Evaluation of the effect of earthquake frequency content on seismic behavior of cantilever retaining wall including soil–structure interaction
Highlights
► 3-D FEM of backfill–cantilever wall–soil/foundation system was proposed. ► Analytical studies were carried out to verify the finite element model. ► Effect of frequency content on seismic behavior of cantilever wall was investigated. ► Soil interaction effect on seismic behavior of cantilever wall was examined. ► It is shown that behavior of cantilever wall is highly sensitive to frequency content.
Introduction
A main goal in seismic design of structures is to make sure that the structure has acceptable performance when it is subjected to ground motions with various intensities and probability of occurrences during its service lifespan. Study of seismic behavior is also essential for the safe design of cantilever walls in the seismic zone since they are widely used as soil retaining systems supporting fill slopes adjacent to roads and residential areas [1]. Many researchers have proposed several seismic analysis and design methods for retaining walls by using different approaches. Even though the quest for reasonable analysis and design methods of retaining structures has been pursued for many years, deformations ranging from slight displacement to catastrophic failure have been observed, and seismically induced retaining wall failures have been reported during the recent major earthquakes incorporating the 1999 Ji–Ji earthquake [2], the 2004 Chuetsu earthquake [3], and the 2008 Wenchuan earthquake [4].
The available methods that have been used for seismic analysis of retaining walls can conveniently be classified into three main categories [5]: (1) those are the traditional approaches developed for verifying geotechnical and structural behavior of walls, in which the relative motions of the wall and backfill material are sufficiently large to induce a limit or failure state in the soil, (2) those in which the wall is essentially rigid and the ground motion is of sufficiently low intensity so that the backfill is presumed to respond within the linearly elastic manner, (3) those in which the soil behaves as a nonlinear, hysteretic material.
The most well-known methods of the first category are the Mononobe–Okabe (M–O) method [6], [7] and its various variants [8], [9], [10], which have found widespread acceptance in codes (e.g., ATC [11], EC-8 [12]). Representatives of the second category are the contributions of Matsuo and Ohara [13], Wood [14], [15], Arias et al. [16], Veletsos and Younan [5], [17], [18], [19], and Younan and Veletsos [20]. By definition, elastic solutions do not consider the true nonlinear hysteretic behavior of the soil, and they are not applicable to walls that can slide [21]. Therefore, in the third category, the finite element method is usually employed to analyze soil–wall systems [22]. Representatives of the third category are the contributions of Siddharthan et al. [23], Siller et al. [24], Elgamal and Alampalli [25], Al-Homoud and Whitman [26], [27]. Moreover, the accuracy of the elastic solutions has been verified with finite element analyzes carried out by Wu and Finn [28] and Psarropoulos et al. [29]. Theodorakopoulos et al. [22], [30] and Theodorakopoulos [31] examined the seismic response of a rigid wall retaining a semi-infinite and uniform soil modeled as a two-phase poroelastic medium. Lanzoni et al. [32] presented a simple method for seismic analysis of a flexible wall retaining a layer of fluid-saturated viscous and poroelastic soil. Elgamal et al. [33] investigated the dynamic characteristics of cantilever wall–backfill system through finite element analysis and forced vibration tests. Madabhushi and Zeng [34] presented the results of both finite element simulation and centrifuge test of a flexible cantilever wall. Mylonakis et al. [35] and Evangelista et al. [36] proposed stress plasticity solutions for evaluating earth pressure coefficients. Stamos and Beskos [37] studied the dynamic response of infinitely long lined tunnels by a special direct boundary element method. Hatzigeorgiou and Beskos [38] investigated the seismic response of 3-D tunnels by assuming inelastic material behavior and considering soil–structure interaction. Cakir and Livaoglu [39] presented a simplified seismic analysis procedure for analysis of backfill-rectangular tank-fluid systems.
Considering previous studies, it is seen that most of them have focused on the determination of earthquake-induced earth pressures. However, limited research has been done on the effects of soil–structure interaction and earthquake frequency content on seismic behavior of cantilever walls in three dimensional space. Due to the importance of these critical parameters, a new study is necessary to investigate the effects of them on the response. As for the codes (e.g., TEC [40], IS 1893 [41], EC-8 [42]) about retaining structures, it is obvious that the analyzes of them are generally carried out by using pseudo-static approximations although these approaches do not properly consider the interaction effects.
The aim of this paper is three-fold: (a) after a brief review of the problem, to present details of finite element model of the system under investigation, (b) to verify the validity of it under fixed-base and elastic soil assumptions through the proposed analytical model, (c) to further investigate the seismic behavior of cantilever wall considering the effects of soil–structure interaction and earthquake frequency content.
Five different ground motions including 1979 Imperial Valley, 1983 Coalinga, 1987 Whittier Narrows, 1989 Loma Prieta and 1994 Northridge are applied to consider the effect of frequency content. All records are scaled in such a way that the horizontal peak ground acceleration reaches 0.37 g. The frequency content characteristic of the ground motion is reflected in predominant period, bandwidth, central frequency, power spectrum intensity, the ratio of peak ground velocity to peak ground acceleration (PGV/PGA), response spectrum intensity, velocity spectrum intensity and acceleration spectrum intensity etc. [43]. Accordingly, consideration of the frequency content can be raised through different ways. Although PGA and PGV are very useful intensity measures for seismological studies, none can provide any information on the frequency content. PGA and PGV have to be supplemented by additional information for the proper characterization of a ground motion [44]. In this connection, the ratio of PGV to PGA is a ground motion parameter which provides information about frequency content. Because PGA and PGV are usually associated with motions of different frequency, the ratio should be related to the frequency content of the motion [45], [46]. Furthermore, Tso et al. [47] have shown that the ratio of PGA/PGV indicates the relative frequency content of the ground motion. So, a good indicator of the frequency content is the ratio of PGA which is expressed in units g to PGV expressed in units m/s. Earthquake records may be classified into three groups according to the frequency content ratio: (a) high PGA/PGV ratio when PGA/PGV>1.2, (b) intermediate PGA/PGV ratio when 1.2≥PGA/PGV≥0.8, (c) low PGA/PGV ratio when PGA/PGV<0.8. [48]. The Loma Prieta record has low frequency content, the Imperial Valley and Northridge earthquakes have intermediate frequency contents, and the Coalinga and Whittier Narrows records have high frequency contents. It can be expressed here that because of the complexity of the response of soil–wall–backfill system, normalization by using the fundamental periods of the wall may lead to misleading results. The considered system response includes the contribution of different parts like backfill and soil foundation responses. Scaling the records in such a way, or in other words, normalization by taking only wall response into account may cause to ignore other effects. Therefore, the abovementioned normalization technique has been selected in this study. However, it should be stated that the best way for normalization is to use the fundamental periods of the system, if the first mode almost controls and characterizes all system response.
Section snippets
Problem definition
The problem under investigation consists of a uniform layer of elastic material, that is free at its upper surface, bonded to a non-deformable rigid base and retained along one of its vertical boundaries by a uniform cantilever wall that is considered to be fixed at the base and to be free at the top. The heights of the wall and soil stratum are considered to be the same, and they are denoted by H. The properties of the soil stratum are defined by its mass density, shear modulus of elasticity,
Finite element modeling
The main advantage of the FEM in analyzing a soil–structure interaction problem is that it can accommodate easily for heterogeneity in the soil or structure medium and for nonlinearity in the materials, as well as in the geometry. Most of the finite element numerical codes perform analyzes in time domain, allowing the introduction of specialized constitutive laws describing the linear and nonlinear behavior of the soil under strong ground motions [49]. In this connection, the proposed numerical
Analytical modeling
The condensation of the multi degree of freedom system to a system with fewer degrees of freedom is a common application in structural dynamics. This technique provides some appealing advantages such as the physical insight, conceptual clarity, the relative easiness of construction and the low computational effort, and may lead to sufficient engineering accuracy. Accordingly, the simple physical models can be used with a small number of degrees of freedom. In addition, these models can be
Numerical application and model verification
In this section, to verify the validity and applicability of the present finite element model, the modal analyzes of a cantilever wall–backfill system are performed. In the numerical example, a 6 m-high cantilever retaining wall with a constant thickness of 0.4 m is considered. As stated before, the critical minimum distance from the face of the wall is taken as 10H=60 m. The Young’s modulus, Poisson’s ratio and unit weight of the concrete were considered as 28,000 MPa, 0.2 and 25 kN/m3,
Seismic analysis
After verifying the validity of the finite element simulation through the analytical model, the versatility of the finite element model allows the treatment of some more realistic situations that are not amenable to analytical solution. Therefore, the modeling was extended to account for the behavior of wall–soil interface, elasto-plastic behavior of soil and soil/foundation interaction effects.
Reasonable modeling of the wall–backfill interaction requires using special interface elements
Results and discussions
Results, obtained by applying the proposed methodology, are presented in terms of the lateral displacements and stresses in two parts. In the first part, a detailed discussion on the effects of soil–structure interaction on seismic behavior of cantilever wall is given. In the second part, the effects of earthquake frequency content on dynamic behavior of cantilever wall subjected to the combined effects of backfill and soil/foundation interactions are discussed. Table 4, Table 5, Table 6, Table
Conclusions
A seismic analysis procedure that can be used for the determination of dynamic behavior of cantilever retaining walls under horizontal ground excitation in three-dimensional space is presented in this study. The study explores different factors such as soil–structure interaction and earthquake frequency content which may have considerable effect on the seismic response of cantilever walls. The soil is modeled as an elasto-plastic medium obeying the Drucker–Prager yield criterion, and
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