Mathematical modelling of monotonic and cyclic undrained clay behaviour

The proposed general analytical model describes the anisotropic, elasto-plastic, path-dependent, stress-strain-strength properties of inviscid saturated clays under undrained loading conditions. The model combines properties of isotropic and kinematic plasticity by introducing the concept of a field of plastic moduli which is defined in stress space by the relative configuration of yield surfaces. For any loading (or unloading) history, the instantaneous configuration is determined by calculating the translation and contraction (or expansion) of each yield surface. The stress-strain behaviour of clays can thus be determined for complex loading paths and in particular for cyclic loadings. The stress-strain relationships are provided for use in finite element analyses. The model parameters required to characterize the behaviour of any given clay can be derived entirely from conventional triaxial or simple shear soil test results. The model's extreme versatility is demonstrated by using it to formulate the behaviour of the Drammen clay under both monotonic and cyclic loading conditions. The parameters are determined by using solely the results from monotonic and cyclic strain-controlled simple shear experimental tests, and the model's accuracy is evaluated by applying it to predict the results of other tests such as (1) cyclic stress-controlled simple shear tests, (2) monotonic triaxial loading compression and unloading extension tests, and (3) cyclic stress- and strain-controlled triaxial tests on, this same clay. The theoretical predictions are found to agree extremely well with the experimental test results.     

Predictions of a continuous hyperplasticity model for Bangkok clay

The performance of a new constitutive model called ‘kinematic hardening modified Cam clay’ (KHMCC) is presented. The model is described using the ‘continuous hyperplasticity’ framework. Essentially this involves an infinite number of yield surfaces, thus allowing a smooth transition between elasticity and plasticity. The framework allows soil models to be developed in a relatively succinct mathematical form, since the entire constitutive behaviour can be determined through the specification of two scalar potentials. An implementation of the continuous hyperplasticity model is also described. The model requires eight parameters plus a viscosity coefficient for rate-dependent analysis. The model is defined in terms of triaxial stress–strain variables for this study, and is used to model monotonic triaxial tests on Bangkok clay. Comparisons of the theoretical predictions with the results of cyclic undrained triaxial compression tests on Bangkok clay are also presented.     

超固结黏土单调和耦合循环的剪切特性研究

针对超固结黏土空心试样,利用土工静力-动力液压三轴-扭转多功能剪切仪,在均等固结条件下进行了单调扭剪和三轴-扭转耦合循环剪切试验。试验结果表明：不同超固结比黏土的单调扭剪强度也可由正常固结黏土的单调扭剪强度得到,得到了不同超固结比下饱和黏土的强度及模量的退化规律;随着超固结比的增大,相同破坏循环次数的动应力比和临界循环应力比均线性增大;超固结比对耦合循环剪切的孔隙水压力的发展模式影响显著。参考Yasuhara的测量方法,采用荷载停止后继续采集孔压的方法可以更好地反映黏土在耦合循环荷载下产生的真实孔压和孔压的增长情况。提出的综合应变式同时考虑了剪切变化和正向偏差变形的共同效应,适合作为主应力连续旋转的耦合循环剪切试验的破坏标准。     

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.     

A simple critical-state-based double-yield-surface model for clay behavior under complex loading

The critical state concept has been widely used in soil mechanics. The purpose of this study is to apply this concept in the framework of multi-mechanism elastoplasticity. The developed model has two yield surfaces: one for shear sliding and one for compression. In this model, the location of the critical state line is explicitly considered and related to the actual material density to control the peak strength and the phase transformation characteristics. The stress reversal technique is incorporated into the model for describing clay behavior under complex loading including changes of stress direction. The determination of the model parameters is discussed; it requires only one drained or undrained triaxial test up to failure with an initial isotropic consolidation stage. The model is used to simulate drained and undrained tests under monotonic loading with different over-consolidation ratios on various remolded and natural clays, including true triaxial tests with different Lode’s angles. Drained and undrained tests under cyclic loadings are also simulated by using the set of parameters determined from monotonic tests. The comparison between experimental results and numerical simulations demonstrate a good predictive ability of this new simple model.     

基于分数阶微积分的粗粒料静动力边界面本构模型

分数阶微分理论在土体静力黏弹性本构模型中得到了广泛应用,然而,其在动力弹塑性模型中的应用尚不多见。为此,基于分数阶微积分理论分析了粗粒料在循环荷载下的变形特性,提出了粗粒料在循环荷载下的分数阶应变率;并以此为基础,进一步建立了粗粒料受静动力荷载作用下的边界面塑性力学本构模型。所提出模型包含10个参数,均可以运用常规三轴试验获得。为了验证所提出模型,选取了几种已有不同文献中的不同粗粒料试验数据进行了模拟,发现,所提出的模型可以较好地模拟粗粒料在静动力加载下的应力-应变行为,对于循环荷载下的长期变形也能较好地预测。     

An elastoplastic constitutive model for cyclic behaviour of sands

The constitutive model of sands is proposed to describe the characteristics of plastic behaviour for cyclic loadings. A non-associated flow rule is used and both yield function and plastic potential are generalized forms of the Modified Cam clay model. The hardening parameter is represented by the plastic work related to different portions of volumetric and deviatoric changes. The boundary surface is employed to describe the plastic strain within the yield surface. The directional independency of yield condition in triaxial compression and extension tests is extended to that in general stress states. Several drained and undrained cyclic tests are predicted and the comparison is made with experimental results. The proposed model is capable of representing the monotonic and cyclic behaviours of sands with reasonable accuracy. The simulation is performed for both included and excluded membrane penetration effects and it is suggested that the membrane penetration causes the significant influences on the results of undrained cyclic tests.     

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.     

Stress–strain behavior of cement-improved clays: testing and modeling

The results of a series of laboratory tests on unimproved and cement-improved specimens of two clays are presented, and the ability of a bounding surface elastoplastic constitutive model to predict the observed behavior is investigated. The results of the oedometer, triaxial compression, extension, and cyclic shear tests demonstrated that the unimproved soil behavior is similar to that of soft clays. Cement-improved specimens exhibited peak/residual behavior and dilation, as well as higher strength and stiffness over unimproved samples in triaxial compression. Two methods of accounting for the artificial overconsolidation effect created by cement improvement are detailed. The apparent preconsolidation pressure method is considerably easier to use, but the fitted OCR method gave better results over varied levels of confining stresses. While the bounding surface model predicted the monotonic behavior of unimproved soil very well, the predictions made for cyclic behavior and for improved soils were only of limited success.     

往返荷载下粘性土的强度及取值标准试验研究

通过对粘性土进行一系列动三轴试验，测定并分析了动荷载作用下为粘性土的动剪应力，轴向应变及超孔隙水压力随时间的变化规律，分析了破坏时不同固结比的粘性土对静，动剪强度和孔隙水压力影响规律，得出了粘性土的动剪强度随固结比变化的关系式，并对粘性土的动剪强度判别方法的标准进行探讨，得出了有益的结果。     

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.     

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。     

Undrained Cyclic and Monotonic Strength of Sand-Silt Mixtures

In an attempt to correlate the monotonic peak strength and the cyclic strength of sand-silt mixtures over a wide range of parameters and to clarify some of the existing confusing conclusions in the literature regarding the undrained strength response of sand-silt mixtures, a series of stress controlled cyclic and strain controlled monotonic triaxial tests was carried out on sand-silt mixture specimens of 50 mm diameter and 100 mm height with varying silt content. In these experiments, various measures of sample density was adopted through different approaches such as constant gross void ratio approach, constant relative density approach, constant sand skeleton void ratio approach, and constant interfine void ratio approach. Also the effect of relative density and confining pressure on these strengths was studied. It is observed that the limiting fines content and the relative density of a specimen play the key role in deciding the cyclic and monotonic resistance of sand-silt mixtures when studied through any approach. For any silt content with relative density more than 70%, cyclic and monotonic resistances are observed to be independent of silt content. When the undrained cyclic strengths of these specimens are plotted against their respective undrained monotonic peak strengths, it is observed that there exists a definite exponential relationship between the two with an excellent correlation coefficient. An expression is proposed in this regard to help engineers assess the cyclic strength of sand-silt mixtures from monotonic test results.     

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.     

Field loading tests of screw micropiles under axial cyclic and monotonic loads

Unlike conventional grouted micropiles, screw micropiles have been recently introduced to the foundation industry. Full-scale field tests of screw micropiles were carried out at a cohesive soil site. The screw micropiles have a diameter varying from 76 to 114 mm and a length varying from 1.6 to 3 m, and spiral threads welded on the lower half of the steel tubular shaft. Site investigation from cone penetration tests (CPT) and laboratory testing implies that the soil was medium to stiff, low plasticity clay. Six axial monotonic and three axial cyclic load tests were performed on three micropiles. One micropile was instrumented with strain gauges to investigate the shaft load distribution during loading. The axial cyclic loading was intended to simulate cyclic inertia load during vertical ground motions. Results showed that the micropiles behave as frictional piles during monotonic tests; the unit shaft resistance and adhesion coefficient were calculated and compared with results in the literature. The end installation torque was estimated using CPT shaft resistance and was shown to agree reasonably with the measured torque. Under axial cyclic loading, the micropiles underwent small cumulative displacements and the magnitude of the displacement decreased with increasing pile length and diameter. Cyclic loading redistributed the load transfer along different segments of the micropile. Negative skin resistance was observed along the smooth pile shaft when the pile underwent decreasing axial loading.

     

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.     

Investigation of monotonic and cyclic behavior of sand using a bounding surface plasticity model

Developing the pore water pressures in loose to medium sands below the water table may lead to liquefaction during earthquakes. The simulation of liquefaction (cyclic mobility and flow liquefaction) in sandy soils is one of the major challenges in constitutive modeling of soils. This paper presents the simulation of sand behavior using a critical state bounding surface plasticity model (Dafalias and Manzari’s model, 2004) during monotonic and cyclic loading. The drained, undrained, and cyclic triaxial tests were simulated using Dafalias and Manzari’s model. The simulation results showed that the model predicts behavior of sand, reasonably well. Also, for CSR?<?0.2, number of cycles for liquefaction is significantly increased. The residual strength of Babolsar sand is produced when it is deformed to an axial strain of 20 to 25%.     

紫坪铺面板坝堆石料颗粒破碎试验研究

采用大型三轴仪对紫坪铺面板坝堆石料进行了单调和循环荷载下的固结排水剪切试验,研究了不同孔隙比情况下颗粒破碎及剪胀的变化规律。试验表明：（1）单调和循环荷载条件下,堆石料颗粒破碎率与塑性功之间存在一致的双曲线关系;（2）峰值应力处剪胀率与颗粒破碎率在半对数坐标中呈近似线性关系;（3）峰值应力处主应力比与相应的剪胀率呈近似线性关系,且上述结果受初始孔隙比的影响不大。研究成果有助于进一步了解堆石料的颗粒破碎特点,对建立复杂应力条件下考虑颗粒破碎和状态相关性的弹塑性本构模型,分析紫坪铺面板堆石坝汶川地震破损机制是十分有益的。     

Monotonic and cyclic characteristics of K0-Consolidated saturated soft clay under a stress path involving a variable confining pressure

In certain field conditions such as offshore projects under wave loads or embankments under traffic loads, both the vertical and horizontal stresses are variable. However, previous investigations rarely considered the variation in horizontal stress. To better understand the characteristics of natural saturated soft clay, a series of monotonic and cyclic triaxial tests with a K₀-consolidation state were carried out under a variable confining pressure (VCP) stress path. The development of axial strain, pore water pressure and effective stress path is analysed. The results show that with the increase in η (the ratio of the variation in the mean effective principal stress to that of the deviatoric stress), the undrained shear strength (q_f) decreases continuously. The pore water pressure generation is slightly improved under a stress path with increasing confining pressure. Based on the test results, a unified formula was established to predict the pore water pressure under VCP stress paths. The unique p–q–e relationship of normally consolidated clay in monotonic VCP triaxial tests was also demonstrated. Under VCP stress paths, the amplitude of the pore pressure increases, and the effective stress path tilts more sharply to the right. Moreover, a unified formula was established that can provide a good reference for predicting effective stress paths under cyclic VCP triaxial tests.