions..................................................................................................................................78
Sum mary, Conclusions and Recom mendations................................................................................104
104
5.1
...................................................................................................................................
Sum ma .ry
5.2
Conclusions................................................................................................................................105
5.3
Recom mendations ....................................................................................................................
107
REFERENCES ..............................................................................................................................................
108
APPENDIX A - Validation of OpenSees Response .....................................................................................
111
Methodology .........................................................................................................................................
111
Vertically Loaded Piles...........................................................................................................................112
Elastic Springs....................................................................................................................................112
Elastic Perfectly Plastic Springs .........................................................................................................
7
113
Laterally Loaded Piles............................................................................................................................114
Elastic Springs....................................................................................................................................114
Elastic Perfectly Plastic Springs .........................................................................................................
114
M acroelem ent Springs ......................................................................................................................
115
Com parison of the Pushover Response of the three Spring Elem ents .................................................
116
Dynam ic M odeling of a single pile ........................................................................................................
116
APPENDIX B -Classification of Dam age for Piled-W harf Structure...........................................................124
8
Table of Figures
Figure 1-1 Seismic hazard for USA by USGS (PGA with 2% PE in 50 year), (USGS, 2008). ........ 19
Figure 1-2 Typical soil-foundation-structural system for pile supported wharf (not to scale)
20
(Shafieezadeh, 20 11) ....................................................................................................................
Figure 1-3 Shearing of a pile by ground displacement in Kobe earthquake, 1995 (Finn and Fujita,
20
20 0 2).............................................................................................................................................
Figure 1-4 Damage to a pile by 2 m of ground displacement in Niigata earthquake, 1964 (Finn
21
and Fujita, 200 2). ..........................................................................................................................
Figure 1-5 Undamaged pile supporting a crane rail in ground which moved more than 1.0 m
during the Great Hanshin Earthquake (Finn and Fujita, 2002)................................................. 21
Figure 2-1 (a) Geometry of soil-pile-structure interaction problem; (b) decomposition into
kinematic and inertial interaction problems; (c) two-step analysis of inertial interaction
29
(modified from Varun 2010).....................................................................................................
Figure 2-2 Various observed modes of pile failure in liquefiable soils (Tokimatsu et al, 1996)... 30
Figure 2-3 Typical Winkler spring and dashpot model for pile foundation analysis (from
30
Kavvadas & Gazetas, 1993).......................................................................................................
Figure 3-1 Schematic Formulation of the Macroelement (modified from Varun, 2010)...... 49
Figure 3-2 Effective vertical stress (Pa) plot after seven loading cycles showing the formation of
local liquefaction zone - approximately five diameters around the pile (from Varun, 2010)...... 50
Figure 3-3 Relationship between excess pore pressure and shear work for undrained cyclic
shear tests on sand (after Towhata and Ishihara, 1985).......................................................... 50
Figure 3-4 Envelope of stress points at equal shear work (Towhata and Ishihara, 1985) ........
51
Figure 3-5 The liquefaction front concept as extent by Varun for pile. The normalized vertical
effective stress S=-- V
can be calculated as a function of the normalized soil resistance
r=p/Ba o ---------------------------
...... ........................................
-..
-----...............................----
52
Figure 3-6 Liquefaction front parameter (S0 ) correlation with normalized shear work for
different values of (a) critical state friction angle (b) pile diameter (c) maximum friction angle
53
(figure from Varun (2010))............................................................................................................
Figure 3-7 (a) Liquefaction front parameter
(S0)
correlation with normalized shear work as a
function of liquefaction resistance parameter X (b) Shear work correlation curves after
53
normalization with parameter w1 (figure from Varun (2010)). ................................................
9
Figure 3-8 Parameter r as a function of Poisson's ratio and power exponent n (from Varun
(20 10 ))...........................................................................................................................................
54
Figure 3-9 Flowchart for calculation of pile response using the macroelement (Varun, 2010).. 55
Figure 3-10 Pile response to small loops of cyclic unloading-reloading after monotonic loading
(Varu n, 20 10 )................................................................................................................................
56
Figure 3-11 p-y curve for the macroelement. We can observe the degradation of the stiffness
and the lateral resistance of the macroelement as a result of the cyclic loading and the pore
pressu re built up...........................................................................................................................
56
Figure 3-12 Sinusoidal Input Displacement motion and b. Assumed pore pressure build up .... 57
Figure 3-13 Physical model of Berth 60-63 and FE model properties as used by Vytiniotis (PhD
2011). (Figure from Vytiniotis (PhD (2011))............................................................................... 58
Figure 3-14 Young's Modulus distribution along the depth of the pile. The darker grey line
corresponds to the upper hydraulic fill, which is modeled with Toyoura Sand of Dr=40 %. The
lighter grey line plots the corresponding distribution along depth of Young's modulus fo
Toyoura Sand of Dr=80%. After the depth of 18.4 m below the surface, for the calibration of
the macroelement we are using the properties of Dr=80 %Toyoura Sand............................. 59
Figure 3-15 p-y curve for the macroelement. Comparison of the medium and the dense
behavior normalized over the vertical effective stress. We have used the same initial stiffness as
the purpose isto presented the qualititave differences in the backbone curves.................... 60
Figure 3-16 p-y curve for the macroelement. Demonstration of the influence on the overall
response of the macroelement of the parameter X.The denser the sand, the lower the value of
X,the larger the soil resistance. Moreover it is worth noticing that the looser sand (X =0.15)
liquefies to a higher degree. All the other parameters used same as Figure 3-11.................. 61
Figure 4-1 Configuration of the Berth 60-63 in Oakland (Shafieezadeh, PhD 2011)................ 80
Figure 4-2 OpenSees model of piled wharf structure. .............................................................
81
Figure 4-3 Constitutive law used to model (a)the moment resistance of the pile section and (b)
the axial resistance . ......................................................................................................................
82
Figure 4-4 Moment curvature curve of the reinforced concrete section of the pile as calculated
by online available softw are KSU_RC (2011)............................................................................. 82
Figure 4-5 Geometry of PV-Drains array for mitigating seismic risk for Berth 60-63 (Vytiniotis,
20 11) .............................................................................................................................................
83
Figure 4-6 Response of the unimproved piled wharf to base case ground motion ,nga0779; (a)
time history of acceleration of rock base excitation (b) acceleration contours of free field
response (from Vytiniotis, 2011) (c) displacement contours of free field response (from
Vytiniotis, 2011) (d) horizontal displacement of the deck ........................................................
84
10
Figure 4-7 Response of the unimproved piled wharf for ground motion nga0779 at t= 5s (a)
Structural displacements (60:1) (b) Snapshot at the same time of the contours of displacement
of the free field analysis (Vytiniotis (PhD, 2011)) (c) Snapshot at the same time of the contours
of excess pore pressure ratio of the free field analysis (Vytiniotis (PhD, 2011)). ..................... 85
Figure 4-8 Response of the unimproved piled wharf for ground motion nga0779 at t= 10s (a)
Structural displacements (60:1) (b) Snapshot at the same time of the contours of displacement
of the free field analysis (Vytiniotis (PhD, 2011)) (c) Snapshot at the same time of the contours
of excess pore pressure ratio of the free field analysis (Vytiniotis (PhD, 2011)). ..................... 86
Figure 4-9 Response of the unimproved piled wharf for ground motion nga0779 at t= 15s (a)
Structural displacements (60:1) (b) Snapshot at the same time of the contours of displacement
of the free field analysis (Vytiniotis (PhD, 2011)) (c) Snapshot at the same time of the contours
of excess pore pressure ratio of the free field analysis (Vytiniotis (PhD, 2011)).. .................... 87
Figure 4-10 Response of the unimproved piled wharf for ground motion nga0779 at t= 20s (a)
Structural displacements (60:1) (b) Snapshot at the same time of the contours of displacement
of the free field analysis (Vytiniotis (PhD, 2011)) (c) Snapshot at the same time of the contours
of excess pore pressure ratio of the free field analysis (Vytiniotis (PhD, 2011)). ..................... 88
Figure 4-11 Performance of the unimproved piled wharf under ground motion nga0779 (a)
bending moment envelopes and (b) location of the plastic hinges in piles............................. 89
Figure 4-12 Time histories of deck displacements for unimproved piled wharf structure for the
90
reference suite of 56 ground motions .....................................................................................
Figure 4-13 Summary of computed deck displacements for unimproved piled wharf structure as
functions of earthquake intensity parameters for the reference suite of 56 ground motions
91
a)PGA, b) PGV, c) PGD, d) Arias Intensity ................................................................................
Figure 4-14 Response of the unimproved piled wharf structure and classification of structural
92
damage for the reference suite of ground motions .................................................................
Figure 4-15 Examples of structural damage in selected seismic ground motions for the
93
unim proved piled w harf structure............................................................................................
Figure 4-16 Comparison with results of Shafieezadeh (2011): a) Time Histories of Horizontal
deck displacements; b) yielded sections as calculated by Shafieezadeh (2011); c) yielded
sections as calculated by Panagiotidou (2013).......................................................................... 94
Figure 4-17 Effectiveness of ground improvement scenarios for piled-wharf structure under
reference suite of ground motions as functions of selected intensity parameters: a)PGA, b) PGV,
95
c) PG D, d) A rias Intensity .........................................................................................................
Figure 4-18 Effect of ground improvement systems on fill and wharf response under ground
96
motio n nga0 779 ............................................................................................................................
11
Figure 4-19 Effect of ground improvement systems on fill and wharf response under ground
motio n nga0753 ............................................................................................................................
97
Figure 4-20 Effect of ground improvement systems on deck displacements under ground
motio n nga0779 ............................................................................................................................
98
Figure 4-21 Effect of ground improvement systems on deck displacements under ground
motio n nga0753 ............................................................................................................................
98
Figure 4-22 Section geometry and reinforcement details of the tested pre-stressed pile (from
Lehm an et al., 2009) .....................................................................................................................
99
Figure 4-23 Bilinear hysteretic model with strength limit (from Ibarra et al.2005).................. 99
Figure 4-24 Modified Ibarra Krawinkler (MIK) Deterioration Model (from Lignos et al. 2011). 100
Figure 4-25 The calibration results of the MIK model for pile-deck connection for the simulated
experim ent (Figure 4-22)............................................................................................................101
Figure 4-26 Effect of deteriorating pile-deck connection on response of the unimproved piledwharf structure under base case ground motion, nga0779....................................................... 102
Figure 4-27 Effect of deteriorating pile-deck connection on response of the unimproved piledwharf structure under base case ground motion, nga0779: (a)MIK, (b) EPP............................ 103
Figure A-1. Settlement along the length of the pile supported on Elastic Springs. ................... 117
Figure A-2 Settlement along the length of the pile supported on Elastic- Perfectly Plastic Springs.
.....................................................................................................................................................
118
Figure A-3 Horizontal deformation along the length of the pile supported on Elastic Support. 119
Figure A-4 Constitutive Behavior of springs in lateral loading ...................................................
119
Figure A-5 Horizontal deformation along the length of the pile supported on Perfectly Plastic
Springs. We can observe a small difference between the numerical and the analytical solution
due to the assumption of the analytical solution that the pile is clamped at the depth where the
deform ation changes sign...........................................................................................................
120
Figure A-6 p-y curve for the macroelement. We can observe the degradation of the stiffness
and the lateral resistance of the macroelement as a result of the cyclic loading and the pore
pressure built up. The excitation is sinusoidal with frequency of 0.1 Hz, amplitude of 0.02 m and
total number of cycles 6. We are assuming a linear pore pressure built-up. ........................... 121
Figure A-7 a. Horizontal Reactions b. Horizontal Displacements c. Force-Displacement curves at
various depths along the pile. The macroelement exhibits a behavior that is bounded but the
responses of the elastic and the elastic-perfectly plastic springs. We can see that the reaction
distribution is smoother as it is anticipated from the Bouc-Wen type hysteresis model.......... 122
Figure A-8 Schematic model of earthquake loading of a single pile ..........................................
12
123
Table of Tables
48
- - - - - - --..............................
.....
-----.. ---------------- .---------..-........................... 48
--- 79
. -------.. . ----------------------...........................----
Table 3-1 .................................................................
Table 3-2 ...................................................................
Table 4-1 ................................................................
Table 4-2 ..............................................................................--..---------------------......................-- -- - - - 79
86
...... --------...... ------------------.........................
Table 4-3 .......................................................................
87
........... - -...------------------------..........................
Tab le 4-4 .....................................................................
13
14
1
Introduction
Liquefaction is a term used to describe the underlying mechanisms of strength loss and ground
deformations that occur due to the accumulation of excess pore pressures. It is most commonly
associated with cyclic shearing during earthquakes and damage is limited over the short
timeframe of the loading event. Liquefaction is commonly observed in seismic events at sites
with loose, saturated granular materials often causing large settlements or lateral movements
within slopes, and causes damage to embedded structures and facilities.
Maritime trade accounts for 80-85 % of international trade and port facilities are exposed to a
variety of natural hazards including earthquakes, tsunamis, and hurricanes that can lead to
significant disruptions in operations and economic losses. The 'Great Hanshin' earthquake
(http://www.city.kobe.lg.ip/foreign/english/disaster/index.html)
resulted
in
almost
complete
destruction of the port facilities resulting in huge short and long-term economic losses for the
city of Kobe. Kobe was one of the world's busiest ports prior to the earthquake. Although the
facilities were rebuilt within 2 years, the port has never regained its former status as Japan's
principal shipping port. More recently, the facilities of the Port au Prince, Haiti seaport were
severely
damaged
in the
January
2010
earthquake
(http://www.telegraph.co.uk/news
/worldnews/centralamericaandthecaribbean/haiti/7032385/Haiti-earthquake-damaged-port-reopens to
-aid-ships.html) due to the liquefaction of the underlying soils and were unable to handle aid
shipments almost a month after the event.
15
Many US ports are located in areas with significant seismic hazard on both the West (Oakland,
Los Angeles, Long Beach, and Seattle) and East coasts (Charleston, SC, and Savannah, GA), as
seen in seismic hazard map from USGS, Figure 1-1. There is a constant need to evaluate the
seismic risk, and suitable mitigation measures, (and their associated costs) that can be
implemented without severe disruption to ongoing port activities. This thesis focuses on
particular mitigation scheme that uses an array of PV drains to prevent pore pressure
accumulation on the landward side of the wharf (originally proposed by Rathje et al, 2004).
This research focuses on the performance of a common type of wharf structure comprising pilesupported deck that typically supports a rail-mounted container crane (also founded on piles
Figure 1-2). The seismic vulnerability of these types of structures is primarily due to the lateral
spreading and slope failure within the embankment fills, which often comprises loose granular
fills (mostly constructed prior to current seismic design codes). Therefore, the piles that are
embedded within these fills can be subjected to large lateral loading due to the spreading (i.e.
lateral deformations within the soil). Figures Figure 1-3 to Figure 1-5 show examples of pile
failures: Figure 1-3 shows a pile-supported warehouse on Port Island (near Kobe City) that
failed completely due to shearing associated with permanent lateral ground displacements
greater than 1.5 m, while Figure 1-4 shows damage to a reinforced concrete pile under a
building in Niigata (1964) earthquake caused by 2 m of ground. In both of these examples the
piles were designed primarily for vertical loads and had limited ability to support bending
moments and shear caused by strong shaking and lateral spreading. Figure 1-5 shows a crane
rail pile that did not sustain any structural damage in the Kobe earthquake even though the
16
ground deformation was approximately 1 m. In this case, the design was adequate for the
imposed structural loads and ground movements.
This thesis focuses on the dynamic response of a pile-supported wharf structure embedded in a
loose granular fill. The performance is evaluated using an uncoupled substructure approach,
which involves separate analyses of the free-field response of the soil mass (i.e. without
structural elements) and of the wharf structure (piles, deck, and crane). This research builds on
prior research by Vytiniotis (2011) and Shafieezadeh (2011). The interaction between the free
field and pile-deck models is handled through 'macro-elements' (Varun, 2010) that require the
time histories of free-field displacements and pore pressures at locations along each of the piles
as input motions. The thesis evaluates structural damage for a reference wharf structure for a
suite of selected earthquake ground motions. It further evaluates the effectiveness of current
soil improvement methods in limiting the structural damage in wharf structures during seismic
loading.
1.1
Thesis Overview
Chapter 2 presents a review of the literature analysis of seismic soil-structure interaction for
pile-supported wharves.
Chapter 3 gives details of the macroelements used to represent pile-soil interaction and the
calibration of the input parameters.
Chapter 4 presents results of two dimensional analyses of the response of a typical piled-wharf
structure under a suite of earthquake ground motions and compare the structural response of
17
the wharf under its existing condition and after installation of a PV drain system. The study
focuses on the effectiveness of the PV drains in mitigation damage to the wharf structure.
Chapter 5 summarizes the research, provides a set of general conclusions drawn from the
outcomes of the research, and outlines future research needs.
18
C'
0O
ui
IL
LA
04
c~IA
E
Figure 1-1 Seismic hazard for USA by USGS (PGA with 2% PE in 50 year), (USGS, 2008).
19
I
Container
Crane
Seaside
Pre-stressed~
batter piles
Pre-stressed
vertical piles
Figure 1-2 Typical soil-foundation-structural system for pile supported wharf (not to scale)
(Shafieezadeh, 2011)
Figure 1-3 Shearing of a pile by ground displacement in Kobe earthquake, 1995 (Finn and Fujita,
2002).
20
I"
Figure 1-4 Damage to a pile by 2 m of ground displacement in Niigata earthquake, 1964 (Finn
and Fujita, 2002).
Figure 1-5 Undamaged pile supporting a crane rail in ground which moved more than 1.0 m
during the Great Hanshin Earthquake (Finn and Fujita, 2002).
21
2
2.1
Literature Review
Soil-Structure Interaction
The term free field motions refers to the situation where the ground response during an
earthquake is not affected by the presence of the structure. For example, a structure founded
on stiff rock, the very high stiffness and strength of the founding rock is often sufficient to
ensure that motions are well approximated by the free field case. However, the foundations of
structures founded on softer soils generally do not conform to the ground response and will
alter the motion experienced by the structure (kinematic interactions), while the dynamic
response of the structure itself can induce deformations of the surrounding soil (inertial
interactions). This process, in which the response of the soil influences the motion of the
structure and vice versa, is referred as soil-structure interaction (SSI).
There are two general methods to quantify soil SSI effects, namely the direct approach and the
substructure approach. The direct approach accounts for the interaction by simultaneously
analyzing the soil and the structure and their interfaces in a single step. While it is possible to
carry out direct analyses, they are usually very computationally demanding. The substructure
approach decomposes the kinematic interaction and inertia interaction problems. The response
of the system is the result of the superposition of the responses (1) due to the kinematic
interaction effect, involving the response to base rock excitation of the system is shown in
Figure 2-1b, which considers a massless super-structure while inertial interactions (Figure 2-1b)
considers the response of the pile-soil system to excitation by D'Alembert forces,
22
-Mii,
where accelerations, ii,, are obtained from the kinematic interaction. This kinematic-inertial
superposition is only theoretically valid for linearly elastic systems. However Gazetas (1984)
observes that in the majority of actual cases, pile deformations due to lateral excitation
(transmitted from the super-structure) attenuate very rapidly with depth (typically within 10-15
diameters from the ground surface). Therefore, shear strains induced in the soil due to inertial
interaction may be significant only near the ground surface. In contrast, vertical S-waves induce
free-field shear strains that are more important at depth. Thus, since soil strains are controlled
by inertial effects near the ground surface and by kinematic effects at greater depths, the
superposition may be approximately valid even if nonlinear soil behavior is expected, during a
strong base excitation. Finally the inertial interaction analyses in the frequency domain can be
conveniently performed in two steps as originally proposed by Kausel and Roesset (1975) for
embedded foundations, (Figure 2-1c). The primary advantage of the substructure approach is
its flexibility and computational efficiency.
2.2
Soil-Structure Interaction for Pile Foundations
The seismic design of pile foundations in loose granular soils poses several difficulties problems
in analysis and design: 1) liquefaction is associated with a large reduction in shear stiffness of
the supporting soil and can induce large shear forces and bending moments within the piles
leading to severe cracking and formation of plastic hinges at specific locations (Finn & Fujita,
2002). After liquefaction, the residual strength of the soil may be less than the shear stresses
needed for slope equilibrium and significant lateral spreading or downslope displacements can
23
also occur (i.e., post-shaking lateral spreading can cause substantial increases in pile cap
displacements above those for the non-liquefied case). In addition, the moving soil can exert
damaging pressures against the piles, leading to failure. Such failures were prevalent during the
1964 Niigata and 1995 Kobe earthquakes. Lateral spreading is particularly damaging when the
piles are embedded in soil profiles including both liquefiable and non-liquefiable (stable) soil
layers.
The most commonly observed modes of pile failure during liquefaction are illustrated in Figure
2-2 (Tokimatsu et al., 1996). For end bearing piles, damage in the pile heads can be caused by
the horizontal forces and/or the overturning moments imposed on the foundation by the
superstructure that can cause excessive shear forces on the piles (Figure 2-2b and f). Another
potential failure can be initiated by the settlement of the adjacent ground that would lead in an
increase in the loads on the piles and cause rigid body vertical settlements on the superstructure (Figure 2-2c). Finally transient ground deformation can apply significant loads to the
supporting piles especially when the pile goes through a non-liquefiable layer, in which case the
moment demand at the interface of the two layers can exceed the moment capacity of the pile
section (Figure 2-2g). Lateral spreading can cause pile bending, and can be accompanied also
with simultaneous loss of pile capacity (Figure 2-2d and h). In the case of friction piles, damage
is mostly associated with large settlement of the superstructure and or tilting due to bearing
capacity failure induced by soil liquefaction (Figure 2-2a and e)..
24
2.3
State of the art methods of analyses
It is apparent from the preceding discussion that seismic response of a pile foundationstructure system should be analyzed using nonlinear dynamic numerical analyses (finite
element or finite difference methods). However, these types of analyses are still not popular in
engineering practice due to their complexity and computational costs. A range of approximate
analysis has been developed, including pseudo-static and simplified dynamic analyses.
Pseudo-static structural analysis of a single pile typically solves the bending moment and shear
force distributions, where soil-structure interactions are represented by a distribution of nonlinear Winkler springs (p-y curves) and the earthquake loading is represented by an equivalent
static inertia force applied at the pile cap (F = PGA'm, where PGA is the peak ground
acceleration and m the mass of the superstructure). The key limitations of this approach relate
to the selection of p-y curves that are derived from static and cyclic lateral load tests, and are
not directly related to mechanisms of stress changes in the soil and pore pressure development
associated with loading. Moreover, it is should be noted that this method tends to over predict
the maximum bending moments because the inertial forces and soil resistance are not always
in phase (Brandenberg et al., 2007).
Simplified dynamic analyses account for both the stiffness of the soil and radiation of energy
away from the pile (radiation damping). Such methods involve an initial calculation of the onedimensional vertical wave propagation, representative of the response of an infinite, level soil
domain (Kavvadas and Gazetas, 1993,). One can then simulate numerically the response for a 1-
25
D column of pile elements in which all nodes at the same vertical elevation are fixed to have the
same vertical displacement, thus ensuring that the one-dimensional soil column deforms as a
shear beam (Figure 2-3). The free-field motions are imposed at the free field end of complex
Winkler springs for the assumed soil profile. The complex spring consists of two frequency
dependent parts (i) a spring that simulates soil stiffness, and (ii) a dashpot that accounts for
radiation damping.
Researchers have developed both closed-form, semi-empirical frequency dependent complex
springs of pile foundation embedded in elastic soil (Novak, 1974; Dobry et al., 1982; Kaynia and
Kausel, 1982; Kavvadas and Gazetas, 1993). These methods are generally formulated in the
frequency domain and give the pile response for a single harmonic excitation. Their application
to earthquake motion therefore requires the application of Fourier transforms. Similar efforts
have led to the development of frequency independent models for elastic soil for example
Kagawa and Kraft (1981), Nogami and Konagai (1988), and Tabesh and Poulos (2001).
Some Winkler type models have been developed by Kagawa (1992) and Liyanapathirana &
Poulos (2005) for liquefying soil. However, those have limited predictive capabilities since they
neglect important features of dynamic pile behavior such as soil-pile gapping and displacement
hardening that istypically observed for sand of medium density (Varun, 2010).
Finally, several attempts have been made to simulate the soil-pile-structure interaction using
macroelements. Macroelements are derived by integrating the material behavior over the
26
locally affected volume. The global stress-strain response is the applied as external loading at
representative locations along the soil-structure interface. Bounded by limit equilibrium
conditions, the macroelements can simulate the coupled effects of soil plasticity and interface
nonlinearities, and thus have a substantial advantage over the simplified analytical procedures.
Successive, decomposition of the far-field and near-field domain allows efficient frequencydomain methods to be employed in the far field, since analysis of the superstructure supported
by macroelements incorporates nonlinear soil-structure interaction effects. However it should
be pointed out that the results are highly dependent on the constitutive soil model and loading
path used to calibrate the model as the mathematical expression describing their behavior has
been mainly derived from curve fitting of the numerical or experimental results.
Boulanger et al. (1999) proposed a macroelement formulation for soil-pile interaction. The
components of the macroelement included scaled replicas of the API p-y curves for nonliquefiable soils. In order to capture the effects of liquefaction, a dashpot was included to
account for radiation damping, and a gap element to account for strain hardening. Boulanger et
al. (1999) report reasonable agreement with centrifuge data, however, as Varun (2010) noted,
the macroelement formulation is unable to distinguish the response of pile in soils that differ in
terms of hydraulic conductivity, liquefaction resistance or dilation angle as the hardening
simulation capabilities of the macroelement are independent of soil properties. Moreover,
Boulanger et al. (1999) macroelement cannot account for seepage effects that may develop
between the far-field and the region around the piles (Gonzalez et al., 2009). Varun (2010)
developed a macroelement for soil-structure interaction analyses of piles in liquefiable soil that
27
attempts to capture efficiently the physical mechanisms of saturated granular material without
the aforementioned drawbacks. The formulation of this macroelement is described in Chapter
3.
28
M
(a)
UU~t
UO t)
U64t)
MU.t)
.
U,(t)
UIt)
(b)
Uct)
Ui)
(i) Knmatc Interaction
(ii) Inrta Interaction
A
(K)
(c)
(ii)
(i)
Figure 2-1 (a) Geometry of soil-pile-structure interaction problem; (b) decomposition into
kinematic and inertial interaction problems; (c) two-step analysis of inertial interaction
(modified from Varun 2010)
29
Setternent of adjacent
Lose of pile cAPacity
Loss of p-e capacity
lateral preading
ground
Failure due to overturning
moment
Failure due to Iteral
apreading
Fallure due to translent
Faillue due to laterel
ground deforntion
spreading
Figure 2-2 Various observed modes of pile failure in liquefiable soils (Tokimatsu et al, 1996)
Seismic
free-field
0
Seismic
pile
0
T
Fu(I
/UOZ
i-1
I
EP, , Lp
ZO
n
747
i
1rm ffr
U 9e''"'
Vertical
S-waves
Figure 2-3 Typical Winkler spring and dashpot model for pile foundation analysis (from Kavvadas
& Gazetas, 1993)
30
3
3.1
Model of Soil-Structure Interaction
Overview of Macroelement Formulation of the Macroelement
During intense seismic events, Soil Structure Interaction (SSI) has been to proven to be a
significant factor of the overall response of pile foundations (Mylonakis and Gazetas, 2000). To
this end, numerous numerical analysis of the soil have been developed to account of this
interaction, including finite element, finite difference and dynamic beam on nonlinear Winkler
foundation (BNWF) methods. The basic assumption of the latter method, more commonly
referred to as the p-y approach, is that the soil-structure interaction can be represented by a
distribution of rheological elements that act independently (i.e., effectively de-coupling the
shear stress transferred between adjacent soil layers). This assumption greatly simplifies the
analyses and reduces computational costs compared to finite element methods that will indeed
describe the aforementioned problem to the fullest.
As described in Chapter 2 the macroelement approach represents a practical compromise
between simplified Winkler methods and full 3D finite element analyses for simulating complex
SSI for piles. The current analyses use a macroelement developed by Varun (2010) that can
capture efficiently the response of piles in cohesionelss soils subjected to cyclic lateral loading
and can account for soil liquefaction, Figure 3-1. The soil resistance around the pile
circumference is modeled along using a nonlinear Winkler spring(dp,), while a viscous damper
(dpd) represents radiation damping that varies with non-linear material behavior. A gap
31
element is included in the formulation to account for the formation of a gap at the interface
between the soil and the pile.
Varun conducted 3D finite element parametric investigation of a single pile in liquefiable soil to
interpret the controlling parameters. The macroelement was originally developed around a
series of 3D finite element simulations using the finite element program Dynaflow
(Prevost,1995) and incorporate the multi yield plasticity model of Prevost (1985) and later
validated with using full-scale, force vibration test data from a blast-induced liquefaction test
bed and centrifuge data for earthquake loading of piles with superstructure (Varun, 2010).
3.1.1 Drained Behavior of Macroelement
Varun (2010) initially considered the response of a pile subjected to lateral loading in dry /
drained soil conditions using a modified Bouc-Wen type hysteresis model (Bouc, 1971; Wen
1976). The equation for the quasi-static case is:
P=P,&
(3.1)
where p is lateral pressure, p, is the ultimate lateral resistance of the pile section and { is a
dimensionless quantity that describes the nonlinear, hysteretic, lateral soil reaction. This
parameter iscomputed incrementally by the following expression:
d
=
{1- f({)[b+
sign(x)={
+1
g -sign(du -{
A
r(3.2)
for
x >0
32
where du is the incremental relative displacement between the pile and the free-field at the
location of macroelement; u, = p,/K , u, is the yield displacement, and K the initial stiffness;
b(= 1-g) and g are input parameters controlling the unloading and reloading stiffness. The case
b = g = 0.5 corresponds to the case where the unloading stiffness is equal to the initial stiffness.
Finally,
f
f({)
= 1 for
is a monotonically increasing function of ( such that
J = 1. Varun
f
= 0 for
=
0 and
(2010) assumes the following analytical expression:
(3.3)
f ({) = tanh(a()/tanh(a)
where a is the backbone curve parameter that is fitted to the results of the numerical (FE)
simulations and depends on the relative density of the surrounding sand. Varun (2010) reports
values of a= 2.7 for dense sands, a= 2.8 for medium sands and a= 2.9 for loose sands. He
also states that the initial stiffness K of the p - y curve, is calibrated to the reference Young's
modulus of the soil (E,),
(p/p,
vs
while b
is fitted to the backbone quasi-static behavior
u/u,) such that b=0.6 (g=1-b=0.4). The ultimate lateral resistance is also
calibrated to the Coulomb friction angle of the sand through the passive earth pressure
coefficient K, and the pile diameter, using a weighting of empirical experiment proposed by
Broms (1964) and Fleming at al. (1992):
(3.4)
p= (3.25K, + 0.3K) -Bov
where K, = tan 2 (45+#/2)
The macroelement includes a dashpot "in series" with the spring (Figure 3-1). This describes
radiation damping caused by energy dissipation and re-distribution. There has been a broad
33
discussion in the literature on whether the dashpot should be placed either in parallel or in
series with the spring element. Wang et al. (1998) reported that, when the dashpot is placed in
a parallel arrangement with the spring, unrealistically large forces may occur when highly nonlinear loading occurs and therefore an upper bound should be applied. To overcome those
Boulanger et al. (1999) placed the dashpot element in "parallel" with the elastic stiffness spring
and in "series" with the plastic slider element, so that the total response never surpasses the
ultimate yield strength of the soil. Varun (2010) argues that the physical interpretation of the
parallel arrangement leads to an incorrect consequence, namely that the soil resistance at
maximum displacement should be almost the same for all loading frequencies in sinusoidal
loading, since at maximum displacement the loading rate is zero, and thus the dashpot does not
contribute to the overall resistance. In his parametric investigation, Varun (2010) proved that
the soil resistance at maximum displacement decreases as the loading frequency increases,
which is something that the series model can capture. Hence he used this arrangement in the
formulation of the macroelement. The total resistance is calculated in an incremental fashion
from the following equation:
dp =dp,+'dp= pyd{s +p,d4
(3.5)
The quasi-static resistance, dp, calculated from equation (3.2), while the dynamic resistance is
given by:
dp =c.du
(3.6)
where c,. is the radiation damping coefficient.
34
The radiation damping coefficient c, is calculated iteratively using an equivalent linear
approach by modifying the linear damping coefficient proposed by Makris and Gazetas (1992)
as:
Cr
=
c(1-f [(b+g-sign(du-{
(3.7)
c = pV-ao 2 QB
where p, is the density of soil, V, is the shear wave velocity in soil,
Q
is a coefficient that
depends on the soil Poisson's ratio and the shape of the foundation as derived by Novak et al.
(1978), ao is the normalized frequency of loading, ao = cB/V , B is the diameter of the pile.
For the case of transient loading co is equated to the dominant frequency of the loading.
Badoni and Makris (1995) showed that
3.1.2
Q =3
is appropriate for shallow depths.
Undrained Behavior of the Macroelement
Varun (2010) observed the formation of a zone around the pile where pore pressures are
considerably different from those in the far-field due to local soil structure interaction. This
zone extends for about five diameters around the pile, Figure 3-2. The same phenomenon has
been reported in the literature, (Gonzalez et al., 2009; Boulanger et al. 1999) and has been
attributed to both dilation effects in the soil and suction acting on the tension side of the pile.
The above observations are indeed in agreement with the principle that soil-structure
interaction alters the stress, pore pressures and displacements in the near field compared to
the conditions in the free-field.
35
In order to incorporate the effects of changes in effective stress at the soil-pile interface Varun
(2010) introduced a pore pressure generator that modifies the drained response to account for
local pore pressure generation and dissipation. The model developed by Varun (2010) extends
the "liquefaction front" concept originally proposed by Iai et al. (1992).
Figure 3-3 summarizes measurements of excess pore water pressure from elemental undrained
torsional shear tests on sands, as a function of the total amount of shear work done per unit
volume of soil (W) as reported by Towhata and Ishihara (1985). In undrained hollow cylindrical
shear tests the total work is calculated in an incremental fashion from the following equation:
dW = a 'de, +2ah'de
+rdvh(.
dW =dW + dW
The above increment, dW, consists of a strain energy contribution due to volumetric
deformations, dW and one due to shearing deformation, dW, . However, since Towhata and
Ishihara (1985) performed undrained tests, the total volumetric change is zero and thus it does
not have any in the total work, dW = 0. Therefore the total work equals the total shear work
done, W = W,. The same authors showed that this behavior is independent of the mode of
shearing and they stated that the excess pore pressure build up depends exclusively on the
current stress state and the accumulated shear work. Towhata and Ishihara (1985) constructed
contour lines for the accumulated shear work in the effecticve stress space (Figure 3-4).
lai et al. (1992) used the above experimental results to formulate a semi-empirical procedure to
describe the effective stress paths, where:
36
= 1
=(1- S)
(3.9)
lai et al. (1992) explained that as shear work is accumulated during dynamic loading, the
envelope of stress points at equal shear work gradually moves from the initial envelope to the
failure line (Figure 3-4). This envelope is called "liquefaction front".
Figure 3-5 shows the implementation of the liquefaction front concept for the pile-soil
macroelement by Varun (2010). The predominant parameter is the liquefaction front
parameter(S 0 ), which can be interpreted as a measure of the cyclic mobility and is defined as
function of shear work, and can be graphically explained as the intersection of the envelope of
stress points at equal shear work with the x-axis in the normalized stress space (Figure 3-5).
Varun (2010) performed a numerical parametric investigation which concluded that So is
independent of critical state friction angle, friction angle and pile diameter as shown in Figure
3-6 a, b and c. However So does depend on the liquefaction resistance parameter of soil, X, a
dimensionless parameter used is the soil model of Prevost as shown in Figure 3-7 (a). The
liquefaction resistance parameter X depends on the relative density and sand type (Popescu,
1995). The liquefaction resistance parameter X is derived by liquefaction strength analysis
using laboratory testing of soil samples or via correlations with field test data. Popescu (1995)
quotes values of the parameter range, X = 0.08 for dense specimens to 0.15 for loose sands.
Varun (2010) found that the liquefaction front parameter correlation with the normalized shear
work could be further normalized by a scaling parameter w, which related to the liquefaction
37
resistance parameterX and to the elastic stiffness properties of the soil through a derived
parameter, 77 (Figure 3-8):
R = n(-n) (1 - 2v) 2 n (I _ V)20-n>
(3.10)
wi
(3.11)
where v is the Poisson's ratio and n is the power exponent describing stiffness variation with
confining pressure 1.
Figure 3-6b shows that the liquefaction front parameter, So, is a unique function of the ratio
The liquefaction front parameter, So, can then be calculated from the following
w/i.
equations:
So = exp --
dSO = KSO (-1ogS
(3.12)
0 )1x
(3.13)
where ris fitted to the simulated behavior shown in Figure 3-5 andFigure 3-6, resulting in a
constant value, K = 1.4 .
Finally Varun (2010) proposed that the liquefaction front excess pore pressure can be used to
represent relations between the vertical effective paths S = d
r = p/BaO :
S2 +
(r:5 r3)
SO
S=
(So-S
2 )2+[(r
-T 3 )/mj2
(r
r)
i.e. E=E0(a/0
38
/O
to the pile resistance,
S2
=
So (1-m 2 /3m)
r3=2Som 2 /3in
where mi is the slope of the failure line, m2 is the slope of the phase transformation line and So
isthe liquefaction front parameter (Figure 3-5).
Figure 3-5 shows clearly how the undrained pile resistance (p) can increase once loading
exceeds the phase transformation state. According to the Varun (2010), the slope of the phase
transformation line to depends on the critical state friction angle,
s:
(3.15)
m2 = 3.25 tan2 (450 +,/2)
Finally the quantity dw is the normalized incremental plastic shear work, and is calculated as
the difference between total incremental shear work (dW) and elastic incremental shear work
(dW) normalized by the product of ultimate soil resistance and yield displacement. From the
results of the parametric investigation, Varun (2010) concluded that the amount of plastic shear
work done when the soil dilates, doesn't contribute significantly to the build-up of excess pore
pressure, therefore only the plastic shear work done in the contractive zone (below the phase
transformation line, r ! r ) is calculated:
dw= 1
dW-dW
pdu-p K
pu,
pYu,
r <r
(3.16)
0r>r
39
3.1.3
Partially Drained Behavior of the Macroelement
Local mechanisms of pore pressure generation contribute to the gradient of excess pore
pressures around the pile hence, provide conditions for partial drainage within the soil mass. In
order to account for this effect, Varun (2010) assumes that there is a linear pressure gradient
between the local field and far/free-field regions in the radial direction, and that Darcy's Law
controls the seepage within the sand. Varun (2010) assumed 1-D radial flow(v, = v = 0):
v,. = k
Ah
L
kU ff-Q
k,
Us =- o (Sg - S)
kL
pg
L
(3.17)
where k is the hydraulic conductivity, Ah is the difference in piezometric head, L the
characteristic length and S = 0v
is the effective stress ratio next to the pile and Sg the
effective stress ratio in the far/free field. Assuming the characteristic length is proportional to
pile diameterL = aB, the first derivative of the drainage velocity is:
d k ,k
kL , (1
-S)=- O(Sfdr L
dr L
dv,d'dd
dr
=-S)=L
,
kS ,
= a2 2 ,0GS) 1 -S)
aB
(3.18)
Using the mass flux equation and assuming that we have flow only in the radial direction and
that the both the soil and the water particles are incompressible -- = -v
at
at
V.vr +an =
at
v + an =
ar at
:
v - aevoi
at
ar
=
where n is the porosity of the soil.
For the case of a linear, isotropic elastic soil:
v
Dr
1 (a OAu
Ky at
a
at
=>
1
ar
K at
_u
1 ad
Ks at
40
(3.19)
where K,' is the elastic bulk modulus of the soil skeleton, and there are no changes in the mean
total stress. For non-linear sand stiffness the value of K ,varies with the effective dense level:
11f
1
Eo
so _ gn
0)
3(1-2v)
(3.20)
where the exponent, n, is obtained from 1-D or hydrostatic compression tests on sands.
v
= sO
Ks K'K
It is then possible to express the radial gradient of specific discharge:
_ o>
dv,
a
"
dr K
at
o
aS
KS at
_
0
ES"
(3.21)
S
at
Equating results in equations 3.18 and 3.21, it is then possible to rewrite change in effective
stress ratio due to partial drainage:
aS
Esok
s"(s'-s)
2
2
at 3(1-2v)a B
s
(Sf - S)
-S"
(3.22)
at
where $ is the partial drainage parameter and depends on the permeability, the Young
modulus of the soil, the diameter of the pile and the Poisson's ratio.
Varun (2010) assumes that the rates of change in effective stress are equivalent to changes in
the liquefaction front parameter (i.e. dS = dS0 ) (from equation 3.14). He makes this
assumption as drainage produces only contraction of the skeleton (which is valid for states
below the phase transformation). The explicit formulation of Equ.17 requires very small time
increments in order to be numerically stable as Varun (2010) reports:
p
dSO (i)
dt -S(i)
(3.23)
(i)]
Instead one can use the implicit formulation for this part which is more stable numerically:
dSo (i)
=
18. dt - S(i)" (S'
(i) - S(i + 1))
41
S(i +1)=S(i)+dS0 (i)
dSo
19-dt-S"
(Sff -S)
(3.24)
The drainage parameter @was obtained as a function of the hydraulic conductivity, Poisson's
ratio and the pile diameter from fitting in the numerical data from the 3D simulations (Varun,
2010):
#J=550 2(1+ v') k-
(3.25)
3(1- 2v') B
Another very important feature that is incorporated in the macroelement behavior is the
formation of a gap between the pile-soil interface. During cyclic loading gapping will occur near
the ground surface on the tension side of the pile, ( as reported in i.e. the 1989 Loma Prieta
Earthquake by Pender and Pranjoto, 1996). To study this behavior, Varun (2010) performed
numerical experiments where the pile is loaded monotonically to a maximum displacement and
then subjected to cyclic loading of magnitude of portions of the original displacement, a
scenario representative of earthquake motion with a strong unidirectional impulse followed by
smaller cycles. Figure 3-10 shows the pile resistance curve during the above loading scenario.
The initial response shows kinematic hardening behavior and afterwards force relaxation is
observed after each cycle of unloading-loading. Varun (2010) states that this kind of kinematic
hardening behavior is indicative of a cohesionelss soil where after the gap becomes infilled
during subsequent load cycles.
To simulate this effect, Varun (2010) implemented a gap element as an additional component
of the macroelement. The gap element is simply an envelope function used as a multiplier to
scale the total p-y response predicted by the macroelement depending on the current
42
displacement and the maximum previous displacement on each side of the pile. A hyperbolic
function is used and the gap multiplier iscalculated as
mg = c +
where
(1- c)
umax
(3.26)
I
is the maximum prior displacement on each side, ng is a power coefficient (avalue
of 2 is recommended by Varun(2010)),
uref =
5u, is a reference displacement value used for
scaling and cd =0.1 -0.2 is the ratio of drag resistance from the sides of the piles to total
resistance. The overall mechanic components of the macroelement are shown in Figure 3-1.
Figure 3-9 shows the sequence of calculations for the macroelement:
1. The drained response ({(i),pd, (i)) is calculated using Eq.(3.5);
2. The shear work done is calculated incrementally using Eq.(3.14)., and is used to
calculate the change in liquefaction front parameter So associated with the undrained
pore pressure generation is obtained from Eq.(3.11);
3. The value of So is updated to account for partial dissipation of excess pore pressure (Eq.
3.19).
4.
Given the current values of (, So and r (=m4S), the current level of average-effective
stress ratio (S)is calculated.
5. The total resistance taking into account also the gapping effect is then calculated as
p = mgpPS and the next increment to the shear work done is computed.
43
The following example presents the behavior of the macroelement in a simplified loading
scenario that allows a better understanding of its mechanical behavior. Figure 3-11 illustrates
the displacement-resistance behavior of the macroelement for 6 cycles of sinusoidal
displacement controlled loading, using the soil parameters shown in the legend (detailed
discussion of the parameters follows in Section 3.2). The vertical axis corresponds to the
normalized lateral resistance p/p, while the horizontal to the lateral displacement of the pile.
The macroelement has as an input a sinusoidal displacement with amplitude of 0.02 m and
frequency of 0.1 Hz (Figure 3-12a). We assume a linear pore pressure build-up (Figure 3-12b) in
order to demonstrate the effect of the phenomenon in the degradation of the soil stiffness.
3.2
Calibration of the Varun (2010) Macroelement for Toyoura Sand
The macroelement
has been calibrated for a specific (but hypothetical) soil profile
corresponding to site conditions for a wharf structure (Berth 30-63, Figure 3-13) that is founded
on piles driven in an hydraulic fill (modeled as loose Toyoura sand). The site consists of three
basic layers whose properties are listed in Table 3-1. The first layer (top 18.3 m of the soil
profile) consists of a hydraulically placed loose sand fill that is susceptible to liquefaction, this is
underlined by a 2.6 m thick layer of dense sand (Dr=80%) on top of stiff-to-hard clay. The water
table level is located 4.6 m beneath the ground surface. Vytiniotis (2011) modeled the hydraulic
fill using the properties of Toyoura sand with Dr=40% (e=0.825), a saturated unit weight,
psat=1.85Mgr/m 3, and hydraulic conductivity, k=3x10 4 m/s, while the two underlying layers are
assumed to have properties of dense Toyoura sand (Dr=80%, e=0.673, psat=2.05Mgr/m 3, and
44
k=3x10 4m/s). The macroelement parameters that are related to the physical properties are the
following:
i.
Initial stiffness of the p-y curve: K =1.25- E,,
where E, is the Young's modulus of the
soil at small shear strain. The small strain, elastic shear modulus of Toyoura Sand is
reported in Dafalias and Manzari (2004) as G= Gopa,
,
1+e
based on
PatI
recommendations from Richart et al. (1970), where pat isthe atmospheric pressure, e is
the current void ratio, and Go is a material property that defines the maximum shear
modulus, Gmax, at P'=Pat. Dafalias and Manzari (2004) report Go=125 and n = 0.5 for
Toyoura Sand and
Vytiniotis (2011) assumes v=0.33 for free field simulations of
Toyoura sand. Figure 3-14 summarizes values of the initial Young's modulus along the
depth of pile H. In the finite element analysis the actual input parameter for each
macroelement- embedded pile node is K, =1.25xE,, (Table 3-2).
ii.
The
slope
of
the
failure
line:
=(3.25K, +0.3K ),
m.,=-
where
B,
K, = tan 2 (45 + / ) is the coefficient of passive elarth pressure and <b is the peak
friction angle of the soil. The peak friction angle for Toyoura sand Dr=40 % and Dr=80 %
was estimated using data from Pestana (Pestana et al (2002) having values of 360 and
430. The critical state friction angle of
#,, =
31' 0 for Toyoura sand, (and is comparable
to soil properties measured for Berth 60-63 Table 3-1).
45
iii.
The slope of the phase transformation line: m2 = 3.25 tan2 45+ s
), where
#,, is the
critical state friction angle of the soil.
iv.
Backbone curve parameter, a describing non-linear p-y relation in first loading
(depends on relative density of the sand, D,).
v.
Shear work correlation parameter w, depending on the power exponent of the soil (n),
the Poisson's ratio (v) and the liquefaction resistance parameter (x)
_n
) (1-
2v) 2n ( 1_
1)2
n>
X
vi.
Partial drainage parameter (0) depending on the Poisson's ratio (v), hydraulic
conductivity (k)and pile diameter (B):
#=
2(1+ v') k
5503(1-2v') B
Following the recommendations of Varun (2010) we assume a= 2.8 for the medium density
sand and a=2.7 for the denser sand. Figure 3-15 compares the macroelement (p-y curve)
response for these loose and dense sand cases. For the sake of simplicity of the figure, we are
using the same initial stiffness for both of cases, which indeed is not true but our intention is to
demonstrate the effect of the others -not so trivial- parameters.
As far as it concerns the shear work correlation parameter w,, the only unknown parameter is
the dilation parameter X. In principle this parameter can be obtained by matching cyclic
laboratory tests with numerical analyses using the Prevost (1985) soil model. The typical range
46
of X = 0.08 to 0.15, with lower values corresponding to denser specimens. In the absence of
specific calibration data from Toyoura sand we assume the same values reported by Popescu et
al. (1995) (based on calibration for fine Nevada Sand). Figure 3-16 shows the influence of the
parameter in the elemental behavior of the macroelement.
Finally, we calculated the radiation damping coefficient (c) . At each macroelement depth, we
calculate the shear modulus (G) and from that the shear wave velocityV, =
-
.
Since we will be
imposing earthquake loading we used an average predominant frequency for the suite of
earthquake loading of about 2 Hz. The macroelement input parameters for the pile No 3 (Figure
3-13) are shown in Table 3-2.
47
Table 3-1: Measure in situ properties of Berth 60-63, data from Vytiniotis (PhD 2011)
Table 3-2: Macroelement properties for pile 3
Dr=40%
Dr=80%
No.
Depth of
Influence
K (kPa)
(kN m)
a
mi
m2
w1
1
2
0.5
1
10181
21063
32
136
2.8
2.8
16.97
16.97
10.15
10.15
1.074
1.074
0.43
0.43
4.40E+05
6.33E+05
3
1
27994
240
2.8
16.97
10.15
1.074
0.43
7.30E+05
4
5
6
1
1
1
34617
40161
45029
366
493
620
2.8
2.8
2.8
16.97
16.97
16.97
10.15
10.15
10.15
1.074
1.074
1.074
0.43
0.43
0.43
8.12E+05
8.74E+05
9.26E+05
7
8
1
1
49419
53450
747
874
2.8
2.8
16.97
16.97
10.15
1.074
9.70E+05
10.15
1.074
0.43
0.43
9
10
11
12
13
1
1
1
1
1
1000
1127
1254
1381
1507
10.15
10.15
10.15
10.15
1.04E+06
1.08E+06
1.10E+06
1.13E+06
1634
16.97
10.15
10.15
1.074
1.074
1.074
1.074
1.074
1.074
0.43
0.43
0.43
0.43
1
2.8
2.8
2.8
2.8
2.8
2.8
16.97
16.97
16.97
16.97
16.97
14
57197
60714
64037
67197
70214
73107
0.43
0.43
1.16E+06
1.18E+06
15
16
1
1
75890
78575
17
1
81170
1761
1888
2015
2.8
2.8
2.8
16.97
16.97
16.97
10.15
10.15
10.15
1.074
1.074
1.074
0.43
0.43
0.43
1.20E+06
1.22E+06
1.24E+06
18
1
83685
2141
2.8
16.97
10.15
1.074
0.43
1.26E+06
19
1
107739
2268
2.7
25.58
10.15
2.013
0.43
1.43E+06
20
1
110210
2373
2.7
25.58
10.15
2.013
0.43
1.45E+06
21
1
113602
2522
2.7
25.58
10.15
2.013
0.43
1.47E+06
22
1
116423
2648
2.7
25.58
10.15
2.013
0.43
1.49E+06
23
0.5
119177
2775
2.7
25.58
10.15
2.013
0.43
1.51E+06
48
(s)
C (Pa's)
1.01E+06
PORE PRESSURE MACROELEMENT
ELEMENT
----------------------------------dp,
dw
Pile response
OUTPUT
GAP
ELEMENT
INPUT
Free-Field
dUff
F
Uf
Displacement of the free field
Sf
Effective Stress Ratio at the free filed
dp,
incrementalforceper unit length exerted by the spring
dpd
incrementalforce per unit length exerted by the dashpot
p,,y
Force per unit length for drained case
dw
Incremental shear work in macroelement
S(w)
Average effective stress ratio in near-field
P
Force per unit length with gap correction
F
Force imposed at pile node in FE analysis
Figure 3-1 Schematic Formulation of the Macroelement (modified from Varun, 2010).
49
Syy-STRESS kPa]
I
I
1.13
4.13
-9.38
14.62
19.87
.
25.12
30.36
35.61
* 40.86
l
H1
OB
46.10
Figure 3-2 Effective vertical stress o, [kPa] plot after seven loading cycles showing the
formation of local liquefaction zone - approximately five diameters around the pile (from
Varun, 2010).
3001 w-u relationship
u UT
=
liquefaction
. 0 kN/ m
0 WN/m"
2 way cyclic torsion shear test
C , x- C , r
=
2
at
E
C', = 294 kNm'
a. 200
K0=1, Toyoura sand
Sym
.
Exp.
No
Tmax
kN/m 2
e
o
37
77.7
0.813
o
45
60.6
0.809
A
47
64.9
0.818
<1
60
70.6
0.811
V
69
55.4
0.784
c>
77
70.6
0.812
5
10
J .0
V
100
*)0
(A
0
.
Average of loading
schemes a,b and e
L..
h
.02
0.05
0.1
0.2
1
0.5
2
Shear work per unit volume w (kJ/m
20
3)
Figure 3-3 Relationship between excess pore pressure and she ar work for undrained cyclic
shear tests on sand (after Towhata and Ishihara, 1985).
50
Toyouro Sand
1
0L
%.
0
V)
1-50
4>
-1
300
Effective Confining Siress -0~'
(kPo)
Figure 3-4 Envelope of stress points at equal shear work (Towhata and Ishihara, 1985)
51
0
Cm1
Failure Line
0
M
Liquefactio
4-J
ront
M2
Phase Transformation Line
--
r2
2/3M2
r3
S2
z
_
F
SO
Vertical Effective Stress Ratio, S =Ta /so
Figure 3-5 The liquefaction front concept as extent by Varun for pile. The normalized vertical
effective stress S=O- 0 oOcan be calculated as a function of the normalized soil resistance
r=/)Bo -
52
1
1I
0.8
0.8
-B=0.5
0-6
. B=0.75
--
0-6
CS
0.4
0.4
0.2
0.2
0
0
0
0.5
1
1.5
2
B=125
A
A
--B=1.5
(b)
0
2.5
0.5
1
1.5
2
2.5
w
w
1
0.8
0
0.6
Co
0.4
0.2
0
0.5
1
1.5
2
2.5
w
Figure 3-6 Liquefaction front parameter (SO)
correlation with normalized shear work w for
different values of (a) critical state friction angle (b) pile diameter (c) maximum friction angle
(figure from Varun (2010)).
1
*X=0.15
0.8
X=0.15
0.8
SX=0. I
X=0.05
-- ------
0.6
A X=0.10
0 .6
U)
-
-
. X=0. 0 5
-
- - -0.4
0.4
-
0.2
(a)
0
0
__
1
_
_0__
2
_
-
0.2
_(b)
3
4
w
0
0.5
1
1.5
w/w 1
Figure 3-7 (a) Liquefaction front parameter (S0 ) correlation with normalized shear work as a
function of liquefaction resistance parameter X (b) Shear work correlation curves after
normalization with parameter w1 (figure from Varun (2010)).
53
2
1
A n=0.6
0.8
0 n=0.7
0.4
0.2
0
0
0.1
0.3
0.2
0.4
0.5
V
Figure 3-8 Parameter r as a function of Poisson's ratio and power exponent n (from Varun
(2010))
54
Total Macroscopic Pile Response
IptParametersK, py, 0, C, M2, W1,y
Z !relative dslcmnu()n~
Compute dramed response (i) and pai)
Compute Plastic shear work (w) and
Liquefaction front, So(i)
I
Input far field excess pwp, 1-Sa(i)
S(i)=S.,(I)I
Compute eff. stress ratio, S(i)
s|S(i)-S (i)|< to
No
Yes
/
Output soil resistance, p(i)
/
Figure 3-9 Flowchart for calculation of pile response using the macroelement (Varun, 2010).
55
1
0.5
IL:
0
-0.5
-1
0
0.025
0.05
0.075
0.1
u (m)
Figure 3-10 Pile response to small loops of cyclic unloading-reloading after monotonic loading
(Varun, 2010).
0.6
0.4
E
0.2
0
0
Lb
0
-0.2
0
NI
F
-0.4
z
-0.6
-0.8I
-0.02
-0.015
-0.01
1
I
-0.005
6
0.005
Horizontal Displacement u (m)
Figure 3-11 p-y curve for the macroelement. The degradation of stiffness and lateral resistance
of the macroelement is a result of the cyclic loading and the accumulation of excess pore
pressure.
56
0.02
E
(a)
0.01
o
E
-
o 0
C
0
0
-0.01 -0.02
T
0.8
1>
.(b)
Lfn
<
0.60.4-
a~>-
CU 0.2-
v Lu.
0
>
0
0
10
20
40
30
50
60
70
Time, t (sec)
Figure 3-12 Sinusoidal Input Displacement motion and b.Assumed pore pressure build up
57
a. Berth Section
4.m
-
ASea
0DOm-
/
Hydraulic Fill
-13.7m -6.3m -
Water Level
\
5 6Facing
Stone
Sand FilI
Old Bay Mud
(Stiff Clay)
Pile Locations
.33,7m -
b. FE Model Properties
I.TI
4,6m
0,0M
'El
-13.7m.-16.3m
-
LI
.33,7m-
LI
Figure 3-13 Physical model of Berth 60-63 and FE model properties as used by Vytiniotis (PhD
2011). (Figure from Vytiniotis (PhD (2011))
58
Young's Modulus distribution along the Macroelement nodes in pile No 3
E(MPa)
100
T----
80
60
40
20
0
0
120
25
0- Toyoura Sand Dr=40%
pTovaura Sand Dr-80%
E -5
*---*-*---*
4-
--
---
20
CL
0.
o
5
-10
-
00
-25
---
-
-
----- -
--
--
------
0
Figure 3-14 Young's Modulus distribution along the depth of the pile. The darker grey line
corresponds to the upper hydraulic fill, which is modeled with Toyoura Sand of Dr=40 %. The
lighter grey line plots the corresponding distribution along depth of Young's modulus fo Toyoura
Sand of Dr=80%. After the depth of 18.4 m below the surface, for the calibration of the
macroelement we are using the properties of Dr=80 %Toyoura Sand.
59
15
a.
10
CL
E
0
5
*
0
0
-1
0
N
-10
-.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Horizontal Displacement u (m)
Figure 3-15 Effect of parameters a and w on the response of the macroelement.
60
0.02
0.6
2
04-
x=0.15
-
x=0.08
-0.015
-0.01
E
$
0.2-
'U
00
C
15 -0.2
-0.4
E
0
-0.6
-0.02
-0.005
t
0.005
0.01
Horizontal Displacement, u (m)
0.015
Figure 3-16 Effect of parameters X on the response of the macroelement.
61
0.02
4
4.1
Seismic Response of Pole-supported Wharf Structures
Problem Description
In this chapter we examine the 2D dynamic response of Berth 60-63 (port of Oakland), which
represents a typical pile-supported wharf structure that was constructed in the 1960s and
hence, reflects now outdated seismic design criteria for loose, liquefiable granular fill. The soil
profile comprises three basic layers whose properties are listed in Table 3-1: a 18.3 m thick
(hydraulically-placed) loose sand fill (average Dr= 40%), that is susceptible to liquefaction,
overlying a 2.6 m base of dense sand (average Dr= 80%) and an underlying stiff-to-hard clay.
The berth structure consists of 7 rows of vertical and 2 rows of batter pre-stressed reinforced
concrete piles supporting a 30 m long, 0.46 m thick reinforced concrete deck (Figure 4-1). A 2-D
finite element (FE) model of this wharf has been developed in OpenSees, an object-oriented FE
analysis framework (McKenna et al. 2010) as shown in Figure 5-2.
The pile-soil model comprises three components at: 1) 2-D beam-column elements
representing the behavior of precast and prestressed piles, 2) vertical spring elements
describing the vertical pile-soil interaction, and 3) macroelements describing the horizontal
response of the pile-soil interaction. Each macroelement has a free field boundary where the
corresponding time histories of free field displacements and excess pore pressure ratio are
imposed as input motions for the dynamic analyses.
62
Vertical loads from the superstructure are transferred to the underlying soil through the shear
resistance along the shafts of the piles and the tip end bearing resistance, while lateral loads
are resisted by the bending action in the vertical piles (the batter piles provide both bending
and axial resistance). The pile nodes have three degrees-of-freedom (2 translational, 1
rotational), while the non-linear beam-column elements (each with 5 integration points) are
capable of simulating the formation of plastic deformations within the element. The properties
of the reinforced piles are represented with an aggregated section in which the momentcurvature response is described by an elastic, perfectly plastic constitutive law with elastic axial
stiffness, EVA, bending stiffness, EI,, and maximum section yielding moment, M, (Figure
4-3).
The piles for Berth 60-63 have width 45.7 cm with a ring of 16 #32 mild steel vertical bars and
10 #13 pre-stressed tendons, covered by 7.5 cm of unconfined concrete. The calculation of the
moment capacity of the section was done using an online available software (KSURC;
Esmaeily, 2011), assuming that pre-stressed tendons provided a fixed axial load across the
section (i.e. increasing the moment capacity). We assume a concrete compressive strength,
f
6.0 ksi = 41.4 MPa, elastic modulus: E, [ksi] = 57 -f 4 [psi], and steel with yield strength
=f60 ksi =414 MPa and modulus, E, = 29,000 ksi = 200 GPa.
63
The deck structure is responsible for transferring the dead and live loads of the wharf structure
to the underlying foundation. The current case considers a cast-in-place concrete deck slab with
thickness, 46 cm, constructed of reinforced concrete (with concrete strength fc=41.4 MPa). Due
to the large thickness and high rigidity, the deck acts as a diaphragm wall in the horizontal
plane. The deck is modeled with linear elastic, beam-column elements, and additional
constraints are imposed (by tying the deformations of all the deck nodes to each other) to
prevent flexural deformation of the deck. The pile-deck connections are modeled in a simplified
way by imposing the same degrees of freedom at the pile head and the connecting pile deck
nodes.
The soil-pile interaction in the vertical direction is represented by elastic springs that simulate
the friction and tip resistance of the soil using zero length elements, which are defined by two
nodes at the same location (the pile node and the corresponding "spring" node). The forcedeformation relationship for the element is prescribed in a uniaxial material. The springs were
assigned stiffness properties following the change of the soil Young's modulus with depth
(Figure 3-14). This simplified modeling of the vertical soil-pile interactions was judged
appropriate as the loading was predominantly horizontal and the vertical displacements are
very small. In the lateral direction, the soil-pile interaction is modeled using the macroelement
developed by Varun (2010), with input parameters calibrated in Chapter 3. The nodes for the
macroelements are offset at a very small distance from the corresponding pile nodes (0.1 m),
such that the orientation of the macroelement is perpendicular to the axis of the pile. Loading is
64
simulated by imposing time histories of free field displacements and excess pore pressure
ratios 2 at the macroelements.
4.2
Ground Motions and Free Field Analyses
The NEES-GC team (Shafieezadeh, 2011) selected a suite of 56 ground motions that are typical
of firm-site conditions in coastal California using records from the Next-Generation Attenuation
of Ground Motions (NGA) project (Chiou et al., 2008), with moment magnitude M=5.5-8.0,
located 15-60 km from rupture zone. A subset of 15 ground motions were randomly selected
from the NGA database at rupture distances less than 15 km.
Vytiniotis (2011) used the selected suite of earthquake ground motions to predict the free field
response at the Berth 60-63 site. The mechanical responses of loose sand fills were computed
using a coupled deformation-flow finite element analyses with appropriate free field boundary
conditions. The DM 2004 (Dafalias & Manzari, 2004) effective stress soil model was used to
simulate the mechanical response of sand in cyclic shearing. Vytiniotis (2011) also investigated
the effectiveness of installing an array of PV-drains as a method of mitigating seismic risk for
Berth 60-63 by using the same suite of free field ground motions. The performance of this
system was evaluated through comparisons with a series of analyses where the whole sand fill
was densified though appropriate compaction methods. The PV-drains system offers a less
, where U0 is the insitu (hydrostatic) pore pressure
2
07o
65
intrusive solution for retrofitting the berth, than conventional compaction methods that would
require a complete reconstruction of the piled wharf structure. Figure 4-5 shows the locations
of the PV drain system analyzed by Vytiniotis (2011). The current research uses free field
analyses to compare the response of: 1) the current unimproved piled wharf structure; 2) the
wharf retrofitted with a PV drain system (Figure 4-5); and 3) the idealized retrofit with complete
densification of the fill.
4.3
Results of Untreated Scenario
We will examine first the response of the structure for the base case analysis of nga0779motion
(Loma Prieta Earthquake, 1989). Figure 4-6a shows the horizontal ground acceleration record of
the event as used by Vytiniotis (2011) as an excitation for the free field analysis of the site of
Berth 60-63. The results of the above analysis are plotted in contours of acceleration and
displacement at 4 snapshots (t = 5, 10, 15, 20 secs) Figures 4-6b and 4-6c. The maximum free
field displacement that occurs in the site is greater than 0.9 m as shown in Figure 4-6c. Figure 46d shows the time history of the horizontal displacement of the deck with a net permanent
displacement Sh = 55 cm.
Figures 4-7 to 4-10 show the evolution of the failure mechanisms within the wharf structure
subjected to the base case ground motion, nga0779. The figures represent snapshots of the
wharf structure and underlying free field fill response (contours of displacement and excess
pore pressure ratio) at 5 sec intervals. At t=5secs (Figure 4-7) no significant displacements or
66
pore pressures have developed in the fill and the deck displacement is less than 1 cm. At t=10
sec, there are significant slope displacements (Figure 4-8b) and pore pressures have already
developed with the outmost regions of the slope reaching excess pore pressure ratio
approachingAu/O = 1.0. Hinges form at the red (landward) pile-deck connections, and there
is a net deck displacement
6
h=
22 cm. The formation of hinges at the most landward pile-deck
connections is indeed the most common type of failure observed as later revealed from our
analyses. At t=15secs, the wharf has failed with a 3-hinge collapse of five rows in piles and large
rotations of the seaward batter piles (Figure 4-9a) and the deck displacement
6
h=
20 cm.
However, it should be noted that the deck displacement has previously reached a local
maximum of 40 cm at t=11 secs (Figure 4-6a) and then decreased to smaller value following the
imposed pulses of the motion. The creation of the 3-hinge collapse mechanism occurs at t = 11
secs. At t = 20 secs; the deck displacement reaches 54 m, while there is a significant spread of
the region with plastic hinges (Figure 4-10a). At the end of the analysis (t = 25 sec) the residual
horizontal displacement is 6 h = 0.55 m. The moment envelope along with the final deformed
shape of the wharf for nga0779 is shown in Figure 4-11.
Figure 4-12 shows the time histories of horizontal displacement of the deck for the suite of 56
motions, categorized in 8 (accordingly to the NGA record locator number). It is worth noticing
that the two motions that give the largest deck displacements are nga0753 and nga0779 (Figure
4-12a) both records from Loma Prieta Earthquake (1989). Figure 4-13 summarizes the
correlations between the computed maximum deck displacements and four measures of
67
earthquake intensity (IM) using power law functions, as proposed by Cornell et al. (2002): PGA,
PGV , PGD and Arias Intensity
Udeck
(4.1)
=a-IMb
where PGA (peak ground acceleration) is the maximum acceleration of the ground motion
recorded to the surface; PGV (peak ground velocity) refers to the maximum velocity of the
ground motion recorded at the surface; PGD (peak ground displacement) is the maximum
displacement of the ground motion recorded at the surface; and finally, the Arias intensity (Ia)
is the measure of total energy content of a seismic excitation defined as:
Ia =
2g
[a(t)]2 dt
(4.2)
Table 4-2 summarizes the values of a, b and the regression efficient, r2 , achieved in these cases.
While the correlations show that deck displacements increases with each of the intensity
measures, there is significant scatter in the results precluding simple predictions. The peak
ground acceleration correlation involves a lot of scatter, but has a having a clear trend (Figure
4-13a). An inherit limitation in the use of PGA is the fact that it does not reflect the frequency
content of the ground motion. PGV represents a better correlation measure, as it incorporates
partially the aforementioned effect but captures only some effect of the sequence of strong
pulses. The correlation of damage measure with PGV is indeed higher than with PGA (Figure
4-13b). The correlation with PGD has again a clear trend but high scatter (Figure 4-13c). As
discussed by Vytiniotis (2011), Arias Intensity provides, perhaps, the most reliable measure of
68
earthquake intensity currently as it includes both the effects of the acceleration, the frequency
content of the record and the sequence of the pulses. Figure 4-13d shows the correlation of
deck displacement with Arias Intensity. This presents a more reliable correlation than PGA, with
two notable outliers nga0753 and nga0739. It is worth commenting that indeed nga0753 is an
outlier for all the above correlation; the reason for this is that the large displacements
associated with this ground motion are attributed to the large lateral spreading of the slope, a
phenomenon than none of the above measures can capture. However, nga0739 is only an
outlier for the correlation with Arias Intensity and indeed follows the trend in the other 3
correlations. This can be attributed to the fact that the nga0739 has a high Arias Intensity value
but consists of a large number of small acceleration pulses that produce little lateral spreading.
Figure 4-14 shows that there is also a very good linear correlation between the maximum deck
displacement and the corresponding maximum free field movement (referred to node 49,
Figure 4-2), as reported by Vytiniotis (2011) to quantify free field slope damage.
Based on an analysis of the wharf structure the seismic performance can be grouped into 4
classes of response:
1. No damage, structural response is elastic;
2. Light damage, where failure occurs only at the pile-deck connections;
3. Moderate damage, where some plastic hinges develop within the piles; and
4. Heavy damage associated with the creation of a plastic collapse mechanism of the
supported wharf.
69
Figure 4-15a illustrates the most commonly observed case of light damage where plastic hinges
develop at the pile-deck connection. Moderate damage,
Figure 4-15b, is associated with the creation of plastic hinges at both the pile-deck connections
and at other locations along the embedded piles. The example shows hinges in vertical piles
close to the surface of the slope and at the interface between layers of strong contrasting
stiffness (Old Bay Mud-dense sand interface, Figure 4-1Figure 4-5) stiffness for the batter piles.
Heavy damage occurs with the creation of a failure mechanism involving plastic hinges at three
distinct locations along the vertical piles at the pile-deck connection, on the upper part of the
loose fill and at the base of the fill, Figure 4-15c.
Of the 56 ground motion records, only two caused extensive damage to the structure, 6
produced moderate damage and 6 light damage. The structure remained elastic for the other
42 ground motions with small permanent displacements, as shown in Table 4-1.
The current analysis for nga0753 can be compared with the results reported by Shafieezadeh
(2011). The main differences in the two analyses is that Shafieezadeh (2011) uses a more
advanced modeling of the reinforced section that can capture the coupled flexural and axial
response of the pile and models the deteriorating behavior of pile-deck connections as studied
by Lehman et al. 2009. In contrast, the current calculations assume an elastic, perfectly-plastic
70
pile response). The results of our analysis show a remarkable agreement in the location of the
plastic hinges and also the time history of the deck displacement (Figure 4-16).
4.4
Effectiveness of Ground Improvement Systems
This section considers the effectiveness of soil improvement methods by comparing the
response of the piled wharf structure under the same suite of ground motions and two ground
improvement systems: 1) a system of PV-drains installed behind the crest of the fill slope (Figure
4-5) and 2) complete densification of the fill (Dr= 80%; e=0.673). The first case assumes the
same input parameters for the soil and macroelements as the untreated case while the latter
uses a revised set of macroelements parameters corresponding to Toyoura sand with Dr= 80%
(Section 3.2).
Figure 4-17 summarizes the computed deck displacements for the piled-wharf with three
ground conditions as functions of the four reference earthquake intensity measures (PGA, PGV,
PGD, and IA). The results show that the predicted (i.e. best fit correlations) deck displacements
for the PV-drain mitigation system lie in the range predicted for unimproved and compacted fill
conditions. Table 4-2 summarizes the power law relations (Equ. 4.1) parameters and regression
coefficients for the four intensity measures. The results show improved regression properties
for the simulations with improved ground conditions. Table 4-1 compares the overall
classification of structural damage for the wharf with the three different ground conditions
(untreated fill, PV-drain system, fully densified fill) for the full suite of reference ground
71
motions. In general, soil improvement methods reduce the number of events where permanent
structural damage occurs. For the PV-drain system, there is only heavy damage for one case
(nga0779), where there is large lateral spreading in the underlying slope; one case of moderate
damage and eleven cases of light damage, (i.e. the installation of the PV-drain system is
efficient in protecting the wharf structure from the plastic hinges formation in the lower section
of the piles and hence, structural retrofit of the wharf can focus on the pile-deck connections).
For the fully densified condition, there are no cases of heavy damage, one case of moderate
damage and eleven cases of light damage. Although the wharf deck undergoes larger
displacement with the PV-drain system than with the fully densified fill (Figure 4-17) the level of
structural damage in both scenarios is quite similar. In this respect, the PV-drain system
represents an efficient method for mitigating the seismic risk for the wharf structure. However,
it is worth noting that the densification method produces less structural damage for the case of
nga0779 where PV drains are ineffective against lateral spreading of the slope. Figure 4-18 and
Figure 4-20 compare the wharf responses and underlying free field results for the three ground
conditions considered for nga0779. The PV-drain system has little effect on the structural
damage of the wharf and displacement for this case. This result occurs as most of underlying
ground conditions are used by lateral spreading in the fill slope. The complete densified slope
undergoes significantly smaller horizontal displacements (Vytiniotis, 2011) and as a result the
structural damage that occurs is moderate (Figure 4-18).
72
Figure 4-19 and Figure 4-21 present a similar survey for nga0753. In this case, damage reduces
significantly with the use of PV-drain system, and deck displacements are comparable to the full
densified fill. In this case, the contour of displacements in the free field analyses show limited
lateral spreading of the loose fill.
The above analyses are indicative that the PV-drain system is effective in protecting the wharf
structure for cases where pore pressures affect response but does offers only marginal
improvement for the case of large induced displacements due to inertial forces. It should be
also stressed out than neither the "ideal" densification of the slope nor the PV-drains
improvement method are proven extremely capable of limiting the failure of the pile-deck
connections (from 6 cases of light damage in the case of untreated, 3 did not sustain any
damage in the ideally densified case and only 1 did not sustain any damage in the case of PVdrains improvement).
4.5
Modeling of Pile-Deck Connection
The prior analyses have used a simplified elastic perfectly-plastic model for the piles and piledeck connections. However, Lehman et al. (2009) have demonstrated in a full-scale test that
pile-deck connections degrade under cyclic loading. The piles and the deck in the wharf for this
study are typically connected by T-headed dowel bars and the nonlinear behavior of this
connection has been calibrated against a full-scale test conducted by Lehman et al. (2009),
Figure 4-22. The pile-deck connection was subjected to lateral cyclic loading at a distance of
73
2.54 m from the interface of the reinforced concrete base while maintaining a constant axial
load on the pile simulating the gravity load.
This section uses a complete representation of the pile-deck connection using a nonlinear
connection element with aggregated section properties that represents a 3.8 cm embedment of
the pile into the wharf deck (Figure 4-22). The axial response of the connection section is the
same as for the piles. However the moment response is modeled using the Modified IbarraKrawinkler (MIK) deterioration model with bilinear hysteretic response (Ibarra et al., 2005). The
MIK model can capture most of the sources of deterioration (i.e. cyclic deterioration of several
modes and softening of the post-yielding stiffness) and accounts for residual strength after
deterioration.
The MIK model is based on standard bilinear hysteretic rules with kinematic strain hardening
but it is modified in a way that during cyclic loading the maximum strength that can be
achieved during unloading is limited by the smallest strength that the has been previously
reached. Had this condition not been established, the strength in the loading path could
increase in later stages of deterioration (Ibarra et al., 2005), Figure 4-23.
The model incorporates an energy-based deterioration parameter that controls four cyclic
deterioration modes once the yield point is surpassed in at least one direction: basic strength,
post-capping strength, unloading stiffness, and accelerated reloading stiffness deterioration as
74
seen in Figure 4-24. However accelerated reloading stiffness is not active in the bilinear version
of MIK. The rates of cyclic deterioration are controlled by a rule developed by Rahnama and
Krawinkler (1993) assuming that every deterioration mode has a reference hysteretic energy
dissipation capacity Et, which is an inherent property of the deterioration mode and it is
independent of the loading history (Ibarra et al.
2005). The reference hysteretic energy
dissipation capacity Et depends on Op, the precapping plastic rotation and My, the effective yield
strength of the component:
E, = A -O, -M,
or
(4.3)
E,, = A, -M,
where A, =1, -d, is the reference cumulative rotation capacity for each mode of deterioration.
The basic and postcapping strength deterioration) is modeled by translating the two strength
bounds (the lines intersecting at the capping point) after every loading cycle in which energy is
dissipated toward the origin at the rate, Figure 4-24:
M, = (1-
#l) -M,
(4.4)
where the moment Mi is any reference strength value on each strength bound line. According
to Lignos and Krawinkler (2011), Mi can be defined as the intersection of the strength bound
line with the y-axis and Pi isthe energy based deterioration parameter:
$,
=(4.5)
E,-XE,
75
where Ei is hysteretic energy dissipated in the loading cycle i; IEj is the total energy dissipated
in past cycles ;and c is an empirical parameter that controls the rate of deterioration, usually
taken as 1.0, a value that we also used in our calibration.
The model can also account for different rates of deterioration in the positive and negative
direction, controlled by parameters dnp which however, the current simulation does not
consider this feature and uses the default dnp= 1.0.
The same concepts apply to modeling of unloading stiffness deterioration, i.e., the deteriorated
stiffness after cycle i isgiven by:
K, =(1-,)-K,
(4.6)
Tables 4-3 and 4-4 list the parameters used for the backbone response and deterioration of the
pile-deck connection, respectively. The parameters modeling the initial backbone response of
the pile-deck connection are listed in Table 4-3, where the initial stiffness and the yield capacity
are taken the same as the elastic- perfectly plastic case (section 4-1). The MIK bilinear model is
used to simulate the deteriorating behavior of our connection and the resulting moment versus
drift ratio (lateral displacement over the height of the column) from the experiment by Lehman
et al. (2009), which was numerically simulated. Figure 4-25 shows that the MIK model captures
reasonably well the measured nonlinear moment-drift response of physical the pile-deck
connection test (note the moment is normalized by the yielding moment of the connection).
76
Figure 4-26a to d summarize the comparison between the elastic perfectly plastic (EPP) piledeck connection and the Modified Ibarra Krawinkler (MIK) pile-deck connection for the base
case ground motion nga0779. The results show that the maximum deck displacement for MIK is
significantly less than for the EPP model, Figure 4-25a. As the pile-deck connection deteriorates,
less and less deformation induced by the lateral spreading on the piles can be transmitted to
the deck. So even though the embedded part of the piles undergoes the same amount of
deformation, the deck exhibits smaller deformations. Figure 4-26b and Figure 4-26c compare
the time histories of the rotation of the connection and of the moment in the pile-deck
connection for pile 3 (Figure 4-1). For the case of MIK, the connection undergoes much larger
rotations than for EPP, as expected from the deteriorating behavior, where the connection
loses its capacity after exceeding the ultimate rotation of capacity. It is worth noting that
damage spreads along the length of the embedded piles for simulations using MIK model as
seen in Figure 4-27.
In conclusion, we see that when the pile deck connection modeling captures the deteriorating
behavior, previously established in model tests, smaller deck displacements occur, while there
is more pronounced structural damage in the piles. It should be pointed out that the location of
the damage is indeed in the same locations are previously identified with the EPP analysis.
77
4.6
Conclusions
The primary conclusions of our analyses are that:
*
The deformations of the piled wharf structure are primarily governed by the lateral
spreading of the soil. Deck displacements are better correlated to Arias Intensity and
PGV than to PGA.
" Three levels of structural damage can be identified for the reference suite of the 56
ground motions. For the non-improved fill only two records cause extensive damage to
the structure, 6 cause moderate damage and 6 cause light damage.
*
The proposed PV-drain system is effective in mitigating seismic damage for most of the
ground motions considered. However, it is ineffective when there is a large lateral
spreading in the loose fill slope. The comparison with the idealized case of fully
densified fill provides a convenient meter for assessing the improvement achieved with
the PV-drain system.
" Analyses using a more advanced modeling of the pile-deck connection, that captures the
deteriorating behavior under cyclic loading, generate smaller deck-displacements but
more extensive structural damage to the embedded piles.
78
Table 4-1: Overall classification of structural damage for the wharf with the three different
ground conditions.
Level of
Damage
None
Light
Moderate
Heavy
Unimproved
Loose Fill
42
6
6
2
Compacted
Fill
45
10
1
0
PV-Drains
System
43
11
1
1
Table 4-2: Values of a and b and the regression coefficient for four earthquake intensity
measures.
PGA
PGV
PGD
Arnas
Intensity
Treatment
NO
PV-DRAINS
Density
40%
40%
a
0.43300
0.36770
b
1.023
1.137
r2
0.6607
0.7273
IDEAL DENSIFICATION
NO
PV-DRAINS
IDEAL DENSIFICATION
NO
PV-DRAINS
IDEAL DENSIFICATION
NO
PV-DRAINS
80%
40%
40%
80%
40%
40%
80%
40%
40%
0.28020
0.00689
0.03500
0.00564
0.03132
0.01970
0.02232
0.13710
0.10090
0.986
0.907
0.997
0.851
0.732
0.819
0.704
0.641
0.709
0.7591
0.7505
0.8367
0.8328
0.7381
0.859
0.8311
0.8115
0.8793
IDEAL DENSIFICATION
80%
0.09350
0.599
0.8894
Table 4-3: Modified Ibarra Krawinkler model properties for initial backbone
900
Effective yield strength My (kNm)
0.0082
Effective yield rotation ey (rad)
Effective stiffness Ke (kNm 2 )
110,000
901
Capping strength for monotonic loading Me (kNm)
Capping rotation for monotonic loading Oc (rad)
0.0083
Pre-capping rotation capacity for monotonic loading E,(rad)
0.0001
Post-capping rotation capacity Oc (rad)
Residual Strength ratio K
0.012
0.0
Ultimate rotation capacity 8u (rad)
0.015
79
Table 4-4 Deterioration Parameters for Modified Ibarra Krawinkler
As
basic strength deterioration
k
unloading stiffness deterioration
0.65
Aa
accelerated reloading stiffness deterioration
1.0
Ad
1.0
dp
post-capping strength deterioration
exponent for deteriorations (c = 1.0 for no deterioration)
rate of cyclic deterioration for positive loading
dn
rate of cyclic deterioration for negative loading
1.0
cs,k,a,d
1.0
Node C3
Nle C2
Node Ci
Figure 4-1 Configuration of the Berth 60-63 in Oakland (Shafieezadeh, PhD 2011)
80
1.0
1.0
*
pile-soil node
$
pile nodes (free space)
*
peck nodes
free -field end macroelement nodes
Figure 4-2 OpenSees model of piled wharf structure.
81
Moment'
Load
My
EcA
curvature
displacement
Figure 4-3 Constitutive law used to model (a)the moment resistance of the pile section and (b)
the axial resistance.
EI= 110,000 kN i 2
1000
M'=-900 kNm
900.~
700
z
600
500
40-
0
30200100
0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
007
Curvature (1/m)
Figure 4-4 Moment curvature curve of the reinforced concrete section of the pile as calculated
by online available software KSU_RC ( Esmaeily, 2011).
82
Drain Locations
Model Berth
4.6m
-F
Fl
F
O.Om
-13.7m
-
-16.3m
-
r
F,
F. p+
43.7m
V
V
Figure 4-5 Geometry of PV-Drains array for mitigating seismic risk for Berth 60-63 (Vytiniotis,
2011)
83
0
0.8
E 0.5-
0.6
0.4-
S0.4
N
0
0
0.2
10
-0.2
-0.4
-0.1
-0.6
-: -0.2-
CL
S-.8
0
-1
10
15
20
time (s)
+4.6m
- +4.6m
- ±O.Om
tO.Om
Ss
5
-16.3m
00
25
time (sec)
-
(b)
-16.3m
(c)
los
15s
Accelerations (m/s0)
S1.
Is
20s
Displacements (m)
0A6
O'
20S
0-
Figure 4-6 Response of the unimproved piled wharf to base case ground motion ,nga0779; (a) time history of acceleration of rock
base excitation (b) acceleration contours of free field response (from Vytiniotis, 2011) (c) displacement contours of free field
response (from Vytiniotis, 2011) (d) horizontal displacement of the deck.
. .. ....
.........
t=5 s
0
~-w I -
mu mimi
U-
mi
Sea Water
-5
Hydraulic Fill
-10 -
/
-15-
-20
Sand Fill
Old Bay Mud
(a)
-25
-10
-5
0
5
10
15
20
25
30
35
Displacements (m)
10.9
Excess Pore pressure
ratio
0.8
0.7
10.5
03
0.2
0.43.0
0.1
10.9
0.7
00.6
0.5
0.3
0.1
F-1
(b)
(c)
Figure 4-7 Response of the unimproved piled wharf for ground motion nga0779 at t= 5s (a)
Structural displacements (50:1) (b) Contours of free-field displacements (c) Contours of freefield excess pore pressure ratio.
85
t=10 s
0
hI31rSearWater
I
-5
Q
Hydraulic Fill
-10
_15
I,
-20
Send Fill
I
Old Bay Mud
(a)
-25 '
-10
-
-5
0
5
10
1s
20
25
30
35
Displacements (m) Excess Pore pressure
ratio
__
0.9
0.8
0.7
0.6
0.5
0.40.
0.3
0.2
0.1
0.9
0.7
0.5
03
0.1
.
(b)
(c)
Figure 4-8 Response of the unimproved piled wharf for ground motion nga0779 at t= 10s (a)
Structural displacements (50:1) (b) Contours of free-field displacements (c) Contours of freefield excess pore pressure ratio.
86
t=15 s
, ,
-~~g-smu -
0
swum smw
A
Sea Water
N
-5
Hydraulic Fill
-10
1/
-15
-20
*-
Sand Fill
Old Bay Mud
(a)
-25
-10
-5
0
5
10
15
20
25
30
35
Displacements (m) Excess Pore pressure
ratio
r7
090.9
00.7
0.5
0.5
00.3
0.2
01
0.1
0.4
0.3
(b)
(c)
Figure 4-9 Response of the unimproved piled wharf for ground motion nga0779 at t= 15s (a)
Structural displacements (50:1) (b) Contours of free-field displacements (c) Contours of freefield excess pore pressure ratio.
87
t=20 s
mnil -
0
A
KK Q
-5
-15
r
Old Bay Mud
(a)
-251
-10
zzz
F !L I
Sand Fill
-5
Sea Water
_ ea Water
r
r
-10 Hydraulic Fill
-20-
m
ml wui siniuu ~s.w
0
5
10
15
20
25
30
35
Displacements (m) Excess Pore pressure
ratio
F_
0.
0.8
0.7
0.6
0.2
01
0.9
0.7
0.1
-1
(b)
(c)
Figure 4-10 Response of the unimproved piled wharf for ground motion nga0779 at t= 20s (a)
Structural displacements (50:1) (b) Contours of free-field displacements (c) Contours of freefield excess pore pressure ratio.
88
(a)
0
( ( 'I 'I A
S"
W~t~
L*V4I
F
-5'
Hydruc Fm
-10
My~O00 kNm
-151-
-20
____II
on6
-10
Say
LII|ILIZZ\I r
F-,
(
ued
-5
0
5
10
is
20
15
20
V
25
30
35
25
30
35
40
(b)
-s
-10V
-20
-25
ki
-10
--
-s
-
------
0
5
---
-
10
----
s
40
Figure 4-11 Response of the unimproved piled wharf under ground motion nga0779 (a) bending
moment
envelopes
and
(b) location
of the
plastic
hinges
in
piles.
89
0.
(a)
(b)
0.4
0.2
--- ---
0
..E-0.2
o
0.6
0)
0.4,
W
0.
0
0.6
-i -
-0.2
(e)
(d)
U
nga0982
0
0
(g)
5
10
is
20
25
(h)
-
I0-4
Case: Unimproved piled wharf
0.2
Elastic Perfectly Plastic Piles
Ground Motions: 56 records
(NGA)
-0.2
0
S
10
15
20
25
0
6
10
16
20
25
time (sec)
Figure 4-12 Time histories of deck displacements for unimproved piled wharf structure for the reference suite of 56 ground motions
.
.
.
. ......
.. ..............
0.7
CD
0.7
0.6
-
)
nga0753
(b) nga0753
nga0779-
.
0.6
nga0779-
0
CD
0.5
0
0.5
0
C
4)
E
) 0.4
0.4
CL,
0 0.3
C
0
N
0 o0.23
r 2=0.6607A
A
A
N
o 0.2
-A
o 0.2
0
M
E
-A
E
E0.1
0.1
0.2
0.3
0.4
0.5
0.7
0.6
0.8
0.9
1
-
-
CU
AAA
r 2=0.7505
AOL A
E0.1
0
10
20
30
40
PGA (g)
50
60
70
80
90
100
PGV (cm/s)
0.7
S0.6
(D
0
0
a,
(D0.5
0
(D
CL
0.4
C
0
o0.3
N
X
0
M
E
E
E
E0.1
CU
0
5
10
15
20
25
30
35
40
45
0
1
2
PGD (cm)
3
4
5
6
7
8
9
Arias Intensity (rms)
Figure 4-13 Summary of computed deck displacements for unimproved piled wharf structure as functions of earthquake intensity
parameters for the reference suite of 56 ground motions a)PGA, b) PGV, c) PGD, d) Arias Intensity
................
.
...........
..........................................
: ::......
::............
.........
0.9
E
~0.8E
*
9
0
Fit
No damage
Light Damage
Moderate Damage
X
Heavy Damage
CU 0. 7 -
(D
0
4
0 0.6N
or
2
0.5C
R2=0.969
CU
0
02
-5
00
02
.406
.
060.
.
Maximum Horizontal Displacement of the Soil (node 49)(m)
Figure 4-14 Response of the unimproved piled wharf structure and classification of structural
damage for the reference suite of ground motions
92
Old Bay
Mud
10
-4
J
5
0
10
15
20
25
5
30
0
(a) Light damage, nga08O2
6
0
10
20
1
25
30
(b) Moderate damage, nga0982
0
A
K
I
-5
rr
r
Hydraulic FIN
1
r
-10
-15
-20
SandFINf11
Sea Water Level
Q
7
~lW
Old Bay Mud
-25
-10
-5
-
0
5
10
15
20
25
30
35
40
(c) Heavy damage, nga0779
Figure 4-15 Examples of structural damage in selected seismic ground motions for the
unimproved piled wharf structure
93
Yielded Section
b)
0.9
0.8
E
W
E
a,
a)
0.7
0.6
0.5
W
VU
0.4
a.
0.3
-Shafieezadeh (2011)
0,2
0
-Panagiotidou
(2013)
0.1
0
-0.1
5
10
15
20
25
30
time (sec)
Figure 4-16 Comparison with results of Shafieezadeh (2011): a) Time Histories of Horizontal deck displacements; b) yielded sections
as calculated by Shafieezadeh (2011); c) yielded sections as calculated by Panagiotidou (2013)
.
.......
..
.
E
3 0.7Symbols
A
p0.6
0
0.5 -0
E
0.4
Case
Unimproved
PV-drain
mitigation system
Compacted fill
0.3
5
0-
0.2
N
b
E 0.1
E
x
0
PGV (m/s)
PGA (g)
E
~0.7
(.0
W,
U 0.6
0
r 0.5
(D
E
(D
80.4
O)
0 0.3
N 0.2
0
E 0.1
_E
.x
0
(U
20
25
PGD (cm)
30
35
40
450
1
2
3
4
5
6
Arlashtensity (n/s)
Figure 4-17 Effectiveness of ground improvement scenarios for piled-wharf structure under reference suite of ground motions as
functions of selected intensity parameters: a)PGA, b) PGV, c) PGD, d) Arias Intensity
......
...............................
......
UntreatedcaseDisplacements
-0
-IC
Untreatedcase-
40-
Excess Pore
0
(a) Unimproved Soil
TreatedcaseDisplacements
-%%,Treated caseExcess Pore
1.I'~6~Pressure Ratio
4
-0
0
6
1*
15
so
20
30
56
40
(b) PV-drains mitigation system
*
Q-%j---------in--
Ezc~
Pore Prnw Rd.~ *S
S------S NS-
A
s~
*~
Q
/ K
contrm'blouml0t
WOvift re
.1 I~
-20
K
-10
1
0
5s
55
0
(c) Compacted fill
Figure 4-18 Effect of ground improvement systems on fill and wharf response under ground
motion nga0779
96
UntreatedcaseExcess Pore
PressureRaio
(a) Unimproved Soil
Treated caseDisplacements
so
I
J
TreatedcaseExcess Pore
Pressure Rado
'M'
4$
ai
13
5
20
2
40
n
(b) PV-drains mitigation system
Sm.PorersPrmaa RanSm.
Ie
WAINe
twe
Codiourbva 01
I
J
-1
0isO18
.
2
2d
30
36
(c) Compacted fill
Figure 4-19 Effect of ground improvement systems on fill and wharf response under ground
motion nga0753
97
40
Horizontal Displacement of the Deck nga0779
0.3-
0.20.10
| -0.10
S-0.20
-0.3-0.4 -015 -
-
0
15
time (sec)
Figure 4-20 Effect of ground improvement systems on deck displacements under ground motion
nga0779
Horizontal Displacement of the Deck nga0753
W
a)
F3
5
10
15
20
25
30
time (sec)
Figure 4-21 Effect of ground improvement systems on deck displacements under ground motion
nga0753
98
AXIAL
LOAD
61cm
HORIZONTAL
LOAD
I-
0
A-A'
E
r'
#32 T-HEADED
REINFORCEMENT BAR
_W11 WIRE
SPACING VARIES
#36 HOOPS
A
#25 HOOPS
P
2-35m
4
Figure 4-22 Section geometry and reinforcement details of the tested pre-stressed pile (from
Lehman et al., 2009)
3
Strength
Limit "
...........
6
8co-
FcO
Envelope
Curve
Fy4
5
Figure 4-23 Bilinear hysteretic model with strength limit (from Ibarra et al.2005)
99
Uniod.
Y
Stiff. Det.y
u
r
r
y
Post -Capping
Strength Det
Basic Strength Det.
Mc
Chord Rotation 8
o
Effective yield strength and rotation (My and 6y)
Effective stiffness K,=M,/6,
Capping strength and associated rotation for monotonic loading (M, and 0c)
Pre-capping rotation capacity for monotonic loading 6 p
Post-capping rotation capacity 6,4
o
Residual strength Mr
o
Ultimate rotation capacity 6.
o
o
o
o
=
KM
Figure 4-24 Modified Ibarra Krawinkler (MIK) Deterioration Model (from Lignos et al. 2011)
100
--
1.5
MIK
ModelTest # 9
Leh man et al. (2009)
1
E
0
rr~
NV
-M
E -0.15
Iff Is
-0.1
0.1
0.15
I-.
0
z
Drift Ratio
f
-1.5
Figure 4-25 The calibration results of the MIK model for pile-deck connection for the simulated
experiment (Figure 4-22
101
0.6 --
0.5
0.12 -
(a)
0.1
=
0.1 -
0.4
0.3
0.08
0.2 -
0.06
MIKMI
0.1 --
o
-
0.04
EPP
0-
0.02
0
N
0* -
- -0.2
x -0.3
-0.02
5
10
Time, t (secs)
E
20
25
0.08
0.1
600
-EPP40(d
(C)
- -MIK
200
.-.
15
Time, t (secs)
600
400 --
EPP
200
0
Z
5
15
20
25
-0.02 -200
-400 -
-400
z
-600 - -
-800 --
-600
0.02
0.04
0.06
-
EPP
-I
-MIK
800
-1000 ---
1000Time, t (secs)
Rotation at Connection (rad)
Figure 4-26 Effect of deteriorating pile-deck connection on response of the unimproved piled-wharf structure under base case
ground motion, nga0779
....
.......
0
(a)
Sea Water Level
Hydraulic Fill
-10-
-15-
-20-
Sand Fill
Old Bay Mud
-25
2;
1
-5
0
5
10
15
20
25
30
35
40
Figure 4-27 Effect of deteriorating pile-deck connection on response of the unimproved piled-wharf structure under base case
ground motion, nga0779: (a) MIK, (b) EPP
......
... ...
5
5.1
Summary, Conclusions and Recommendations
Summary
This thesis focuses on the study of the dynamic response of a piled-wharf structure supported
within a loose, liquefiable sandy fill soil. The method of analysis that has been used is the
uncoupled substructure approach that involves separate analyses for the response of the soil
mass "free-field" and for the wharf structure (piles, deck, and crane). The soil-structure
interaction between the two models is handled through macro-elements that require the time
histories of displacements and pore pressure of the free field response in the locations of the
piles supporting the wharf as input motions (Varun, 2010). This research supplements the prior
studies by Vytiniotis (2011) on free field behavior and Shafieezadeh (2011) on piled-wharf
response. The current study evaluates the effectiveness of ground improvement methods
(densification, PV-drains) in terms of limiting structural damage and permanent deformations.
To study the seismic response of the wharf structure, we developed a finite element model in
OpenSees that can predict the permanent deformations of the structure and the along the piles
during seismic loading. The earthquake loading is imposed at specific locations along the
embedded length of piles at the free nodes of the macroelements in terms of time histories of
free field displacements and excess pore pressures. The soil-pile interaction phenomena are
incorporated through the use of the macroelement developed by Varun (2010) that is
calibrated using standard engineering soil properties for the site of interest. A suite of 56
ground motions that are typical of firm-site conditions in coastal California was used to evaluate
104
the dynamic response of the wharf of interest. We then compared the effectiveness of 2
ground improvement scenarios for piled-wharf structure under reference suite of ground
motions, a PV-drains mitigation system and an ideally compacted fill. Finally, we implemented a
more advanced model of the pile-deck connection that can capture the deteriorating behavior
exhibited by the connection.
5.2
Conclusions
The use of the sophisticated macroelement in the analyses provides significant advantages over
the full 3D finite element analyses for simulating complex SSI for piles especially in terms of
modeling complexity and computational time. The macroelement captures efficiently the
fundamentals
mechanics
of saturated
granular soil-pile
interaction.
Moreover,
the
macroelement is easily calibrated using standard parameters obtained from laboratory tests
and other available correlations. However, further research is required to identify the validity of
the macroelement predictions using experimental data. Moreover, the results of the
predictions of the analyses with the macroelement should be compared with 3D analyses using
other constitutive models than the ones used in the original analyses
Our major conclusion is that the permanent deformations of the structure are primarily
governed by the lateral spreading of the soil and therefore retrofitting methods should be
targeted in decreasing the soil deformations. We can also support the fact that due to the high
nonlinear nature of the phenomenon, no single measure of earthquake intensity can be used as
a definite predictive tool for the anticipated damage on the structure. However, reasonably
105
good correlations were achieved with Arias Intensity and PGV. Furthermore, we identified 4
ranges of response which were highly associated with the lateral deformations of the slope : (a)
zero damage, structure remains elastic; (b) light damage, where failure occurs only at the piledeck connections; (c) moderate damage, where some failure occurs also inside the soil mass;
(d) heavy damage associated with the creation of failure mechanisms. In total for the untreated
fill, from the 56 motions, only two caused extensive damage to the structure, 6 of them caused
moderate damage and 6 caused light damage.
The analyses also show that a system of PV-drains can be used to mitigate permanent
deformations of the deck and reduce structural damage to the wharf. In fact, the results
indicate a general reduction of the level of damage within the piles. Hence, further
improvements can be obtained by retrofitting the more susceptible pile-deck connections. The
results of our analyses indicated that the PV-drains mitigation system results are comparable to
that of the "ideal" full densification of the slope.
Finally, we implemented a more advanced modeling of the pile deck connection that can
capture the deteriorating behavior exhibited by the connection. The results of this analysis
indicated that the computed deck displacements are reaching smaller values than in the elasticperfectly plastic case. Nevertheless, the structural damage that occurs in the embedded part of
the piles is indeed more extended.
106
5.3
Recommendations
Future research efforts should be concentrated on development and validation of constitutive
laws that can predict more reliably the cyclic response of saturated sandy soils. The lateral
spreading is the main cause of the structural damage in the wharf structures; therefore better
free-filed prediction capabilities are needed. Other important topics include strategies for
structural retrofitting of the wharf and low intrusive improvement methods such as colloidal
silica. Future studies should be also directed at modeling newer wharf designs and assess their
vulnerability, thus testing the design suggestions given by current design codes. Finally,
research efforts should be targeted in validating the developed tools of analysis with 3D
numerical analyses and experimental data.
107
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110
APPENDIX A - Validation of OpenSees Response
Methodology
One important task of this research was to validate the OpenSees framework in vertical and
lateral loading of single piles supported on springs. This was done by comparing analytical
solutions of the response of a single pile embedded in one soil layer under laterally and
vertically loading with the finite element model. In the finite element model, the pile is
simulated by beam elements and a series of springs are used to represent the soil. The soil
springs are generated and are assigned separate uniaxial material objects in the vertical and 4and lateral directions. The validation of the response of the pile embedded in one soil involved
two different constitutive behaviors of the soil: 1) vertically loaded pile with elastic and elastic,
perfectly-plastic materials and, 2) laterally loaded pile with elastic and perfectly-plastic
materials.
The embedded pile length is 20 m and the pile with diameter, D=1.0 m. The mesh is defined by
the number of the elements. The spring nodes are created with three dimensions and three
translational degrees-of-freedom. The soil springs are generated using zero-length elements to
which separate uniaxial material are assigned to represent the force-displacement relationship
in the lateral and vertical directions, therefore two sets of nodes are created, sharing the same
set of locations. One set of spring nodes, the fixed-nodes, are initially fixed in all three degreesof-freedom. The other set of nodes, the slave nodes, are initially fixed in only two degrees-offreedom, and are later given equal degrees-of-freedom with the pile nodes. The constitutive
behavior of the springs is defined such that the springs oriented in the lateral direction
111
represent p-y springs, and the vertically-oriented springs represent t-z and Q-z springs for the
pile shaft and tip, respectively.
The pile nodes are created with three dimensions and six degrees-of-freedom (3 translational, 3
rotational). With the exception of the uppermost pile head node, the pile nodes are fixed
against translation in the y-direction and rotations about the x- and z- axes. The pile head node,
where the load is applied, has no rotational fixity, thus simulating a free-head pile. The pile is
given elastic behavior for simplicity. Displacement Beam Column elements with elastic section
were used to model the pile, with a modulus of elasticity, E = 25 GPa and shear modulus, G =
9.6 GPa (Poisson ration v = 0.3). The use of displacement based elements can allow simulating
the spread of plasticity along the element in future research.
Vertically Loaded Piles
Elastic Springs
Vertical-oriented springs were assigned uniaxial Elastic material behavior with elastic spring
constant of the shaft k,= 20 MN/m 3 and elastic spring constant of the tip kp=35 MN/m 3 . In order
to verify our numerical solution, we compared it with the analytical solution proposed by
Veruijt (2010) for pile supported on continuous elastic springs along the length of the pile and
at the tip. In Figure A-1, we can see that we are achieving identical response with numerical and
analytical solutions. The results presented are for vertical load, P=10 MN. The analytical fpr
vertical displacement and the normal force in the pile are:
ph cosh[(L- z)/ h]
W=EEA
n (L
sinh
/h)
(Ah(1)
112
N = -P
sinh[(L -z) / h]
(A.2)
sinh (L / h)
where h is the characteristic length h = EA/k, O,
k, has the character of a subgrade
modulus (r = kw) and 0 is the circumference of the pile.
Elastic Perfectly Plastic Springs
Vertical-oriented springs were assigned uniaxial Elastic Perfectly Plastic material behavior with
elastic spring constant of the shaft k= 20 MN/m
3
MN/m
3
and elastic spring constant of the tip kp=35
and quake (displacement where the perfectly plastic behavior begins) wo=0.01D. For
this particular case, we derived the analytical solution, for pile supported on elastic-perfectly
plastic springs along the length of the pile and at the tip.:
E +k h
M=E
E-k~h
C
Uei
exp 2Lh
(P-roOd)h B= M (P-ro0d)h
(1-M) (1-M)EA
(1-M)EA
=Cexp
-)
xhdj+Bexp
eh
Ne =-EA[-exp
h
U
A00
2EA
h
h
P
EA
(A.3)
h
exp
(_h
(M+1)(P--ro0d)h
(1-M)
EA
N,,= -(P+r 0Ox)
where ro = (k, wo) is the maximum shear stress, d isthe plastic region
Figure A-2 shows very good agreement between numerical and analytical solutions. The results
presented are for four different levels of loading starting for small loads where the system
exhibits purely elastic behavior, to higher loads where there is only a region where the soil
113
exhibits plastic behavior and to finally to the ultimate load.
Laterally Loaded Piles
For the horizontal case, the embedded length of the pile was 50m in order to secure a perfect
match with the analytical solutions derived by Veruijt (2010) for the case of infinite long pile:
Figures A-3 and A-5 show that our assumption was correct and indeed only the upper 20 meter
of the pile undergo lateral displacement.
Elastic Springs
Horizontally-oriented springs were assigned uniaxial Elastic material behavior with elastic spring
constant, k= 20 MN/m 3 . We reproduced the analytical solution proposed by Verruijt (2008) for
pile supported on elastic springs along the length of the pile:
u -
PA 3
exp(-z/ 2)cos(z/)
2EI
(A.4)
where A4_ 4E1 k is the characteristic length of the pile.
Figure A-3 shows that we are achieving a perfect match between numerical and analytical
solution. The results presented are for P=10 MN.
Elastic Perfectly Plastic Springs
Horizontally-oriented springs were assigned uniaxial Elastic Perfectly Plastic material behavior.
Since we verify our analysis using the analytical solution produced by Brum (reported by Veruijt,
2010), the springs have to be simulated as Perfectly Plastic (Figure A-4).:
(K, -K,)7'D(8h2+9hz+3)
360EI
Z)
3
(
114
+K)cD(h+z)
12EI
3
where h is determined by solving (Equ. A.6) for a given level of loading P
P= (K, -K.)jDh2+( K-+
(A.6)
JK)cDh
These springs were modeled by springs with very high stiffness and very small yielding strain.
From Figure A-5, we present results for P=3000 kN.
We can observe a small difference between the numerical and the analytical solution, this is
because of the Blum's assumption that the pile is clamped at the depth where the deformation
changes sign. In Brum's assumption the soil pressure at that depth is replaced by a point load in
order to maintain equilibrium. It is worth noticing that in this case the strength of the springs
depends on the depth of the soil.
Macroelement Springs
Horizontally-oriented springs were modeled with the Macroelement elements created by Varun
(2010). Figure A-6 presents the displacement vs. resistance curves of the macroelements for 6
cycles of consecutive loading using the soil parameters mentioned in the figure. The vertical
axis corresponds to the normalized lateral resistance while the horizontal to the imposed
displacement at the element. The macroelement has as an input a sinusoidal displacement with
amplitude of 0.02 m and frequency of 0.1 Hz, and assumes a linear pore pressure accumulation
in order to demonstrate the effect of the phenomenon in the degradation of the soil stiffness.
The properties of macroelement necessary for this analysis, which were homogeneous along
the depth of the model, are shown in the same figure.
115
Comparison of the Pushover Response of the three Spring Elements
Figure A-7 shows the lateral response of an elastic pile embedded in 3 different scenarios
(elastic springs, elastic-perfectly plastic springs and macroelements). The finite element mesh is
the same as used for the vertical cases as the pile length is 20 m. The macroelement soil springs
are generated using special elements PYMacro2D elements (implemented in OpenSees by
Shafieezadeh, 2011). In order to be able to compare the results, the same modulus of elasticity
has been used for all three scenarios (E = 20 MPa) and for the two latter scenarios the same
ultimate resistance at each depth (friction angle 30 degrees). The results presented are for P=10
MN. We can notice that the macroelement exhibits a more realistic and smooth behavior and it
is bounded by the two extreme idealized cases. The reaction of the soil springs is pressure
depended for the elastic- perfectly plastic spring and the macroelement.
Dynamic Modeling of a single pile
Figure A-8 presents schematically the model that has been used for the preliminarily dynamic
analysis of a single pile. The main difference in the finite element mesh is that for the seismic
analysis, a mass element is added at the free node of the pile. The analysis is driven by time
histories from free field analysis (displacements and excess pore pressure ratio) at the free
nodes of the macroelements. This particular example imposes displacements reordered from
the field analysis (Vytiniotis, 2011) using as an outcrop motion from Parkfield earthquake (2004,
M= 6.19). In Figure A-9, the recorded displacement, velocities and accelerations at the mass are
presented, along with the excitation.
116
0
2
4
6
81Verruijt (2010)
Numerical Solution
r- 10-o
1214.
16-
P (kN)
10000
ks (kN/m 3 )
20000
kp (kN/m 3 )
35000
-
18 20
6
0.0011
LPmax (M)
6.5
7
7.5
8
8.5
9
settlement (m)
9.5
Figure A-1. Settlement along the length of the pile supported on Elastic Springs.
117
10
10.5
11
x 10 3
E
E
10-
lo~11
12-.---
NumericalSolution
AnalyticalSolution,Elastic Region
AnalyticalSolution,Plastic Region
14-
-
Numerical Solution
Analytical Solution,Elastic Region
Analytical Solution,Plastic Region
14-
Large Plastic
Region
,0
18
20
0.008
a*NmrclSuto
12
12-
0.009
0.01
0,011
0.012
settlement(m)
0.013
0.014
Failure
1618-
0.015
20
0.014
0.015
0.016
0.017
0.018
0.019
settlement(m)
0.02
0.021
0.022
Figure A-2 Settlement along the length of the pile supported on Elastic- Perfectly Plastic Springs.
118
P
A
.4
510
15
ks
20 -
Veirutt(1 7
Analytical Solution
-
2530-
P (kN)
10000
35
ks (kN/m 3 )
20000
40-
6 max
0.24
(M)
.
45
I
50
-4
-0.8
-0.6
-0.4
I-
I
0.2
0
.0.2
horizontal displacement (m)
0.4
0.6
0.8
1
Figure A-3 Horizontal deformation along the length of the pile supported on Elastic Support.
h
KpO ' +2 c Kp
passive
0.5
Ka O' -2 c Ka
active
Horizontal Displacement
Figure A-4 Perfectly plastic soil response
119
c 25-
3035404550
-0.05
0
I
0.05
I
I
0.15
0.1
horizontal displacement (m)
I
0.2
0.25
0.3
Figure A-5 Horizontal deformation along the length of the pile supported on perfectly plastic
springs.
120
0.6
0.4>)
a) 0.20
CU)
0-
4-
0
CD,
CU
-0.2
-0.4
a)
N
0
z -0.6-
-0.8
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Horizontal Displacement, u (m)
Figure A-6 p-y curve for the macroelement. The excitation is sinusoidal with frequency of 0.1
Hz, amplitude of 0.02 m and total number of cycles 6. This case assumes a linear pore pressure
build-up.
121
2
4
6
8
Macroelement
Elastic- Perfectly Plastic
E
10
.c
Elastic
-e-
=t 12
14
16
18
-600
-500
-400
-300
-200
-100
0
100
200
-0.05
0
0.05
0.1
reaction
(kN)
0.15
0.2
0.25
0.3
horizontal displacement (m)
200
-
-
100-
-
Depth=15 m
Depth=10 m
Depth=7.5 m
Depth=5 m
Depth=2.5 m
Depth=0.5 m
02
.2-100-
-200-
-300-
-400
-0.02
'
0
'
0.02
L
0.04
L
L
0.1
0.08
0.06
displacement (m)
0.12
0.14
0.16
0.18
Figure A-7 a. Horizontal Reactions b. Horizontal Displacements c. Force-Displacement curves at
various depths along the pile. The macroelement exhibits a behavior that is bounded but the
responses of the elastic and the elastic-perfectly plastic springs.
122
I I1
444Figure A-8 Schematic model of earthquake loading of a single pile
43-
.2
2-
jN
-2
0
time(s)
5
10
15
time (s)
20
25
30
0
E1
4)
10
15
time (s)
20
25
15
time (s)
30
30
Figure A-9 a Outcrop Horizontal Acceleration used in the free field analysis to produce the free
field displacement, b. Recorder Horizontal Displacement at the mass center, c. Recorder
Horizontal Velocity at the mass center, d. Recorder Horizontal Acceleration at the mass center.
123
APPENDIX B -Classification of Damage for Piled-Wharf Structure
Dwaae Level
Record
Nube
Numiber
33
145
150
Earthquake
me
AUmasproed
Intent
Loose Fil
Deck Displacemnent im)
Compacted
Fill
PV-Drains
System
Unimproved
Loose Fit
Compacted
FiH
Dins
Di
0
0
0.077
0.067
0.061
0.047
0.037
0.153
0.131
(I)Sse
0.45
0.29
Parkfield
0.22
Lake
__
__
0.40
Lake
0
0.19
_
__
__
_
_
0.77
__
_
_
_
_
_
_
__
_
_
__
_
__
__
_
_
0.030
_
_
_
0.136
_
448
n
0.34
0.68
0.126
0.099
0.101
451
n
0.97
2.89
0.234
0.171
0.203
472
n
0.07
0.10
0.038
0.029
0.026
0.14
0.17
0.025
0.017
0.013
0.032
0.024
0.018
0.034
0.024
632
648
649
669
676
Whittier
Narrows01
Whittier
Narrows01
Whittier
Narrows01
Whittier
Narrows01
Whittier
Narrows1
01
0.15
0.13
0.15
0
0
0
0.21
0.20
_
0.035
0.26
0.028
0.043
0.21
II
-
0
-
-
- -- -
-
-
-
_
.,.
0.026
0.030
1
1
I I
0.021
_
_
_
0.16
0.017
0
_
- - - - -- -
......................................
...............
..
0_
00
..
...........
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1
_
1
llamage Level
Record
AisPV-
SeEathquake
ame
NNber
Whe
Narrows01
684
739
__
_
_
Loma
Prieta
0.03
0.02
0.24
__
_
Unmproved
Loose FAd
0.012
4.97
_
_
_
_
_
753
0.50
3.24
X
8.37
X
0.78
791
Pnieta
_________en
0.07
_
_
0.10
01ve
Loma
Unimproved Compacted
Fin
Loose Fil
PV-Drains
System
U
System
0.009
0.006
_
0.09
_________ao
Compacted
FI
0
751
779
U,
Ias
(mis)
PGA (g)
_
_
_
_
_
_
_
X
_
_
_
__
_
_
_
_
_
___
0.169
_
_
_
_
_
0.138
_
0.041
0.035
0.032
0.584
0.226
0.285
0.551
0.373
Deck___
0.08
0.134
_
_
_
0.506
_
(m)_ _
_
0.035
0.029
0.031
_____
802
Loma
0.38
1.45
0.209
0.160
0.178
810
ora
0.46
2.66
0.167
0.129
0.137
897
Landers
0.07
0.12
0.037
0.036
0.042
0.20
0.43
0.036
0.027
0.021
0.06
0.06
0.022
0-017
0.012
982
0.76
3.24
0.334
0.225
0.275
983
0.76
3.24
0.334
0.225
0.275
954
969
Nodig-
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I
Damae Level
ReNuc
Nmber
r~J
Ea
ake
Name
Arias
PGA (g)
Intensity
(MIS)
Unimped
Fig
Compacted
Fill
PV-Drains
System
Deck Di~4acenent (m~
Unimproved
Loose Fif
Compacted
Fill
PV-
Sse
2374
ahi-2
0.02
0.01
0.006
0.005
0.004
2393
Tahi-2
0.03
0.01
0.007
0.005
0.004
2397
Chi-Chi,
Taiwan-2
0.02
0.01
0.008
0.006
0.004
2399
TCi-Chi2
0.05
0.02
0.008
0.006
0.005
2490
Taiwan-3
0.08
0.09
0.032
0.023
0.024
2498
Chi-Chi,
Taiwan-3
0.08
0.17
0.081
0.061
0.063
2658
Tai-n3
0.61
0.81
0.055
0.046
0.040
2716
Chi-Chi,
Tain-4
0.03
0.02
0.008
0.006
0.005
2804
Chi-Chi,
Tauan-04
0.02
0.00
0.003
0.002
0.000
2867
Chi-Chi,
0.02
0.0
0.01
0.011
0.009
0.007
0.022
0.015
0.015
_____TaiWan-04
2871 281Taiwan-04
Chi-Chi,
2883
3008
Ch-Chi
TChi-nh,
_____
0.05
_____
0.05
____
0.03
0.03
0.016
0.014
0.012
0.06
0.05
0.010
0007
0.005
....
.......