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.     

Assessment of soil liquefaction incorporating earthquake characteristics

This paper investigates the effect of nature of the earthquake on the assessment of liquefaction potential of a soil deposit during earthquake loading. Here, the nature of the earthquake is included via the parameter V, the ‘pseudo-velocity’, that is the gross area under the acceleration record of the earthquake at any depth below the ground surface. By analysing a number of earthquake records from different parts of the world, a simple method has been outlined to assess the liquefaction potential of a soil deposit based on the pseudo-velocity. For many earthquakes occurred in the past, acceleration records are available or can be computed at the ground level or some other depth below the ground surface. Therefore, this method is a useful tool at the preliminary design stage to determine the liquefaction potential before going into a detailed analysis. Validation of the method is carried out using a database of case histories consisting of standard penetration test values, acceleration records at the ground surface and field observations of liquefaction/non-liquefaction. It can be seen that the proposed method has the ability to predict soil liquefaction potential accurately, despite its simplicity.     

A practical reliability-based method for assessing soil liquefaction potential

The current simplified methods for assessing soil liquefaction potential use a deterministic safety factor in order to judge whether liquefaction will occur or not. However, these methods are unable to determine the liquefaction probability related to a safety factor. An answer to this problem can be found by reliability analysis. This paper presents a reliability analysis method based on the popular Seed'85 liquefaction analysis method. This reliability method uses the empirical acceleration attenuation law in the Taiwan area to derive the probability density distribution function (PDF) and the statistics for the earthquake-induced cyclic shear stress ratio (CSR). The PDF and the statistics for the cyclic resistance ratio (CRR) can be deduced from some probabilistic cyclic resistance curves. These curves are produced by the regression of the liquefaction and non-liquefaction data from the Chi-Chi earthquake and others around the world, using, with minor modifications, the logistic model proposed by Liao [J. Geotech. Eng. 114 (1988) 389]. The CSR and CRR statistics are used in conjunction with the first order and second moment method, to calculate the relation between the liquefaction probability, the safety factor and the reliability index. Based on the proposed method, the liquefaction probability related to a safety factor can be easily calculated. The influence of some of the soil parameters on the liquefaction probability can be quantitatively evaluated.     

Learning of pore pressure response and dynamic soil behavior from downhole array measurements

Downhole arrays are deployed to measure motions at the ground surface and within the soil profile, with some arrays instrumented to also record the pore pressure response within soft soil profiles during excitation. The measurements from these arrays have typically been used in conjunction with parametric and nonparametric inverse analysis approaches to identify soil constitutive model parameters for use in site response analysis or to identify averaged soil behavior between locations of measurement. The self-learning simulations (SelfSim) inverse analysis framework, previously developed and applied under total stress conditions, is extended to effective stress considerations and is employed to reproduce the measured motions and pore pressures from downhole arrays while extracting the underlying soil behavior and pore pressure response of individual soil layers. SelfSim is applied to the 1987 recordings from the Imperial Valley Wildlife Liquefaction Array. The extracted soil behavior suggests a new functional form for modeling the degradation of the shear modulus with respect to excess pore pressures. The extracted pore pressure response is dependent on the number and amplitude of shear strain cycles and has a functional form similar to current strain-based pore pressure generation models.     

A numerical model for the dynamic analysis of inclined pile groups

The paper presents a numerical model for the dynamic analysis of pile groups with inclined piles in horizontally layered soil deposits. Piles are modelled with Euler–Bernoulli beams, while the soil is supposed to be constituted by independent infinite viscoelastic horizontal layers. The pile–soil–pile interaction as well as the hysteretic and geometric damping is taken into account by means of two‐dimensional elastodynamic Green's functions. Piles cap is considered by introducing a rigid constraint; the condensation of the problem permits a consistent derivation of both the dynamic impedance matrix of the soil–foundation system and the foundation input motion. These quantities are those used to perform inertial soil–structure interaction analyses in the framework of the substructure approach. Furthermore, the model allows evaluating the kinematic stress resultants in piles resulting from waves propagating in the soil deposit, taking into account the pile–soil–pile interactions. The model validation is carried out by performing accuracy analyses and comparing results in terms of dynamic impedance functions, kinematic response parameters and pile stress resultants, with those furnished by 3D refined finite element models. To this purpose, classical elastodynamic solutions are adopted to define the soil–pile interaction problem. The model results in low computational demands without significant loss of precision, compared with more rigorous approaches or refined finite element models. Copyright © 2015 John Wiley & Sons, Ltd.     

Study on wall-type gravel drains as liquefaction countermeasure for underground structures

One of the most dramatic causes of damage to engineering structures during earthquakes has been the development of soil liquefaction beneath and around the structures. In order to dissipate the excess pore water pressures near structures, gravel drains are usually employed. In this study, the use of recycled concrete crushed stones as gravel drain materials is addressed. In order to investigate the performance of wall-type gravel drains, two series of shaking table tests were performed. The test results showed that gravel drains, when appropriate grain size distribution is considered, effectively dissipate the excess pore water pressure underneath the structure, and consequently reduce the magnitude of uplift. To supplement the laboratory tests, finite element analyses were also performed. For specified structure, ground and earthquake conditions, there is a critical width of gravel drain at which no uplift of structure will occur. The results of the model tests and the finite element analyses were then employed in developing design charts for determining the critical width of gravel drain to prevent buoyant rise of structure when the surrounding soil mass liquefies.     

A method for nonlinear dynamic response analysis of semi-infinite foundation soil

This paper presents development of a special finite difference method for the nonlinear dynamic response analysis of semi-infinite foundation soil. Semi-infinite domain is mapped into the finite domain using special mapping. For the region of engineering interest, mapping is isometrical, and for far field, shrink mapping which transforms an infinite interval into a finite interval is adopted. Using linear and nonlinear constitutive models, the responses of semi-infinite foundation soil are computed using a proposed method with a small mesh model and an extensive mesh model. Surface loadings or incident earthquake waves are applied to the models in the computations. Good agreements were obtained among the theoretical and computed results of the two models and the effectiveness of the proposed method was demonstrated.     

A novel framework integrating downhole array data and site response analysis to extract dynamic soil behavior

Seismic site response analysis is commonly used to predict ground response due to local soil effects. An increasing number of downhole arrays are deployed to measure motions at the ground surface and within the soil profile and to provide a check on the accuracy of site response analysis models. Site response analysis models, however, cannot be readily calibrated to match field measurements. A novel inverse analysis framework, self-learning simulations (SelfSim), to integrate site response analysis and field measurements is introduced. This framework uses downhole array measurements to extract the underlying soil behavior and develops a neural network-based constitutive model of the soil. The resulting soil model, used in a site response analysis, provides correct ground response. The extracted cyclic soil behavior can be further enhanced using multiple earthquake events. The performance of the algorithm is successfully demonstrated using synthetically generated downhole array recordings.     

砂土液化大变形本构模型及在ABAQUS软件上的实现

基于Yang和E lgam al等人提出的砂土液化大变形本构模型,对该模型的建立过程进行了详细的推导,基于新的嵌套屈服面硬化规则,对原有模型的硬化规则的不连续性做了改进,把该本构模型扩展应用到三维液化大变形的数值分析中,实现了基于ABAQUS大型商用软件计算平台上砂土液化大变形的计算子程序的开发,基于该计算平台和开发的本构模型,对动三轴试验体系中砂土试样的液化过程进行了数值试验分析,给出了试验过程中试样的竖向动位移、整体竖向应力应变关系滞回曲线和动孔压时程曲线的数值计算结果。文中初步验证了该模型在ABAQUS上开发的子程序的可靠性和数值计算模型的可行性,模型的可靠性及其子程序的稳定性还需通过试验结果和数值计算结果的对比分析与进一步验证。     

Decoupled seismic analysis of an earth dam

The seismic stability of an earth dam is evaluated via the decoupled displacement analysis using the accelerograms obtained by ground response analysis to compute the earthquake-induced displacements. The response analysis of the dam is carried out under both 1D and 2D conditions, incorporating the non-linear soil behaviour through the equivalent linear method. Ten artificial and five real accelerograms were used as input motions and four different depths were assumed for the bedrock.1D and 2D response analyses were in a fair agreement with the exception of the top third of the dam where only a 2D modelling of the problem could ensure that the acceleration field is properly described. The acceleration amplification ratio obtained in the 2D analyses was equal to about 2 in all the cases considered, consistently with data from real case histories.The maximum permanent displacements computed by the sliding block analysis were small, being less than 10% of the service freeboard; a satisfactory performance of the dam can then be envisaged for any of the seismic scenarios considered in the analyses.     

On the applicability of neural networks for soil dynamic amplification analysis

Artificial Neural Networks (ANN) have gained a solid status as a tool for modeling complex phenomena in different areas of research and engineering practice. In this paper, their applicability to estimate the mapping of seismic acceleration from bedrock to free surface in a complex soil profile is explored. Such a use is intended to serve as a hypothesis-free alternative to the dynamic amplification analysis, which is currently based on geophysical and soil dynamics procedures. Were the neural networks to be useful to such a mapping, they could in principle be employed for several purposes, such as soil identification using instrumental data, design of early warning systems and estimation of probabilistic spectra via Monte Carlo simulation, in which the ANN act as an efficient solver surrogate. The conditions under which these ambitious purposes can be reached are discussed. Two classes of multi-layer perceptrons were tested, which are characterized by time-independent and time-dependent connections. It is shown that the first class of networks is useful for response spectrum mapping, while the second performs very well in the assessment of free-surface time series. It arises as the main conclusion that the most promising perspective of application of ANN in this respect is for the estimation of probabilistic free-surface spectra, which is an important goal for the modern trend of reliability-based aseismic design. The limitations to the other said applications are also highlighted.     

A practical numerical method for large strain liquefaction analysis of saturated soils

Accurate prediction of the liquefaction of saturated soils is based on strong coupling between the pore fluid phase and soil skeleton. A practical numerical method for large strain dynamic analysis of saturated soils is presented. The u–p formulation is used for the governing equations that describe the coupled problem in terms of soil skeleton displacement and excess pore pressure. A mixed finite element and finite difference scheme related to large strain analysis of saturated soils based on the updated Lagrangian method is given. The equilibrium equation of fluid-saturated soils is spatially discretized by the finite element method, whereas terms associated with excess pore pressure in the continuity equation are spatially discretized by the finite difference method. An effective cyclic elasto-plastic constitutive model is adopted to simulate the non-linear behavior of saturated soils under dynamic loading. Several numerical examples that include a saturated soil column and caisson-type quay wall are presented to verify the accuracy of the method and its usefulness and applicability to solutions of large strain liquefaction analysis of saturated soils in practical problems.     

液化区埋地管线的数值模拟分析

利用ANSYS有限元分析软件,建立了由场地土液化引起的地下管道上浮反应的分析模型。用土弹簧模型模拟地下管道的受力特点,考虑了管土之间相互作用的非线性特征,通过算例分析了管道在发生上浮反应时的应力应变曲线,探讨了液化区埋地管道在发生上浮位移时的受力特征,得出了一些有意义的结果。主要有:管线的应力应变以轴向为主,并且管顶和管底的受力最大,管侧相对于管顶和管底轴向应力应变很小可以忽略;最大应变位于液化区和非液化区交界处;管线中点处等效应力达到极值等等。     

结构动力反应分析的三阶显式方法

本通过对传统动力反应分析方法的总结，阐明了建立隐式和显式方法的一般思路及数学本质，提出了使用系统位移反向向量三阶导数的隐工和实用显式积分方法－3阶显式方法，分析了该显式方法的精度和稳定性，并对建立更高阶隐式和显式方法以及方法的精度和稳定性作了初步讨论。最后，通过算例对本方法、献[1]方法和经典的常平均加速度法（隐式方法、视为精确解）的精度和稳定性进行了比较分析。结果表明，本方法具有明显的优点。     

考虑非线性的建筑物地基地震液化简化分析方法

本文在建筑物地基地震液化总应力简化判别方法的基础上，考虑地基土壤的剪切非线性及饱和砂土Martin非线性孔压增长模型，提出了估计建筑物地基孔压增长的简化分析方法，这一方法可用来判别地基的初始液化问题。     

Nonlinear shear mass participation factor (rd) for cyclic shear stress ratio evaluation

Most methods for assessment of in situ seismic soil liquefaction potential require evaluation of the earthquake-induced cyclic shear stress ratio (CSR). Estimates of the in situ CSR can be developed directly, using dynamic response analyses, but it is common in ‘simplified’ analysis methods to develop estimates of the in situ CSR using empirical relationships. Unfortunately, the most widely used existing empirical relationships are based on limited response analyses and do not take full advantage of current knowledge of factors affecting this response problem. As a result, they are both biased and unnecessarily imprecise. This paper presents the results of a relatively comprehensive suite of site response studies (2153 site response analyses), performed using carefully selected suites of site conditions and input time histories, to provide an improved basis for development of estimates of in situ CSR using the r_d-approach. The resulting empirical correlations, developed using the Bayesian updating method, provide a much improved basis for simplified empirical evaluation of CSR as a function of (1) depth; (2) earthquake magnitude; (3) intensity of shaking; and (4) site stiffness.     

Successive formula method for numerical analysis of vibrating response

The algorithm of successive formulas for computing numerical vibrating response of unequal time interval for a single-degree of freedom oscillator in linear cases are more systematically introduced in the paper. Some numerical analysis characteristics of the algorithm are discussed. It is proved that the algorithm is unconditionally stable and convergent. A computer program for simultaneous calculation of the relative displacement, the relative velocity and the absolute acceleration response spectra is edited in the paper. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 236–242, 1992.     

结构-地基动力相互作用时域数值计算模型研究

完全在时域数值分析范畴内，本文对结构一地基动力相互作用系统运动方程进行了深入推导，给出了统一的基本表达形式，简化可获得目前应用的各类主要时域模型。其中，基于结构一地基交界面的位移协调条件及作用力与反作用力平衡方程，推导了动力相互作用分析子结构法模式的时域基本方程。从结构的一般动力平衡方程出发，推导了相互作用直接法模式的基本平衡方程，并基于有限元模型对两类模式间的等价性条件进行了理论验证。     

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。     

Physical model for dynamic analysis of structures with FPS isolators

This article presents a physical model for frictional pendulum isolators (FPS) that is ready to be implemented in most commercial software. The model is capable of accounting for effects such as large deformations, sticking, and uplift and impact by sensing the normal loads in the isolators through a gap element. Sticking has been incorporated into the model by extending the Park–Wen hysteretic model to the case of large deformations. The proposed model has been tested against a theoretically ‘exact’ formulation leading to essentially identical results. To facilitate its use, the physical FPS model has been cast into a typical non‐linear structural element format, i.e. with deformation as input and restoring force as output. Examples of a building and a bridge have been chosen to show the potential of the element and to provide further insight into the earthquake response of structures with FPS isolators; in particular, in aspects such as the orientation in placement of the isolator, sticking, P? Δ, and other large deformation effects. Copyright © 2003 John Wiley & Sons, Ltd.