Conference PaperPDF Available

Investigation of Post-Failure Axial Capacity of Lightly Reinforced Concrete Piles

Authors:

Abstract and Figures

Occurrence of man-induced earthquakes in areas of low tectonic seismicity, where most structures have not been designed to resist earthquake loading, created the need for seismic performance evaluation of existing structures. Evaluations performed revealed that in some cases seismic demands on existing structures and their foundations may be larger than the available capacity and therefore a retrofit scheme is often proposed and designed. This paper presents a numerical study in order to investigate whether a pile whose shear structural capacity has been exceeded is still able to carry the vertical loads of the superstructure following an earth-quake. A methodology useful for the preliminary seismic evaluation of poorly reinforced pile foundations was developed that is based on analytical models developed for lightly reinforced columns. Analysis of a case-study from northern Europe using the proposed methodology showed that piles can bear vertical loads even after shear failure has initiated, as long as the imposed drifts on the pile are less than a critical value. For most of the cases analyzed, the pile fails in shear, but appears to continue to carry the vertical loads. This finding is likely to have a significant influence on the design of retrofit approaches.
Content may be subject to copyright.
1 INTRODUCTION
Retrofit of the foundation (and especially of a pile foundation) is an expensive and cumbersome
task. It is for this reason that in seismic areas piles are designed to remain elastic following a
design earthquake and nonlinearity is typically allowed in the superstructure where inspection,
repair, and retrofit can occur relatively easily. Nevertheless, several case-histories (especially
from the Kobe 1995 earthquake in Japan) have shown that pile yielding under strong shaking
cannot be avoided, especially for piles embedded in soft soils. Pile yielding is also probable in
existing piles that have not been designed to resist seismic loads and are therefore lightly rein-
forced subjected to man-induced seismicity. However, a number of cases have been reported in-
dicating that piles continue to bear the vertical loads of a building, preventing collapse, even when
they have sustained severe cracking due to shear or bending capacity exceedance. The most char-
acteristic of these cases is the NHK Building in Niigata, Japan. Despite the failure in shear due to
liquefaction of the coarse-grained soil during the Niigata earthquake in 1964, interestingly, the
pile yielding was only identified 20 years after the earthquake when the soil was excavated for a
new project construction. During this 20-year period the building was in service despite the hid-
den shear failure of the piles.
Although direct extrapolation of this experience cannot be applied to areas of very low tectonic
seismicity, such as those encountered in northern Europe, since the detailing of existing piles in
there does not resemble that used in earthquake prone regions, it may still be possible that existing
lightly-reinforced concrete piles provide sufficient vertical capacity to prevent collapse, even
when the seismic demand exceeds the estimated/assumed shear and/or bending capacity of the
pile.
Investigation of Post-Failure Axial Capacity of Lightly
Reinforced Concrete Piles
V. Drosos
GR8 GEO, Athens, Greece (formerly: Fugro)
A. Papageorgiou
STRUSUS Consulting, Rhodes, Greece
A. Giannakou, J. Chacko
GR8 GEO, Athens, Greece (formerly: Fugro)
S. De Wit
Shell Global Solutions International B.V., Rijswijk, the Netherlands
ABSTRACT:
Occurrence of
man
-
induced earthquakes
in areas of
low
tectonic seismicity,
where
most structures have not been designed to resist earthquake loading, created the need for seismic
performance evaluation of existing structures. Evaluations performed revealed that in some cases
seismic demands on existing structures and their foundations may be larger than the available
capacity and therefore a retrofit scheme is often proposed and designed. This paper presents a
numerical study in order to investigate whether a pile whose shear structural capacity has been
exceeded is still able to carry the vertical loads of the superstructure following an earthquake. A
methodology useful for the preliminary seismic evaluation of poorly reinforced pile foundations
was developed that is based on analytical models developed for lightly reinforced columns. Anal-
ysis of a case-study from northern Europe using the proposed methodology showed that piles can
bear vertical loads even after shear failure has initiated, as long as the imposed drifts on the pile
are less than a critical value. For most of the cases analyzed, the pile fails in shear, but appears to
continue to carry the vertical loads. This finding is likely to have a significant influence on the
design of retrofit approaches.
A numerical study was undertaken with the goal to investigate whether a pile whose shear
structural capacity has been exceeded is still able to carry the vertical loads of the superstructure
following an earthquake. Considering the limited information/research available on the post-fail-
ure behavior of reinforced concrete piles and given that the structural function of a pile resembles
that of a column, the relative literature on post-failure capacity of columns provides the best avail-
able source of knowledge on the topic.
2 POST-FAILURE BEHAVIOR OF COLUMNS AND PILES
Despite the structural resemblance of piles to columns, the presence of soil differentiates the re-
sponse of the pile from that of a column. The role of the soil is twofold: it may apply additional
loads on the pile due to kinematic interaction, but at the same time, it may provide an extra con-
finement to the concrete of the pile increasing its ductility thus improving the post-failure behav-
ior. Maki and Mutsuyoshi (2004) and Mohammed and Maekawa (2012) explored the impact of
soil confinement on the behavior of the piles and concluded that soil confinement around plastic
hinges restrain the spalling of cover concrete and local buckling of reinforcement, hence increas-
ing the pile ductility. The effect of soil confinement diminishes close to the pile head.
While research on the post-failure behavior of reinforced concrete piles is very limited, several
researchers have studied the post-failure axial capacity of reinforced concrete columns (e.g. Yo-
shimura and Yamanaka, 2000; Shirai et al., 2001; Sezen, 2002; Elwood and Moehle, 2003). Ex-
periments have shown that the lateral capacity of a poorly-reinforced column after failure de-
grades to a small residual value. This has a major effect on the axial capacity of the column. Based
on the experimental results, researchers have drawn the following key conclusions: a) axial failure
occurs when the shear capacity of the structural member reduces to almost zero; b) drift at axial
failure decreases with increasing axial load; and c) columns with smaller hoop spacing can bear
the vertical load at larger drifts compared to columns with larger hoop spacing.
3 ANALYTICAL MODEL USED FOR THE NUMERICAL SIMULATION OF POST-
FAILURE BEHAVIOR OF PILES
The empirical model proposed by Elwood and Moehle (2003) to estimate the drift at shear and at
axial failure of existing lightly-reinforced concrete columns was used to develop a methodology
for the preliminary seismic evaluation of poorly reinforced pile foundations. According to this
model, the behavior of a poorly reinforced column can be idealized with the backbone curve
presented in Figure 1a. Four regimes are identified: a) at the beginning the structural member
deforms almost linearly with the initial stiffness up to the point where yielding occurs (δy); b) the
column reaches the ultimate lateral capacity (Vu) and it continues deforming up to a drift δs which
denotes failure in shearing and formation of a shear crack; c) for larger deformations, the lateral
capacity of the column reduces as the column cross-section further disintegrates; d) at the point
where lateral capacity reduces to almost zero (δa) the column starts losing its axial capacity as
well. After this point, and if the drift continues increasing, the axial capacity of the column de-
grades according to a limit curve as shown in Figure 1b.
Elwood and Moehle (2003) provided the following empirical equation for the estimation of the
drift at shear failure δs [= Δs/L].
 =
 +4𝜌


 (𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑀𝑃𝑎) (1)
where ρ΄΄ is the transverse reinforcement ratio defined as the cross-sectional area of the transverse
reinforcement over the product of the column width b and hoop spacing s (Ast / bs), c is the
concrete compressive strength, P is the axial load, Ag is the gross cross-sectional area of the col-
umn, and ν is the nominal shear stress (V / bd). In accordance with experimental data, the model
suggests that the drift to denote shear failure increases with more transverse reinforcement and
decreases with increasing axial load.
Figure 1. Idealized behavior of a lightly-reinforced column according to Elwood and Moehle (2003).
For the estimation of the drift at axial failure a), Elwood and Moehle (2003) developed a
simplified shear-friction model and calibrated it using experimental data. For a damaged column
with the characteristic diagonal crack developed, any axial load supported by this column must
be transferred across the crack. The load that can be transferred across the crack is a function of
the normal stress on the failure surface. Reviewing the experimental data, Elwood and Moehle
empirically determined the equation for the estimation of the drift at axial failure δa [= (Δ/L)axial].
 =
  

 (2)
where θ is the angle of the crack relative to the horizontal (typically 65o), fyt is the steel yield
strength, and dc is the depth of the column core from center line to center line of the ties.
Having developed empirical models for the assessment of the drift at shear (δs) and at axial (δa)
failure, Elwood and Moehle (2003) developed a macro-element to describe the behavior of lightly
reinforced columns. The model of the shear-critical column consists of three elements. A nonlin-
ear beam element models the flexural nonlinear behavior of the column. A shear spring is added
on top of the column (in series) to simulate the behavior of the column in shear according to the
model by Elwood and Moehle (2003). Finally, one more spring is added in series to simulate the
axial behavior of the column after failure.
According to Elwood and Moehle (2003) recommendations, the behavior of the shear spring is
defined by a trilinear relationship. The first branch of the envelope describes the shear behavior
of the column before failure. It is defined by the initial stiffness which can be approximated by
the shear stiffness of the column, Kini = GA/L. This initial segment of the envelope continues until
the shear load reaches the shear capacity of the column, Vo or the drift at shear failure, δs, whatever
comes first. At this point, the second branch of the response starts with a negative stiffness, Kdeg.
This negative stiffness can be determined as follows:
𝐾 =

 (3)
where 𝐾 is the unloading stiffness of the beam element (flexural response) —which is usu-
ally taken equal to the initial loading stiffness of the beam, and 𝐾
is the (negative) stiffness of
the resultant response (beam + shear spring) and is determined from the line connecting the point
of shear failure (δs, Vo) and the drift at axial failure, δa (δa, 0). Finally, the third branch of the
response envelope is defined by the residual shear capacity of the column, Vres (typically assumed
equal to 15% of the ultimate shear capacity according to seismic codes).
The empirical model described above was implemented in the finite element software Open-
Sees (Mazzoni et al., 2010) to be used for the numerical simulations of lightly-reinforced piles
under seismic loading. The uniaxial hysteretic material Pinching4 (Lowes et al., 2004) was se-
lected from the OpenSees material library to simulate the shear behavior of a lightly reinforced
pile elements (shear spring). Pinching4 is a general one-dimensional hysteretic load-deformation
relationship that can be calibrated to represent the response of a structural member under mono-
tonic or cyclic loading. The constitutive relationship includes a response envelope, an unload-
reload path, and three optional damage rules that control the evolution of the response. The re-
sponse envelope and the unloading-reloading path are defined as multilinear relationships and
thus the model is able to describe rather complicated hysteretic loops. The axial spring proposed
by Elwood and Mohle (2003) for modeling the axial capacity degradation after failure was omit-
ted, conservatively assuming that pile loses all its axial capacity as soon as the drift at axial failure
is reached.
We note that the macro-element developed by Elwood and Moehle (2003) for lightly reinforced
columns (i.e. LimitState material in OpenSees material library) could not be readily implemented
for the simulation of pile behavior since the pile needed to be discretized into a series of elements
with connected soil springs that model the nonlinear soil-pile interaction behavior with depth.
4 MODEL VALIDATION
Due to lack of experiments on the post-axial failure capacity of lightly reinforced piles, the model
was validated against shake table tests performed by Elwood and Moehle (2003) that investigated
the dynamic response of shear-critical columns and their post-failure axial capacity. A frame con-
sisting of three columns with the central one designed to be shear-critical (wider spacing of trans-
verse reinforcement) was tested. Details of the experiment are provided in Elwood and Moehle
(2003). Using the finite-element code OpenSees and the analytical model described above, the
shake table experiment was modeled in order to validate the analytical model. The Pinching4
material was calibrated for the experiment following the procedure described earlier.
The results of the numerical analysis of the experiment are compared with the measured re-
sponse of the central column in Figure 2.The shear force horizontal displacement hysteretic
loops illustrate that the numerical model is able to reproduce efficiently all the components of the
column behavior: the initial stiffness of the column, the ultimate shear capacity, the strength deg-
radation and the residual strength, and the unloading stiffness. The calculated response of the
column is bounded by the backbone curve defined from a push-over analysis. The numerical
model has predicted sufficiently the shear force variation with time/displacement and the charac-
teristic points of shear and axial failure are clearly identified at about the same point as in the
experiment.
Figure 2. Analysis results vs. experiment measurements of the response of the central column to horizontal
cyclic load. Hysteretic loops of shear force against horizontal relative displacement (the idealized backbone
curve [black line] according to the empirical model by Elwood and Moehle is superimposed) and shear
force time histories
5 NUMERICAL INVESTIGATION OF POST-FAILURE BEHAVIOR OF LIGHTLY
REINFORCED PILES
5.1 Approach
For the numerical investigation of post-failure behavior of lightly reinforced piles a 2-story build-
ing located in northern Europe was selected as a case study. The building is constructed of precast
concrete wall elements and steel frames supporting the slabs with a foundation consisting of cast
in-situ foundation beams supported on concrete bored piles. One pile from this building was se-
lected for application of the proposed methodology.
The pile was modeled as a beam-on-nonlinear-Winkler foundation (BNWF). The pile elements
were connected to the soil through a set of springs simulating the soil-pile interface behavior (i.e.
p-y and t-z springs based on the soil deposit properties and using API (2000) recommendations).
The free ends of the springs were excited by the free-field soil motion at the corresponding depth.
A one-dimensional site response analysis performed separately to calculate the free-field motion
at these depths. The inertial loads imposed to the foundation by the oscillation of the superstruc-
ture were considered in a simplified manner (i.e. through a 1-dof oscillator added above the pile
head with a fundamental fixed-base period of 0.3 s).
Shear springs following Elwood and Moehle’s model were added between consecutive beam
elements at locations where significant shear forces were expected to develop and shear failure
was likely to occur. To identify locations of substantial shearing, an analysis considering the pile
with infinite shear capacity was conducted first. Shear springs were then placed at the location of
these critical points and analyses were repeated.
5.2 Development of Free-Field Time Histories Along Pile
The soil profile consists of a thick layer of soft clay (about 9 m thick) overlying an approximately
3-m thick medium dense sand layer. A clay layer of 1 m thickness is encountered between the
medium dense sand layer and a deeper dense sand layer that was present to the maximum depth
explored (about 23 m depth). Figure 3 illustrates the stratigraphy of the idealized soil profile and
presents the interpreted shear wave velocity (Vs) profile. Following the applicable seismic code
provisions, the input motion was applied at a stiff-soil horizon with shear wave velocity of 300
m/s which was encountered at 22.5 m depth.
Nonlinear site response analyses were performed to develop free-field soil motion along the
pile that were applied at the free end of the p-y springs. Since no site-specific dynamic laboratory
tests are available for the site, Darendeli’s (2001) modulus reduction and damping curves were
used. For the clay layers a plasticity index (PI) equal to 40 was assumed.
Input motions were derived according to the applicable seismic code that incorporated demands
due to man-induced earthquakes resulting in a design PGA value at stiff soil conditions of 0.54 g
for 1500-year return period. The response spectrum of the input motion at depth and the ground
surface response spectrum are presented in Figure 3. Deamplification was observed due to the
nonlinear response of the soft soil deposit. Analysis with an input motion of increased PGA at
depth (0.81 g) was also performed to investigate the influence of the rather conservative partial
factors recommended by the seismic code when nonlinear time history analyses are performed.
5.3 Pile Modeling
The geometry of the pile and the detailing are presented in Figure 3. Material properties provided
by the structural engineer have been used in this study. The shear capacity VRd,c of the upper and
the lower part of the pile is 77.2 kN and 59.8 kN, respectively. An axial load of 550 kN has been
assumed for the examined pile based on the seismic evaluation of the building.
The pile was modeled with 0.5m-long nonlinear beam elements. For the simulation of the non-
linear behavior in bending moments and axial loads the cross-section of the beam is discretized
in small areas, called fibers, whose behavior is described by the constitutive law of their material.
In this way all the components of the cross-section are modeled in detail (i.e. confined con-
crete/core, unconfined concrete/cover, and longitudinal reinforcement). Concrete fiber behavior
is described using the Concrete02 material from the OpenSees library and reinforcement behavior
is modeled with Steel02 material. During the analysis the resultant response of the fiber section
defines the response of the beam element where the section belongs to. The two material models
that describe the pile section behavior (i.e. concrete and steel) were calibrated based on the mate-
rial properties reported by the structural engineer.
As mentioned above shear springs are placed at locations of substantial shearing. Three critical
points of increased shear demands were identified along the pile for the reference motion. These
locations are associated with depths where interfaces of significant soil stiffness contrast are en-
countered (i.e. sand–clay interfaces at about 9 and 12 m depth). A shallower point (~7m depth)
was considered also critical due to the increased shear forces. In light of the above, three shear
springs were added into the pile model at the specific depths. An additional shear spring was
placed at the pile head where the presence of the foundation beam (i.e. fixed-head boundary con-
ditions) and the superstructure is likely to impose significant demands on the pile.
Figure 3. Case study from man-induced seismicity area in northern Europe: idealized soil profile at the site
(left), ground motions (bottom right), and analyzed pile geometry and detailing (top right)
5.4 Calibration of the Shear Springs
From the analysis performed to identify the critical points, it was concluded that the pile is likely
to suffer a pure shear failure (i.e. for shear forces close to the ultimate shear capacity of the pile,
the bending moments developed are considerably lower than the moment capacity). Since the
shear capacity V0 is known, the only parameter to be estimated for the calibration of the shear
springs is the drift at axial failure, δa.
For the upper part of the pile, application of Equation 2 is straightforward. Given the transverse
reinforcement of the pile (Ast = 10-4 m2, s = 0.75 m, fyt = 550 MPa), and assuming a critical crack
angle θ = 65ο, an axial load P = 550 kN, and a depth of the pile core dc = 0.28 m, the drift at axial
failure for the upper part of the pile is estimated (Δ/L)axial,upper 1.5 %.
For the lower part of the pile, direct application of Equation 2 is not possible since transverse
reinforcement does not exist, the spacing s tends to infinity and thus drift at axial failure tends to
zero. At this point, we note that Elwood and Moehle (2003) ignored the dowel action of the lon-
gitudinal reinforcement in the derivation of Equation 2. The justification for disregarding this
action is that spalled cover concrete and hoop wide spacing cannot provide enough resistance for
the dowel action to develop. Nonetheless, this is not the case for the central rebar of the pile
foundation. The central reinforcement runs along the axis of the pile and has sufficient concrete
cover and anchor length to warrant the development of dowel action to some extent. The magni-
tude of the lateral force that can be provided by the central rebar is limited to the minimum of the
steel bar shear capacity and the dowel action due to concrete resistance. The model proposed by
Rasmussen (1963) was used to estimate the dowel action force.
𝑉= 1.3 𝑑
𝑓 𝑓<
𝑓 (4)
where db is the rebar diameter, fc is the concrete compressive strength, fs is the steel yield strength,
and A is the rebar cross-sectional area. To account for cyclic degradation during seismic loading,
a partial factor of 2 was applied to Vd (EPPO, 2012).
Rewriting Equation 2 as follows:
 =
  

(5)
where Ft is the resisting force provided by the hoops in the free-body diagram, and assuming that
this force is provided by the dowel action of the central bar for the lower part of the pile, then the
drift at axial failure can be estimated according to Equation 5. From the properties of the central
rebar of the pile (db = 25 mm, fs = 550 MPa) and the concrete (fc = 20 MPa), and assuming a
critical crack angle θ = 65ο, and an axial load P = 550 kN, the drift at axial failure for the lower
part of the pile is estimated (Δ/L)axial,lower 1.7 %.
5.5 Results
Figure 4 shows the profiles of shear force (V), pile relative horizontal displacement (upile), and the
shear force – horizontal displacement hysteretic loop of the pile at 11.5 m depth using the refer-
ence input motion (PGA = 0.54 g). Each line in the plots corresponds to a specific time during the
shaking. The shear capacity is reached only at two points (i.e. 9.5m and 11.5m depth) which indi-
cate the points of shear failure. Indeed, the abrupt change in the pile displacement profile at 11.5m
depth [marked with the red circle] reveals the formation of a plastic hinge at this depth. This is
better illustrated in the hysteretic loop of the pile at the specific depth. After shear failure the drift
continues increasing and the shear force following the backbone curve starts degrading. At a dis-
placement of about 5 mm the seismic motion reverses and the imposed drift reduces again. After
this cycle, the seismic motion does not impose larger displacement on the pile and shear capacity
does not degrade further. Given that axial failure initiates when the shear capacity reduces to
almost zero, it is concluded that the pile is unlikely to lose its axial capacity under this seismic
load. Figure 5 shows analysis results for the highest input motion considered with a PGA of 0.81
g. Shear capacity is reached at three points (i.e. at 7 m, 9.5 m and 11.5 m depth) indicating loca-
tions of shear failure. The behavior of the pile at 9.5 and 11.5 m depth is similar to this observed
in the previous case. At 7 m depth though, after the shear failure the drift continues increasing
and the shear force following the backbone curve starts degrading and eventually reaches the
residual shear capacity. At this point axial failure is imminent.
Figure 4. Profiles of shear force (V) and pile relative horizontal displacement (upile), and hysteretic loop of
the pile cross-section at 11.5m depth [red circle marks a critical point with increased shear demands; black
dashed line in the shear force plot denotes the shear capacity of the pile; red dashed line denotes the response
envelope of the specific pile cross-section]
6 CONCLUSIONS
A preliminary investigation of the post-failure axial capacity of poorly reinforced piles has been
carried out using a developed methodology/approach based on the research findings of Elwood
and Moehle (2003) who examined the residual axial capacity of lightly reinforced columns that
are prone to fail in shear. Analysis of a case study from northern Europe have shown that poorly-
reinforced piles can bear vertical loads even after shear failure has initiated, as long as the imposed
drifts on the pile are less than a critical value. Given the seismic demand in the area, for most of
the cases analyzed, the pile fails in shear, but it seems that it can continue bearing the vertical
loads. Although the development of the proposed approach lies on solid scientific evidence, in-
evitably, application of Elwood and Moehle (2003) model to piles includes several assumptions
and hypotheses that require experimental verification. Main assumptions of the developed meth-
odology as presented in this paper to be verified include the extrapolation of model application
from columns to piles and the contribution of the central rebar to the shear resistance of the cross-
section. This paper is about single structural pile performance. It is important to note that seismic
assessments of global building response consider the full foundation system, including all piles
and (partial) embedded foundation beams. The full building-foundation-soil system should be
analyzed to ensure that all force and shear resisting components and load retribution effects are
taken into account and to arrive at a representative individual seismic pile loading regime.
Figure 5. Profiles of shear force (V) and pile relative horizontal displacement (upile), and hysteretic loop of
the pile cross-section at 7m depth
REFERENCES
American Petroleum Institute (2000) “Recommended Practice for Planning, Designing, and Constructing
Fixed Offshore Platforms,” RP 2AWSD, 21st Edition, API, Washington, D.C., December.
Darendeli, M. (2001) Development of a new family of normalized modulus reduction and material damping
curves. Ph.D. Thesis, Dept. of Civil Eng., Univ. of Texas, Austin.
Elwood, K., and Moehle, J. P., (2003) Shake Table Tests and Analytical Studies on the Gravity Load Col-
lapse of Reinforced Concrete Frames, PEER Report 2003/01, Pacific Earthquake Engineering Research
Center, University of California.
EPPO (2012) Code of Structural Interventions 2012, GG 42/B/20-01-2012, Earthquake Planning and Pro-
tection Organization, Athens, Greece.
Lowes, L.N., Mitra, N., and Altoonash, A. (2004) A Beam-Column Joint Model for Simulating the Earth-
quake Response of Reinforced Concrete Frames, PEER Report 2003/10, Pacific Earthquake Engineer-
ing Research Center, University of California.
Maki, T. and Mutsuyoshi, H. (2004) “Seismic Behavior of Reinforced Concrete Piles under Ground”. Jour-
nal of Advanced Concrete Technology, 2(1), pp. 37-47.
Mazzoni, S., McKenna, F., Fenves, G.L. (2010) OpenSees Online Documentation, http://opensees.berke-
ley.edu/wiki/index.php/Main_Page, Pacific Earthquake Engineering Center, University of California.
Mohammed, A.Y.M. and Maekawa, K. (2012) “Global and Local Impacts of Soil Confinement on RC Pile
Nonlinearity Global and Local Impacts of Soil Confinement on RC Pile Nonlinearity”. Journal of Ad-
vanced Concrete Technology, 10. pp. 375-388.
Rasmussen, H.B. (1963) “Resistance of Embedded Bolts and Dowels Loaded in Shear”, Bygningsstatiske
Meddelelser, Vol.34(2).
Sezen, H., (2002) Seismic Response and Modeling of Reinforced Concrete Building Columns, Ph.D. Dis-
sertation, Department of Civil and Environmental Engineering, University of California, Berkeley.
Shirai N., Moriizumi, K., and Terasawa, K., (2001) Cyclic Analysis of Reinforced Concrete Columns:
Macro-Element Approach, Modeling of Inelastic Behavior of RC Structures under Seismic Load, Amer-
ican Society of Civil Engineers, Reston, Virginia, pp. 435-453.
Yoshimura, M., and Yamanaka, N., (2000) Ultimate Limit State of RC Columns, Second US-Japan Work-
shop on Performance-Based Earthquake Engineering Methodology for Reinforced Concrete Building
Structures, Sapporo, Japan, PEER report 2000/10. Berkeley, Calif.: Pacific Earthquake Engineering
Research Center, University of California, pp. 313-326.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
Abstract Experimental investigation of the ,earthquake response ,of reinforced ,concrete sub- assemblages,indicates that stiffness and strength loss resulting from beam-column,joint damage may be substantial. To simulate inelastic joint action, a joint element is developed that is appropriate for use with traditional beam-column elements,in two-dimensional nonlinear frame analysis. The proposed ,element ,formulation includes four external nodes ,with a total of 12 external degrees-of-freedom; however, the element is a super-element and includes four additional internal degrees-of-freedom. The super-element comprises ,13 one-dimensional
Thesis
As part of various research projects [including the SRS (Savannah River Site) Project AA891070, EPRI (Electric Power Research Institute) Project 3302, and ROSRINE (Resolution of Site Response Issues from the Northridge Earthquake) Project], numerous geotechnical sites were drilled and sampled. Intact soil samples over a depth range of several hundred meters were recovered from 20 of these sites. These soil samples were tested in the laboratory at The University of Texas at Austin (UTA) to characterize the materials dynamically. The presence of a database accumulated from testing these intact specimens motivated a re-evaluation of empirical curves employed in the state of practice. The weaknesses of empirical curves reported in the literature were identified and the necessity of developing an improved set of empirical curves was recognized. This study focused on developing the empirical framework that can be used to generate normalized modulus reduction and material damping curves. This framework is composed of simple equations, which incorporate the key parameters that control nonlinear soil behavior. The data collected over the past decade at The University of Texas at Austin are statistically analyzed using First-order, Second-moment Bayesian Method (FSBM). The effects of various parameters (such as confining pressure and soil plasticity) on dynamic soil properties are evaluated and quantified within this framework. One of the most important aspects of this study is estimating not only the mean values of the empirical curves but also estimating the uncertainty associated with these values. This study provides the opportunity to handle uncertainty in the empirical estimates of dynamic soil properties within the probabilistic seismic hazard analysis framework. A refinement in site-specific probabilistic seismic hazard assessment is expected to materialize in the near future by incorporating the results of this study into state of practice.
Article
This paper reports the results of experimental and analytical investigation on the response behavior of reinforced concrete piles under ground. From the experimental results, it was clarified that the axial load at pile head affects the restoring force degradation and the maximum damage point is dependent on the relative stiffness between the pile and surrounding soil. From the analytical study using 3-dimensional FEM analysis, the experimental behavior could be adequately simulated by the applied method. Further investigations on the shapes or areas of hysterisis loops will be needed for the future application of this method to seismic performance evaluation of the entire structure-pile foundation-soil system.
Article
Thesis (Ph.D in Engineering--Civil and Environmental Engineering)--University of California, Berkeley, Fall 2002. Includes bibliographical references (leaves 276-290).
Article
Thesis (Ph.D. in Engineering-Civil and Environmental Engineering)--University of California, Berkeley, Fall 2002. Includes bibliographical references (leaves 277-289).
Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms
  • American Petroleum Institute
American Petroleum Institute (2000) "Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms," RP 2AWSD, 21st Edition, API, Washington, D.C., December.
Earthquake Planning and Protection Organization
  • Eppo
EPPO (2012) Code of Structural Interventions 2012, GG 42/B/20-01-2012, Earthquake Planning and Protection Organization, Athens, Greece.
OpenSees Online Documentation
  • S Mazzoni
  • F Mckenna
  • G L Fenves
Mazzoni, S., McKenna, F., Fenves, G.L. (2010) OpenSees Online Documentation, http://opensees.berkeley.edu/wiki/index.php/Main_Page, Pacific Earthquake Engineering Center, University of California.
Resistance of Embedded Bolts and Dowels Loaded in Shear
  • H B Rasmussen
Rasmussen, H.B. (1963) "Resistance of Embedded Bolts and Dowels Loaded in Shear", Bygningsstatiske Meddelelser, Vol.34(2).
Cyclic Analysis of Reinforced Concrete Columns: Macro-Element Approach, Modeling of Inelastic Behavior of RC Structures under Seismic Load
  • N Shirai
  • K Moriizumi
  • K Terasawa
Shirai N., Moriizumi, K., and Terasawa, K., (2001) Cyclic Analysis of Reinforced Concrete Columns: Macro-Element Approach, Modeling of Inelastic Behavior of RC Structures under Seismic Load, American Society of Civil Engineers, Reston, Virginia, pp. 435-453.