Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 723904, 12 pages

http://dx.doi.org/10.1155/2015/723904

## Effects of Upstream Water Level on Dynamic Response of Earth Dam

^{1}Department of Civil Engineering, National Taipei University of Technology, Taipei 10608, Taiwan^{2}Institute of Engineering Technology, National Taipei University of Technology, Taipei 10608, Taiwan

Received 23 October 2014; Revised 18 March 2015; Accepted 18 March 2015

Academic Editor: U. E. Vincent

Copyright © 2015 Shong-Loong Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

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 [1].

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 [2], the earthquake resulted in a 3 cm wide, 75 cm deep, and 15 m long crack across the crest of the dam at the Hutoupi Reservoir, which was about 25 km away from Jiaxian. These are just some of the examples showing how frequent seismic activities occurred in the region and the consequences of the seismic activities on the integrity of earth dam. Earth dams may crumble under seismic loads as the result of soil liquefaction. The significance of conducting thorough dam investigation has been emphasized by Zhang [3].

Finite element (FE) analysis has been widely used for the evaluation of the seismic response and safety of earth dam. Clough and Chopra [4] first introduced the application of FE analysis in the dynamic analysis of earth dam. Seed et al. [5] and Seed [6] back analyzed the response of the 1971 San Fernando earthquake on the deformation of the Lower and Upper San Fernando dams, also using FE analysis. Zienkiewicz et al. [7] included material nonlinearity and liquefaction analysis to study the behavior of the dam materials. Zienkiewicz and Mroz [8] and Pastor et al. [9] proposed the use of the generalized plasticity theory in the response analysis of earth dams under seismic activities. Khoei et al. [10] compared the performance of Pastor-Zienkiewicz and cap plasticity models through the dynamic analysis of the failure of lower San Fernando dam under the 1971 earthquake and the Mahabad and Doroodzan dams under the 1978 Tabas earthquake. Wu et al. [11] employed the computer program LIQCA to simulate the dynamic responses of an earth dam. Gui and Chiu [12] simulated the dynamic response of Renyitan earth dam using the Finn model [13] provided in the two-dimensional finite difference program FLAC. All of these studies yielded convincing results.

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.

#### 2. Governing Equations

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 [15] incorporated Darcy’s law for the representation of the fluids flow in the soil to the linear elastic solid mechanics framework and thus formulated the so-called two-phase mixing theory to deal with the pore-water pressure issues that the total stress analysis failed to handle. The equations of motion for elastic porous media saturated with a pore fluid consist of two variables’ fields: (i) pore pressure and (ii) skeleton displacements . A simplified numerical framework, known as the formulation, was formulated by assuming Darcy’s flow rule (laminar flow) and neglecting the fluid inertia [7, 16–18]. By denoting was the flow rate of the fluid, we thus have the overall balance or momentum equilibrium equation of soil-liquid mixture as [19]where and are the total mass and total stiffness matrixes, is the discrete gradient operator coupling the soil and fluid phase, is the permeability matrix, and is the compressibility matrix. Vectors and represent the effect of body forces along with prescribed boundary conditions for the solid-fluid mixture and fluid phases.

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 [19]. The model was proposed in 1985 by Pastor et al. for saturated sands subjected to dynamic excitation and liquefaction was imminent. The main advantage of the theory is that neither the yield surface nor the plastic potential surface needs to be explicitly defined; see, for example, Merodo et al. [20] and Khoei et al. [10]. Detailed description of the theory and constitutive relation for P-Z III can be found in, for example, Merodo et al. [20]; Khoei et al. [10]; Borowiec [19], Zienkiewicz and Mroz [8]; they are thus not repeated here.

#### 3. Calibration of Soil Model and FE Program

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.

##### 3.1. Centrifuge Model

A dynamic centrifuge test, performed at the University of Colorado at Boulder, was selected for this purpose [11, 14, 21]. The centrifuge model test selected for this study was one of the three tests performed in the University of Colorado to obtain data for safety assessment of a dam in Taiwan that was rocked by a strong earthquake on 21 September, 1999. The soil used in the construction of the model dam was taken within the reservoir of the dam so that a better representation of the behavior of the prototype dam could be simulated in the centrifuge. The centrifuge has a maximum capacity of 400 g-ton and equipped with an electrohydraulic shaking table. Thus, the shock wave was generated by this in-flight electrohydraulic shaker table, which is a displacement-controlled system [21].

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 [21]. Model II was analogous to Model I but with a 33 m thick low-plasticity silt (ML) foundation. Model III was built to mimic the actual section of the prototype dam, as shown in Figure 1. The materials used to construct the model dam included low-plasticity clay (CL) for the core, low-plasticity silt (ML) for the upstream and downstream slopes, and silty-sand (SM) for the 33 m thick foundation. All the models were scaled down 150 times from the actual dam; the models were then subjected to 150 g of gravitational acceleration to replicate the field stress state as in the actual dam [21]. Model III is the subject of this study.