Using centrifuge tests data to identify the dynamic soil properties: Application to Fontainebleau sand

Knowledge of the dynamic properties of the soil is of great importance as the dynamic shear modulus and damping ratio are necessary input data in finite element modeling programs. This paper presents a post-processing strategy to identify the shear modulus and damping ratio vs. shear strain curves using the experimental results of a dynamic centrifuge program. Application is presented for the Fontainebleau sand. The proposed methodology is fast, robust and able to capture the nonlinear hysteretic behavior of the material. Based on the results, specific parameters for the Fontainebleau sand are identified for the empirical equation of shear modulus and damping ratio proposed by Ishibashi and Zhang [1]. It is found that confining pressure has an important influence on both shear modulus evolution and damping ratio.     

Centrifuge modeling of seismic response of layered soft clay

Centrifuge modeling is a valuable tool used to study the response of geotechnical structures to infrequent or extreme events such as earthquakes. A series of centrifuge model tests was conducted at 80g using an electro-hydraulic earthquake simulator mounted on the C-CORE geotechnical centrifuge to study the dynamic response of soft soils and seismic soil–structure interaction (SSI). The acceleration records at different locations within the soil bed and at its surface along with the settlement records at the surface were used to analyze the soft soil seismic response. In addition, the records of acceleration at the surface of a foundation model partially embedded in the soil were used to investigate the seismic SSI. Centrifuge data was used to evaluate the variation of shear modulus and damping ratio with shear strain amplitude and confining pressure, and to assess their effects on site response. Site response analysis using the measured shear wave velocity, estimated modulus reduction and damping ratio as input parameters produced good agreement with the measured site response. A spectral analysis of the results showed that the stiffness of the soil deposits had a significant effect on the characteristics of the input motions and the overall behavior of the structure. The peak surface acceleration measured in the centrifuge was significantly amplified, especially for low amplitude base acceleration. The amplification of the earthquake shaking as well as the frequency of the response spectra decreased with increasing earthquake intensity. The results clearly demonstrate that the layering system has to be considered, and not just the average shear wave velocity, when evaluating the local site effects.     

Validation of a new endochronic liquefaction model for granular soil by using centrifuge test data

The application of a new liquefaction constitutive model, based on the endochronic theory applied to densification of sandy soil, to a set of centrifuge tests from the University of British Columbia, is presented in this paper. The model employed herein takes into account, in a unified formulation, contractive and dilative behaviours, and considers the soil collapse as well. First of all, the model is calibrated by means of undrained cyclic simple shear stress test data. The constitutive law of the soil is implemented in the bidimensional coupled finite element code CMLIQ (Cyclic Mobility and LIQuefaction), developed by the authors. Three centrifuge tests are analysed, the seismic loading and the geometry being the same for all of them, namely an improved slope with drain devices or denser soil at some locations. Comparisons between the data provided by the numerical model and the experimental measurements are shown, and, as a result, the accuracy of the model is explored and evaluated.     

砂-锯末混合模型土的动力特性试验研究

为研究砂-锯末混合模型土的动力参数规律特性,采用动三轴试验,研究了此类土的滞回圈特性以及其动剪切模量和阻尼比随循环加载次数的变化规律.试验结果表明:分级循环加载过程中,随着荷载级别的增加,滞回圈的面积逐渐增大,形状从柳叶形向新月形发展;模型土的动剪切模量在各循环下基本为常量而阻尼比呈上下波动;而随荷载级别的增大,动剪切...     

基于等效线性化方法的一维土层地震反应通用计算程序对比

基于等效线性化的一维土层地震反应计算是目前国内外普遍采用的方法,国外的SHAKE91、DEEPSOIL和我国的LSSRLI-1即是根据这一方法编制的通用计算程序。本文采用这3个程序进行了不同地震波、不同输入地震动幅值下不同场地类型的土层地震反应计算,并对三者的结果进行了全面的比较分析。结果表明:①SHAKE91和DEEPSOIL程序的计算结果完全相同;②当土层最大剪应变均采用时域计算时,LSSRLI-1程序的计算结果与SHAKE91和DEEPSOIL程序基本相同,但有微小差别,其原因是:在基于等效剪应变通过离散形式的剪切模量和阻尼比随等效剪应变变化的关系曲线确定等效剪切模量和阻尼比时,DEEPSOIL和SHAKE91采用的插值方法与LSSRLI-1不同;③当LSSRLI-1程序采用频域经验关系计算土层最大剪应变时,特别是在强地震动输入下得到的土层地表加速度峰值和加速度反应谱与另外两个程序的计算结果有差别,且土层最大剪应变随着输入加速度的增大出现较大的差别。因此,本文建议:当采用LSSRLI-1程序计算土层地震响应时,应使用程序中的时域解方法代替以往默认的频域经验关系方法。     

Bounding surface plasticity model for the seismic liquefaction analysis of geostructures

This paper presents the constitutive relations and the simulative potential of a new plasticity model developed mainly for the seismic liquefaction analysis of geostructures. The model incorporates the framework of critical state soil mechanics, while it relies on bounding surface plasticity with a vanished elastic region to simulate the non-linear soil response. Key constitutive ingredients of the new model are: (a) the inter-dependence of the critical state, the bounding and the dilatancy (open cone) surfaces on the basis of the state parameter ψ, (b) a (Ramberg–Osgood type) non-linear hysteretic formulation for the “elastic” strain rate, (c) a discontinuously relocatable stress projection center related to the “last” load reversal point, which is used for mapping the current stress point on model surfaces and as a reference point for introducing non-linearity in the “elastic” strain rate and finally (d) an empirical index of the directional effect of sand fabric evolution during shearing, which scales the plastic modulus. In addition, the paper outlines the calibration procedure for the model constants, and exhibits its accuracy on the basis of a large number of laboratory element tests on Nevada sand. More importantly, the paper explores the potential of the new model by presenting simulations of the VELACS centrifuge tests of Models No 1 and 12, which refer to the free-field liquefaction response of Nevada sand and the seismic response of a rigid foundation on the same sand, respectively. These simulations show that the new model can be used successfully for the analysis of widely different boundary value problems involving earthquake soil liquefaction, with the same set of model constants calibrated on the basis of laboratory element tests.     

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.     

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。     

幂函数剪切模量成层土非线性地震反应的半解析算法

运用文献[1]所建议的动态应力一应变关系及其推广的Masing加卸载准则,考虑土料在地震等产生的不规则加载条件下的非线性滞回特征,将增量法与相应场地地震线性反应解析解[2]相结合,提出了该动力非线性方程的半解析时域算法,基于改进的一维剪切梁模型,对剪切模量是其深度的某一幂函数的成层非均质土层,建立了求解土体地震反应的非线性分析技术。针对文献[2]中的土层剖面,做了计算、分析和讨论。     

Modal identification of a centrifuge soil model using subspace state space method

In this paper, modal parameters of a layered soil system comprising of a soft clay layer overlying a dense sand layer are identified from accelerometer recordings in a centrifuge test. For the first time, the subspace state space system identification (4SID) method was employed to identify the natural frequencies, damping ratios, and complex valued mode shapes while considering the non-proportional damping in a soil system. A brief review of system identification concepts needed for application of the 4SID techniques to structural modal identification is provided in the paper. The identified natural frequencies were validated against those estimated by transfer function spectra. The computed normal mode shapes were compared with closed-form solutions obtained from the one-dimensional shear wave propagation equation. The identified modal parameters were then employed to synthesize state space prediction models which were subsequently used to simulate the soil response to three successive base motions. The identified models captured acceleration time-histories and corresponding Fourier spectra reasonably well in the small and moderate shaking events. In the stronger third shaking event, the model performed well at greater soil depths, but was less accurate near the surface where nonlinearities dominated.     

1D harmonic response of layered inhomogeneous soil: Analytical investigation

The seismic response of inhomogeneous soil deposits is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The problem under investigation comprises of a continuously inhomogeneous stratum over a homogeneous layer of higher stiffness, with the excitation defined in terms of vertically propagating harmonic S waves imposed at the base of the system. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous layer. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, rate of inhomogeneity and hysteretic damping ratio. Equivalent homogeneous soil approximations are examined. The effect of vanishing shear wave propagation velocity near soil surface on shear strains and displacements is explored by asymptotic analyses.     

Simulation of soil–foundation–structure interaction of Hualien large-scale seismic test using dynamic centrifuge test

Understanding the soil–structure interaction (SSI) mechanism is crucial in the seismic design of nuclear power plant (NPP) containment systems. Although the numerical analysis method is generally used in seismic design, there is a need for experimental verification for the reliable estimation of SSI behavior. In this study a dynamic centrifuge test was performed to simulate the SSI behavior of a Hualien large-scale seismic test (LSST) during the Chi-Chi earthquake. To simulate the soil profile and dynamic soil properties of the Hualien site, a series of resonant column (RC) tests was performed to determine the model soil preparation conditions, such as the compaction density and the ratio of soil–gravel contents. The variations in the shear wave velocity (V_S) profiles of the sand, gravel, and backfill layers in the model were estimated using the RC test results. During the centrifuge test, the V_S profiles of the model were evaluated using in-flight bender element tests and compared with the in-situ V_S profile at Hualien. The containment building model was modeled using aluminum and the proper scaling laws. A series of dynamic centrifuge tests was performed with a 1/50 scale model using the base motion recorded during the Chi-Chi-earthquake. In the soil layer and foundation level, the centrifuge test results were similar to the LSST data in both the time and frequency domains, but there were differences in the structure owing to the complex structural response as well as the material damping difference between the concrete in the prototype and aluminum in the model. In addition, as the input base motion amplitude was increased to a maximum value of 0.4g (prototype scale), the responses of the soil and containment model were measured. This study shows the potential of utilizing dynamic centrifuge tests as an experimental modeling tool for site specific SSI analyses of soil–foundation–NPP containment system.     

Nonlinear response of single piles under lateral inertial and seismic loads

A macroscopic model that consists of distributed hysteretic springs and frequency dependent -pots is utilized to model the lateral soil reaction and a practical method based on one-dimensional finite element formulation is developed to compute the nonlinear response of single piles under dynamic lateral loads. The model is physically motivated, adequate for cohesive and cohesionless soils, and involves standard geotechnical parameters. Only two parameters have to be calibrated by fitting experimental data. Hysteretic and radiation damping are modeled realistically within the practical range of amplitudes and frequencies. The model is calibrated and validated against five well instrumented full-scale experiments and typical values for the range of the model-parameters are provided. Subsequently, the developed model is utilized to study the nonlinear seismic response of single piles. Finally, the developed method and the calibrated model are used to predict the inertial and seismic response of one of the piles used in the foundation of the Ohba bridge near Tokyo, Japan.     

Comparison of relative permeability-saturation-pressure parametric models for infiltration and redistribution of a light nonaqueous-phase liquid in sandy porous media

To test and evaluate the ability of commonly used constitutive relations for multifluid flow predictions, results of numerical flow and transport simulations are compared to experimental data. Three quantitative experiments were conducted in 1-m-long vertical columns. The columns were filled with either a uniform sand, a sand with a broad particle-size distribution, or with a layered system where a layer of a course-textured uniform sand was placed in an otherwise finer-textured uniform sand. After establishing variably water-saturated conditions, a pulse of a light nonaqueous-phase liquid (LNAPL) was injected uniformly at a constant rate. Water and LNAPL saturations were measured as a function of time and elevation with a dual-energy gamma-radiation system. The infiltration and redistribution of the LNAPL were simulated with nonhysteretic and hysteretic parametric relative permeability-saturation-pressure (k-S-P) models. The models were calibrated using two-phase air-water retention data and an established scaling theory. The nonhysteretic Brooks-Corey k-S-P model, which utilizes the Burdine relative permeability model, yielded predictions that closely matched the experimental data. Use of the nonhysteretic and hysteretic k-S-P models, based on the van Genuchten S-P relations and k-S relations derived from the Mualem relative permeability model, did not agree as well with the experimental data as those obtained with the Brooks-Corey k-S-P model. Explanations for the differences in performance of the three tested parametric k-S-P models are proposed.     

Centrifuge model tests on liquefaction-induced settlement and pore water migration in non-homogeneous soil deposits

This paper presents the results of dynamic centrifuge model tests conducted to investigate the liquefaction mechanism in non-homogeneous soil deposits. Four types of model tests were conducted: one model test involved a uniform soil deposit; one involved continuous layered soil deposit; and two involved discontinuous layered soil deposits. Non-homogeneity in the tests was incorporated by including periodically distributed discontinuous silty sand patches. It was found that more excess pore water pressure (EPWP) remains for a longer period of time in the discontinuous region in non-homogeneous soil deposits compared with the continuous layered and uniform soil deposits. The generation of pore water pressure ceases the supply of a new mass of water after seismic excitation; therefore the dissipation of EPWP becomes the dominant factor for settlement after seismic excitation. The rapid dissipation of EPWP through the discontinuous part in the non-homogeneous soil deposits manifests as a larger settlement in the discontinuous part, causing non-uniform settlements.     

水平成层均质土地震反应非线性分析的半解析算法

采用动态应力-应变关系及其推广的Masing加卸载准则,考虑土体在地震等不规则加载条件下的非线性滞回特征,将增量法与相应场地地震线性反应解析解相结合,提出了该动力非线性方程的半解析时域算法,以水平成层场地一维剪切梁模型为例,建立了求解土体地震反应的非线性分析技术。针对Seed-Idriss给出的砂土平均曲线,分析计算了非均匀层状密砂的线性和非线性地震反应。     

Liquefaction potential and strain dependent dynamic properties of Kasai River sand

The availability of efficient numerical techniques and high speed computation facilities for carrying out the nonlinear dynamic analysis of soil-structure interaction problems and the analysis of ground response due to earthquake loading increase the demand for proper estimation of dynamic properties of soil at small strain as well as at large strain levels. Accurate evaluation of strain dependent dynamic properties of soil such as shear modulus and damping characteristics along with the liquefaction potential are the most important criteria for the assessments of geotechnical problems involving dynamic loading. In this paper the results of resonant column tests and undrained cyclic triaxial tests are presented for Kasai River sand. A new correlation for dynamic shear damping (D_s) and maximum dynamic shear modulus (G_max) are proposed for the sand at small strain. The proposed relationships and the observed experimental data match quite well. The proposed relationships are also compared with the published relationships for other sands. The liquefaction potential of the sand is estimated at different relative densities and the damping characteristics at large strain level is also reported. An attempt has been made to correlate the G_max with the cyclic strength of the soil and also with the deviator stress (at 1% strain) from static triaxial tests.     

Shear modulus degradation model for cohesive soils

One of the key issues in cyclic behaviour of soft clays is gradual degradation of shear modulus. In most of the cyclic soil models such degrdation of shear modulus of soil with the progression of loading cycle was incorporated, addition to the standard non-linear backbone curves. Such cyclic degradation was usually represented by a parameter, degradation index, which is a function of loading cycles and cyclic shear strain amplitude. However it is well understood from the past experimental studies that the degradation index depends on various other factors as well. The present paper aims to develop a simple empirical model involving degradation index as a function of number of loading cycles, plasticity index, cyclic shear strain, overconsolidation ratio, loading frequency based on the experimental results. It is then fitted with the hyperbolic hysteretic model to estimate the modulus degradation for different cycles. Finally the damping ratio is calculated based on Masing rule with correction factors and validated through experimental results.     

Cyclic shearing and liquefaction of soil under irregular loading: an incremental model for the dynamic earthquake-induced deformation

The paper presents a mathematical model for the deformation of soil under irregular cyclic loading in the simple-shear conditions. The model includes the possible change in the effective pressure in saturated soil due to the cyclic shearing, the reciprocal influence of the effective pressure on the response of the soil to the shear loading, and the pore pressure dissipation due to the seepage of the pore fluid. The hysteresis curves for the strain–stress relationship are constructed in such a way that they produce both the required backbone curve and the required damping ratio as functions of the strain amplitude. At the same time, the approach enables the constitutive functions involved in the model to be specified in various ways depending on the soil under study. The constitutive functions can be calibrated independently of each other from the conventional cyclic shear tests. The constitutive model is incorporated in the boundary value problem for the dynamic site response analysis of level ground. A numerical solution is presented for the dynamic deformation and liquefaction of soil at the Port Island site during the 1995 Hyogoken-Nambu earthquake.