Advances in Civil Engineering

Volume 2018, Article ID 3129471, 10 pages

https://doi.org/10.1155/2018/3129471

## A Modified Newmark Methodology for Permanent Deformation Analysis of Rock-Fill Dams

State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100048, China

Correspondence should be addressed to Hongjun Li; moc.rhwi@jhil

Received 8 December 2017; Accepted 13 February 2018; Published 1 April 2018

Academic Editor: Haiyun Shi

Copyright © 2018 Hongjun Li 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

Newmark sliding block approach has been extensively studied by many researchers in the past decades. Significant progress has been made to alleviate its deficiencies and overcome its simplifying assumptions, but some aspects such as the cyclic shear strength and time history vertical acceleration in the Newmark sliding displacement analysis are seldom considered strictly. In the presented research, a modified Newmark methodology for sliding deformation analysis of rock-fill dams subjected to strong earthquake is proposed. In order to make the seismic safety evaluation of dams more realistic, the influence of cyclic shear strength (earthquake-induced reduction of shear strength) and time history vertical acceleration obtained from the dynamic response analysis on the critical acceleration and accumulative sliding displacement of the flexible sliding body is considered. Detailed comparison between the proposed method and existing methods is performed via the analysis of two typical dams, that is, a virtual rock-fill dam with a height of 100 m which is assumed to be situated on rock formation and a real core rock-fill dam with a height of 150 m built on deep overburden layers. It is demonstrated that the cyclic shear strength and time history vertical acceleration within flexible sliding body, as highlighted in the proposed method, have significant effect on the seismic safety evaluation, critical acceleration, and accumulation of sliding deformation of rock-fill dams subjected to strong earthquake loading. The existing approaches tend to provide unconservative evaluation on the consequences of earthquakes on rock-fill dams.

#### 1. Introduction

Nowadays, the evaluation on the seismic performance of rock-fill dams and Earth slopes subjected to strong earthquakes is performed utilizing not only the traditional force-oriented factor of safety, but also the magnitude of the accumulative earthquake-induced sliding displacement [1–3]. A strict and simple prediction of earthquake-induced sliding displacement can directly show the potential consequences of earthquakes on rock-fill dams. In 1965, an original procedure for the prediction of earthquake-induced sliding displacement was formulated by Newmark [4]. Through this research, it is revealed that irregular inertial force induced by earthquake acceleration could exert a driving force sufficient to reduce temporarily the factor of safety below one and then result in several sliding episodes during the shaking. As pointed out by Newmark, sliding episodes in earthquakes occur when the critical acceleration is exceeded and continues until the velocity of downward movement reduces to zero. So the accumulation of permanent sliding displacement (Newmark sliding displacement), with its magnitude equal to the summation of all downward movements during the shaking, could be a useful index to evaluate the stability of slopes during earthquakes.

In the early Newmark-type method, the flexible sliding body is modeled as a rigid block, and only two parameters are used, that is, the input ground motion and the critical acceleration (*k*_{y} g, the horizontal acceleration that results in unit pseudostatic factor of safety). Due to its effectiveness and simplicity, the Newmark sliding rigid block approach has been extensively adopted and studied by many engineers and researchers in the past decades. Much great progress has been made to alleviate its limitations and overcome its simplifying assumptions; for example, the flexibility of the sliding mass is firstly considered instead of the assumption of rigid body by Makdisi and Seed [5]. However, the research on the influence of the cyclic shear strength (or dynamic pore pressure) and time history vertical acceleration on the critical acceleration and accumulation of sliding displacement is still limited. Meanwhile, the application of this approach for the seismic stability evaluation of high rock-fill dams with a height over 250 m or around 300 m is also limited. Thus, with the development of testing apparatus and technology for cyclic shear strength of rock-fill materials under cyclic loading, it is suggested that the seismic design and assessment of the effectiveness of mitigation measures for rock-fill dams subjected to earthquake be performed strictly based on the cyclic shear strength [6–9].

On the other hand, a theoretically reasonable and practically feasible method for prediction of earthquake-triggered sliding displacement is required necessarily for the seismic design and stability analysis for emerging high rock-fill dams. Therefore, special emphasis of this paper will be placed on the determination of critical acceleration of flexible sliding body based on the cyclic shear strength and time history vertical acceleration aiming at more realistic evaluation of earthquake-induced sliding displacement of high rock-fill dams.

#### 2. Cyclic Shear Strength of Rock-Fill Materials

The first aim of this study is to analyze the effect of cyclic shear strength on earthquake-induced sliding displacements using the modified Newmark method in order to improve the ability of predicting seismic stability of rock-fill dams. It must be noted that the liquefaction-induced instability has not been included in this paper. As we know, in the earthquake, instability occurs when the dynamic shear stresses required to maintain equilibrium of a soil deposit exceed the static shear strength of that deposit. Then it will recombine the structure character of soil's particle until the new equilibrium can reach. The shear strength of soil in this new equilibrium will be regarded as cyclic shear strength.

The cyclic shear strength is an important parameter in seismic design and stability analyses of rock-fill dams. For some typical rock-fill materials, such as fine sand, clay, and sand gravel, the significant cyclic loading induced by irregular strong earthquake usually leads to the obvious degeneration of the undrained shear strength [10, 11]. Some accidents of rock-fill dams occurred due to the decrease of cyclic shear strength. The postcyclic undrained shear behavior of rock-fill materials under cyclic loading has been the focus in the past decades. Nowadays, some considerable advances of testing apparatus and technology for cyclic shear strength of rock-fill materials have been obtained; for example, the cyclic triaxial undrained compress tests and simple shear tests have been used extensively to study the cyclic shear strength of rock-fill materials. From the tests, it is shown that the cyclic undrained shear strength is often related to the confining pressure , failure number of cycles , and the failure strain criterion (5% or 10%). In general, the correlation of undrained cyclic shear strength , confining pressure, and cyclic shear stress acting on the failure surface can be formulated by (1–5). In addition, it is noted that the lower value between the static shear strength and cyclic shear strength should be adopted in the seismic design and stability analysis of rock-fill dams.

Here, and are the major principle effective stress and minor principle effective stress, respectively; is the cyclic shear stress; is the initial effective confining pressure with ; is the initial static shear stress with ; is the correction coefficient of cyclic shear strength; and are the initial shear stress and normal stress acting on the failure surface, respectively; is the variation of cyclic shear strength at a given number of cycles; *n* is the number of cycles; is the effective friction angle; and *α* is the initial shear stress ratio on the failure surface.

For the sake of simplicity and convenience in application, based on the available data of rock-fill materials obtained by the dynamic triaxial compress tests and by referring to the mode of Mohr–Coulomb principle, the cyclic shear strength can be represented by a simple equation, as (6). Then, the cyclic shear strength of rock-fill materials can be easily determined from the number of cycles, confining pressure, and shear stress ratio on the failure surface.

Here, and are the equivalent cyclic cohesion and friction coefficient, respectively, which can be directly introduced into the modified Newmark sliding displacement analysis. Both of them are in proportion to the initial shear stress ratio on the failure surface, as in (7) and (8). and are the cyclic shear strength parameters as *α* equals zero, and and are proportional coefficients.

Based on the above mentioned description and formulations, the two main steps to obtain the cyclic shear strength are outlined as follows. First, the total shear strength under different confining pressures and consolidation ratios can be obtained from the cyclic triaxial undrained compress tests as shown in Table 1. Second, the parameters of cyclic shear strength can be determined by linear approximation as shown in Table 2.