The island of Taiwan is located between the boundaries of the Eurasia and the Philippines Plates and thus earthquakes occurred frequently. The excitation of earthquake affects the integrity of earth dams situated in the mountainous area of the island. A study was conducted to evaluate the dynamic response and safety of one of the earthquake dams. The computer program and soil model used were calibrated for their appropriate use for the subject dam against a well-instrumented centrifuge model. Numerical simulation was then conducted to examine the influence of upstream water storage level on the response of the earth dam. The numerical results identified three locations in the dam where attentions are required because these locations were found susceptible to liquefaction.
Earthquakes due to active tectonic movements are frequent in Taiwan, which is located between the boundary of Eurasian and Philippines Sea Plates. The plate boundary tectonics are generally dominated by the subduction of the Philippines Sea Plate beneath Eurasia along the Ryukyu Trench that runs from southwest Japan to Taiwan [
A magnitude 7.3 earthquake on the Richter scale struck a small town, Chi-Chi (pronounced as Ji-Ji), in central Taiwan on September 21, 1999, as a result of the violent movement of the Chelongpu fault. On October 22 of the same year, another magnitude 6.4 earthquake on the Richter scale struck the town of Jiayi in southern Taiwan, and one of the accelerometers located on the right shoulder of the Renyitan Reservoir dam, which was located four kilometers away from the Jiayi town, detected a maximum ground acceleration of 992 gal. Cracks were observed at the crest of the dam. On March 4, 2010, a magnitude 6.4 earthquake on the Richter scale, with epicenter near the town of Jiaxian, jolted southern Taiwan especially the Gaoxioang county. According to the report summarized by Water-Watch Nongovernmental Organization [
Finite element (FE) analysis has been widely used for the evaluation of the seismic response and safety of earth dam. Clough and Chopra [
When an earth dam is subjected to a seismic load pore-water pressure responded faster than the deformation at the top of dam. Thus, for safety management of earth dam, pore-water pressure response is an important indicator. This study aims at investigating the influence of the upstream water storage level on the pore-water pressure response in the body of an earth dam subjected to synthetic earthquake excitation. Experimental results from a dynamic centrifuge test were first used to calibrate the appropriate use of the chosen constitutive law for the following numerical simulation. Subsequently, effective stress analysis was conducted to evaluate the safety of the study earth dam under the synthetic seismic loading.
Total stress analysis yields only the deformation of soil from the given stress-strain relationship but provides no information on the changes in excess pore-water pressure (EPWP) when the soil is subjected to excitation. Thus, the use of the total stress analysis for liquefaction study is insufficient. Biot [
The model used to simulate the dynamics behavior of the soil is the Pastor-Zienkiewicz mark III (P-Z III) model, which has been recognized as the model most suitable for modeling materials susceptible to liquefaction [
To calibrate the appropriateness of the soil model chosen for this study, it is necessary to calibrate the result obtained from the finite element analysis with that of a well-instrumented experimental test.
A dynamic centrifuge test, performed at the University of Colorado at Boulder, was selected for this purpose [
For all the three centrifuge models tested at the University of Colorado, the slope at the upstream and downstream sides was 1 : 3 and 1 : 3.5, respectively. Model I of the earth dam was built entirely using the prototype core material, which is the low-plasticity clay (CL), and it was founded directly on the impervious and rigid base of the aluminum model container [
Cross-section of model dam and its instrumentation layout (prototype dimensions).
To provide a better representation and understanding of the responses of the dam during excitation, a number of accelerometers, pore-water pressure transducers, and linear variable differential transformers were installed in the body of the model dam as shown in Figure
The finite element program used for the following dynamic numerical analysis is called DIANA-SWANDYNE II. The Pastor-Zienkiewicz (P-Z) model was already built-in as its constitutive model. The parameters of the P-Z constitutive model were determined through a series of one-dimensional consolidation test, drained and undrained monotonic triaxial consolidated test (see, e.g., [
Parameters used for the Pastor-Zienkiewicz model.
Soil type |
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CL | 1.50 | 1.3 | 9.5 | 210 | 200 | 125 | 4 | 8 | 196.2 |
ML | 1.54 | 1.3 | 30 | 318 | 280 | 300 | 8 | 4 | 196.2 |
SM | 1.54 | 1.4 | 30 | 155 | 150 | 400 | 4 | 10 | 196.2 |
The time-history accelerations and time-history pore-water pressure obtained from both the centrifuge test and the numerical analysis are compared and discussed in this section. The time-history of accelerometer ACC1, installed at the base of the centrifuge model, was used as the input of the earthquake acceleration in the numerical analysis.
The full 35 seconds of time-history horizontal accelerations recorded in the centrifuge and the numerical analysis are compared in Figure
Dominant frequency and maximum amplitude obtained from centrifuge and FE analysis.
Parameter | ACC1 (g) | ACC2 (g) | ACC3 (g) | ACC4 (g) | ACC5 (g) | ACC6 (g) | ACC7 (g) | ACC8 (g) | |
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Maximum Amplitude, g | Centrifuge | 0.099 | 0.125 | 0.070 | 0.005 | 0.109 | 0.086 | 0.076 | 0.109 |
FE | 0.099 | 0.156 | 0.131 | 0.049 | 0.118 | 0.111 | 0.101 | 0.091 | |
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Dominant | Centrifuge | 0.7 | 0.7 | 2.5~3.3 | 1.8~2.0 | 0.7 | 0.7 | 0.7 | 0.7 |
Frequency, Hz | FE | 0.7 | 0.7 | 0.7 | 2.2~2.5 | 0.7 | 0.7 | 0.7 | 0.7 |
Comparison of time-history acceleration of Model III.
Pore-water pressure transducer PPT6 was installed at the upstream toe of the model dam to monitor whether the upstream water storage level was kept at the predetermined level during the in-flight test. Five more pore-water pressure transducers were installed in the body and the foundation of the dam, as shown in Figure
Figure
Comparison of time-history of EPWP of Model III.
The contour of the initial hydrostatic PWP and the EPWP at
Distribution of (a) hydrostatic PWP, and EPWP at (b)
The 1,535 m long Renyitan dam is an off-stream dam with a height of 20.3 m and a 9 m wide crest; the dam has a water-storage area of about 3.66 km2 with a total water-storage capacity of about 29.11 million cubic meters, of which the effective water-storage capacity is 27.31 million cubic meters [
The cross-section selected for the dynamic numerical analysis is shown in Figure
Cross-section of the Renyitan earth dam (after [
Layout of numerical PWP monitoring points.
The acceleration time history to be used in numerical analysis may be selected from the (i) past acceleration time history captured in real earthquakes; (ii) simulated synthetic ground acceleration from theoretical seismological models of seismic fault rupture; and (iii) simulated spectrum matched artificial acceleration using stochastic or random vibration theory [
A trapezoidal spectrum was selected for deriving the synthetic earthquake. The trapezoid envelope rises to its highest point and then stays at the plateau before falling back down to zero. The trapezoid envelope thus represents the components of the rise time
With the above information as input parameters and using the principle of natural random excitation, the synthetic earthquake program, SIMQKE-II [
Earthquake acceleration and acceleration spectrum used in the FE analysis.
Twelve (PPT1–PPT12) of the 28 pore-water pressure monitoring points were placed in the body of the earth dam and the rest (PPT13–PPT28) were installed in the foundation layers. PPT1, PPT6, and PPT10 were located in the outer shell of the dam at the upstream side, which is made of silty-sand (SM). PPT2, PPT7, and PPT11 were in the transition shell at the upstream side, which is made of low plasticity silt (ML). PPT3, PPT8, and PPT12 were in the low plasticity clay (CL) core of dam. PPT4 and PPT5 were in the transition shell and outer shell, respectively, of the downstream side. PPT9 was placed in the filter layer at the downstream side. PPT13 through PPT28 was in the foundation layers.
A filter layer was present on the right side of the core at the downstream side because of the need to reduce the phreatic surface running across the dam. The seepage and stress analyses provided the initial hydrostatic pore-water pressures and the initial vertical stresses of the dam for the dynamic analysis. The subsequent dynamic analysis provided the EPWP generated in the dam as a result of the synthetic earthquake excitation. Table
Initial stresses and EPWPs obtained from FE analysis.
Water pressure gauge | PPT1 | PPT2 | PPT3 | PPT4 | PPT5 | PPT6 | PPT7 | PPT8 | PPT9 |
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Initial vertical effective stress (kPa) | 13.0 | 91.7 | 242.7 | 271.8 | 82.4 | 11.1 | 130.3 | 301.9 | 263.2 |
Initial pore-water pressure (kPa) | 28.6 | 65.1 | 14.8 | −31.6 | −19.7 | 90.0 | 70.0 | 64.4 | −8.5 |
EPWP (kPa) | −7.3 | 28.7 | 215.0 | −0.9 | −0.1 | 1.8 | −10.2 | 167.9 | −0.0 |
EPWP ratio (%) | −56.2% | 31.3% | 88.6% | −0.3% | −0.1% | 16.1% | −7.8% | 55.6% | 0.0% |
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Water pressure gauge | PPT10 | PPT11 | PPT12 | PPT18 | PPT19 | PPT21 | PPT23 | PPT24 | PPT25 |
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Initial vertical effective stress (kPa) | 20.9 | 192.5 | 330.8 | 19.3 | 398.7 | 286.1 | 445.1 | 437.1 | 258.2 |
Initial pore-water pressure (kPa) | 127.6 | 79.7 | 29.5 | 27.2 | 126.8 | 125.5 | 284.7 | 254.1 | 247.8 |
EPWP (kPa) | 12.5 | −4.8 | 37.6 | 21.8 | 153.8 | 167.1 | 64.4 | 202.2 | 195.5 |
EPWP ratio (%) | 59.6% | −2.5% | 11.4% | 113.2% | 38.6% | 58.4% | 14.5% | 46.3% | 75.7% |
The dynamic numerical results are evaluated in terms of the normalized EPWP, defined as the ratio of the EPWP to the initial vertical effective stress. It is shown in Table
To examine the effect of upstream water storage level on the stability of the dam at the end of the synthetic earthquake excitation, five hypothetical upstream water storage levels at 7.6 m, 10.2 m, 12.7 m, 15.2 m, and 17.3 m were assumed to take place at the 20.3 m high Renyitan earth dam. The distribution of the EPWPs generated in the dam for water storage level of 0.37, 0.50, and 0.75 of the dam height is shown in Figure
Locations of maximum EPWP in the dam.
Water level ratio ( |
0.37 | 0.50 | 0.62 | 0.75 | 0.85 |
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Max. EPWP (kPa) | 274.3 | 289.4 | 312.7 | 340.4 | 354.9 |
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82.4 | 101.4 | 101.4 | 101.4 | 101.4 |
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34.7 | 33.7 | 33.7 | 33.7 | 33.7 |
Location in dam | Upstream shell | Core | Core | Core | Core |
Distribution of EPWP for various upstream water storage levels.
Figure
Figure
The distribution of the EPWP when the water storage level was at 75% of the dam height is shown in Figure
In general, it was seen that the area bounded by the 200 kPa EPWP in the foundation layer expanded with the increased of the upstream water storage level. The critical EPWP tended to occur near the bottom of the upstream transition shell and the core of the dam; this is because the filter layer placed on the right shoulder of the core and the bottom of the downstream transition shell was able to dissipate almost all the EPWPs generated at the end of the excitation.
The generation of excess pore-water pressure (EPWP) varied across the earth dam as the water storage level increased. The final EPWPs, normalized by their corresponding initial effective vertical stress, across the dam at the end of the earthquake excitation are presented in Figure
EPWP ratio versus normalized water storage level from FE analysis.
Figure
The profiles of the EPWP ratio registered by PPT3, PPT8, and PPT12 in the dam core are shown in Figure
Figure
The EPWP ratio profile registered by the PPTs in the upper layer of SM foundation is shown in Figure
The EPWP generated in the middle layer of the ML foundation did not seem to approach the critical value, at which liquefaction would occur (Figure
The relationship between the EPWP, normalized by the initial vertical stress, of all the 28 pore-water pressure monitoring points and the initial hydrostatic pore-water pressure is plotted in Figure
Normalized EPWP versus hydrostatic PWP.
A series of dynamic finite element analysis under a synthetic earthquake was conducted using a two-dimensional program in this study. The computer program, DIANA-SWANDYNE II, and the soil model adopted in this study were first calibrated by simulating the response of a model earth dam under an earthquake excitation in the centrifuge. The following conclusions can be made.
The amplification of the earthquake wave as it was transmitting to the top of dam and the response of the EPWPs were captured and compared between the centrifuge test result and the numerical result. Good agreement has been achieved between both sets of result, indicating the reliability of the chosen program and soil model.
The silty-sand filter layer placed on the right shoulder of the core and the bottom of the downstream transition shell was effective in dissipating almost all the EPWPs generated at the end of the excitation.
The result of the analysis revealed that the EPWP near the top-third of the upstream outer shell was becoming more and more negative (suction) until the water level reached 75% of dam height indicating that this region will be in a stable state as no liquefaction is possible during excitation.
The results from dynamic analysis with five different water storage levels suggested that the zone just above the interfaces between the foundation soil and the upstream ML transition shell and the CL core was susceptible to liquefaction if the level of the upstream water storage was close to the dam height. In addition, it was observed that EPWP built up quickly in the middle ML layer of the downstream foundation.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors are grateful to the financial support provided by Taiwan Water Corporation for conducting the above centrifuge tests.