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.

     

Multi-surface Cyclic Plasticity Sand Model with Lode Angle Effect

A Drucker-Prager J ₂ multi-surface-plasticity sand model is modified to employ the Lade-Duncan failure criterion as the yield function. This function includes the first and third stress invariants to account for the dependence of cyclic shear stress–strain behavior on confining pressure and the Lode angle. Related modifications to the flow rule and hardening rule are described. Dependence of dilatancy on confinement is also included. Salient features of the model performance are presented under general three-dimensional (3D) loading conditions, where the yield function provides a more accurate representation of nonlinear shear response. Dynamic response analyses of a mildly inclined infinite slope are performed to illustrate the influence of excitation direction on the accumulation of liquefaction-induced lateral ground deformation.     

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.     

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.     

A Consistent Soil Fatigue Framework Based on the Number of Equivalent Cycles

Cyclic soil degradation and hardening affects soil stiffness and strength, and is linked to an increase or decrease in the mean effective confining stress due to void ratio or pore pressure changes. This change of state can be explicitly modeled by using effective stress methods, or implicitly modeled using total stress methods. In the latter, this is achieved by using empirical functions based on the number of loading cycles that are derived from constant-amplitude stress or strain laboratory tests. To suite generalized loading conditions, these functions must be extrapolated to variable-amplitude loading. This falls under the general class of a fatigue-based problem. The main focus of this paper is to present a generalized consistent soil fatigue formulation for soils under cyclic loading. The paper then goes on to discuss the implementation of various cyclic soil degradation and hardening models reported in the literature, and highlights their important underlying assumptions, capabilities and limitations.     

循环荷载作用下考虑非达西渗流的软黏土一维流变固结分析

基于Hansob渗流理论和Merchant流变模型,将微分型流变方程耦合到一维固结理论中,建立了循环荷载作用下双变量表述的软黏土一维流变固结耦合方程组。采用FlexPDE软件对方程组进行了求解,通过与已有文献结果对比,验证了算法的可靠性,在该基础上研究了循环荷载作用下饱和软黏土的一维流变固结特性,分析了Hansob渗流参数、Merchant流变模型参数以及循环荷载类型对饱和软黏土固结特性的影响。研究结果表明,按超孔压定义的平均固结度 和按变形定义的平均固结度 均呈现循环变化特征,且 > ;当循环周次较大时, 进行稳定循环状态,由于流变效应, 峰值仍呈逐渐增大趋势;随着Hansob渗流参数 和 的逐渐增大,地基固结速率逐渐降低,同一循环周次内 、 的峰值也随之降低;随着流变参数F的逐渐增大,同一循环周次内 的峰值逐渐降低, 的峰值显著提高;随着 的逐渐增大,同一循环周次内 、 的峰值逐渐降低。循环荷载作用下地基的平均固结度始终处于循环状态,无法达到固结完成状态,其最大平均固结度也远小于线性荷载的情况。     

Influence of cyclic wetting and drying on swelling behavior of mudstone in south west of Iran

Mudstone experience periodic swell and shrink behavior due to alternate wetting and drying cycles at arid and semi-arid regions with distinctive seasonal changes. This paper examines the influence of cyclic wetting and drying on swelling strain and swelling pressure to simulate the behavior of such rocks under heavy structures (such as building foundations) and behind the stiff support systems (such as concrete linings). Mudstone samples from Bakhtiari formation of Masjed-Soleiman region in south west of Iran were chosen to perform the laboratory tests. The swelling strain under different dead pressures and also swelling pressure under oedometeric condition were measured over time. The maximum swelling strain and pressure increased with each cycle but it had a bound. Increasing the number of wetting and drying cycles reduces the time required to reach ultimate swelling of mudstone. This is a very important conclusion which helps to determine ultimate swelling behavior in a faster way as opposed to performing standard swelling tests for very long periods. The laboratory’s results are also in good correspondence with field measurements.     

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.     

循环荷载对粉质黏土力学性质的影响

通过等压固结静、动三轴试验,研究了渤海湾粉质黏土在循环荷载作用下的动力性质和循环荷载后不排水静力性质。试验结果表明,循环应力幅值比越大,平均轴向应变和轴向应变幅值越大;循环应力幅值比达到0.4时,平均轴向应变和轴向应变幅值随着循环周数增加迅速增大;循环应力幅值比相同,固结应力越大,轴向应变幅值越大,而平均轴向应变越小。在较大的循环应力幅值比下,平均孔压比值和孔压幅值比值随着循环周数的增大会达到稳定;循环应力幅值比越大平均孔压比值和孔压幅值比值均越大;相同循环应力幅值,固结应力越大平均孔压比值越小,而固结应力对孔压幅值比值影响较小。循环荷载的作用会导致循环荷载后不排水剪在q-p’平面上有效应力路径和孔压发展表现出超固结土的性质。     

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.     

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。     

上海软土动剪切模量衰减规律的试验研究

为了获得上海软土在循环动力荷载作用下的动力特性,特别是动剪切模量的衰减规律,采用原状第④层上海软土进行等向固结不排水动三轴试验,分析了加载频率和动应力比 对动剪切模量的影响。试验结果表明,对于上海第④层软土,动应力比达到0.2时,土样才发生破坏;土样的剪切模量-累积轴应变曲线不受加载频率和动应力比的影响;剪切模量的衰减下降主要发生在轴应变0～1%区间。最后提出了一个描述剪切模量衰减规律的数学模型。     

考虑循环应力比和频率影响的动荷载下软土微观结构研究

以杭州原状软土为研究对象,借助扫描电镜和PCAS微观定量测试技术,采用分形理论对波浪荷载下的饱和软土微观结构进行研究,探讨不同循环应力比和不同频率条件下孔隙的分布特征及其变化规律。结果表明：循环应力比越大或频率越低,试样破坏所需的循环次数越少;试样临界破坏应变水平随循环应力比的增加呈升高趋势,而不同频率下的临界破坏应变水平则基本一致;孔隙的尺度、排列、形态等特征均随循环应力比的变化呈规律性变化,但随频率变化没有明显的规律性;循环剪应力作用下,孔隙破碎的同时兼并生长,这是剪切带上褶皱现象的微观本质,并且孔隙排列方向与剪切带方向基本一致。通过循环加载前、后微观结构特征参数的变化规律,揭示了波浪荷载下循环应力比和频率对土体微观结构的影响以及土体宏观变形的微观机制。     

Laboratory Investigation of the Resistance of Tailings and Natural Sediments to Cyclic Loading

A number of cyclic triaxial tests were carried out on mine tailings and natural sediment samples under undrained conditions to investigate their resistance to cyclic loading. The tests were performed on more than 100 samples with a cyclic shear stress ratio ranging from 0.10 to 0.40 under varying void ratio and the same confining pressure. It was observed that the axial strain and excess pore water pressure increased with the number of loading cycles while the effective stress decreased with increasing number of loading cycles. The liquefaction resistance of the tailings was also observed to be higher than that of natural soils with similar particle size distribution, void ratio and plasticity index. It was observed that the influence of specific gravity on the cyclic strength of mine tailings is significant. The results showed that the cyclic resistance of the tailings was not strongly influenced by plasticity index for low plasticity tailings. A boundary relationship between void ratio and normalized cyclic resistance ratio was established based on the results.     

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。     

粉土循环累积应变和残余动模量的试验研究

粉土地基上建造的铁路或公路在交通荷载作用下易产生各种病害,导致基础设施不能正常工作。为研究交通循环荷载作用下粉土的累积变形和动力性能,针对钱塘江粉土开展一系列的循环三轴试验,探讨土体物理条件（相对压实度、含水率）和应力特征（频率、围压、动应力比）等对粉土累积轴向应变、动模量和阻尼比等的影响。试验结果表明,钱塘江粉土的临界动应力比约为0.11,当轴向动应力小于临界动应力时,粉土的动模量变化很小,相应的累积轴向应变也很小;当动应力超过临界动应力后,土样的动模量快速下降,残余动模量约为初始弹性模量的20%,同时,动模量和阻尼比随着累积轴向应变（或名义振次）的发展变化显著。粉土的动模量和阻尼比在归一化后可得到统一规律：在轴向应变（或名义振次）小于一定值时,动模量几乎不变,而后呈指数形式衰减,最终趋于稳定值;粉土阻尼比随着轴向应变（或名义振次）的发展呈指数关系增长。     

粉质黏土周期荷载后的不排水强度衰化特性

在3种不同围压下进行了一系列重塑粉质黏土的静三轴和动-静三轴不排水剪切试验,得到了不同动应力水平条件下粉质黏土的孔压、动应变和不排水剪切强度值。通过对土样的不排水强度、孔压和动应变的无量纲化处理,确定了周期荷载作用后粉质黏土的不排水强度比与动载引起的孔压比和动应变比之间的相关关系。试验结果表明：粉质黏土在周期荷载作用后的不排水强度衰减程度取决于动载引起的动应变比值和孔压比值。当周期荷载引起的动应变比值小于0.1时,孔压比增长较快,土样的不排水强度几乎没有衰减;当动应变比大于0.1时,孔压比增长变慢,土样的不排水强度明显衰减;当动应变比值接近1时,孔压比值达到0.9,土样的不排水强度衰减程度约达到55 %     

循环剪切荷载作用下软土的力学性状研究

利用从现场取得的原状土样,通过室内动三轴试验对循环荷载作用下的变形、孔压和强度特性进行研究。试验研究主要考虑了周围固结压力、循环剪切应力比、荷载频率和循环次数等因素的影响。研究表明,在循环荷载作用下,孔隙水压力和轴向应变均是一个波动上升的过程。当循环应力比增大时,动孔隙水压力变化幅值显著增加,而残余孔压也较大。同时,孔隙水压力值也随着周围压力的增大而明显增大。当作用荷载频率比较大时,需要更多的循环次数才能达到小频率作用荷载能达到的孔隙水压力值。但是,随着循环荷载作用次数的增加,频率对孔隙水压力的影响有减小的趋势。     

循环应力比和振动频率对盐渍土微观结构影响分析

以青海省察尔汗地区盐渍土为研究对象, 借助扫描电子显微镜（SEM）设备和颗粒孔隙及裂隙图像识别与分析系统（PCAS）, 应用图像分割原理和分形理论, 对交通循环荷载作用下的盐渍土微观结构进行研究, 探讨不同循环应力比和不同振动频率下孔隙分布特征及其微观机制。结果表明： 循环应力比R由0.375增加到0.75, 临界破坏动应变由2.32%增高到3.17%, 动载循环次数相应减少; 振动频率f由0.5 Hz增加到2.0 Hz, 临界破坏动应变由2.82%减小到2.48%, 动载循环次数相应增多; 盐渍土孔隙参数随循环应力比的增大, 孔隙尺度分维值D_v 增长了0.12, 概率熵H_m 减小了0.017, 孔隙的形态分形维数D减小了0.27, 平均形状系数F增加了0.14, 变化规律较明显; 随振动频率的增大, D_v 增长了0.014, H_m 减小了0.002, D变化了0.06, F变化了0.003, 变化规律不明显; 在动荷载作用下, 试样的孔隙空间排列与宏观上的褶皱鼓状变形具有一致性。通过未加载试样与加载后试样的微观结构参数变化对比, 从循环应力比和振动频率对盐渍土微观孔隙特征的影响到宏观变形的相互作用机制进行了系统分析。     

循环荷载下黏土应变积累积强化模型研究

循环加载历史是影响土的动力特性的一个重要因素。通过对一种原状粉质黏土进行高循环次数单剪试验,研究了黏土体应变随剪应变幅值及循环次数的变化规律,以及由于体应变的累积对黏土动力特性产生的影响。试验结果表明,黏土的体应变随着循环次数的增多和循环剪应变幅值的增大而增大,而土的动力特性则随着体应变的不断累积而出现强化现象,表现为动剪模量增加,阻尼比减小。对累积体应变与动剪模量、阻尼比之间的关系进行了研究,提出了相应的强化关系式。在常用的非线性模型基础上,通过引入动剪模量的强化系数和阻尼比的衰减系数,建立了一种能考虑循环应变历史影响的土动力模型。