Nonlinear numerical simulation of physical shaking table test, using three different soil constitutive models

Abstract

Dynamic response records of pile performance during earthquakes are limited mainly due to the challenges of recording the seismic soil–pile response. This limitation has led to an inadequacy in providing a standardized basis for the calibration and validation of the available analytical and numerical methods developed for seismic soil–pile superstructure interaction problems. To bridge this gap, a series of numerical simulations of scaled, shaking table tests of model piles in soft clay has been developed in the current study. This paper aims to accurately identify all aspects and critical parameters in the numerical simulation and propose the most suitable soil constitutive model. Three soil constitutive models are selected as advanced models for soft soil, namely, the modified Mohr–Coulomb, Drucker–Prager/cap plasticity, and Cam–clay models. Similar to the physical test case study, this numerical analysis uses dimensional analysis techniques to identify scale modelling criteria and develop a scaled soil and pile-supported structure model correctly. The 3D nonlinear numerical models are developed using the Abaqus software.

Introduction

Seismic soil-structure interaction (SSI) analysis is a sophisticated process that simultaneously involves pore water pressure generation, ground and foundation/pile deformation and a gap-/slap mechanism. In traditional seismic design, the effect of the pile on the ground motions applied to the structure is typically ignored or simplified to facilitate the analyses [[1], [2], [3]]. This practice is generally accepted as a conservative design hypothesis for spectral analysis because flexible pile foundations lengthen the natural period of the structure and increase the damping provided [2]. Moreover, SSI effects are presumed advantageous during earthquake excitation because they can increase the structural flexibility and natural period of the structure and consequently decrease the base shear forces. Simplified and non-standardised analyses are widely used to assess pile integrity during seismic loading [3].

Two of the most relevant discussions currently in SSI research are (i) increasing residual deformations and (ii) decreasing the stiffness of the pile foundation system, which in turn may affect the seismic response and structural displacement [6]. The ground motions experienced by a superstructure are influenced by the pile system, and piles may experience extreme damage and/or failure under earthquake loading. In general, there is insufficient information in the public domain regarding seismic soil–pile response cases, and several of the cases that are published only involve piles equipped to record the dynamic response. These cannot provide a reliable basis for calibrating and validating the analytical techniques which have been developed for seismic soil–pile–superstructure interaction (SSPSI) problems.

In this context, in recent years researchers have been conducting centrifuge and shaking table tests under controlled laboratory conditions. The majority of these tests have investigated seismic responses in cohesionless soils with liquefaction potential [4]. However, many piles are located on soft clays that have the potential for cyclic strength degradation during seismic loading [[7], [8], [9]]. Therefore, the need for a greater research focus into SSPSI is clear. Laboratory shaking table tests on specimens with a flexible wall offer an opportunity to extend the limited performance data of SSPSI in soft clays, under various controlled test conditions [7]. The flexible wall container allows the soil to move horizontally along the depth and therefore this test method can provide a realistic response compared with those using other types of container [8]. Moreover, these experiments can fully represent the coupled behaviour of the soil–pile–superstructure system.

In the past, the majority of numerical soil-pile/foundation models presented in the available literature have employed a Winkler spring model, which uses beam elements to represent the pile, spring elements for the soil along the pile surface that is embedded in the ground, and applied earthquake time history at the bottom of the structure or at the side boundary condition [9]. The wave propagation and output data are unrealistic however as the soil model is usually restricted to being either linear elastic or viscoelastic, owing to the limitations of finite element analysis (FEA) and computer resources. Moreover, to apply the nonlinear FEA approach in engineering practice, the resulting numerical simulations should be further verified through experiments [10]. Zhang et al. [11] described the damping characteristics of the soil–structure system using physical shake table tests. The study observed that the predominant period and the system mode shape tend to be compatible, the amplitude of transfer function rises, the interface motion state is coordinated, and the modal damping ratios are identical. The SSI system can be considered as the engineered classical damping mechanism by selecting a dynamic analytical approach in practical projects. Yang et al. [12] captured the effect of SSPSI on the dynamic behaviour of structure and soil by employing two groups of large‐scale shaking table tests of 12 storey RC frame-founded pile group embedded in soft soil for two different test conditions, considering the SSI effect. The results revealed that SSPSI amplifies the storey drift and peak displacements. However, the peak acceleration and base shear force of the structure were reduced. It was recommended that the SSI must be realistically considered in order to provide an accurate seismic design for structures on soft soils.

Chen et al. [13] investigated the effect of seismic excitation on the behaviour of granular landslides subjected to horizontal and vertical seismic motion using a small-scale shaking table model test. The results demonstrated that the soil deposit shape is affected significantly by the motion frequency characteristics, where the maximum measured displacement of the system increases with the natural frequency for both the horizontal and vertical applied motion scenarios. The slope and sidewall angles of the landslide deposits are examined under different seismic waves in order to provide preliminary guidelines for the design of protective structures. Zhang et al. [14] studied the soil-structure interaction system and seismic behaviour of double box utility tunnels with joint-connections using shaking table model tests. The input motion in this study was an earthquake with a scaled PGA of 0.2 g, 0.4 g, 0.8 g or 1.2 g. Moreover, in order to examine the influence of frequency characteristics on the seismic behaviour, a series of artificial sine waves with a PGA of 0.2 g and five different frequencies ranging between 5-30 Hz were also examined as a second group of input motions. The study revealed that the effect of soil-structure interaction on the seismic behaviour of this system is significantly greater when the PGA value of the input motion is increased. The acceleration response of the system is considerably affected by the dynamic property of the soil, such as dynamic shear strain and damping ratio. The motion frequency content was shown to have a significant effect and therefore the recommendation was that a natural frequency should be used when the utility tunnel is under construction.

One of the key challenges in modelling geotechnical materials is representing the dynamic response of the soil accurately under various external loading conditions. Soil materials can have a range of diverse and complex properties, including their elasticity, viscosity and plasticity. Nevertheless, reliable constitutive models are capable of simulating the material as a complex, heterogeneous and strongly nonlinear material [15] for various soil types and conditions, such as cohesive or non-cohesive and saturated or unsaturated soils [16]. Dynamic response records of co-seismic pile performance are limited due to the complexity of an accurate reading as well as a lack of well-documented soil–pile response case histories. These limitations lead to inadequate provision of a standardised basis for the calibration and validation of the methods developed for seismic soil–pile superstructure interaction (SSPSI) problems. To address this, a series of numerical simulations (using finite element analysis FEA) for shaking table tests of scaled model piles in soft clay were developed. All of the numerical simulation aspects and the soil constitutive criteria are successfully identified. The shaking table test programme developed by Philip Meymand was adopted as a physical test case. The study uses dimensional analysis to identify scale modelling criteria and develop a scaled soil and pile-supported structure model with a good degree of accuracy. A unique numerical methodology is designed to permit multi-directional shear deformations, minimise boundary effects and replicate the free-field site response. Soil–structure interaction (SSI) effects, including the gap/slap mechanism and the consequences of kinematic and inertial force, are clearly demonstrated. In this context, a three-dimensional (3D) finite element (FE) model to simulate a physical shaking table test with a flexible wall barrel, to simulate the dynamic response of a soil structure interaction system founded in a soft clay is developed. The paper proceeds with a description of the shaking table tests which are later employed to validate the numerical analysis [17]. This is followed by a detailed description of the finite element model, which is developed using the Abaqus software [18]. The model is then employed to further understand the behaviour.