Centrifuge modelling of flexible retaining walls subjected to dynamic loading

This paper outlines the results of an experimental program carried out on centrifuge models of cantilevered and propped retaining walls embedded in saturated sand. The main aim of the paper is to investigate the dynamic response of these structures when the foundation soil is saturated by measuring the accelerations and pore pressures in the soil, displacements and bending moment of the walls. A comparison among tests with different geometrical configurations and relative density of the soil is presented. The centrifuge models were subjected to dynamic loading in the form of sinusoidal accelerations applied at the base of the models. This paper also presents data from pressure sensors used to measure total earth pressure on the walls. Furthermore, these results are compared with previous dynamic centrifuge tests on flexible retaining walls in dry sand.     

Significance of small strain damping and dilation parameters in numerical modeling of free-field lateral spreading centrifuge tests

Lateral spreads are complex dynamic phenomena that are challenging to represent numerically. In this paper numerical models are developed and calibrated using the displacement, acceleration, and pore water pressure time histories recorded in a free-field lateral spreading centrifuge test. The calibrated numerical model then is used to predict another free-field lateral spreading centrifuge test using the same soil profile but different input acceleration time history. The computed response shows good agreement with the centrifuge test measurements. This paper demonstrates that even in a large strain problem, such as lateral spreading, small strain damping plays an important role in numerical simulation results; it also shows the need to have pressure dependent dilation parameters in the employed soil constitutive model implemented in order to simultaneously reproduce measurements of pore water pressure, acceleration and lateral displacement.     

Study of pore pressure variation during liquefaction using two constitutive models for sand

Numerical analyses of liquefiable sand are presented in this paper. Liquefaction phenomenon is an undrained response of saturated sandy soils when they are subjected to static or dynamic loads. A fully coupled dynamic computer code is developed to predict the liquefaction potential of a saturated sandy layer. Coupled dynamic field equations of extended Biot's theory with u–P formulation are used to determine the responses of pore fluid and soil skeleton. Generalized Newmark method is employed for integration in time. The soil behavior is modelled by two constitutive models; a critical state two-surface plasticity model, and a densification model. A class ‘B’ analysis of a centrifuge experiment is performed to simulate the dynamic response of level ground sites. The results of the numerical analyses demonstrate the capability of the critical sate two-surface plasticity model in producing pore pressures that are consistent with observations of the behavior of liquefiable sand in the centrifuge test.     

An investigation into the seismic behaviour of dams using dynamic centrifuge modelling

Dynamic response of dams is significantly influenced by foundation stiffness and dam-foundation interaction. This in turn, significantly effects the generation of hydrodynamic pressures on upstream face of a concrete dam due to inertia of reservoir water. This paper aims at investigating the dynamic response of dams on soil foundation using dynamic centrifuge modelling technique. From a series of centrifuge tests performed on model dams with varying stiffness and foundation conditions, significant co-relation was observed between the dynamic response of dams and the hydrodynamic pressures developed on their upstream faces. The vertical bearing pressures exerted by the concrete dam during shaking were measured using miniature earth pressure cells. These reveal the dynamic changes of earth pressures and changes in rocking behaviour of the concrete dam as the earthquake loading progresses. Pore water pressures were measured below the dam and in the free-field below the reservoir. Analysis of this data provides insights into the cyclic shear stresses and strains generated below concrete dams during earthquakes. In addition, the sliding and rocking movement of the dam and its settlement into the soil below are discussed.     

Experimental p-y loops for estimating seismic soil-pile interaction

Seismic soil-pile interaction is evaluated in this study based on back-calculated p-y loops constructed from sampled data of pile bending moments. Fundamental properties of p-y loops are implemented to derive distributed springs and dashpots, thereby quantifying soil-pile interaction in the realm of a Beam on Dynamic Winkler Foundation modeling. The procedure is validated by means of well-documented centrifuge tests of a single pile supported structure founded on a two-layer soil profile that comprises of soft clay overlying dense sand. Two shaking levels of a real earthquake motion applied at the base of the soil profile were examined and the generated seismic p-y loops were compared to cyclic p-y curves commonly used in pile design practice. The results demonstrate the strong influence of intensity of the input motion on seismic p-y loops while cyclic p-y curves established for soft clays tend to overestimate soil stiffness under strong excitation. Typical sets of recorded and computed structural response are presented, denoting the ability of the BDWF model related to p-y loops in reproducing adequately fundamental aspects of seismic soil-pile interaction.     

土-桩-框架结构非线性相互作用的精细数值模型及其验证

利用有限元软件ABAQUS,建立了土-桩-框架结构非线性相互作用（SSI）的二维精细有限元模型,分别采用记忆型粘塑性嵌套面模型和损伤塑性模型模拟土体和混凝土材料,采用梁单元和rebar单元模拟RC桩基及其内部纵筋,采用接触面对法模拟桩土接触效应,取得了良好的计算效果。将自由场、框架、土-桩-框架结构模型的分析结果和其它成熟的计算软件进行对比,验证了数值模型的有效性。分析发现：桩基外侧靠近承台处的土体的非线性反应很强烈,而桩基内部土体的非线性反应较小,很大程度上只是跟随群桩一起运动。由于桩土动力接触,桩顶的加速度反应可能超出上部结构,并且桩顶的加速度时程曲线上有非常明显的＂针＂状突变。随着地震动强度的增加,上部框架逐渐表现出单自由度体系的动力特征,加速度反应谱有从多个波峰退化为单一波峰的趋势。     

Local system identification analyses of the dynamic response of soil systems

The seismic behavior of massive geotechnical systems exhibits complex response patterns and mechanisms under severe loading conditions. Some of these mechanisms are localized in space, but nevertheless impact significantly the entire system response and ultimately its stability. A thorough monitoring and identification of the whole response of a distributed soil system commonly constitutes a significant challenge, and would generally be prohibitively expensive. This study presents a point-wise identification technique of soil-systems using the acceleration records provided by local instrument arrays. The newly developed identification algorithm consists of: (1) evaluation of strain tensor time histories using the motions recorded by a cluster of instruments (arranged in an appropriate multi-dimensional configuration), (2) estimation of the stress tensors corresponding to the evaluated strains utilizing a pre-selected class of constitutive models of soil response, (3) computation of accelerations associated with estimated stresses using the equations of motion, and (4) calibration and evaluation of an optimal model of soil response by minimizing discrepancies between recorded and computed accelerations. Computer simulations and analysis of centrifuge tests of a soil–quay wall system showed that the proposed technique provides an effective tool to identify local soil characteristics and properties.     

Dynamic characteristics of lateral load-deflection relationships of flexible piles

Most offshore platforms are supported on long and large-diameter piles with variable wall-thickness along the length, and soil properties varying with depth. The design and analyses of these piles are made by modelling the soil-pile system with a beam-on-Winkler foundation. Therefore, evaluation of appropriate soil-pile springs for use in such analyses is a matter of concern. Fundamental characteristics of dynamic lateral load-deflection relationships for piles were studied analytically considering the soil-pile-structure interaction under seismic loading conditions. The soil layer was assumed homogeneous, linearly elastic with hysteretic type material damping, and overlying a rigid base. A superstructure with multi-degrees of freedom was supported by a single vertical pile hinged at the rigid base. Parametric studies were carried out to identify the influence of the system parameters on the behaviour of the dynamic lateral load-deflection relationships of piles. The lateral load-deflection relationships vary considerably with depth and are influenced not only by the dynamic properties of soil but also by the structural properties of a pile and loading conditions. These lateral load-deflection relationships can be used to define the soil-pile springs for the seismic response analysis of a soil-pile-structure system, and the results can be extended to problems with soil profiles with layering and non-linearity.     

Seismic analysis and design of rigid bridge abutments considering rotation and sliding incorporating non-linear soil behavior

A two-dimensional (2D) finite element analytical model is developed to analyze the seismic response of rigid highway bridge abutments, retaining and founded on dry sand. A well verified finite element code named FLEX is used for this purpose. The proposed model has the following characteristics: (1) The soil (dry sand in this study) is modeled by a 2D finite element grid; (2) The bridge abutment is molded as a rigid substructure; (3) The strength and deformation of the soil are modeled using the viscous cap constitutive model. This model consists of a failure surface and hardening cap together with an associated flow rule. The cap surface is activated for the soil under the wall to represent compaction during wall rocking. In addition, viscoelastic behavior is provided for representing the hysteretic-like damping of soil during dynamic loading; (4) Interface elements are used between the wall and the soil (at the backface of the wall and under its base) to allow for sliding and for debonding/recontact behavior; (5) The finite element grid is truncated by using an absorbing boundary approximation. Using this boundary at both sides of the grid simulates the horizontal radiation of energy scattered from the wall and the excavation. Shear beams are placed adjacent to the lateral boundaries from each side which give the far-field ground motion, for comparison with those computed adjacent to the boundaries. The analytical model is verified comparing predictions to results from dynamic centrifuge tests, with satisfactory agreement. The proposed model is used to study the dynamic response of an 8.0 m high and 3.0 m wide rigid bridge abutment (proportioned using the traditional approach to design) for different sinusoidal and earthquake acceleration input motions. The results from the analysis show that outward tilting of rigid bridge abutments is the dominant mode of response during dynamic shaking and that these abutments end up with a permanent outward tilt at the end of shaking. The results from all the analyzed cases of the 8.0 m high gravity retaining wall together with those from the analysis of the tilting wall centrifuge tests are discussed and used for proposing a practical method for evaluating the seismic response of rigid abutments during earthquakes.     

Circular tunnels in sand: dynamic response and efficiency of seismic analysis methods at extreme lining flexibilities

The paper discusses the seismic response of circular tunnels in dry sand and investigates the efficiency of current seismic analysis methods at extreme lining flexibilities. Initially, a dynamic centrifuge test on a flexible circular model tunnel, embedded in dry sand, is analyzed by means of rigorous full dynamic analysis of the coupled soil–tunnel system, applying various non-linear soil and soil–tunnel interface models. The numerical results are compared to the experimental ones, aiming to better understand the recorded response and calibrate the numerical models. Then a series of numerical analyses are conducted using the validated numerical model, in order to investigate the effect of the tunnel lining rigidity on the dynamic response of the soil–tunnel system. In parallel, the accuracy of currently used simplified analysis methods is evaluated, by comparing their predictions with the results of the a priori more accurate and well validated numerical models. The comparative analyses allow us to highlight and discuss several crucial aspects of the soil-tunnel system seismic response, including (1) the post-earthquake residual values of the lining forces, which are amplified with the increase of the flexibility of the tunnel and (2) the importance of the soil-tunnel interface conditions. It is finally concluded that simplified analysis methods may provide a reasonable framework for the analysis at a preliminary stage, under certain conditions.     

基于动力BNWF法的冻土-桩相互作用模型研究

基于水平循环荷载作用下不同负温冻土环境中单桩动力特性模型试验结果,在已有分析桩-土-结构相互作用的动力BNWF模型的基础上,提出改进的冻土-桩基动力相互作用非线性反应分析模型。在该模型中,利用改进的双向无拉力多段屈服弹簧考虑桩侧冻土的水平非线性力学特性,同时兼顾桩侧与冻土间的竖向非线性摩擦效应、桩尖土的挤压与分离作用以及远场土体阻尼对桩基动力特性的影响。其中桩侧水平多段屈服弹簧参数根据冻土非线性p-y关系获得,该关系曲线以三次函数曲线段及常值函数段共同模拟,并由室内冻土压缩试验结果确定。最后基于改进的动力BNWF模型,提取动位移荷载作用下该桩顶力-位移滞回曲线及桩身不同埋深处的弯矩动响应数值分析结果,并与相应的模型试验结果对比,二者具有较好的拟合度,表明本文所提出的改进模型在分析冻土-桩动力相互作用时有较好的适用性。     

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics.Two practical pile inclinations of 5° and 10° in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered.Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles.Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases.Distinct values of horizontal impedance functions are obtained for the ’positive’ and ’negative’ cycles of harmonic loadings,leading to asymmetric force-displacement relationships for the inclined piles.Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses,and the results from the numerical models are in good agreement with the experimental data.Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.     

土-桩-钢结构相互作用体系的振动台模型试验

本项试验是研究土-结构相互作用对结构TLD减震控制影响的系列振动台模型试验的组成部分,主要目的是提供相应的对比试验数据。在这组试验中,突出的问题是TLD、上部被控结构和土层三个子系统模型基频间的协调。为了尽可能降低土层模型基频,文中采用了一种具有低剪切波速特性的土层模拟介质。最后,通过土-桩-钢结构系统的振动台模型试验,研究了土-结构相互作用对钢结构动力特性和地震反应的影响。     

瑞利阻尼对砂土场地非线性地震响应的影响分析

在地震荷载作用下,自由场地会产生土体侧向变形和地表响应放大现象。由于土体的高度非线性,计算自由场地地震响应时,不同的阻尼比及剪切模量取值是造成其计算结果与试验结果相差较大的原因之一。目前动力计算常采用瑞利阻尼方法,其系数取值会在一定程度上影响计算结果。选用两模态简化瑞利阻尼系数计算方法,分析土体阻尼比及控制频率的取值对计算结果的影响,对比离心机模型试验,利用开源有限元平台OpenSees,采用适合于土体动力分析的多屈服面本构模型(PDMY),建立剪切梁模型模拟三维自由场地,并分析瑞利阻尼参数对自由场地地震响应和侧向变形计算结果的影响。结果表明,针对相对密度为60%的Nevada干砂,阻尼比为4%、控制频率比为5时,场地响应计算结果与试验结果较为符合。综合分析显示场地非线性响应时域计算时,应特别注意选用的瑞利阻尼参数值。     

土工动力离心模型试验在边坡工程中的应用综述

总结了土工动力离心模型试验在边坡的地震响应、动力破坏机理、液化大变形和土与结构物动力相互作用等研究中的应用现状，提出了目前边坡动力模型试验中存在的问题，以及今后的发展方向。     

Liquefaction-induced deformation of earthen embankments on non-homogeneous soil deposits under sequential ground motions

Damage of embankments during earthquakes is widely attributed to the liquefaction of foundation soil. Previous studies have investigated the dynamic response of embankments by mainly considering uniform sand foundation and a single earthquake event. However, the foundation of an embankment consists of many sublayers of soil from liquefiable sand to relatively impermeable layer, and during earthquakes a mainshock may trigger numerous aftershocks within a short time which may have the potential to cause additional damage to soil structures. Accordingly, the investigation of liquefaction-induced deformation of earthen embankments on various liquefiable foundation conditions under mainshock–aftershock sequential ground motions is carried out by a series of dynamic centrifuge tests in this study. The liquefiable foundation includes uniform sand profile, continuous layered soil profile, and non-homogeneous soil profiles. Effects of various foundation conditions on embankment deformations are compared and analyzed. From the test results, it is found that the embankment resting on non-homogeneous soil deposits suffer more damage compared to the uniform sand foundation of same relative density. The test results also suggest that the sequential ground motions have a significant effect on the accumulated deformation of embankment.     

Seismic response of adjacent dense and loose saturated sand columns

Compaction or densification of loose saturated soils has been the most popular method of reducing earthquake related liquefaction potential. Such compaction of a foundation soil is only economical when limited in extent, leading to a case of an ‘island’ of improved ground (surrounded by unimproved ground). The behavior of the densified sand surrounded by liquefied loose sand during and following earthquakes is of great importance in order to design the compacted area rationally and optimize both safety and economy. This problem is studied herein by means of dynamic centrifuge model tests. The results of three heavily-instrumented dynamic centrifuge tests on saturated models of side-by-side loose and dense sand profiles are discussed. The test results suggest the following concerns as relates to ‘islands’ of densified soil: (1) there is a potential strength degradation in the densified zone as a result of pore pressure increase due to migration of pore fluid into the island from the adjacent loose liquefied ground; (2) there is a potential for lateral deformation (sliding) within the densified island as the surrounding loose soil liquefies.     

Simplified dynamic analysis to evaluate liquefaction-induced lateral deformation of earth slopes: a computational fluid dynamics approach

Lateral deformation of liquefiable soil is a cause of much damage during earthquakes, reportedly more than other forms of liquefaction-induced ground failures. Researchers have presented studies in which the liquefied soil is considered as viscous fluid. In this manner, the liquefied soil behaves as non-Newtonian fluid, whose viscosity decreases as the shear strain rate increases. The current study incorporates computational fluid dynamics to propose a simplified dynamic analysis for the liquefaction-induced lateral deformation of earth slopes. The numerical procedure involves a quasi-linear elastic model for small to moderate strains and a Bingham fluid model for large strain states during liquefaction. An iterative procedure is considered to estimate the strain-compatible shear stiffness of soil. The post-liquefaction residual strength of soil is considered as the initial Bingham viscosity. Performance of the numerical procedure is examined by using the results of centrifuge model and shaking table tests together with some field observations of lateral ground deformation. The results demonstrate that the proposed procedure predicts the time history of lateral ground deformation with a reasonable degree of precision.     

Dynamic effects in a saturated layered soil deposit: centrifuge modeling

The dynamic response of a saturated layered soil deposit was modeled on the Princeton University geotechnical centrifuge using various centrifugal acceleration levels. The layered soil deposit consists of a saturated Nevada sand layer overlaid by a silt layer of low permeability. Measured acceleration and pore-water pressure time histories are used to validate the scaling laws used in interpreting dynamic centrifugal modeling test results. Careful measurements of the settlements at the silt surface are performed using a non-contact displacement transducer, and comparisons are made with measurements obtained with a standard linear voltage displacement transducer. Finally, the experimental results are used to verify the validity of the numerical procedures encompassed in the computer code DYNAFLOW.     

Experimental p-y curves for liquefied soils from centrifuge tests

The present study aims to obtain p-y curves(Winkler spring properties for lateral pile-soil interaction) for liquefied soil from 12 comprehensive centrifuge test cases where pile groups were embedded in liquefiable soil. The p-y curve for fully liquefied soil is back-calculated from the dynamic centrifuge test data using a numerical procedure from the recorded soil response and strain records from the instrumented pile. The p-y curves were obtained for two ground conditions:(a) lateral spreading of liquefied soil, and(b) liquefied soil in level ground. These ground conditions are simulated in the model by having collapsing and non-collapsing intermittent boundaries, which are modelled as quay walls. The p-y curves back-calculated from the centrifuge tests are compared with representative reduced API p-y curves for liquefied soils(known as p-multiplier). The response of p-y curves at full liquefaction is presented and critical observations of lateral pile-soil interaction are discussed. Based on the results of these model tests, guidance for the construction of p-y curves for use in engineering practice is also provided.