A middle surface concept (MSC) model for saturated sands in general stress space

An elastoplastic constitutive model is proposed for saturated sands in general stress space using the middle surface concept (MSC). In MSC, different features of stress–strain response of a material are divided into different pseudo‐yield surfaces. The true‐yield surface representing the true response is established by using various links between the yield surfaces. In this MSC sand model, several well‐known features of sand response are represented by three different pseudo‐yield surfaces, which are developed in a simple and straightforward way. These features include the critical state behaviour, the effects of state parameter, unloading and reloading plastic deformation, the influence of fabric anisotropy, and phase transformation line related behaviour. Finally, the model predictions and test results are compared for two different types of sands under a variety of loading conditions and good comparisons are obtained. The application of MSC to saturated sand modelling shows the versatility of MSC as a general concept for modelling stress–strain response of materials. Copyright © 2006 John Wiley & Sons, Ltd.     

Liquefaction and cyclic mobility model for saturated granular media

A new constitutive law for the behaviour of undrained sand subjected to dynamic loading is presented. The proposed model works for small and large strain ranges and incorporates contractive and dilative properties of the sand into the unified numerical scheme. These features allow to correctly predict liquefaction and cyclic mobility phenomena for different initial relative densities of the soil. The model has been calibrated as an element test, by using cyclic simple shear data reported in the literature. For the contractive sand behaviour a well‐known endochronic densification model has been used, whereas a plastic model with a new non‐associative flow rule is applied when the sand tends to dilate. Both dilatancy and flow rule are based on a new state parameter, associated to the stiffness degradation of the material as the shaking goes on. Also, the function that represents the rearrangement memory of the soil takes a zero value when the material dilates, in order to easily model the change in the internal structure. Proceeding along this kind of approach, liquefaction and cyclic mobility are modelled with the same constitutive law, within the framework of a bi‐dimensional FEM coupled algorithm developed in the paper. For calibration purposes, the behaviour of the soil in a cyclic simple shear test has been simulated, in order to estimate the influence of permeability, frequency of loading, and homogeneity of the shear stress field on the laboratory data. Copyright © 2006 John Wiley & Sons, Ltd.     

适用于砂土循环加载分析的边界面塑性模型

基于临界状态土力学框架,建立了一个适用于砂土排水循环加载的边界面塑性模型。采用了考虑虚拟峰值应力比的偏应变硬化准则,初始加载阶段应力点位于边界面上,反向加载阶段以历史最大屈服面作为边界面,同时实现了对密砂软化现象的模拟和对历史所受最大应力的记忆。边界面采用修正的椭圆形,引入考虑密度与应力水平的状态相关剪胀函数,采用非相关联流动法则和以应力反向点作为映射中心的径向映射准则。模型仅有10个参数,通过常规三轴试验即可确定,并且使用一套参数可以模拟不同围压、密度的单调和循环加载情况。分别对饱和砂土的单调、循环排水三轴试验进行模拟,结果表明,该模型能够合理地反映饱和砂土排水条件下的应力-应变特性。     

A unified plasticity model for large post-liquefaction shear deformation of sand

Based on previous experimental findings and theoretical developments, this paper presents the formulation and numerical algorithms of a novel constitutive model for sand with special considerations for cyclic behaviour and accumulation of large post-liquefaction shear deformation. Appropriate formulation for three volumetric strain components enables the model to accurately predict loading and load reversal behaviour of sand, fully capturing the features of cyclic mobility. Compliance with the volumetric compatibility condition, along with reversible and irreversible dilatancy, allows for physically based simulation of the generation and accumulation of shear strain at zero effective stress after initial liquefaction. A state parameter was incorporated for compatibility with critical state soil mechanics, enabling the unified simulation of sand at various densities and confining pressures with a same set of parameters. The determination methods for the 14 model parameters are outlined in the paper. The model was implemented into the open source finite-element framework OpenSees using a cutting-plane stress integration scheme with substepping. The potentials of the model and its numerical implementation were explored via simulations of classical drained and undrained triaxial experiments, undrained cyclic torsional experiments, and a dynamic centrifuge experiment on a single pile in liquefiable soil. The results showed the model’s great capabilities in simulating small to large deformation in the pre- to post-liquefaction regime of sand.     

Stress‐driven integration strategies and m‐AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces

The paper proposes a stress‐driven integration strategy for Perzyna‐type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity‐like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m‐AGC tangent operator. This operator is combined with the stress‐prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra‐step iterations (in physical viscoplasticity), or to a variable time‐step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero‐thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed. Copyright © 2016 John Wiley & Sons, Ltd.     

Modelling of sand behaviour under earthquake excitation

In this paper, liquefaction potential of loose sand deposit subjected to an earthquake loading is evaluated. The analysis is performed by using a finite element technique incorporating the equations of dynamics of saturated porous elastoplastic media. The soil response is modelled by an anisotropic hardening rule, similar to that as proposed by Poorooshasb and Pietruszczak.¹ The concept is based on the theory of bounding surface plasticity incorporating a non-associated flow rule and the idea of reflected plastic potential. The present paper provides a modified formulation to that discussed in Reference 1. Modifications are aimed at simplifying the concept for numerical implementations.     

考虑砂土密实度影响的单桩竖向循环加载模型试验

采用自主设计的长期循环加载装置,进行了不同密实度砂土中单桩竖向循环加载模型试验,考虑砂土密实度的影响,建立了循环累积位移预测模型,并对其适用范围进行了探讨。试验结果回归分析表明,第1次循环累积位移与循环荷载比呈指数函数模型变化,模型参数与砂土密实度有关。在一定循环累积位移速率范围内,桩顶循环累积位移与循环次数幂函数模型的预测值与实测值吻合较好,但循环累积位移速率受砂土密实度的影响,因此,应对桩顶循环累积位移的发展规律进行分区,以考虑砂土密实度的影响。     

A Modified Mohr-Coulomb Model to Simulate the Behavior of Pipelines in Unsaturated Soils

At the present time, it is very common in practice to utilize Mohr-Coulomb model to simulate the soil behaviour in the application of soil-pipeline interaction problems. However, the traditional Mohr-Coulomb model is unable to predict the realistic loading that can apply on buried pipes during large ground deformation. Especially, the linear elastic-perfectly plastic Mohr-Coulomb model is not capable of simulating the unsaturated soil loading which can result larger than anticipated loading due to suction induced additional normal force between the soil particles. A user defined unsaturated modified Mohr-Coulomb model is developed within a generalized effective stress framework considering suction hardening effects to capture the realistic loading induced by unsaturated soil medium. Firstly, the model has been developed considering microscopic and macroscopic suction hardening mechanisms, and was implemented into a commercial finite element program associated with user subroutine written in FORTAN. Then the model was validated through a series of unsaturated triaxial compression tests conducted on the basis of different sand types having various initial conditions. Finally, the model has been applied to simulate the behaviour of pipelines subjected to lateral soil loading in unsaturated soils. The results revealed that the modified Mohr-Coulomb model has reasonable predictions when compared to the load-displacement response of pipes obtained from two large scale testing programs. The developed model can be used to predict the increased strength and stiffness associated with soil suction that increases lateral loads on pipelines, and thus has widespread relevance for simulating the pipeline response in unsaturated soils under externally imposed ground movement.     

Numerical investigation of the stabilisation behaviour of shallow foundations under alternate loading

This article presents a stability criterion for shallow foundations on sand for various loading conditions. By means of laboratory model tests, a behaviour called self-healing is shown. Numerical simulations of these tests prove the suitability of the employed numerical model. Based on this validation, a numerical parametric study is done to analyse the influence of loading condition and initial state of the soil on the self-healing. Main focus is on the rotational behaviour and settlement of the foundation. The observations and numerical results are discussed and an explanation is presented based on results of cyclic laboratory tests.     

Analysis of coupled axial and lateral deformation of roots in soil

Plant roots can help to stabilise slopes. Existing analytical models to predict their mechanical contribution are however limited: they typically focus on the ultimate limit state, employ various empirical factors, and ignore much of the underlying root-soil interaction. A new model was developed based on large deflection Euler-Bernoulli elastic beam theory that can be used to study the mobilisation of root strength under various loading conditions (direct shear and pull-out). Both lateral and axial loading of the root by the soil were incorporated, based on existing methodologies for foundation piles (p-y and t-z curves). The model is able to take the key parameters into account (root biomechanical properties, root architectural properties, and soil properties) while remaining quick to solve using a numerical boundary value problem solver. The model was compared with experimental direct shear test data using various root analogues (rubber, plastic, and wood) in dry sand with various densities and effective stress levels and was able to accurately predict the measured shear force-displacement behaviour. Comparison with experimentally measured pull-out force-displacement curves using rubber and wooden root analogues with various architectures in dry and partially saturated sands was also satisfactory. In the future, this model can aid with addressing long-standing problems in the root-reinforcement community: quantifying the effect of (sequential) mobilisation of root strength in direct shear, the effect of the angle at which the root crosses a shear plane, the effect of root topology on root-reinforcement or the effect of root bending, and root shear shear forces on root-reinforcement.     

Modelling and simulation of load transfer in reinforced soils: Part 1

Results of both triaxial and direct shear tests on reinforced soil samples performed by different investigators have shown that soil dilatancy and extensibility of the reinforcements have a significant effect on the generated tension forces in the inclusions. An appropriate soil--reinforcement load transfer model, integrating the effect of soil dilatancy and reinforcement extensibility is therefore needed to adequately predict forces in the inclusions under expected working loads. This paper present a load transfer model assuming an elastoplastic strain hardening behaviour for the soil and an elastic--perfectly plastic behaviour for the reinforcement. This model is used to analyse the response of the reinforced soil material under triaxial compression loading. A companion paper present the application of this model for numerical simulations of direct shear tests on sand samples reinforced with different types of tension resisting reinforcements. The model allows an evaluation of the effect of various parameters such as mechanical characteristics and dilatancy properties of the soil, extensibility of the reinforcements, and their inclination with respect to the failure surface, on the development of resisting tensile stresses in the reinforcements. A parametric study is conducted to evaluate the effect of these parameters on the behaviour of the reinforced soil material. An attempt is also made to verify the proposed model by comparing numerical predictions with available experimental results of both triaxial and direct shear tests on reinforced soil samples. This model can be used for analysis and design of reinforced soil walls with different types of tension resisting inclusions to predict tension forces under expected working loads.     

利用旁压试验的砂土初始状态反演分析

讨论了砂土旁压试验的反分析问题。建议利用旁压试验实测数据反演确定土体的初始状态而非材料参数,材料参数可以通过实验室常规试验确定。主要利用了新型的亚塑性本构模型参数不受土体状态影响的特点。主要内容包括：建立有限元数值模型,利用文献中的试验数据确定了特定砂土的材料参数;通过模拟砂土的实验室旁压试验,验证了数值模型;通过改变土体初始应力状态和相对密实度进行数值计算,并利用数值计算成果,建立了可适用于砂土初始状态反演分析的实测旁压荷载和土体中应力与相对密度的数学关系。     

Numerical simulation of the seismic response of tunnels in sand with an elastoplastic model

The number of larger tunnels in seismic regions has grown significantly over the last decades. The behaviour of tunnels under seismic actions may be assessed using simplified or more complex approaches. Plane–strain centrifuge tests with dynamic loading on a model tunnel are used as experimental benchmark on the seismic behaviour of tunnels, with the ultimate aim of calibrating numerical and analytical design methods. Two models with dry uniform fine sand were prepared at two different densities, in which an aluminium-alloy tube was installed. This paper describes the numerical simulation of these tests with an elastoplastic model. The tunnel response recorded in the centrifuge tests is compared with the numerical prediction, showing the evolution of accelerations and internal forces along the tunnel lining during the model earthquakes. In general, the numerical simulation diverges from the recorded at the centrifuge tests. The numerical simulation largely amplifies the motion at the fundamental frequency of the soil deposit, while this effect is not significant in the centrifuge tests. It is shown that the peak increments in lining forces during dynamic loading measured in the centrifuge test disagree with the values from the numerical simulation and from the Wang’s elastic solution. The divergence observed between simulation and centrifuge tests may result mainly from the real initial stiffness of the sand in the centrifuge tests which are lower than those measured in laboratory tests and to the insufficient knowledge of all relevant stress paths to be imposed to soil for the calibration of model parameters.     

某砂土液化大变形本构模型参数的敏感性分析

基于Yang和Ahmed[1－5]等提出的砂土液化大变形本构模型,对该模型的硬化规则和弹塑性模量确定方法作了改进,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开发。基于该计算平台,对该模型的主要参数在描述砂土液化动孔隙水压力增长和动应力-应变关系曲线等方面的可靠性和敏感性进行了研究。给出了模型全过程参数、剪胀过程参数、剪缩与剪胀状态转换点流动变形量控制参数对试样的应力-应变关系曲线的影响程度及其规律,并对模型的主要参数的敏感性进行了分析,所得结论为通过动三轴试验获得相关模型参数提供了有效的指导和帮助,同时也发展了砂土液化大变形新的数值计算方法。     

穿越不同密实度饱和砂土地层的盾构隧道地震响应三维数值分析

地震液化对隧道结构有重大威胁,且位于不同抗液化能力地层交界处的盾构隧道段更易发生严重的地震破坏。采用三维数值方法研究穿越不同密实度状态饱和砂土地层的盾构隧道的地震响应规律。饱和砂土用一种描述不同密实度砂土液化行为的边界面模型进行模拟,首先通过隧道液化上浮的振动台试验结果验证该本构模型的合理性。其次,应用多自由度连接弹簧表征管片环间相互作用,采用文献中的拼装管片的逐级加载试验结果验证该方法的可行性。最后,建立穿越两种不同密实度饱和砂土地层的盾构隧道三维数值模型,研究相对密实度、输入加速度峰值和交界面倾角对砂土地层-盾构隧道系统动力响应的影响。结果表明,可液化地层中隧道结构位移模式是水平地震激励下产生的水平位移与由于液化上浮效应产生的竖向位移的耦合作用,加之隧道在不同土层中变形存在差异,从而导致隧道呈现扭转的变形形态。在靠近交界面处,隧道整体上浮量急剧变化且该处结构上浮量随着交界面倾角增大而增大,同时管片结构弯矩出现突变,接头螺栓的环间剪切和拉伸位移也显著增加。分析结果进一步印证地震作用下盾构隧道在不同性质饱和砂土地层交界面处更易破坏,在设计阶段应予以重点关注。     

Incrementalization of a single hardening constitutive model for frictional materials

The governing equations for an elasto‐plastic constitutive model for frictional materials such as soil, rock, and concrete are presented, and the incremental form is indicated in preparation for implementation of the model in a user‐defined module for finite element calculations. This isotropic, work‐hardening and ‐softening model employs a single yield surface, it incorporates non‐associated plastic flow, and its capability of capturing the behaviour of different types of frictional materials under various three‐dimensional conditions has been demonstrated by comparison with measured behaviour, as presented in the literature. The incrementalization procedure is indicated and the resulting equations for the single hardening model are presented together with parameters for a dense sand. Following the implementation of the model, these parameters are used for evaluation of different integration schemes as presented in a companion paper by Jakobsen and Lade (Int. J. Numer. Anal. Meth. Geomech. 2002; 26 :661). Copyright © 2002 John Wiley & Sons, Ltd.     

循环荷载下砂土的剪切硬化边界面本构模型

基于临界状态土力学框架,建立了一个适用于往返循环荷载作用的砂土边界面本构模型。采用无纯弹性域假设,认为受到反向荷载的瞬时土体就产生塑性变形,砂土的弹性区域退化为一个点。屈服面为倒子弹头型,由于砂土孔隙比与压力之间不存在惟一对应的关系,使得屈服面大小无法与体积应变直接耦合,故采用塑性偏应变而不是剑桥模型那种塑性体应变作为硬化参数。流动法则采用加入状态参数的修正的Rowe应力剪胀关系,体现了依赖状态的剪胀思想。屈服面大小的比值 反映了塑性模量的演化,并推导了 的表达式。只用1套参数,该模型就能合理地模拟砂土在不同密度和固结压力下循环荷载的应力-应变关系曲线。     

Employing a variable permeability model in numerical simulation of saturated sand behavior under earthquake loading

Despite advances in the numerical analysis of saturated sand behavior under earthquake loading, accurate prediction of liquefaction-related phenomena by numerical simulation remains a challenge. Variation of the coefficient of permeability is a key issue which has not obtained due attention in most previous modeling. In this study, a revised form of a recently proposed variable permeability function was implemented in a fully coupled dynamic model adopting modern two-surface plasticity constitutive law to evaluate the effects of permeability variations on the results of numerical modeling. The variable permeability model is comprised of a simple function relating the permeability coefficient of soil mass to the excess pore water ratio. In this study, the constants of the variable permeability function were attained based mainly on theoretical evidence and experimental observation. Well-documented centrifuge experiments were examined to evaluate how well the proposed model captures the main features of soil response to earthquake loading. The results indicate that the proposed function greatly enhanced the capability of numerical modeling to predict the behavior of saturated sand under cyclic loading. Particularly, the variable permeability model with proposed constants significantly improved the amount of liquefaction-induced settlement predicted by numerical modeling.     

Numerical modeling of changes in anisotropy during liquefaction using a generalized constitutive model

A constitutive model with rotation hardening was generalized from the triaxial compression state to a general stress state. With the generalized model, numerical simulations of cyclic and monotonic undrained triaxial tests were conducted to reproduce the phenomenon of continuous, orderly and rapid changes in anisotropy during liquefaction. The simulated results demonstrated that when sand enters the liquefaction stage, the yield surface in the stress space rotates quickly, causing continuous and rapid changes in anisotropy. Through comparison of the simulated and experimental results, the generalized constitutive model was shown to be able to capture the fundamental behaviors of sand demonstrated by the experimental data, and the rotational hardening rule adopted in the generalized model was proven suitable for describing the continuous, orderly and rapid changes in anisotropy that occur during liquefaction.