Modelling of seismic actions in earth retaining walls and comparison with shaker table experiment
Introduction
Retaining walls is an important part of the built infrastructure in the surrounds of highway and railway tracks, an essential feature in multi-level interchanges in both rural and urban environments, and where space for urban development is in demand in a hilly terrain. Performance of retaining wall's during past earthquakes was highly influenced by retaining wall type, foundation type, base soil conditions, and distance from earthquake epicenter [32,44,45]. During the Kobe earthquake (1994, 0.8g maximum recorded PGA) most of retaining wall failure occurred due to excessive sliding and rotation of retaining wall [26,28,52]. Evaluating the safety of retaining walls in high seismic regions requires seismically induced inertial actions on the backfill to be considered for ensuring adequate stability of the wall and its foundation in a projected intensity of ground shaking [38,47]. The enactment of new seismic design provisions in countries away from the tectonic plate margins has also raised attention to the need of assessing the ability of retaining wall to withstand the projected earthquake actions in both regions of low and high seismic activities [50].
Numerous studies employing numerical simulations for predicting the potential seismic performance of retaining wall have been reported in the literature (e.g. Refs. [21,35]. The importance of incorporating detailed hysteresis properties of the backfill materials into the numerical model has been highlighted [6,8]. In many of the cited references the numerical simulations were not paralleled by any dynamic experimentations for validation purposes. Simulations that have neglected the variability in the properties of the backfill materials affecting its response behaviour can be misleading [51]. Literature references that are related to the modulus properties of soil materials are therefore important. The seismic response behaviour of the backfill can be sensitive to soil type, conditions of confinement and loading conditions [10,11,13,19,24].
Experimental studies involving dynamic testings of scaled down retaining wall specimens complete with the backfill have also been reported in the literature [12,25,46,60,63]. Similar dynamic testings have also been carried out on different wall types [59], flexible vertical underground structures [23], earth retaining structures employing geo-synthetics [27] and reinforced soils [31]. The common emphasis of these studies was in studying the peak dynamic earth pressure that could be developed behind the retaining wall in the context of a force-based design framework. The duration of the pressure that can be influential to the displacement behaviour of the retaining wall and the resulting damage has not been modelled.
The role of backfill pressure on earthquake response of retaining wall has been studied by various researchers [33,35,38,46,62]. Veletsos and Younan [54,55] studied backfill pressure behind rigid and flexible retaining wall's and observed that the wall flexibility could affect the backfill pressure. The conventional force based seismic design of retaining wall considers a pseudo-static backfill pressure behind the retaining wall which could be estimated using the Mononobe-Okabe (MO) method [38,42]. The capability of MO method has been examined by various researchers. Mikola and Sitar [35] observed that MO method can effectively estimate seismic soil pressure on different retaining wall's, whereas some studies questioned the capability of MO method [46,49].
Based on extensive literature review it was observed that a detailed experimental investigation focused on the seismic displacement and dynamic characteristics of the retaining wall followed by a detailed geotechnical investigation for characterizing the backfill material is not addressed in the literature. Moreover, a reliable finite element (FE) modelling approach to simulate the seismic actions on retaining wall which could also address the calibration of backfill material model with simple geotechnical experiments, and accurate damping modelling of backfill is not present in the literature.
This article is aimed at investigating the time-dependent seismic response behaviour of retaining wall and the backfill through dynamic experimentations in conjunction with numerical modelling. In order to allow for results from physical experimentation and numerical simulations to be compared a simple scaled down wall specimen was considered throughout the article. The key objective is to establish credibility of the presented numerical model which can be employed in subsequent studies to undertake simulations of the prototype in order to inform designers, regulators and researchers over their seismic response behaviour of retaining wall of different forms and dimensions. Following the introduction is presentation of the experimental setup for shaker table testing of a scaled down model of a retaining wall along with observations from the dynamic testing (section 2), static testing of soil samples for determining the value of the relevant soil parameters (section 3), numerical modelling based on the derived soil parameters (section 4) and validation of the numerical model based on comparison of experimental recordings with numerical simulations (section 5).
Section snippets
Experimental setup and instrumentation
Shaking table experiments were performed on a scaled down model of a retaining wall which was base restrained and was made of aluminum consistent with experimental setup that was adopted in previous research [12,23,25]. A scale down factor (λ) of 10 has been considered in the present study. It should be noted herein that the authors tried to establish a benchmark numerical modelling approach which should be able to replicate the rigorous shaking table experiment results along with nonlinear
Sieve analyses
Samples of crushed rocks (the backfill materials) were subject to sieve tests to obtain the particle size gradation curve as per identification procedures stipulated by the standards [4,5]. The gradation curve so obtained shows D60 (i.e. 60% finer) at 6.0 mm, D30 at 4.2 mm, and D10 at 2.8 mm (Fig. 8). The coefficient of conformity (Cu) was identified to be 2.14 whereas the coefficient of curvature (Cc) was identified to be 1.05 suggesting a poorly graded soil with a narrow range of particle
Numerical modelling of the scaled down retaining wall
In order to evaluate the capability of the FE models for replicating the results of shaking table testings a 2D numerical model of a (scaled down) base restrained retaining wall and the backfill was developed in FE software Abaqus [1]. The retaining wall and backfill was modelled in plane strain conditions consistent with numerical simulation studies that had been reported in the literature [41,62].
Validation of the shaking table experiment results with FE simulations
An important stage of the shaking table experiments was to apply six excitation pulses with the purpose of validating the accuracies of the numerical model. Two half cycle sine pulse (shown in Fig. 3b), two one cycle sine pulse (shown in Fig. 3c) and two multiple pulses (shown in Fig. 3d) which were the targeted base excitations. Displacement of the shaking table base was captured during all the tests using laser sensors. The captured horizontal displacement time histories of the shaking table
Conclusions
This article presents the experimental setup and the dynamic testing of a scaled down model of a retaining wall and backfill on the shaker table. A series of pulse type excitations of varying amplitude and gradual increase in duration, and complexity, was applied. The response of the backfill was shown to be dominated by its fundamental mode of vibration. Active residual displacement of the backfill which has been shown to be sensitive to the amplitude of the applied excitations was observed.
In
CRediT authorship contribution statement
Rohit Tiwari: Conceptualization, Investigation, Numerical Investigation, Figures, Writing – review & editing. Nelson Lam: Methodology, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The support of the Commonwealth of Australia through the Cooperative Research Centre program is sincerely acknowledged. Stipendiary scholarship received from The University of Melbourne, Australia for supporting living expenses of the first author during the period of his PhD candidature is also acknowledged.
List of Notations
- Acceleration at time t
- ,
- Coefficients of Equation 1
- D,
- Damping ratio
- f
- Frequency
- t
- Time
- VSH
- Shear wave velocity of the elastic soil column
- Dimensionless ratio
- Ratio of time step
- Ratio of length
- Ratio of velocity
- Ratio of Stiffness
- Ratio of density
- Velocity in the prototype model
- Velocity in the scaled model
- Cu
- Coefficient of uniformity
- Cc
- Coefficient of curvature
- D60
- Particle size of the crushed rock (backfill) at 60% finer
- D30
- Particle size of the crushed rock (backfill) at 30% finer
- D10
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