Fully coupled finite element model for dynamics of partially saturated soils

Understanding the response of partially saturated earth structures under various static and dynamic loads is important for the design and construction of economical and safe geotechnical engineering structures. In this study, the numerical approach is used to understand the dynamics of partially saturated soils. The mathematical equations governing the dynamics of partially saturated soils are derived based on the theory of mixtures and implemented within a finite element framework. The stress–strain behavior of the soil is represented by an elasto-plastic constitutive model for unsaturated soil based on bounding surface concept and the moisture-suction behavior is modeled using van Genuchten model. Fully coupled finite element simulations are performed to study the response of partially saturated soil embankment under earthquake loading and validated with centrifuge test results available in the literature. The predicted displacement responses are in good agreement with the measured responses. The pore water pressure, pore air pressure, matric suction, the degree of saturation in various elements and the response of the embankment under different initial moisture content are also discussed.     

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.     

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated. A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils. The accuracy of the model is validated using a classic example in literature. The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils. The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model. The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy. The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model, which provides a weaker confining action to the underground structure.     

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.     

饱和砂土液化研究进展

根据国内外文献资料,从三方面总结了饱和砂土的最新进展:饱和砂土液化判别方法、砂土液化的试验研究以及液化后分析,特别是探讨了液化对上部结构的影响。最后指出了存在的问题和今后的研究方向。     

A generalized Ross method for two- and three-dimensional variably saturated flow

A numerical method has been proposed by Ross [Ross PJ. Modeling soil water and solute transport-fast, simplified numerical solutions. Agron J 2003; 95(6): 1352–1361.] to solve one-dimensional soil water movement problems. The Ross method is a noniterative numerical scheme, that can reduce computational time without sacrificing computational accuracy. The main aim of this study is to present a general form of the Ross method for two- and three-dimensional variably saturated flow. The established numerical model (R3D) is widely tested using five problems, in which the numerical solutions of R3D are compared with analytical solutions, laboratory data, and solutions from a traditional iterative numerical model. The comparison shows that R3D accommodates various hydraulic functions and boundary conditions. Results from R3D, which does not require iteration, are as accurate as results from iterative model. With the help of the primary variable switching technique, this model is unconditionally mass conservative, and computes infiltration into dry soil more efficiently. R3D is thus considered as an efficient tool for its high accuracy and efficiency for solving two- and three-dimensional variably saturated flow problems.     

用于钢框架结构二阶分析的一种实用塑性区数值模型

提出了一种基于有限元的考虑初始缺陷的塑性区模型,详细介绍了这种模型的单元类型、网格密度、材料属性、边界条件、求解方法以及残余应力和初始几何缺陷的施加,并通过和经典的Vogel框架计算结果的对比,验证了模型的可靠性。并利用这种模型分析了初始缺陷对于钢框架二阶弹塑性受力性能的影响。     

Acoustic and electromagnetic properties of soils saturated with salt water and NAPL

Electrical, seismic, and electromagnetic methods can be used for noninvasive determination of subsurface physical and chemical properties. In particular, we consider the evaluation of water salinity and the detection of surface contaminants. Most of the relevant properties are represented by electric conductivity, P-wave velocity, and dielectric permittivity. Hence, it is important to obtain relationships between these measurable physical quantities and soil composition, saturation, and frequency. Conductivity in the geoelectric frequency range is obtained with Pride's model for a porous rock. (The model considers salinity and permeability.) White's model of patchy saturation is used to calculate the P-wave velocity and attenuation. Four cases are considered: light nonaqueous phase liquid (LNAPL) pockets in water, dense nonaqueous phase liquid (DNAPL) pockets in water, LNAPL pockets in air, and DNAPL pockets in air. The size of the pockets (or pools), with respect to the signal wavelength, is modeled by the theory. The electromagnetic properties in the GPR frequency range are obtained by using the Hanai–Bruggeman equation for two solids (sand and clay grains) and two fluids (LNAPL or DNAPL in water or air). The Hanai–Bruggeman exponent (1/3 for spherical particles) is used as a fitting parameter and evaluated for a sand/clay mixture saturated with water.Pride's model predicts increasing conductivity for increasing salinity and decreasing permeability. The best-fit exponent of the Hanai–Bruggeman equation for a sand/clay mixture saturated with water is 0.61, indicating that the shape of the grains has a significant influence on the electromagnetic properties. At radar frequencies, it is possible to distinguish between a water-saturated medium and a NAPL-saturated medium, but LNAPL- and DNAPL-saturated media have very similar electromagnetic properties. The type of contaminant can be better distinguished from the acoustic properties. P-wave velocity increases with frequency, and has dissimilar behaviour for wet and dry soils.     

A robust empirical model to estimate earthquake-induced excess pore water pressure in saturated and non-saturated soils

In engineering practice, the liquefaction potential of a sandy soil is usually evaluated with a semi-empirical, stress-based approach computing a factor of safety in free field conditions, defined as the ratio between the liquefaction resistance (capacity) and the seismic demand. By so doing, an estimate of liquefaction potential is obtained, but nothing is known on the pore pressure increments (often expressed in the form of normalized pore pressure ratio r_u) generated by the seismic action when the safety factor is higher than 1. Even though r_u can be estimated using complex numerical analyses, it would be extremely useful to have a simplified procedure to estimate them consistent with the stress-based approach adopted to check the safety conditions. This paper proposes such a procedure with reference to both saturated and unsaturated soils, considering the latter as soils for which partial saturation has been artificially generated with some ground improvement technology to increase cyclic strength and thus tackle liquefaction risk. A simple relationship between the liquefaction free field safety factor FS, and r_u(S_r) is introduced, that generalizes a previous expression proposed by Chiaradonna and Flora (Geotech Lett, 2020. https://doi.org/10.1680/jgele.19.00032) for saturated soils. The new procedure has been successfully verified against some experimental data, coming from laboratory constant amplitude cyclic tests and from centrifuge tests with irregular acceleration time histories for soils having different gradings and densities.

     

Dynamic analysis of slab track on multi-layered transversely isotropic saturated soils subjected to train loads

The dynamic responses of a slab track on transversely isotropic saturated soils subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate the rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground systems are solved using the double Fourier transform, and the dynamic responses in the time domain are obtained by the inverse Fourier transform. The results show that a train load with high velocity will generate a larger response in transversely isotropic saturated soil than the lower velocity load, and special attention should be paid on the pore pressure in the vicinity of the ground surface. The anisotropic parameters of a surface soil layer will have greater influence on the displacement and excess pore water pressure than those of the subsoil layer. The traditional design method taking ground soil as homogeneous isotropic soil is unsafe for the case of RE 1 and RG 1, so a transversely isotropic foundation model is of great significance to the design for high train velocities.     

Wave propagation in marine sediments and water saturated soils

Summary A unification of the theories of Biot and Weiskopf has been made to form the suitable equations of motion for porous water saturated soils and marine sediments. It has been shown that the velocities of the body waves depend on the direction of propagation. In the vertical direction there are three, one distortional and two dilatational waves. In the horizontal direction there are two dilatational and two distortional waves. Finally, propagation of Love waves and Rayleigh waves have been discussed. Suitable potential functions have been derived to find the frequency equation for Rayleigh waves.     

关于软弱粉质粘土地震液化或震陷的判别标准

文中简要介绍了判别细粒土地震液化分析方法的发展历程,指出了工程建设中考虑细粒土地震液化问题的必要性。基于已有研究成果,阐述了可用于工程设计的软弱粉质粘土地震液化简化判别方法,并对建筑抗震设计新规范中增加的相关条款进行了说明解释。     

Direct differentiation method for response sensitivity analysis of a bounding surface plasticity soil model

Finite element (FE) response sensitivity analysis is an important component in gradient-based structural optimization, reliability analysis, system identification, and FE model updating. In this paper, the FE response sensitivity analysis methodology based on the direct differentiation method (DDM) is applied to a bounding surface plasticity material model that has been widely used to simulate nonlinear soil behavior under static and dynamic loading conditions. The DDM-based algorithm is derived and implemented in the general-purpose nonlinear finite element analysis program OpenSees. The algorithm is validated through simulation of the nonlinear cyclic response of a soil element and a liquefiable soil site at Port Island, Japan, under earthquake loading. The response sensitivity results are compared and validated with those obtained from Forward Finite Difference (FFD) analysis. Furthermore, the results are used to determine the relative importance of various soil constitutive parameters to the dynamic response of the system. The DDM-based algorithm is demonstrated to be accurate and efficient in computing the FE response sensitivities, and has great potential in the sensitivity analysis of nonlinear dynamic soil-structure systems.     

基于Finn本构模型的饱和砂土地震液化分析

天然地震作用下的饱和砂土液化问题是岩土地震工程研究的重要课题之一。目前,国内推荐使用的规范法是基于实际地震液化调查而建立的判别方法,方法本身缺乏理论基础。采用Finn液化本构关系建立了砂土液化数值分析模型,运用有限差分法的动力时程分析模块,分析了饱和砂土地基的地震液化问题。结果表明,将Finn本构模型应用于砂土液化分析,可以较好地给出地震作用过程中孔隙水压力和有效应力变化的规律。     

Steady flow patterns in saturated and unsaturated,isotropic soils

A comprehensive analysis of steady flow patterns in saturated and unsaturated, possibly heterogeneous, isotropic soils is presented. It is shown that, at any point, the divergence of the unit tangent vector field to the streamlines is equal to the directional derivative along the streamlines of the orthogonal cross-sectional area of an infinitesimal stream tube divided by that area and also equal to the mean curvature of the surface of constant total head. Expressions are derived for the distribution of the flux, the water content, the velocity, the hydraulic conductivity, the total head, and the pressure head along a stream line or an infinitesimal, stream tube. Among the results is a simpler derivation, further interpretation, and extension of earlier work on calculating the hydraulic conductivity distribution from detailed measurements of the total head distribution in combination with measurements of the hydraulic conductivity at a few locations. In the last section, the jumps of various quantities at an interface are discussed.     

Velocity and attenuation of compressional waves in nearly saturated soils

Based on the two-phase theory of Biot, we present exact and approximate expressions for the velocity and attenuation of compressional waves within nearly saturated poroelastic media. We use the approximate solutions to model the low-frequency compressional waves within nearly saturated soils. The model accounts for the effective stress, degree of saturation, and void ratio, and is capable of describing experimental results on Ottawa sand. The three-phase theory of Vardoulakis and Beskos and the two-phase theory of Biot similarly describe the velocity and attenuation of compressional waves in most soils. However, the former theory breaks down for nearly saturated gravels and dense sands.     

Efficient methods for solving water flow in variably saturated soils under prescribed flux infiltration

The non-linear solvers in numerical solutions of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties and in this paper we address the gravity term and the prescribed-flux boundary in the Picard iteration. The problem of the gravity term in the Picard iteration is iteration-to-iteration oscillation as the gravity term is treated, by analogy with the time-step advance technique, ‘explicitly’ in the iteration. The proposed method for the gravity term is an improvement of the ‘implicit’ approach of Zhang and Ewen [Water Resour. Res. 36 (2000) 2777] by extending it to heterogeneous soil and approximating the inter-nodal hydraulic conductivity in the diffusive term and the gravity term with the same scheme. The prescribed-flux boundary in traditional methods also gives rise to iteration-to-iteration oscillation because there is no feedback to the flux in the solution at the new iteration. To reduce such oscillation, a new method is proposed to provide such a feedback to the flux. Comparison with traditional Picard and Newton iteration methods for a wide range of problems show that a combination of these two proposed methods greatly improves the stability and consequently the computational efficiency, making the use of small time step and/or under-relaxation solely for convergence unnecessary.     

基于广义极值分布的巴颜喀拉块体中部地震危险性分析

本文对广义极值分布模型的构建机理进行了深入详细的阐述,给出了逻辑意义更加合理的的重现期和重现水平定义,以及相关的地震危险性评价指标。在此基础上,应用构建模型对巴颜喀拉块体中部的地震危险性做了客观的评价,得出巴颜喀拉块体中部每年的平均最大发震为M_s5.1,每20年发生M_s6.0以上强震可能性超过97%,M_s7.5左右的超强震约100年一遇,块体内部孕育地震的能量积累迅速。