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.     

Modeling cyclic shearing of sands in the semifluidized state

Liquefaction is associated with the loss of mean effective stress and increase of the pore water pressure in saturated granular materials due to their contractive tendency under cyclic shear loading. The loss of mean effective stress is linked to loss of grain contacts, bringing the granular material to a “semifluidized state” and leading to development and accumulation of large cyclic shear strains. Constitutive modeling of the cyclic stress-strain response in earthquake-induced liquefaction and post-liquefaction is complex and yet very important for stress-deformation and performance-based analysis of sand deposits. A new state internal variable named strain liquefaction factor is introduced that evolves at low mean effective stresses, and its constitutive role is to reduce the plastic shear stiffness and dilatancy while maintaining the same plastic volumetric strain rate in the semifluidized state. This new constitutive ingredient is added to an existing critical state compatible, bounding surface plasticity reference model, that is well established for constitutive modeling of cyclic response of sands in the pre-liquefaction state. The roles of the key components of the proposed formulation are examined in a series of sensitivity analyses. Their combined effects in improving the performance of the reference model are examined by simulating undrained cyclic simple shear tests on Ottawa sand, with focus on reproducing the increasing shear strain amplitude as well as its saturation in the post-liquefaction response.     

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.     

常剪应力路径下含气砂土的三轴试验

天然气水合物完全分解时,产生的气体使得能源土孔隙压力急速增加,有效应力减小,进而引起土体液化破坏。此时深海能源土斜坡的应力状态与静力液化失稳过程可简化为含气土在常剪应力排水(或不排水)应力路径下的破坏问题。以此为背景,提出了制备含气砂土试样的改进充气管法,并开展了含气砂土的常剪应力路径三轴试验。22组试验结果表明:同一孔隙比的含气密砂在不同围压与常剪应力下具有相同的失稳线;含气砂土试样失稳时的应力比和体变均随初始相对密实度的增大而增大;含气密砂在常剪应力路径下饱和度对失稳特征影响的规律性在排水与不排水条件下均不明显,但在不排水条件下含气砂土的孔压(或体变)对变形的敏感性降低;含气密砂在常剪应力路径到达失稳点之后,排水条件下是瞬变的液化鼓胀破坏,不排水条件下是渐变的剪切破坏。     

Effects of boundary conditions and partial drainage on cyclic simple shear test results—a numerical study

Owing to imperfect boundary conditions in laboratory soil tests and the possibility of water diffusion inside the soil specimen in undrained tests, the assumption of uniform stress/strain over the sample is not valid. This study presents a qualitative assessment of the effects of non‐uniformities in stresses and strains, as well as effects of water diffusion within the soil sample on the global results of undrained cyclic simple shear tests. The possible implications of those phenomena on the results of liquefaction strength assessment are also discussed. A state‐of‐the‐art finite element code for transient analysis of multi‐phase systems is used to compare results of the so‐called ‘element tests’ (numerical constitutive experiments assuming uniform stress/strain/pore pressure distribution throughout the sample) with results of actual simulations of undrained cyclic simple shear tests using a finite element mesh and realistic boundary conditions. The finite element simulations are performed under various conditions, covering the entire range of practical situations: (1) perfectly drained soil specimen with constant volume, (2) perfectly undrained specimen, and (3) undrained test with possibility of water diffusion within the sample. The results presented here are restricted to strain‐driven tests performed for a loose uniform fine sand with relative density D_r=40%. Effects of system compliance in undrained laboratory simple shear tests are not investigated here. Copyright © 2004 John Wiley & Sons, Ltd.     

An experimental database for the development,calibration and verification of constitutive models for sand with focus to cyclic loading: part II—tests with strain cycles and combined loading

For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of initial conditions and load characteristics are necessary. It is the purpose of these two companion papers to provide such database collected for a fine sand. Part II concentrates on the undrained triaxial tests with strain cycles, where a large range of strain amplitudes has been studied. Furthermore, oedometric and isotropic compression tests as well as drained triaxial tests with un- and reloading cycles are discussed. A combined monotonic and cyclic loading has been also studied in undrained triaxial tests. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.     

An experimental database for the development,calibration and verification of constitutive models for sand with focus to cyclic loading: part I—tests with monotonic loading and stress cycles

For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such a model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of initial conditions and load characteristics are necessary. The purpose of these two companion papers was to provide such database collected for a fine sand. The database consists of numerous undrained cyclic triaxial tests with stress or strain cycles applied to samples consolidated isotropically or anisotropically. Monotonic triaxial tests with drained or undrained conditions have also been performed. Furthermore, drained triaxial, oedometric or isotropic compression tests with several un- and reloading cycles are presented. Part I concentrates on the triaxial tests with monotonic loading or stress cycles. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.     

纤维加筋砂土抗液化试验与数值模拟

砂土液化是导致重大地震灾害的主要原因之一。本研究探讨了天然纤维加筋砂土在循环荷载作用下的抗液化性能。在不排水条件下,对具有不同纤维含量的加筋砂土试样进行了一系列循环三轴试验,研究了饱和砂土的液化特性以及循环剪应变幅值、纤维含量对饱和砂土抗液化性能的影响。此外,通过模拟已完成的循环三轴试验,建立了二维有限元数值模型,并对具有不同纤维含量的加筋砂土进行了参数标定。研究结果表明:(1)增加循环剪应变幅值将促进超孔压累积,使得滞回曲线斜率和平均有效应力减小速度加快;(2)纤维的存在能够减缓超孔压的累积,随着纤维含量增加,加筋砂土抗液化能力得到明显提高;(3)标定后的本构模型参数能可靠地用于模拟纤维加筋砂土的液化响应。研究结果为饱和砂土抗液化问题与纤维加筋砂土的数值模拟提供了有价值的参考。     

Effects of initial static shear on cyclic resistance and pore pressure generation of saturated sand

In practical engineering, cyclic shear stresses induced by earthquakes, traffic, and waves are superimposed on the initial static shear stress in sand fills or deposits, leading to complex responses of soils such as their deformation characteristics, pore pressure generation, and susceptibility (or cyclic resistance) to liquefaction. To experimentally investigate the undrained cyclic response of saturated sand, a series of triaxial tests were performed, covering a broad range of initial static and cyclic deviatoric stress levels. The results indicate that different stress conditions lead to two types of cyclic behavior: cyclic mobility and residual deformation accumulation. The compressional static stress is beneficial to the cyclic resistance of the dense sand, whereas the extensional static stress is regarded as detrimental as it tended to reduce the cyclic strength. Moreover, by comparing the available test data obtained from the same sand with varying initial densities and confining pressures, the static shear effect on cyclic resistance was found to be dependent on the state of the sand. Compared to the interpretation made using the limiting pore pressure-based criterion, the conventional failure criterion using a cyclic axial strain of 5% may lead to a substantial overestimation of the cyclic resistance, thus resulting in unsafe assessment and design. Hence, by employing the pore pressure criterion, the pore pressure generated in the cyclic tests was investigated and was found to be significantly influenced by the static shear stress. A pore pressure generation model is proposed to obtain the pore pressure characteristics of sand under various static shear stress conditions.     

Laboratory Investigation into the Effects of Silty Fines on Liquefaction Susceptibility of Chlef (Algeria) Sandy Soils

In a number of recent case studies, the liquefaction of silty sands has been reported. To investigate the undrained shear and deformation behaviour of Chlef sand–silt mixtures, a series of monotonic and stress-controlled cyclic triaxial tests were conducted on sand encountered at the site. The aim of this laboratory investigation is to study the influence of silt contents, expressed by means of the equivalent void ratio on undrained residual shear strength of loose, medium dense and dense sand–silt mixtures under monotonic loading and liquefaction potential under cyclic loading. After an earthquake event, the prediction of the post-liquefaction strength is becoming a challenging task in order to ensure the stability of different types of earth structures. Thus, the choice of the appropriate undrained residual shear strength of silty sandy soils that are prone to liquefaction to be used in engineering practice design should be established. To achieve this, a series of undrained triaxial tests were conducted on reconstituted saturated silty sand samples with different fines contents ranging from 0 to 40 %. In all tests, the confining pressure was held constant at 100 kPa. From the experimental results obtained, it is clear that the global void ratio cannot be used as a state parameter and may not characterize the actual behaviour of the soil as well. The equivalent void ratio expressing the fine particles participation in soil strength is then introduced. A linear relationship between the undrained shear residual shear strength and the equivalent void ratio has been obtained for the studied range of the fines contents. Cyclic test results confirm that the increase in the equivalent void ratio and the fines content accelerates the liquefaction phenomenon for the studied stress ratio and the liquefaction resistance decreases with the increase in either the equivalent void ratio or the loading amplitude level. These cyclic tests results confirm the obtained monotonic tests results.     

砂土液化大变形模型在FLAC3D中的开发与应用

通过FLAC3D二次开发平台,在VC++环境下实现了基于砂土液化大变形机制的变动映射中心边界面弹塑性模型的二次开发。基于饱和砂土液化大变形本构理论,该模型符合三维应力空间边界面映射规则,并引入临界状态变量,可实现对不同密度和围压状态下砂土液化大变形分析。针对FLAC3D程序混合离散技术与数据调用模式和模型的体积相容性条件,测试分析了将模型采用不同植入方案的计算稳定性,开发了在FLAC3D混合离散技术下不同子区共享映射中心,进入与离开液化状态保持同步的开发方案,并给出模型开发的关键技术与实施方法。利用开发的模型,对饱和砂土开展了不排水/排水/循环三轴试验与不排水循环扭剪试验模拟,及三维地基的动力反应分析。计算结果表明,模型及所开发程序具有很好的模拟与分析砂土液化后大变形的能力。     

饱和砂土液化后大变形机制的离散元细观分析

采用颗粒流软件模拟了饱和砂土在不排水条件下的循环剪切试验,研究了不同因素对液化的影响,并进一步分析了饱和砂土液化后宏观变形的基本规律。在此基础上,从孔隙分布角度解释了砂土液化后的大变形的细观物理机制。通过自编程序对颗粒排列和孔隙分布的演化过程进行定量描述,给出孔隙率标准差作为液化后体积收缩势的度量,并研究了孔隙率标准差与液化后大变形的关系。离散元细观数值模拟再现了室内试验中的宏观现象,证实了室内试验中饱和砂土液化后的有限剪切大变形是客观真实的材料响应。土体体积收缩势的累积所导致的孔隙均匀化以及土颗粒间自由空隙增大正是饱和砂土液化后循环剪应变逐渐增大的细观机制。孔隙率标准差作为孔隙均匀化的量化指标,与循环剪应变各周次幅值有良好的相关性。     

Large post-liquefaction deformation of sand, part I: physical mechanism, constitutive description and numerical algorithm

This paper presents a theoretical framework for predicting the post-liquefaction deformation of saturated sand under undrained cyclic loading with emphasis on the mechanical laws, physical mechanism, constitutive model and numerical algorithm as well as practical applicability. The revealing mechanism behind the complex behavior in the post-liquefaction regime can be appreciated by decomposing the volumetric strain into three components with distinctive physical background. The interplay among these three components governs the post-liquefaction shear deformation and characterizes three physical states alternating in the liquefaction process. This assumption sheds some light on the intricate transition from small pre-liquefaction deformation to large post-liquefaction deformation and provides a rational explanation to the triggering of unstable flow slide and the post-liquefaction reconsolidation. Based on this assumption, a constitutive model is developed within the framework of bounding surface plasticity. This model is capable of reproducing small to large deformation in the pre- to post-liquefaction regime. The model performance is confirmed by simulating laboratory tests. The constitutive model is implemented in a finite element code together with a robust numerical algorithm to circumvent numerical instability in the vicinity of vanishing effective stress. This numerical model is validated by fully coupled numerical analyses of two well-instrumented dynamic centrifuge model tests. Finally, numerical simulation of liquefaction-related site response is performed for the Daikai subway station damaged during the 1995 Hyogoken-Nambu earthquake in Japan.     

Constitutive model for cyclic behaviour of cohesionless sands

This paper presents a constitutive model for describing the stress-strain response of sands under cyclic loading. The model, formulated using the critical state theory within the bounding surface plasticity framework, is an upgraded version of an existing model developed for monotonic behaviour of cohesionless sands. With modification of the hardening law, plastic volumetric strain increment and unloading plastic modulus, the original model was modified to simulate cyclic loading. The proposed model was validated against triaxial cyclic loading tests for Fuji River sand, Toyoura sand and Nigata sand. Comparison between the measured and predicted results suggests that the proposed modified model can capture the main features of cohesionless sands under drained and undrained cyclic loading.     

车辆荷载作用下软土地基塑性变形的计算

对于低路堤公路,合理地预测车辆荷载引起的地基塑性累积变形对于低路堤公路的设计有着重要的意义。从机制上讲,可将地基的塑性应变分为塑性体积应变和塑性剪切应变。其中对于塑性体积应变,提出采用不排水条件下的残余孔压模型与一维固结理论相耦合进行计算;对于塑性剪切应变,考虑了塑性体积应变引起的土体硬化,提出了修正的塑性剪切应变计算模型。然后基于所提模型,对萧山黏土的不排水与排水条件下的动三轴试验进行模拟,初步验证了所提模型的有效性。对于实际工程问题,首先运用数值的方法求得车辆荷载在地基中引起的附加应力,然后运用所提模型计算各土层的塑性应变,再结合分层总和的方法求得地基的累积塑性变形。以日本佐贺机场1号测点为例,说明了模型在工程边值问题中的有效性。     

Experimental investigation on the deformation characteristics of granular materials under drained rotational shear

Rotational shear is the type of loading path where samples are subjected to cyclic rotation of principal stress directions while the magnitudes of principal stresses are maintained constant. This paper presents results from an experimental investigation on the drained deformation behaviour of saturated sand in rotational shear conducted in a hollow cylinder apparatus. Two types of granular materials, Leighton Buzzard sand and glass beads are tested. A range of influential factors are investigated including the material density, the deviatoric stress level, and the intermediate principal stress. It is observed that the volumetric strain during rotational shear is mainly contractive and most of strains are generated during the first 20 cycles. The mechanical behaviour of sand under rotational shear is generally non-coaxial, i.e., there is no coincidence between the principal axes of stress and incremental strain, and the variation of the non-coaxiality shows a periodic trend during the tests. The stress ratio has a significant effect on soil response in rotational shear. The larger the stress ratio, the more contractive behaviour and the lower degree of non-coaxiality are induced. The test also demonstrates that the effect of the intermediate principal stress, material density and particle shape on the results is pronounced.     

Coupling pore-water pressure with distinct element method and steady state strengths in numerical triaxial compression tests under undrained conditions

The undrained shear behaviour of sands has been a key topic after the devastating geo-disasters during the 1964 Niigata Earthquake in Japan. Extensive geo-technical soil tests, especially undrained triaxial compression tests, have revealed that the liquefaction phenomenon was the major cause for the disaster expansions. To numerically reproduce the liquefaction phenomenon, the pore-water pressure was coupled with a distinct element method. In this model, the dynamic changes in pore-water pressure were taken into consideration by the changes in volumetric strain and modulus of compressibility of water in the respective measurement spheres. Fluid-flows among the measurement spheres were controlled by Darcy’s law. The effective stress paths and steady state strengths in undrained triaxial compression tests associated with the wide ranges of initial void ratio were investigated. The effective mean stresses of medium-dense to dense numerical specimens at the steady state were negatively proportional to the initial void ratio. Loose numerical specimens reproduced quasi-liquefaction with the effective mean stresses that were less than 25% of the initial value. The medium-dense numerical specimens reproduced the phase transformation that was a typical characteristic of granular materials. The rolling restraints did not much influence of the effective angle of internal friction but strongly affected pore-water pressure behaviour within a certain range of initial void ratio.     

An anisotropic hardening model for soils and its application to cyclic loading

An anisotropic hardening model for soils is proposed by applying the concept of a field of hardening moduli developed previously for metals. Besides the yield surface, a set of nesting surfaces in the stress-space specifies the variation of hardening moduli during the deformation process. Both drained and undrained soil behaviour can be treated and distortional as well as volumetric strain cycles can be considered. The model can be applied in studying soil behaviour under cyclic loading and in particular to describe densification or liquefaction phenomena.     

饱和悬浮塑料砂流动变形可视环剪试验研究

为了分析剪切条件下零有效应力状态砂土的流动变形规律,对传统环剪仪进行了试样可视化改造,研制了透明环形剪切盒,通过对剪切盒膨胀性能分析及与标准砂的剪切试验对比,验证了环剪装置改造的合理性。通过分析不排水条件下饱和悬浮塑料砂的剪应力-应变曲线,发现其剪切强度具有应变软化的特性。通过分析环剪仪中饱和悬浮塑料砂试样的有效应力,证实了可视环剪试验中的土体基本处于零有效应力状态。开展了饱和悬浮塑料砂的流动变形可视环剪试验研究,结果表明：饱和悬浮塑料砂在固结不排水条件下剪切变形不连续,直接在剪切面发生断裂;在不固结不排水的条件下饱和悬浮塑料砂的剪切变形表现出流动形态,且与剪切速率有关：在低剪切速率下,剪切变形仅在剪切面处形成具有曲线轨迹的流动变形而在其他区域不发生变形;而在高剪切速率下剪切变形为整体的倾斜变形,符合黏性流体的流动变形特征。