A two-scale constitutive framework for modelling localised deformation in saturated dilative hardening material

Undrained deformation of dilative sand generates negative excess pore pressure. It enhances the strength, which is called dilative hardening. This increased suction is not permanent. The heterogeneity at the grain scale triggers localisations causing local volume changes. The negative hydraulic gradient drives fluid into dilating shear zones. It loosens the soil and diminishes the shear strength. It is essential to understand the mechanism behind this internal drainage and to capture it numerically. The purpose of this paper is to develop a macroscopic constitutive relationship for the undrained deformation of saturated dense sand in the presence of a locally fully or partially drained shear band. Separate constitutive relations are generated for the band and intact material. Both time and scale dependence during pore fluid diffusion in saturated sand are captured, eliminating the mesh dependency for finite element implementations. The model is applied to the Gauss points that satisfy the bifurcation criterion. The proposed method is calibrated to recreate the undrained macroscopic response bestowed by an extra-small mesh. The microscopic behaviours inside and outside shear band predicted by this model are qualitatively in good agreement with individual material point behaviours inside and outside the shear band in the extra-small mesh. Depending on the loading rate and the shear band thickness, the response inside the band can be fully or partially drained, which governs the ultimate global strength. The calibrated model is exploited to simulate an upscaled biaxial compression test with semipermeable boundaries.     

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.     

A non-linear numerical model for soil mechanics

A new computer program (CONBAL-2) is developed for 2D numerical simulations of granular soil by random arrays of spheres. CONBAL-2 uses the discrete-element method and is based on 3D program TRUBAL, previously presented by Cundall. As in TRUBAL, the new program models a random array of elastic spheres in a periodic space. The main modification of TRUBAL is the implementation by the authors of a rigorous solution for the force–displacement relation at the interparticle contacts. This force-displacement relation is a function of the elastic constants, friction coefficient and sizes of the spheres, with the properties of quartz used to simulate sand. Other specific features of CONBAL-2 include its 2D character, the lack of particle rotation and its capability to simulate shear loading on any plane. Simulated laboratory test results are presented using CONBAL-2 and several random arrays of 531 spheres having two particle sizes. These simulations include monotonic loading drained and undrained (constant volume) ‘triaxial’ experiments, as well as a cyclic-loading, constant-volume ‘torsional shear’ test. The stress–strain curves, effective stress paths, volume changes, as well as the ‘pore water pressure’ build-up behaviour obtained in the simulations compare favourably—qualitatively and in some aspects quantitatively—with similar laboratory results on sands. However, the simulated soil is somewhat stiffer and stronger due to the perfectly rounded particles, limited range of grain sizes, lack of particle rotation and 2D character of the model.     

DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

In an effort to study undrained post-liquefaction shear deformation of sand, the discrete element method (DEM) is adopted to conduct undrained cyclic biaxial compression simulations on granular assemblies consisting of 2D circular particles. The simulations are able to successfully reproduce the generation and eventual saturation of shear strain through the series of liquefaction states that the material experiences during cyclic loading after the initial liquefaction. DEM simulations with different deviatoric stress amplitudes and initial mean effective stresses on samples with different void ratios and loading histories are carried out to investigate the relationship between various mechanics- or fabric-related variables and post-liquefaction shear strain development. It is found that well-known metrics such as deviatoric stress amplitude, initial mean effective stress, void ratio, contact normal fabric anisotropy intensity, and coordination number, are not adequately correlated to the observed shear strain development and, therefore, could not possibly be used for its prediction. A new fabric entity, namely the Mean Neighboring Particle Distance (MNPD), is introduced to reflect the space arrangement of particles. It is found that the MNPD has an extremely strong and definitive relationship with the post-liquefaction shear strain development, showing MNPD’s potential role as a parameter governing post-liquefaction behavior of sand.     

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。     

Development of a Nonlinear Model for Soft Rock and its Applications

A phenomenological model has been developed for soft rock based on the results of a series of triaxial compression (TC) tests conducted on Kobe sandstone with a very high precision measurement. From the analysis and interpretation of the test results, it has been found that small strain Young’s modulus (E^e) was a function of the major principal stress. E^e for elastic strains of soft rock was assumed to be cross-anisotropic. A damage function has been used to derive the appropriate elastic Young’s modulus when subjected to shear loading. As the basic stress–strain relation, the relationship between the tangent modulus and the shear stress level was used. The differential form of which was subsequently integrated by a 4th order Runge–Kutta solver to obtain the stress–strain relation. The model of soft rock is based on an isotropic strain hardening elasto-plastic framework which takes into account the pressure sensitivity, cross-anisotropy, degradation of Young’s modulus with the degree of mobilized shear stress and the nonlinearity of the shear stress-shear strain relationship. Although the model was developed from the analysis of the TC tests results of Kobe sandstone, it was also applied to the other types of soft rock or stiff geomaterials. Plate loading tests were conducted at a level of 61 m below the ground level at the bottom of a large excavated shaft at four locations. Finally, the model was used to simulate the plate loading test results successfully. This model was successfully calibrated with Akashi sandstone and applied in the simulation for the settlement of Akashi-Kaikyo Bridge piers. The simulations were carried out for both drained and undrained condition by changing the Poisson’s ratio. The layering information beneath the foundations were used in the FEM simulation. The use of very accurate Young’s modulus from the field shear wave velocity test was the key to the successful simulation of the settlement under bridge pier foundations.     

Model for large strain consolidation under constant rate of strain

A numerical model, called CCRS1, is presented for one‐dimensional large strain consolidation under constant rate of strain loading conditions. The algorithm accounts for vertical strain, general constitutive relationships, relative velocity of fluid and solid phases, changing compressibility and hydraulic conductivity during consolidation, and an externally applied hydraulic gradient acting across the specimen. Soil compressibility is rate independent, and as such, the current model is most appropriate for less‐structured clays. Verification checks show excellent agreement with analytical and numerical solutions for small and large strain conditions. A series of numeric examples indicates that compressibility and hydraulic conductivity constitutive relationships can have an important effect on constant rate of strain consolidation response. Results also indicate that analytical solutions obtained using small strain theory can be in significant error for large strain conditions with changing coefficient of consolidation. Copyright © 2012 John Wiley & Sons, Ltd.     

Thermo-hydro-mechanical modeling of unsaturated soils using isogeometric analysis: Model development and application to strain localization simulation

This study presents a thermo-hydro-mechanical (THM) model of unsaturated soils using isogeometric analysis (IGA). The framework employs Bézier extraction to connect IGA to the conventional finite element analysis (FEA), featuring the current study as one of the first attempts to develop an IGA-FEA framework for solving THM problems in unsaturated soils. IGA offers higher levels of interelement continuity making it an attractive method for solving highly nonlinear problems. The governing equations of linear momentum, mass, and energy balance are coupled based on the averaging procedure within the hybrid mixture theory. The Drucker-Prager yield surface is used to limit the modified effective stress where the model follows small strain, quasi-static loading conditions. Temperature dependency of the surface tension is implemented in the soil-water retention curve. Nonuniform rational B-splines (NURBS) basis functions are used in the standard Galerkin method and weak formulations of the balance equations. Displacement, capillary pressure, gas pressure, and temperature are four independent quantities that are approximated by NURBS in spatial discretization. The framework is used to simulate strain localization in an undrained dense sand subjected to plane strain biaxial compression under different temperatures and displacement velocities. Results show that an increase in the displacement rate leads to reduction in the equivalent plastic strain while an increase in the temperature leads to an increase in the equivalent plastic strain. The findings suggest that the proposed IGA-based framework offers a viable alternative for solving THM problems in unsaturated soils.     

Triaxial tests on the fluidic behavior of post-liquefaction sand

Liquefaction-induced ground deformation is a major cause of structural damage during earthquakes. However, a better understanding of seismic liquefaction is needed to improve earthquake hazard analyses and mitigate structural damage. In this paper, a dynamic triaxial test apparatus was employed to investigate the fluidic characteristics of post-liquefaction sand. The specimens were vibrated to the point of liquefaction by dynamic loading, and then the liquefied sand was further sheared by triaxial compression in an undrained manner. It was found that a non-Newtonian fluid model can accurately describe the shear stress and the shear strain rate of post-liquefaction sand during undrained triaxial compression. The apparent viscosity, a major parameter in a constitutive model of a non-Newtonian fluid, decreases with an increase in the shear strain rate.     

饱和黏土不排水剪切的热破坏

试验资料表明：饱和黏土在不排水常载升温条件下会产生很大的变形并最终可发生热破坏现象,因此,升温也成为一种加载方式。基于姚仰平等提出的热UH临界状态模型,推导了受温度影响的热不排水抗剪强度表达式,对不同超固结度饱和黏土在升温下的不排水抗剪强度模拟与试验结果对比表明：所提公式能够合理反映试验资料中受温度影响的不排水抗剪强度变化规律。利用热UH模型对不排水常载-升温过程进行了模拟,模拟结果表明,热UH模型可合理地反映不排水常载-升温条件下饱和黏土的应力-应变关系以及强度变化规律。针对能影响热破坏过程的几种因素如升温初始时的偏应力比、升温幅度、超固结度以及先期固结压力等进行了讨论分析,得到了各因素对于饱和黏土不排水剪切下的应力-应变关系及强度特性的影响规律。     

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。     

两种粉质黏土的动、静强度特性对比研究

以京津高铁和杭州地铁沿线的两种典型粉质黏土为研究对象,并采用英国GDS多功能三轴仪完成了静、动力强度测试,研究了两种土的静力不排水抗剪强度和在交通荷载高振次循环下的动强度、临界动应力比、应变发展模式以及振后抗剪强度等方面的差异。对比发现,长期循环荷载作用下两种土的应变发展和振后强度均有很大不同。与京津地区粉质黏土相比,杭州地铁沿线土含水率高、孔隙比大、密度低、灵敏度高、强度低。两种原状土在小幅振动后土体强度略有增大,而随振幅增大,振后强度将低于未经历振动时的不排水强度值;而重塑土振后强度均低于静剪强度。     

Kinematic hardening of soft clay in simple shear

In a separate paper, the authors have proposed a normalized, non-degrading form of the shear stress–shear strain relationship for undrained, cyclic simple shear of soft clay. This relationship is described in the present paper, and it is seen to include a single fatigue parameter—the mean effective stress. Application of the relationship therefore requires knowledge of the history of the mean effective stress during any loading history. The present paper proposes an effective stress path model which may be used for prediction of this history. The model is developed within the framework of bounding surface kinematic and isotropic hardening plasticity. It incorporates an isotropic hardening bounding surface, and a kinematic hardening yield surface, in which the elastic region vanishes, and so the yield surface reduces to the stress point. The normalized shear stress–shear strain relationship, developed on the basis of Iwan's model, is used to establish the shape of the cap of the bounding surface. A new translation rule is also incorporated in the model, allowing improved prediction of stress path development within the bounding surface during regular or irregular cyclic loading. Use of the proposed model to simulate the behaviour of soft clay in laboratory undrained cyclic simple shear tests shows excellent qualitative agreement, with most of the major features of the actual behaviour being predicted.     

Theoretical Evaluation of the Mechanical Behavior of Unsaturated Soils

An evaluation method for the mechanical behavior of unsaturated soils is studied in this paper. Although the mechanical behavior of unsaturated soils is complicated, a simple modeling is preferable in practice. This is because the soil properties are not homogeneous and ground data is limited when structures are being designed. In addition, in order to evaluate the reliability of the design, the physical meanings of the parameters applied in the prediction model should be clear. Firstly, the authors study the relationship between compaction curves and compression indexes in the unsaturated state that is used in the proposed constitutive model. Based on the constitutive model, the stress paths for constant volume shear tests are formulated under a constant void ratio condition and the stress paths for undrained shear tests are calculated under a constant water content condition. In the case of unsaturated specimens, the volume of these specimens changes with the shear deformation and the stress paths depend on the initial degree of saturation. The results of the calculation qualitatively describe the test results by considering the changes in effective confining pressure in the undrained condition and the water retention curves.     

循环荷载作用下软土的孔压模式和强度特征

通过循环三轴剪切试验,研究原状软土的变形和孔压发展规律。建议了一个循环荷载作用下孔隙水压力的发展模式。研究了不排水循环荷载作用下软土的动强度以及作用后饱和软土静强度的衰减特征,讨论了周围固结压力和荷载作用频率对动强度的影响。研究表明,在某一轴向应变条件下,循环次数随循环剪应力比的增加而迅速减小;随循环剪切应力比的增大,饱和软土的静强度有一定衰减。     

Delayed plastic model for time‐dependent behaviour of materials

A delayed plastic model, based on the theory of plasticity, is proposed to represent the time‐dependent behaviour of materials. It is assumed in this model that the stress can lie outside the yield surface and the conjugate stress called static stress is defined on the yield surface. The stress–strain relation is calculated based on the plastic theory embedding the static stress. Thus, the stress–strain relation of the model practically corresponds to that of the inviscid elastoplastic model under fairly low rate deformation. The delayed plastic model is coupled with the Cam‐clay model for normally consolidated clays. The performance of the model is then examined by comparing the model predictions with reported time‐dependent behaviour of clays under undrained triaxial conditions. It is shown that the model is capable of predicting the effect of strain rate during undrained shear and the undrained creep behaviour including creep rupture. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

原状和重塑海洋粘土经历动载后的静强度衰减

根据海洋粉质粘土原状和重塑土样的动三轴试验结果, 比较和分析了两种土样应力、应变、孔隙水压力和不排水抗剪强度行为, 得到了土样的静不排水抗剪强度衰减与波浪荷载作用下土样产生的动应变以及平均累积孔压之间的关系。 并将波浪荷载作用使土样内孔压升高, 有效应力降低, 形成拟超固结现象的理论, 应用到土样不排水抗剪强度衰减与平均累积孔压之间关系的分析;同时与重塑土样的超固结静态剪切试验结果进行比较, 得到了土样在波浪荷载作用后的归一化不排水抗剪强度与拟超固结比之间的关系式。 建议以少量原状土样, 配合大量重塑土样的动三轴试验结果, 实现对实际海洋粘土地基在波浪荷载作用后的静不排水抗剪强度衰化规律的评估。     

结构性黄土的剪切带及强度特性的真三轴试验研究

采用西安理工大学自主研发的真三轴仪,对西安白鹿原黄土进行了不同中主应力比值、不同固结围压的试验研究,探讨了黄土剪切带形成与峰值强度、中主应变与大主应变关系曲线、体应变与大主应变关系曲线特征点之间的联系以及子午平面、 平面上的强度变化规律。分析了真三轴应力条件下黄土强度变形规律和试样剪切带破坏模式和黄土在复杂应力状态下剪切带形成的判断依据和原因,研究表明,真三轴压缩原状黄土具有明显的剪切带,围压和中主应力比值较小时表现为软化,围压和中主应力比值较大时则表现为硬化;中主应变、体应变与大主应变关系曲线较为一致的转折点反映了土变形性状发生变化;与中主应变方向一致的剪切带两侧土结构块体产生相对滑移,剪切带开始形成和发展;土应变曲线的转折点可以作为土固结结构内剪切带形成的判断依据;子午平面上强度线呈线性变化规律, 平面上呈曲边三角形非线性变化规律,并且与 -SMP强度准则较为接近。不同应力条件下剪切带变化复杂的破坏模式与黄土原生的结构特征和加载共同作用的变化有密切联系。     

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.