Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction

This paper presents a new plasticity model developed for the simulation of monotonic and cyclic loading of non‐cohesive soils and its implementation to the commercial finite‐difference code FLAC, using its User‐Defined‐Model (UDM) capability. The new model incorporates the framework of Critical State Soil Mechanics, while it relies upon bounding surface plasticity with a vanished elastic region to simulate the non‐linear soil response. Stress integration of constitutive relations is performed using a recently proposed explicit scheme with automatic error control and substepping, which so far has been employed in the literature only for constitutive models aiming at monotonic loading. The overall accuracy of this scheme is evaluated at element level by simulating cyclic loading along complex stress paths and by using iso‐error maps for paths involving change of the Lode angle. The performance of the new constitutive model and its stress integration scheme in complex boundary value problems involving earthquake‐induced liquefaction is evaluated, in terms of accuracy and computational cost, via a number of parametric analyses inspired by the successful simulation of the VELACS centrifuge Model Test No. 2 studying the lateral spreading response of a liquefied sand layer. Copyright © 2009 John Wiley & Sons, Ltd.     

A multi‐mechanism constitutive model for plastic adaption under cyclic loading

As is well known, granular soils under cyclic loading dissipate a large amount of energy and accumulate large irreversible strains. Usually, with time, this second effect reduces and the accumulation rate decreases with the number of cycles until obtaining a sort of ideal stationary cyclic state at which ratcheting disappears. In this paper, only this ideal state is taken into consideration and simulated by means of a multi‐mechanism constitutive model for plastic adaptation. For this purpose, the concept of cycle is discussed, many different categories of cyclic stress/strain paths are considered and some theoretical issues concerning both the flow and the strain‐hardening rules are tackled. Even though the paper focuses on soil behaviour, the conclusions can be extended to all materials exhibiting ratcheting due to volumetric behaviour.Copyright © 2013 John Wiley & Sons, Ltd.     

A two-mechanism soil–structure interface model for three-dimensional cyclic loading

A three-dimensional (3D) soil–structure interface model is proposed within the two-mechanism constitutive theory and bounding surface theory originally established for soils. The proposed model has two main characteristics: first, the model is formulated based on two different and superposed deformation mechanisms. The first mechanism is due to the stress ratio increment, and the second is due to the normal stress increment. Each mechanism induces a shear strain component and a normal strain component. The proposed model can be reduced to the conventional single-mechanism interface model. Second, the plastic modulus and stress dilatancy are defined using the bounding surface theory. The plastic flow rule under cyclic loading is modified and assumed to be dependent on both the stress state of the mapping point and the stress reversal loading direction. The proposed model was validated against the available 3D interface tests and was found to satisfactorily reflect the salient features of the interfaces under monotonic and cyclic loading paths with different normal boundaries. The problem in which the elastic normal stiffness in conventional single-mechanism interface models is often underestimated to enhance the simulation performance under varying normal stress conditions is solved by incorporating the second mechanism. And the effect of the second mechanism on the modeling behavior is discussed. The modified plastic flow direction accurately simulates the 3D cyclic shear response, and the difference between the model simulation and test result increases with the number of cycles by use of the plastic flow direction defined in conventional bounding surface theory.     

基坑工程侧向卸、加载应力路径试验及模量计算

分析认为,基坑支护外侧的土体有可能产生侧向卸载和加载两种应力路径,因此进行了侧向卸载、加载的应力路径试验,并根据邓肯-张模型的思路和试验结果,推导了侧向卸载、加载的切线弹性模量公式。通过实例计算发现,用推导的切线弹性模量公式,可以得到很好的计算结果,这说明考虑侧向卸载、加载的应力路径的模量公式能够更好地模拟基坑问题。     

An AI-based model for describing cyclic characteristics of granular materials

Modelling cyclic behaviour of granular soils under both drained and undrained conditions with a good performance is still a challenge. This study presents a new way of modelling the cyclic behaviour of granular materials using deep learning. To capture the continuous cyclic behaviour in time dimension, the long short-term memory (LSTM) neural network is adopted, which is characterised by the prediction of sequential data, meaning that it provides a novel means of predicting the continuous behaviour of soils under various loading paths. Synthetic datasets of cyclic loading under drained and undrained conditions generated by an advanced soil constitutive model are first employed to explore an appropriate framework for the LSTM-based model. Then the LSTM-based model is used to estimate the cyclic behaviour of real sands, ie, the Toyoura sand under the undrained condition and the Fontainebleau sand under both undrained and drained conditions. The estimates are compared with actual experimental results, which indicates that the LSTM-based model can simultaneously simulate the cyclic behaviour of sand under both drained and undrained conditions, ie, (a) the cyclic mobility mechanism, the degradation of effective stress and large deformation under the undrained condition, and (b) shear strain accumulation and densification under the drained condition.     

The effects of unloading on drained cyclic behaviour of Sydney sand

New excavation or tunnelling affects the stress state of soils in ground. The change of stress state due to excavation may affect the cyclic behaviour of soils. Cyclic loading, such as traffic and earthquake loading, induced ground deformation may be greater than expected if such effect is not considered. A series of cyclic triaxial tests were performed on Sydney sand with different relative densities. The effect of unloading sequence on deformation of the sand under cyclic loading was simulated by reducing lateral stress in steps between loading cycles. The dependence of strain accumulation on the magnitude of confining pressure reduction and on unloading stress paths was studied. The results indicate that the sand has a memory of stress history and the stress history of such unloading enlarges the strain accumulation during the subsequent cycles, and the greater the reduction of lateral stress, the greater the accumulated strain. Under cyclic loading, the accumulated axial strain could increase nonlinearly or linearly with the ratio of unloading magnitude to initial mean effective stress, depending on the stress state before cyclic loading. The unloading stress paths have limited effects on the final accumulated strain if the initial and final stress states are the same. The variation of strain accumulation direction attributes to the change of average stress ratio resulting from lateral stress reduction, but hardly depends on relative density and unloading stress paths. The strain accumulation direction after unloading roughly agrees with the modified Cam Clay flow rule.

     

Orthogonal test and regression analysis of the strain on silty soil in Shanghai under metro loading

Cyclic triaxial test by means of the geotechnical digital system is conducted for the soil near the Guoquan Road Station of Metro Line 10 in Shanghai to analyze the strain characteristics and the variation law of saturated silty soil under subway loading. Orthogonal design method is used to arrange the experiment, considering the following factors: frequency ratio f _R, cyclic stress ratio σ _R, vibration time ratio N _R, and the interaction function among them. Results show that the cyclic stress ratio σ _R, the frequency ratio f _R, the vibration time ratio N _R, and the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R have a significant effect on the axial strain of the subway tunnel. The effect of the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R is also significant. From the analysis of variance and regression theory, the nonlinear regression equation of the cumulative plastic strain of silty soil under subway loading is established. Residual analysis proves that the equation is ideal and credible. The results have important value for the design of subway tunnels.     

A two-surface plasticity model for cyclic behavior of saturated clay

This paper presents a two-surface plasticity model for describing some important features of saturated clay under cyclic loading conditions, such as closed hysteresis loops, cyclic shakedown and degradation, and different stress–strain relations for two-way loading. The model, namely ACC-2-C, is based on the elastoplastic model ACC-2 (an adapted Modified Cam Clay model with two yield surfaces) developed by Hong et al. (Acta Geotech 11(4):871–885, 2015). The small-strain nonlinearity concept is adopted to achieve the nonlinear characteristics of clay during unloading–loading stage. The new hardening law related to accumulated deviatoric plastic strain is proposed for the inner surface to describe the cyclic shakedown and degradation. Following the advantages of the ACC-2 model, the constitutive equations are simply formulated based on the consistency condition for the inner yield surface. The model is conveniently implemented in a finite element code using a stress integration scheme similar to the Modified Cam Clay model. The simulation results are highly consistent with experimental data from drained and undrained isotropic cyclic triaxial tests in normally consolidated saturated clay under both one-way and two-way loadings.

     

Kinematic hardening plasticity formulation of small strain behaviour of soils

An objective of this paper is to demonstrate that the small strain model developed by the authors can be incorporated into the conventional kinematic hardening plasticity framework to predict pre‐failure defor mations. The constitutive model described in this paper is constituted by three elliptical yield surfaces in triaxial stress space. Two inner surfaces are rotated ellipses of the same shape, representing the boundaries of the linear elastic and small strain regions, while the third surface is the modified Cam clay large‐scale yield surface. Within the linear elastic region, the soil behaviour is elastic with cross‐coupling between the shear and volumetric stress–strain components. Within the small strain region, the soil behaviour is elasto‐plastic, described by the kinematic hardening rule with an infinite number of loading surfaces defined by the incremental energy criterion. Within the large‐scale yield surface, the soil behaviour is elasto‐plastic, described by kinematic and isotropic hardening of the small strain region boundary. Since the yield surfaces have different shapes, the uniqueness of the plastic loading condition imposes a restriction on the ratio between their semi‐diameters. The model requires 12 parameters, which can be determined from a single consolidated undrained triaxial compression test. Copyright © 2000 John Wiley & Sons, Ltd.     

Monotonic and cyclic tests on kaolin: a database for the development,calibration and verification of constitutive models for cohesive soils with focus to cyclic loading

A database with about 60 undrained monotonic and cyclic triaxial tests on kaolin is presented. In the monotonic tests, the influences of consolidation pressure, overconsolidation ratio, displacement rate and sample cutting direction have been studied. In the cyclic tests, the stress amplitude, the initial stress ratio and the control (stress vs. strain cycles) have been additionally varied. Isotropic consolidation leads to a failure due to large strain amplitudes with eight-shaped effective stress paths in the final phase of the cyclic tests, while a failure due to an excessive accumulation of axial strain and lens-shaped effective stress paths was observed in the case of anisotropic consolidation with \(q^{\text{ ampl }}< |q^{\text{ av }}|\). The rate of pore pressure accumulation grew with increasing amplitude and void ratio (i.e. decreasing consolidation pressure and overconsolidation ratio). The “cyclic flow rule” well known for sand has been confirmed also for kaolin: With increasing value of the average stress ratio \(|\eta ^{\text{ av }}| = |q^{\text{ av }}|/p^{\text{ av }}, \) the accumulation of deviatoric strain becomes predominant over the accumulation of pore water pressure. The tests on the samples cut out either horizontally or vertically revealed a significant effect of anisotropy. In the cyclic tests, the two kinds of samples exhibited an opposite inclination of the effective stress path. Furthermore, the horizontal samples showed a higher stiffness and could sustain a much larger number of cycles to failure. All data of the present study are available from the homepage of the first author. They may serve for the examination, calibration or improvement in constitutive models dedicated to cohesive soils under cyclic loading, or for the development of new models.     

削坡作用土质边坡变形分布式光纤监测试验研究

采用高空间分辨率的PPP-BOTDA光纤感测技术,研发出一种适合于土体变形监测的特种感测光缆。通过水平向和垂直向感测光缆植入,对边坡模型在坡顶局部加载和削坡过程土体内部变形场进行了分布式监测,获得了荷载和削坡作用下坡体变形场的分布规律,并对边坡模型进行了有限元数值分析和计算评价。分布式光纤感测技术监测结果表明:在坡顶局部加载作用下土体水平向拉张变形最大值发生在坡体中部,这与数值模拟结果一致;但在削坡作用下,坡体水平向拉张变形最大值发生在坡体上部,表明削坡作用改变了边坡模型的变形规律,上层土体在坡顶局部荷载作用下易发生倾倒变形。研究结果也表明,作者研制的特种感测光缆具有良好的感测性能,可以对土体变形场进行准确有效监测。     

多维地震荷载等效循环周数计算模型

地震波是一种多维的随机荷载,一般在参数测定中应将其转化为等效循环荷载。采用有限元模拟多向地震荷载作用下的砂土动力响应,介绍了弹塑性边界面模型及其参数的含义,阐述了确定参数的方法,选取涵盖大震、中震、近场、远场及不同土质条件的155组多向地震输入时程进行单向、多向加载。利用混合效应回归分析法,建立了多向地震荷载作用下等效循环周数计算模型,分析验证了该模型的准确性。提出了基于等效循环周数比的多维地震荷载作用下等效循环周数计算方法。研究表明：模型预测值能较好地反映等效循环周数实际值的变化趋势;震级和震中距对等效循环周数比影响不明显;砂土特性对等效循环周数比的影响具有主导作用, 在不同震级范围内,等效循环周数比均随着相对密度的增大而增大,对应于相对密度为45%、60%、80%、100%的砂土,等效循环周数比分别近似为1.60、1.85、1.90和2.05。     

Resilient and plastic strain behavior of freezing–thawing mucky clay under subway loading in Shanghai

Depending on artificial freezing method applied in subway tunnel construction, a series of stress-controlled cyclic triaxial tests were conducted on freezing–thawing mucky clay to investigate their resilient and plastic strain behavior. In terms of practical engineering, this study focuses on three significant influencing factors which are artificial freezing temperatures, dynamic stress amplitude and loading frequency. This study demonstrates how these influence factors effect on the resilient strain or dynamic elastic modulus and accumulated plastic strain which are crucial to better understanding the strain behavior of freezing–thawing soil. The results indicate that the value of freezing temperature has slight influence on dynamic elastic modulus, but the freeze–thaw action can truly decrease the dynamic elastic modulus of soil, and soil with higher freezing temperature possesses larger accumulated axial strain. Besides, the dynamic elastic modulus decreases remarkably with the increasing of the cyclic stress amplitude, while the accumulated plastic strain behaves adversely. In addition, loading frequency has the least effect compared with other two factors, but lower frequency can generate larger accumulated plastic strain.     

竖向循环荷载作用下砂土中单桩承载特性模型试验研究

采用自主设计的竖向循环加载装置,通过室内模型试验研究竖向循环荷载作用下砂土中单桩承载特性和桩周土体变形机制。根据试验结果,桩体累积位移可以划分为不发展区域、渐变发展区域、破坏区域3种区域;滞回曲线的滞回圈包络面积随着循环次数的增加,呈现逐渐减小的趋势,滞回曲线由不闭合发展为闭合曲线,桩周土体由弹塑性变形逐渐转变为弹性变形。采用粒子图像测速（particle image velocimetry,简称PIV）技术对循环荷载作用下桩周土体变形进行实时量测,得到桩周土体完整的位移场和剪切应变场。结果表明：循环周期、幅值和密实度为桩周土体变形的主要影响因素,随着循环周期的增加,剪切破坏带在接近土体表面处呈现内敛趋势,剪切破坏面最终近乎平行于桩-土界面。循环荷载幅值越大,表层土体在循环荷载作用下越趋于密实,侧向土压力增大,位移影响区域减小,对应剪切应变场呈现“耳”状分布,幅值比循环周期更容易导致桩周土体出现沉陷。不同砂土密实度中的桩体累积位移随着循环周期呈现出不同的特征,松砂状态下桩周土体位移场呈现倒截锥形,密砂则呈现圆柱形。     

Application of a Hill-Climbing technique to the formulation of a new cyclic nonlinear elastic constitutive model

In the field of constitutive modelling of soil behaviour, optimisation techniques have been mostly employed as a calibration tool, particularly when several model parameters lack clear physical meaning. In this paper, however, a procedure based on a Hill-Climbing optimisation algorithm is presented as a form of improving the performance of constitutive models. Specifically, a simple cyclic nonlinear elastic model, which is shown to be unable to simulate adequately the damping ratio measured under small and large strain amplitudes, is modified by applying the Hill-Climbing technique to the determination of a new relationship describing the unloading/reloading behaviour of soil under cyclic loading. The performance of the proposed model is assessed by evaluating its parameters based on three distinct sets of empirical damping ratio curves and computing the corresponding error in their simulation. It is shown that the introduction of the new unloading/reloading expression formulated based on the outcome of the optimisation procedure increases substantially the precision of the constitutive model.     

低围压循环荷载作用下饱和粗粒土的动力特性与骨干曲线模型研究

基床层是铁路路基的核心组成部分,一般为粗颗粒土,厚约2.5～3.0 m,长期直接承受行车荷载的反复作用,其在动载反复作用下的变形特性是评价路基工作性能的关键要素之一。为研究粗粒土在列车循环荷载作用下的应力-应变特性,开展了一系列应力控制的单向循环加载大型动三轴试验,模拟列车动载和路基粗粒料填筑实际情况,包括不同动应力幅值（模拟不同列车轴重）、不同围压（模拟不同埋深）的动三轴持续振动试验。结果表明,在循环荷载作用下,土体刚度变化与振动次数、围压关系密切。根据动应力幅值大小的不同,循环荷载作用下饱和粗粒土的动应变随振次的发展形态可分为3种类型：稳定型、破坏型和临界型。根据试验所得出的动应力-应变关系曲线特点,建立了含围压和循环振次的骨干曲线模型。与传统的骨干曲线模型相比,该模型能反映土体刚度随循环振次的变化,更能反映列车往复作用的实际情况;同时该模型能用于估算路基土体动强度,对铁路路基核心层的动力变形稳定性评价和基于动力变形控制的路基设计具有参考价值。     

A hypoplastic macroelement model for shallow foundations under monotonic and cyclic loads

In this work, a macroelement for shallow foundations on sands has been developed based on the theory of hypoplasticity. The incrementally nonlinear constitutive equations of the macromodel are defined in terms of generalized forces and displacements and are constructed based on the general approach proposed by Niemunis (Extended Hypoplastic Models for Soils. Habilitation Thesis, Bochum University, 2002). A suitable vectorial internal variable—mimicking the concept of intergranular strain introduced by Niemunis and Herle (Mech Cohes Frict Mater 2:279–299, 1997) for continuum hypoplasticity—is employed to provide the model sufficient memory of past displacement history to be able to reproduce the observed behavior under cyclic loading paths. As compared to similar macroelements formulated within the framework of the theory of elastoplasticity, the proposed approach has the advantage of a much simpler mathematical structure, which allows a straightforward implementation in existing structural analysis FE codes. The model performance has then been evaluated by comparing the model predictions with available experimental results from a series of small-scale model tests reported by Nova and Montrasio (Géotechnique 41:243–256, 1991). Overall, the model captures reasonably well the observed response under nonproportional, complex loading paths. A series of simulations reproducing the tests performed by di Prisco et al. (Shallow footing under cyclic loading: experimental behaviour and constitutive modelling. Patron, Bologna, 2003) has also demonstrated the potential of the proposed model to simulate the observed behavior of footings under cyclic loading paths, at least from a qualitative point of view.     

竖井地基的大应变固结分析

简单介绍了真空-堆载联合预压下饱和软土竖井地基大变形固结沉降模型（VRCS1模型）,该模型能考虑大应变、材料非线性、非达西流、真空折损和竖井未打穿等因素。使用该模型对澳大利亚巴利纳支路某现场沉降进行预测,结果与现场实测数据吻合良好。基于该工程案例,讨论了分级堆载、循环荷载、真空联合堆载、上边界为等应力/等应变条件以及排水板打入深度等因素对竖井地基固结过程的影响规律。计算结果表明：分级堆载可降低土体超静孔压峰值进而改善土体稳定性;循环荷载使土体固结过程发生震荡,且土体沉降峰值迟于超静孔压峰值和荷载峰值出现;真空荷载和堆载作用机制有本质区别,真空荷载不可简单以堆载替代;上边界等应变条件下的固结速率一般快于等应力条件,工程真实条件一般介于两者之间;排水板打入深度超过0.9倍土层厚度时,再加大打入深度加速固结效果不明显。     

基于广义塑性力学的土体次加载面循环塑性模型(Ⅱ):本构方程与验证

按广义塑性力学原理，导出了土体次加载面循环塑性模型的本构方程，建立了相应的加卸载准则以及模型参数的确定方法。通过多种应力路径下土的本构响应的模拟，表明次加载面循环塑性模型能较好地反映循环荷载作用下土体呈现的非线性、滞回性与变形的积累性三方面主要特征，初步验证了模型的有效性。