1.
Effect of Earthquake on Embankment Dams 1577
EFFECT OF EARTHQUAKE ON EMBANKMENT DAMS
Dr. Gopi Siddappa1
ABSTRACT
An earthquake is a vibration of the earth produced by a rapid release of energy. An
earthquake only occurs for a few brief moments; the aftershocks can continue for weeks;
the damage can continue for years. The present work deals with an important and
complex issue in geotechnical and earthquake engineering, which concerns the influence
of both elasticity and pore water pressure on the seismic response of earthen dams to
artificial earthquake records using the finite element program GEOSTUDIO QUAKE/ W.
The study includes observation during earthquake loading, the different methods of
seismic analysis of earth dams, such as the simplified methods, the empirical methods, the
equivalent-linear analyses and the non linear methods. The study presents numerical
analyses of the seismic behavior of homogeneous and cored earthen dams. The analysis is
first conducted for a simple case which concerns the elastic response of the earthen dam.
This analysis provides some indications about the response of the dam, mainly the
dynamic amplification and pore water generation. For the elastic analyses, a parametric
study is conducted for the investigation of the influence of major parameters such as the
mechanical properties of the earth material density and soil stiffness. If the post-
earthquake stability analyses indicate factors of safety against sliding above 1.0, the
expected amount of deformation can be estimated using several methods. The most
rigorous method is to use finite element or finite difference programs.
INTRODUCTION
Dams can be classified according to their purpose as diverting dams, storage dams and
detention dams. According to the materials used for its construction, dams are classified
as earth fill dams, rock fill dams, concrete gravity dams etc. Earth fill dam can be
classified into homogeneous and core dam. Homogeneous dam is one which uses same
material and core dam is one in which different materials are used. The core material can
be different from shell and it comprises of less permeability. The core can be designed to
be placed at the center of dam or at other locations.
Like most of engineering structures, earth dams may fail due to faulty design, improper
construction and poor maintenance practices, etc. The various causes of failure may be
hydraulic failure, seepage failure, piping through dam body, structural failure and due to
earthquake. An earthquake is a vibration of the earth produced by a rapid release of
energy (Tarbuck et. al. 1996). The main features include the focus, the location within the
earth where the earthquake rupture starts, and the epicentre, the point on the earth's
surface directly above the focus. Earthquakes have a greater effect on society than most
people think. These effects range from economical to structural to mental. An earthquake
1
Professor, Department of Civil Engineering, P.E.S. College of Engineering, MANDYA– 5710401,
Karnataka State, INDIA. Phone: 91-9448745759. e-mail: gopisiddappa@gmail.com
2.
1578 Innovative Dam and Levee Design and Construction
only occurs for a few brief moments; the aftershocks can continue for weeks; the damage
can continue for years. Accurate records of earthquake magnitudes have been kept only
for some 100 years since the invention of the seismograph in the 1850s. Recent records of
casualties are likely to be more reliable than those of earlier times. There are estimated to
be some 500,000 seismic events each year. Out of these, about 100,000 can be felt and
about 1,000 cause some form of damage. Experience has shown that well-compacted,
impervious rolled-fill dams are resistant to earthquake forces, provided they are
constructed on rock or overburden foundations resistant to liquefaction. There are two
major issues that need to be resolved in assessing the seismic performance of earth dams
under earthquakes:
a) Stability: Is dam stable during and after earthquake?
b) Deformation: How much deformation will occur in the dam?
The first failure of a dam due to earthquake reported in the literature is Augusta Dam,
GA, during 1886 Charleston, SC earthquake. Worldwide, fewer than 30 dams have failed
completely during earthquakes (USCOLD 2000). These were primarily tailings or
hydraulic fill dams, or relatively small embankments of questionable design. Few large
embankment dams have been severely damaged. In 1925, an earthquake (M 6.3) caused
catastrophic slope sliding failure of the 25-feet high Sheffield Dam in Santa Barbara, CA.
This was the first recognition that shaking of embankments with low relative density
materials may cause liquefaction failures. The 2001 Bhuj (India) earthquake (M 7.7)
resulted in widespread soil effects and liquefaction in low-lying estuaries and young
alluvial deposits. Strong ground motion lasted more than 85 seconds, and lower-level
shaking several minutes. Numerous embankment dams were damaged in the epicenteral
area, including seven medium-sized (40 to 120 feet high) earth dams. Fourteen smaller
dams were also damaged, some extensively. The reservoirs were very low at the time of
the earthquake but liquefaction of the foundation caused moderate to severe failure of the
upstream and, locally, the downstream slopes of the dams.
Simplified procedures are used for small dam’s analysis or to assess the need for detailed
studies of large dams. Two common procedures are described in the following. Other
simplified approaches for estimating dam deformations can be found in the literature (e.g.,
Jansen, 1987; Romo and Resendiz, 1981). If liquefaction is of concern to the dam or its
foundation, the simplified procedure of Seed and Idriss (1970a) can be implemented for
dams with flat slopes. A better approach is to assess the liquefaction potential from
corrected field penetration data (Seed, 1983). Newmark (1965) computed earthquake-
induced displacements in embankments by assuming that movements occur when an
inertia forces on a rigid block of soils above a fixed potential failure surface exceed its
sliding resistance. He assumed that the slope deformed only during those portions of the
earthquake when the out-of-slope earthquake forces cause the pseudo static factor of safety
to drop below 1.0
A dam responds as a flexible body, and accelerations vary as a function of depth within the
embankment. To take this into account, Makdisi and Seed (1977) estimated the peak crest
acceleration (ü max) from a specified response spectrum and a square-root-of-the-sum- of-
the-squares (SRSS) combination of the spectral accelerations of the first three modes of
3.
Effect of Earthquake on Embankment Dams 1579
dam vibration. In 1987, the authors tested the correlation with friction angles lower than
ncountered in rock fill, using the results of physical model tests on dry sand
embankments (Roth et al., 1986). Finite element analyses used to define the initial state of
static stresses often rely on hyperbolic soil models (Duncan et al., 1984) and variations of
the initial tangent static Ei with the confining pressure, as originally suggested by Janbu
(1963).
Strain-dependent equivalent dynamic shear moduli and damping ratios as first introduced
by Seed and Idriss (1970a) are essential to EQL analyses. EQL response is sometimes
obtained for representative soil columns within the dam section using SHAKE91 (Idriss
and Sun, 1992). For prediction of the shear strength of an unsaturated soil, two
approaches had been proposed y Bishop (1959—effective stress approach) and
Fredlund et al.(1978— independent stress variables approach). Many researchers have
demonstrated both theoretical and empirical formulations to estimate unsaturated shear
strength, e.g. the verification of the nonlinear change in cohesion of an unsaturated soil
(Escario and Sáez1986) an analytical model based on a soil–water retention curve
(Vanapalli et al. 1996); an empirical formulation based on Bishop’s concept (Khalili and
Khabbaz 1998); the prediction of soil cohesion using hyperbolic equation (Lee et al. 2003).
The response and behaviour of earth structures subjected to earthquake shaking is highly
complex and multifaceted (Steven Kramer, 2005). Generally, there are the issues of:
(a) the motion, movement and inertial forces that occur during the shaking, (b) the
generation of excess pore-water pressures, the potential reduction of the soil shear
strength, (c) the effect on stability created by the inertial forces, excess pore-water
pressures and possible shear strength loses, and (d) the redistribution of excess pore-water
pressures and possible strain softening of the soil after the shaking has stopped.
OBJECTIVES OF THE STUDY
The main objective of this investigation is to study the seismic behaviour of homogenous
and core earthen dam by using a finite element software QUAKE/W. QUAKE/W is a
geotechnical finite element software product used for the dynamic analysis of earth
structures subjected to earthquake shaking and other sudden impact loading such as
dynamiting or pile driving. The study includes the analysis to investigate the response of
the ground and the structure when it is subjected to an earthquake, and to examine the
possibility that there may be some generation of excess pore-pressures, which in turn
could lead to some liquefaction.
Problem Configuration : Figure 1 shows the problem configuration of a homogeneous and
a core earth dam with mesh. Basically it is an earth dam founded on an 8-metre stratum of
gravel soil. The embankment is 5-m high with 2H : 1V side slopes. The dam retains a
reservoir with a full supply level (FSL) at an elevation of 12 m with a water head of 4
meters. The properties of the materials considered for the study is shown in Table 1.
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1580 Innovative Dam and Levee Design and Construction
Table 1. Material Properties for Earth Material Stiffness Analysis
Parameter Units Shell Material Core Material Foundation
Unit Weight (γ) kN/m3
16 18 19
Poisson’s Ratio (ν) - 0.3 0.3 0.3
Damping Ratio (ξ) - 0.1 0.1 0.1
Elastic Shear
Modulus (Gmax)
MPa 5000 5000 5000
(a) Homogeneous Earth Dam
(b) Core Earth Dam
Figure 1. Problem Configuration with Mesh
The dam has a granular under drain to control the seepage through the dam. The drain
itself is actually not included in the analysis, but is considered when defining the phreatic
surface. For the analysis, the geometry can be represented by two GeoStudio regions; one
region for the foundation and the second region for the embankment. The emphasis here
is on QUAKE/W because the cases involve earthquake shaking, but SEEP/W, SLOPE/W
and SIGMA/W are also used. SEEP/W is used to establish the long-term steady-state
seepage conditions and pore-pressures (Figure 2). On the downstream side, the water
table is taken at the ground surface. A granular blanket was placed between the original
dam and the downstream berm, assuming that the blanket functioned as intended, the
piezometric line will daylight somewhere in the granular blanket. This is modelled by
tagging the boundary between the dam and the berm as a potential seepage face.
Approximate conductivity functions and Ksat (Saturated conductivity) values are adequate
for this steady-state analysis, since the piezometric surface is high up in the dam and
much of the seepage flow is in the saturated zone. Also, the pore-pressure distribution is
not sensitive to Ksat.
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Effect of Earthquake on Embankment Dams 1581
Figure 2. Long Term Steady-state Seepage and Pore-pressure Conditions
The QUAKE/W Initial Static analysis type is conducted to establish the initial, total and
effective static stress distribution throughout the dam. This is done with a QUAKE/W
Static-type analysis or a SIGMA/W Insitu analysis: To compute the initial static stresses,
it is necessary to specify Poisson’s ratio and the total unit weight of the soils. The
previously computed SEEP/W pore-pressures are used in the static stress analysis. It is
important to include the weight of the reservoir water in the static stress analysis. This is
done by applying a fluid pressure boundary on the region edges in contact with the
reservoir and is illustrated in Figure 3. The resulting total and effective vertical stress
contours, as in Figure 4 and Figure 5.
(a) Homogeneous dam (b) Core dam
Figure 3. The Reservoir Water Weight Boundary Condition
(a) Homogeneous Dam (b) Core Dam
Figure 4. Total Vertical Stress Contours
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1582 Innovative Dam and Levee Design and Construction
(b) Homogeneous Dam (b) Core Dam
Figure 5. Initial Static Effective Vertical Stress Contours
Based on the SEEP/W pore-pressures and QUAKE/W static stresses, the factor of safety
is well above 2.0 as illustrated in Figure 6. This is consistent with the findings by Seed et
al., who concluded that the margin of safety against instability under the static conditions
was fairly high.
(c) Homogeneous Dam (b) Core Dam
Figure 6. Stability before the Earthquake
The purpose of the dynamic analysis is to determine the excess pore-pressures that may
develop, and identify zones where the soil may have liquefied. The Equivalent Linear
Dynamic analysis type is used here with an impervious boundary condition adopted as
shown in Figure 7. In QUAKE/W, selected points can be flagged where the results will be
saved for each and every time step while integrating through the earthquake record which
is defined as History Points. Two History Points marked as ( ) have been specified in
each model as shown in Figure 7.
(d) Homogeneous Dam (b) Core Dam
Figure 7. Impervious boundary for the Dynamic Analysis and History Points ( )
7.
Effect of Earthquake on Embankment Dams 1583
The structure will be subjected to earthquake shaking according to the time-history record
shown in Figure 8. The peak acceleration is assumed as 0.12g and the duration is 10
seconds. The data points are presented at a constant 0.02 second interval. The constitutive
behaviour of the soil is treated as being linear elastic. The shear modulus Gmax is 5000
kPa for both the foundation and embankment soil. The damping ratio is a constant 0.1
(10%). The Equivalent Linear method of analysis in QUAKE/W is formulated to
compute the generation of excess pore-pressures on the basis of Cyclic Stress Ratios
(CSR), and on the basis of the number of uniform cycles experienced by the soil during
the shaking, relative to the number of cycles required for the soil to liquefy.
Dynamic Analysis Results : Figure 9 shows the relative displacements as a deformed
mesh which illustrate the swaying of the ground during the earthquake. Figure 10 shows
contours of q/p΄ stress ratios under the initial static stresses. A point of significance is the
high q/p΄ ratios in the central part of the foundation. This means that there is a zone where
the initial q/p΄ points are above the collapse surface. The soil strength in this zone could
easily fall down to the steady-state strength with a small amount of shaking. With stress
ratios greater than about 1.2 indicate a stress point above the collapse surface.
(a) Homogeneous Dam (b) Core Dam
(b)
Figure 8. Earthquake Time-History Record
(a) Homogeneous Dam (b) Core Dam
(b)
Figure 9. Relative Displacements at 4.52 Seconds into the Shaking (100x Exaggeration)
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1584 Innovative Dam and Levee Design and Construction
(a) Homogeneous Dam (b) Core Dam
Figure 10. q/p΄ Stress Ratios under Initial Static Stresses
Liquefaction : In an Equivalent Linear analysis, a key parameter obtained is the Cyclic
Stress Ratio (CSR). This number is used together with the Cyclic Number function
(Figure 11) to indicate the possibility of liquefaction. Generally higher the CSR, higher
will be the possibility of liquefaction. During the shaking, excess pore-pressures will
develop, causing other elements to reach the collapse surface to liquefy. In this study,
CSR’s greater than about 0.2 will indicate liquefaction is possible. Figure 12 shows the
liquefied zone at the end of the shaking. The high excess pore-pressures are seen on the
upstream side (Figure 13), where there is pocket of excess pore-pressures that exceed
5 kPa and 2kPa for homogeneous and core dam respectively.
(a) Homogeneous Dam (b) Core Dam
Figure 11. Cyclic Stress Ratio Contours
(a) Homogeneous Dam (b) Core Dam
Figure 12. Liquefied Zone at the end of Shaking.
9.
Effect of Earthquake on Embankment Dams 1585
(a) Homogeneous Dam (b) Core Dam
Figure 13. Contours of Excess Pore-pressure at the end of Shaking
Post-Earthquake Stability : SLOPE/W has the capability to use the specified steady-state
strength along the portion of a potential slip surface that passes through an element
that QUAKE/W has marked as liquefied. Figure 14 illustrates that repeating the pre-
earthquake stability analysis, but with post-earthquake pore-pressures and with steady-
state strengths in the liquefied zones, results in a factor of safety of greater than unity.
Post-Earthquake Deformations : There is strong evidence that the major slide movements
did not start until after the strong earthquake shaking. Seed et al. (1978) note that, “… the
slide probably did not occur until near or just after the end of the stronger earthquake
motions.” The post-earthquake conditions can be taken into SIGMA/W to do a stress re-
distribution. Clearly some zones were over-stressed after the earthquake due to the
strength loss. With SIGMA/W, it is possible to attempt to re-distribute the stresses in the
over-stressed zones.
Figure 15 shows the displacement vectors from the post-earthquake SIGMA/W stress re-
distribution. The movements seem to be a reasonable approximation of what happened as
the movement started. In the crest area, the start of the movement is close to where the
head scarp was, and the movements are downward at a steep angle, which is consistent
with the actual head scarp. Figure 16 and 17 shows the contours of excess pore-pressure
and liquefied zone after earthquake shaking.
(a) Homogeneous Dam (b) Core Dam
Figure 14. Post-earthquake Stability.
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1586 Innovative Dam and Levee Design and Construction
(a) Homogeneous Dam (b) Core Dam
Figure 15. Post-earthquake Deformation at 16 sec
(a) Homogeneous Dam (b) Core Dam
Figure 16. Contours of Excess Pore-pressure after Earthquake Shaking
(a) Homogeneous Dam (b) Core Dam
Figure 17. Liquefied Zone after Earthquake Shaking.
CONCLUSION
Many of the material properties used in this analysis are simple estimates. They are,
however, adequate for understanding the key issues and mechanisms. The response of the
homogeneous dam under earthquake loading with comparing to core dam was
investigated and evaluated. Concentration of stress in core model is less than
homogeneous model. Therefore, it can be concluded that the core dam section has better
static behaviour compare to simple homogeneous dam. Displacement, acceleration, and
spectral response in homogeneous dam are similar to those in core dam. Therefore, it
seems that natural frequency of homogeneous dam is close to that of core dam to the
frequency of earthquake. Changing material in core zone does not have enough effect on
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Effect of Earthquake on Embankment Dams 1587
response of dam. Therefore, core model has shown more safety against failure from
tensile stresses under pore water pressure.
SEISMIC RESPONSE OF THE EARTH DAMS: INFLUENCE OF ELASTICITY
In this study, dynamic analysis of earth dam considering dam-foundation interaction,
under Horizontal Earthquake Record αmax = 0.12g is assumed as input motion, carried out
by using QUAKE/W, a finite element package for solving geotechnical problems. The
seismic response of the dam is affected by the mechanical properties of the earth
material. The reference example concerns an earth dam with a clay core constructed
on a homogeneous soil layer (Figure 1b).
Dynamic Analysis: The numerical modelling for the dynamic analyses has been
performed using the QUAKE/W program, on the geometry of the dam foundation coupled
model as shown in (Figure 1b) which is based on finite element method. Results of
earthquake analysis at History Point of dam crest as shown in Table 2 and Table 3
indicates that core earth dam performs better than the homogeneous dam during
earthquake. Dynamic analyses were performed for the end of construction stage using the
linear elastic model for material dynamic behaviour. Material properties of dam body and
foundation have been presented in Table 4 and Table 5. The structure is subjected to
earthquake shaking according to the time-history record as shown in the Figure 18. The
peak acceleration assumed is 0.12g and the duration is 10 seconds. The data points are
presented at a constant 0.02 second interval.
Table 2. Earthquake Analysis Results at History Point at Dam Crest
Parameter Homogeneous Dam Core Dam
X-Peak Displacement (m) 0.0850 0.0761
X-Peak Velocity (m/sec) 0.4011 0.4012
X-Peak Acceleration (g) 0.3667 0.3667
Max. Total Stress (kPa) 13.095 14.454
Maximum Effective Stress (kPa) 28.526 30.292
Max. Shear Stress (kPa) 3.6336 4.8621
Deviatoric Stress (q) (kPa) 7.5655 9.4262
Pore-Water Pressure (kPa) -15.431 -15.837
Excess PWP (kPa) 0.2562 0.1113
Maximum Strain 5.36E-05 5.90E-06
Max. Shear Strain 8.72E-05 1.82E-05
Cyclic Stress Ratio 0.1142 0.0593
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1588 Innovative Dam and Levee Design and Construction
Table 3. Post Earthquake Analysis Results at History Point at Dam Crest
Figure 18. Earthquake Time-History Record
Table 4. Material Properties for Earth Material Density Analysis
Model
No.
Parameter Unit
Weight
(γ)kN/m3
Poisson’s
Ratio
(ν)
Damping
Ratio
(ξ)
Elastic
Shear Modulus
(Gmax)MPa
1
Shell 16 0.3 0.1 23
Core 18 0.3 0.1 15
Foundation 19 0.25 0.1 400
2
Shell 18 0.3 0.1 23
Core 20 0.3 0.1 15
Foundation 19 0.25 0.1 400
3
Shell 20 0.3 0.1 23
Core 22 0.3 0.1 15
Foundation 19 0.25 0.1 400
Parameter Homogeneous Dam Core Dam
X-Peak Displacement (m) -1.09E-08 4.15E-08
X-Peak Velocity (m/sec) 2.4E-08 -
Max. Total Stress (kPa) 13.0789 15.1812
Mean Total Stress (p) (kPa) 8.1902 8.6145
Maximum Effective Stress (kPa) 28.5101 30.8846
Mean Effective Stress (p') (kPa) 23.6214 24.3179
Max. Shear Stress (kPa) 3.6286 5.2413
Deviatoric Stress (q) (kPa) 7.3342 9.9107
Pore-Water Pressure (kPa) -15.4312 -15.7034
Excess PWP (kPa) 0.2562 -
Maximum Strain 2.29E-06 1.30E-08
Max. Shear Strain 6.97E-06 3.65E-08
Cyclic Stress Ratio 0.1142 0.0593
13.
Effect of Earthquake on Embankment Dams 1589
Table 5. Material Properties for Earth Material Stiffness Analysis
Parameter Units Shell Material Core Material Foundation
Unit Weight (γ) kN/m3
16 18 19
Poisson’s Ratio (ν) - 0.3 0.3 0.3
Damping Ratio (ξ) - 0.1 0.1 0.1
RESULTS
Earth material density: Analyses were conducted for the dam subjected to the Horizontal
Earthquake Record αmax = 0.12g as input motion for the three densities of the core(18, 20
and 22 kN/m3
and three densities of the shell (16, 18 and 20kN/m3
). Figure 19 shows the
influence of the variation of the core density on the seismic amplification in the dam. It
can be observed that this variation does not affect the dam response. This result is
expected, because the mass of the core presents a small part of the mass of the dam. The
influence of the variation of the shell density on the seismic amplification of the dam is
illustrated in Figure 20. It can be observed that the decrease in the shell density leads to
an increase in the dynamic amplification. This result is also expected, because the
decrease in the mass of the dam leads to an increase of its fundamental frequency as
shown in Figure 21.
Figure 19. Horizontal Acceleration Time History at the Dam Crest
Figure 20. Horizontal Velocity Time History at the Dam Crest
-0.1
0
0.1
0.2
0 10 20 30 40 50 60 70
X-Velcoity(m/sec)
Time(sec)
Velocity Time History
Model 1 Model 2 Model 3
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 50 100 150 200 250 300 350 400 450 500
Acceleration(g)
Time (sec)
Acceleration Time History
Model 1 Model 2 Model 3
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1590 Innovative Dam and Levee Design and Construction
Figure 21. Spectral Response at the Dam Stiffness on Crest
Earth Material Stiffness : Analyses were also conducted for Horizontal Earthquake Record
αmax = 0.12g as input motion for three values of the Young’s modulus and elastic shear
modulus as shown in Table 6.
Table 6. Young’s Modulus and Elastic Shear Modulus Values
Core Shell Foundation
Young’s
modulus(MPa)
40 60 80 30 40 60 500 750 1000
Elastic shear
modulus(MPa)
15 23 31 11 15 23 200 300 400
Figure 22 shows the influence of the variation of the shear modulus of the core on the
seismic amplification of the dam. It can be observed that this variation leads to a moderate
increase in the dynamic amplification. This increase results from the increase of the
fundamental frequency of the dams towards the dominate frequency of the loading.
CONCLUSION
The influence of the variation of the shearing modulus of the shell on the seismic
amplification in the dam is illustrated in Figure 23. It can be observed that the increase
in the shell shearing modulus leads to a significant increase in the dynamic amplification.
This result is also expected, because the increase in the shell shearing modulus leads to an
increase in its fundamental frequency towards the frequency of the major peak of the input
motion. The influence of the variation of the shear modulus of the foundation on the
dynamic amplification is depicted in Figure 24. It can be observed that an important
variation of this parameter (100%) slightly affects the seismic response of the dam.
Elastic analyses showed that the seismic loading induces mainly lateral displacement,
which increases with the distance from the dam foundation. The maximum value is
observed near the dam crest. The mechanical properties of the core (shear stiffness and
density) moderately affect the elastic response, while those of the shell affect significantly
the response of the dam.
0
0.2
0.4
0.6
0.8
0 10 20 30 40 50 60 70 80 90 100
X-SpectralVelocity
(m/sec)
Period (sec)
Spectral Response at Dam Crest
Model 1 Model 2 Model 3
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Effect of Earthquake on Embankment Dams 1591
Figure 22. Influence of the Core Stiffness on the Seismic Response of the Dam
Figure 23. Influence of the Shell Stiffness on the Seismic Response of the Dam
Figure 24. Influence of the Foundation Stiffness on the Seismic Response of the
Dam
ACKNOWLEDGEMENT
I am thankful to SHILPA U, PG student in Computer Aided Design of Structures, Civil
Engineering Department, P.E.S. College of Engineering, Mandya, Karnataka, India who
has helped in producing this paper.
0
0.2
0.4
0.6
0 10 20 30 40 50 60 70 80 90 100
X-SpectralVelocity
(m/sec)
Period (sec)
Spectral Response at Dam Crest
G = 31MPa G = 23MPa G = 15MPa
0
0.2
0.4
0.6
0 20 40 60 80 100
X-SpectralVelocity
(m/sec)
Period (sec)
Spectral Response at Dam Crest
G = 23MPa G = 15MPa G = 11MPa
0
0.2
0.4
0.6
0 10 20 30 40 50 60 70 80 90 100
X-SpectralVelocity
(m/sec)
Period (sec)
Spectral Response at Dam Crest
G = 400MPa G = 300MPa G = 200MPa
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1592 Innovative Dam and Levee Design and Construction
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Effect of Earthquake on Embankment Dams 1593
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