Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 404712, 7 pages

http://dx.doi.org/10.1155/2015/404712

## Application of Effective Stress Model to Analysis of Liquefaction and Seismic Performance of an Earth Dam in China

School of Earth Sciences and Engineering, Hohai University, Nanjing 210098, China

Received 17 February 2015; Accepted 17 June 2015

Academic Editor: Francesco Tornabene

Copyright © 2015 Changqing Qi 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

Earthquake-induced liquefaction is one of the major causes of catastrophic earth dam failure. In order to assess the liquefaction potential and analyze the seismic performance of an earth dam in Fujian, Southeastern China, the in situ shear wave velocity test was firstly carried out. Results indicate that the gravelly filling is a type of liquefiable soil at present seismic setting. Then the effective stress model was adopted to thoroughly simulate the response of the soil to a proposed earthquake. Numerical result generally coincides with that of the empirical judgment based on in situ test. Negative excess pore pressure developed in the upper part of the saturated gravelly filling and positive excess pore pressure developed in the lower part. The excess pore pressure ratio increases with depth until it reaches a maximum value of 0.45. The displacement of the saturated gravelly soil is relatively small and tolerable. Results show that the saturated gravelly filling cannot reach a fully liquefied state. The dam is overall stable under the proposed earthquake.

#### 1. Introduction

Earth dams usually have better seismic performance during earthquakes. According to statistics, seldom earth dams have been totally out of service after earthquakes in the past few decades in China [1]. But when the dam contains or is situated on liquefiable materials, earthquake-induced liquefaction may cause considerable reduction in stiffness and strength of soil, resulting in dam failure [2]. A number of dam failures or damages have been reported due to seismically induced liquefaction. The most classic example is the lower San Fernando dam during the 1971 San Fernando earthquake. Liquefaction induced flow slide on the upstream side of the dam nearly caused the dam to be out of service [3]. The liquefaction slide of Baihe dam of Miyun Reservoir during the 1976 Tangshan earthquake was another representative example. The estimated 0.15 million m^{3} volumetric slide in the upstream part of the dam aroused great panic at that time [4]. Several dam failures in Chilean [5], Japan [6], and India [7] were also reported causing great damage.

In sight of its immense economic damage and loss of life, earth dam failures due to liquefaction have drawn great concern in the past half century. Several types of approaches have been developed to study this problem. The empirical relationships based on tested indexes are commonly used methods at present [8–10]. The empirical relationship methods can give an overall and quick judgment on liquefaction potential of gravelly soil. But for thoroughly understanding the response of coarse soil to cyclic shear loads, numerical modeling technique is better [11–13]. The seismic response of soil has a direct relation to the progressive build-up of pore pressure during an earthquake. The increasing pore pressure and decreasing effective stress control the resistance of the soil to deformation [14]. Thus, assessment on progressive degradation of soil strength is important in dynamic soil liquefaction analysis.

The effective stress method is a useful tool in modeling the progressive loss of soil strength caused by development of pore pressure. Liyanapathirana and Poulos [15] summarized four main categories of liquefaction models based on effective stress analysis method, which are (1) models based on plasticity theory; (2) stress path methods; (3) correlations between pore pressure response and plastic volume change tendency; and (4) use of experimentally observed undrained pore pressure response. The model of the third category, which is often referred to as the Finn model, is explicit and has a lesser number of parameters. The model can take into account stiffness and strength degradation due to pore pressure development and was used in this paper for dam liquefaction and seismic performance assessment.

#### 2. Methodology

The strength and stiffness of soil are primarily governed by effective stress, and so it is desirable to evaluate seismic response of soil in terms of effective stress. For saturated granular material, adopted numerical model should reflect the variation of pore pressure and thus can predict the effective stress level.

For saturated soil under undrained conditions, Martin et al. [16] suggested that the pore pressure increment is related to the change of plastic volumetric strain of the soil skeleton:where is pore pressure increment, is bulk compressibility, and is the plastic volumetric strain increment. The referred model can adequately reflect the response of pore pressure until liquefaction triggering point [17] and thus is an effective tool for assessment of soil liquefaction risk.

The plastic volumetric strain increment could be obtained by various constitutive theories. In this paper, the expression presented by Byrne [18] was adopted. The plastic volumetric strain increment was expressed as follows:where is the shear strain in the current cycle, is the accumulated volumetric strain from prior cycles, and and are constants that depend on the relative density :

In this paper, the model was incorporated into the finite difference computer program to perform a nonlinear fully coupled dynamic analysis. is based on a continuum finite difference discretization using the Lagrangian approach [19]. The equations of motion are utilized to obtain the velocities and displacements when dynamic load is excreted. The equation of motion can be expressed aswhere is material density, is time domain, is coordinate vector, is stress tensor, and is body force.

For a fully nonlinear method, any given function can be used in dynamic analysis of . The general constitutive equation is expressed aswhere is stress rate tensor, is strain rate tensor, is the parameter taking the loading history into account, and is the given functional expression.

The Mohr-Coulomb elastic-perfectly plastic constitutive relation is the commonly used constitutive models for soil. In order to adapt the model for dynamic analysis, several modifications have been achieved. In this paper, the modification defined by Puebla et al. [20] was used. The secant shear modulus and bulk modulus were considered to be stress-dependent and given as follows:where and are shear and bulk modulus numbers, and are modulus exponents, is the mean effective stress, and is atmospheric pressure.

#### 3. Statement of Dam Conditions

Dongzhen reservoir, located about 6.0 km upstream Putian City in Fujian Province, Southeastern China, has a normal storage capacity of 435 million m^{3}. The reservoir has a comprehensive function of flood control, irrigation, and power generation. The water retaining dam has an irregular geometry (Figure 1). The longitudinal profile of the dam has an asymmetric U-shape which is steep on the right flank and gentle on the left (Figure 2(a)). The dam is a core-wall earth dam with a maximum height of 58.6 m. The normal dammed water level is about 8.1 m to the dam crest (Figure 2(b)). The core wall made of lean clay and the filling is gravelly soil. A layer of rock blocks revetment was placed on the surface to protect the slope. The thickness of the blocks revetment on the upstream surface is about 2.0 m.