小应变硬化土模型参数的确定与敏感性分析

地下工程施工引起的土体扰动区可分为剧烈扰动区、扰动区、微扰动区和未扰动区。为全面反映土体在扰动下的应力路径和力学响应,必须考虑全应变范围的土体特性,尤其是小应变范围内的力学响应,因此对小应变硬化土本构模型关键参数(初始剪切模量和剪应变阀值)的确定方法进行介绍。开展上海典型软土的三轴固结排水剪切试验和固结试验研究,给出确定上海软土小应变硬化土模型(HSSmall)参数的方法,建议采用原位测试的方法确定土体的初始弹性模量。基于土单元数值模拟进行初始弹性模量和剪应变阀值的参数敏感性分析。随着初始弹性模量的增大,初始压缩曲线与卸载-再压缩曲线的斜率均增大。由于对应的回弹模量不变,初始弹性模量与回弹模量的差值增大,应变与偏应力试验曲线的回滞环宽度也随之增大。随着剪应变阀值的增大,初始压缩曲线和再压缩曲线的近似直线段增长,在同样剪应力情况下,土体的应变值减小,土体保持初始弹性模量刚度的区间增大。     

滩海桶形基础承载力三维弹塑性有限元仿真

在经典的D rucker-Prager(以下简称D-P)弹塑性本构模型基础上,通过将线性屈服准则改为抛物线型屈服准则来模拟静水压力对土体的屈服与破坏,并根据实验确定的硬化曲线建立了改进的D-P模型,使该本构模型能很好地模拟大港滩海软土的应力应变关系。利用MARC程序作为平台,建立了滩海桶形基础承载力有限元分析模型,计算了实验桶形基础的承载力。将计算结果进行了与模型试验结果的比较,证明了该模型的有效性。     

考虑阻尼拟合的动态骨架曲线函数式

根据土体动力实验结果所示土体应力－应变关系的基本特征，本文提出了描述土体应力－应变骨架曲线及动态骨架曲线的一种简单合理的函数表达式，并将其引入作者建立的土体动力剪切动态骨架曲线应力－应变关系模型中，导出了能拟合土体实验阻尼值且形式简单合理，应用方便的土体动力剪切应力－应变关系的经验函数式。     

软土等向固结与K0固结条件下的三轴试验研究

对某软土重塑样分别进行等向固结和K0固结条件下的三轴试验,研究了不同固结条件、不同围压下软土的强度和应力应变特性,并对试验结果进行了分析和对比。结果表明：低围压下,等向固结三轴压缩试验和K0固结三轴压缩试验土样破坏时的主应力差差别不大,随着围压增大,K0固结条件下试验土体的主应力差要明显大于等向固结条件下的试验土体;与等向固结相比,K0固结条件下的土体粘聚力c值减小,而内摩擦角增大;土体呈现剪缩特性。运用等向固结三轴压缩试验确定的邓肯模型参数模拟K0固结条件下土体的试验曲线,吻合较好,初步验证了邓肯模型参数对K0固结土体的适用性。     

岩石损伤软化的修正本构模型

利用服从Weibull分布的岩石微元强度表示方法,基于Drucker-Prager破坏准则,通过引入损伤变量的修正系数,利用应力-应变关系曲线峰值点处的应力、应变确定Weibull分布参数的关系式,建立不同围压下的损伤软化本构模型。该模型参数较少且易于确定,其参数的确定方法揭示了模型参数的物理意义。与前人的研究成果进行对比分析,结果表明该模型比未修正前有着明显的优越性,且与实测结果吻合较好,分析结果显示出该模型的合理性。     

波浪荷载作用下软黏土软化模型研究

波浪荷载能引起海床土体的主应力轴连续旋转。不同于地震、交通等循环荷载,在周期性波浪荷载作用的土体应力路径方式下,软黏土的软化效用更为明显。本文分别对天然和扰动的海床土体在波浪荷载作用下的应力响应进行模拟,并分析应力路径的特点;为描述软化后的应力-应变关系,将软化效用和累积塑性应变的参数引入到能够反应土体动力非线性的Hardin-Drnevich模型中,建立修正模型,使之能够反应软黏土体软化与塑性应变累计特性;通过与模拟波浪荷载下土体应力特征的循环耦合试验结果进行对比分析,验证该修正模型的可靠性。     

循环荷载下南京片状细砂的动应力——应变关系

以片状颗粒成分为主的片状结构砂与常用的圆形颗粒标准石英砂相比,在物理力学特性上有显著的差异。循环荷载作用下,饱和砂土振动孔压上升会导致土体刚度发生软化,当振动孔压累积达到一定水平时,会产生液化现象,从而引起土体结构发生破坏。采用英国WFI动三轴仪,研究了南京片状细砂在循环荷载作用下,静偏应力水平、循环应力比水平和循环次数对其动应力一应变关系的影响,考虑每一次循环过程中动应力—应变关系滞回曲线的卸载及再加载割线动剪切模量Gsec和最大割线模量Gmax的变化特性,建立了动剪模量软化的经验公式;静偏应力水平对动剪模量软化有显著影响,随着循环次数的增加,动应力—应变滞回圈逐渐向应变累积方向滑移和向应变轴方向倾斜,且彼此分离;考虑循环软化特性,采用修正的Masing准则,描述了循环荷载下南京片状细砂的动应力—应变关系。     

基于双参数损伤阈值的高延性混凝土损伤本构模型研究

通过9组不同配合比高延性混凝土试件的单轴受压试验,研究了纤维桥联应力的约束作用对高延性混凝土试件单轴受压破坏形态的影响。根据高延性混凝土单轴受压应力-应变曲线的形状和特点,引入两个损伤阈值参数γ和β,建立了基于双参数损伤阈值的高延性混凝土单轴受压损伤本构模型。试验结果表明:高延性混凝土单轴受压损伤本构模型的初始损伤阈值γ远高于普通混凝土和钢纤维混凝土;达到峰值应变时,高延性混凝土的损伤值D远小于钢纤维混凝土的;纤维桥联应力的横向约束作用,显著提高了高延性混凝土单轴受压的耐损伤能力。本文建立的模型曲线与试验曲线吻合良好,能较好地描述纤维桥联作用的影响以及高延性混凝土单轴受压应力状态下的损伤发展过程。     

基于三轴试验红层泥岩的邓肯-张模型参数研究

兰州地区红层泥岩形成于干旱、半干旱环境,其物理力学特性与其他地区的红层泥岩不同。以G6京藏高速兰海养护维修工程的红层泥岩路基填料为研究对象,通过大量的常规三轴试验,研究含水率对其力学特性及邓肯-张模型参数的影响。结果表明:在不同含水率下兰州地区红层泥岩的应力-应变曲线关系符合双曲线模型。含水率小于最优含水率时,破坏形式为剪切破坏;含水率大于最优含水率,破坏形式为鼓状破坏;随着含水率的增加,黏聚力和内摩擦角逐渐减小,内摩擦角减小的幅度更大,究其原因是含水率对黏聚力和内摩擦角的影响机理不同而导致。采用数学模型进行拟合发现:黏聚力、内摩擦角与含水率分别呈二次抛物线与对数曲线关系。不同含水率下邓肯-张模型参数破坏比R_f在区间(0.869,0.984)内波动,K值随含水率增大而减小呈负线性关系,n值随含水率的增大而增大呈线性关系。     

描述软土不排水循环应力应变响应的拟动力关系

依据等效黏弹性理论与蠕变理论,建立了描述一般应力状态饱和软土不排水循环应力应变响应的拟动力本构关系。该关系包括三个基本参数：循环剪切模量,阻尼比与增量循环累积应变。利用循环剪切模量与阻尼比随土单元八面体剪应变的变化描述循环荷载作用下软土的不排水循环应变,依据Mises蠕变势函数与正交流动法则确定循环累积应变增量。通过饱和软土不固结不排水循环三轴压缩试验确定这些变化关系。按确定出的参数预测循环三轴拉伸与循环扭剪试验结果。预测出的循环拉伸试验剪切模量和阻尼比随八面体剪应变的变化与试验结果吻合。对于循环扭剪试验,当循环偏应力与静偏应力方向一致时,预测出的循环累积应变随循环次数的变化与试验结果基本一致;当循环偏应力与静偏应力作用方向不一致时,预测出的循环累积应变与试验结果相比偏小。     

Volume changes during fracture and frictional sliding: A review

Summary Volume changes in geologic materials have been measured with strain gauges, cantilever displacement gauges, or through observation of either pore or total volume. When porosity is less than 0.05, compaction is small or absent; apart from elastic strains in the minerals, dilatancy predominates, beginning at 50 to 75 percent of the fracture stress difference. When initial porosity exceeds about 0.05, compaction and dilatancy may overlap. The onset of dilatancy has not been identified, but most of the dilatancy occurs within about 10 percent of the fracture stress difference. In low porosity rocks, dilatancy increases initial porosity by a factor of 2 or more; in porous rocks or granular aggregates the increase is only 20 to 50 percent. However, the actual pore volume increase is larger in rocks of high initial porosity. Hence, earthquake precursors which depend on the magnitude of dilatancy should be more pronounced in porous rocks or in fault gouge. In contrast, precursors which are based on fractional changes in some porosity-related property may be more pronounced in rocks of low initial porosity. Future work is particularly needed on constitutive relations suitable for major classes of rocks, on the effects of stress cycling in porous rocks, on the effects of high temperature and pore fluids on dilatancy and compaction, and on the degree of localization of strain prior to fracture.     

Bounding surface plasticity model for the seismic liquefaction analysis of geostructures

This paper presents the constitutive relations and the simulative potential of a new plasticity model developed mainly for the seismic liquefaction analysis of geostructures. The model incorporates the framework of critical state soil mechanics, while it relies on bounding surface plasticity with a vanished elastic region to simulate the non-linear soil response. Key constitutive ingredients of the new model are: (a) the inter-dependence of the critical state, the bounding and the dilatancy (open cone) surfaces on the basis of the state parameter ψ, (b) a (Ramberg–Osgood type) non-linear hysteretic formulation for the “elastic” strain rate, (c) a discontinuously relocatable stress projection center related to the “last” load reversal point, which is used for mapping the current stress point on model surfaces and as a reference point for introducing non-linearity in the “elastic” strain rate and finally (d) an empirical index of the directional effect of sand fabric evolution during shearing, which scales the plastic modulus. In addition, the paper outlines the calibration procedure for the model constants, and exhibits its accuracy on the basis of a large number of laboratory element tests on Nevada sand. More importantly, the paper explores the potential of the new model by presenting simulations of the VELACS centrifuge tests of Models No 1 and 12, which refer to the free-field liquefaction response of Nevada sand and the seismic response of a rigid foundation on the same sand, respectively. These simulations show that the new model can be used successfully for the analysis of widely different boundary value problems involving earthquake soil liquefaction, with the same set of model constants calibrated on the basis of laboratory element tests.     

Finite strain rock plasticity: stress triaxiality, pressure, and temperature effects

An elasto-plasticity theory is used to model the deformation of geological materials under various confining pressures and moderate temperatures. The effects of material hardening (or softening due to volumetric strains) are included, and the corresponding elasto-plastic rate constitutive relations are developed. To study the influence of pressure and temperature on the constitutive parameters, we use some published data of laboratory experiments on certain rocks. It is shown that over a wide range of pressures and low to moderate temperatures, when the rate effect can be ignored, the model can be used to describe the behaviour of geological materials. Based on this theory, dilatancy (i.e., inelastic volumetric expansion) of an intact granite is studied under conventional triaxial stress states. The effect of pressure and temperature on the magnitude of dilation and on the stress (measured relative to the peak stress) at the onset of dilatancy is investigated. It is found that, consistent with experimental data, the theory predicts this stress to be about 50% of the peak stress, but its specific value depends on pressure and temperature. As an illustration, stress-strain curves for intact granite at relatively shallow crustal depths are then predicted for possible application to the study of crustal deformation and for the prediction of fault behaviour.     

地壳岩石剪切失稳的应力与应变准则

本文建立了岩石体膨胀起点与峰值点之间应力与应变关系的解析表达式,分别给出了其剪切失稳应力与应变准则.考虑到地壳岩石缓慢加载作用使其均匀性指标的减小效应,本文也分别给出了简化的适用于脆性破坏预测的应力与应变准则.实例表明该应变准则可用于崩塌与强震等脆性破坏问题的预测分析.     

Statistical damage constitutive model for rocks subjected to cyclic stress and cyclic temperature

A constitutive model of rocks subjected to cyclic stress–temperature was proposed. Based on statistical damage theory, the damage constitutive model with Weibull distribution was extended. Influence of model parameters on the stress–strain curve for rock reloading after stress–temperature cycling was then discussed. The proposed model was initially validated by rock tests for cyclic stress–temperature and only cyclic stress. Finally, the total damage evolution induced by stress–temperature cycling and reloading after cycling was explored and discussed. The proposed constitutive model is reasonable and applicable, describing well the stress–strain relationship during stress–temperature cycles and providing a good fit to the test results. Elastic modulus in the reference state and the damage induced by cycling affect the shape of reloading stress–strain curve. Total damage induced by cycling and reloading after cycling exhibits three stages: initial slow increase, mid-term accelerated increase, and final slow increase.     

Force–displacement response of in‐plane‐loaded URM walls with a dominating flexural mode

This article presents a new mechanical model for the non‐linear force–displacement response of unreinforced masonry (URM) walls developing a flexural rocking mode including their displacement capacity. The model is based on the plane‐section hypothesis and a constitutive law for the masonry with zero tensile strength and linear elastic behaviour in compression. It is assumed that only the compressed part of the wall contributes to the stiffness of the wall and therefore the model accounts for a softening of the response due the reduction of the effective area. Stress conditions for limit states are proposed that characterise the flexural failure. The new model allows therefore linking local performance levels to global displacement capacities. The limit states criteria describe the behaviour of modern URM walls with cement mortar of normal thickness and clay bricks. The model is validated through comparison of local and global engineering demand parameters with experimental results. It provides good prediction of the effective stiffness, the force capacity and the displacement capacity of URM walls at different limit states. Copyright © 2015 John Wiley & Sons, Ltd.     

预静载对全级配混凝土梁动弯拉强度的影响

为了探讨预静载对全级配混凝土梁动弯拉强度的影响,本文从全级配混凝土的细观层次出发,将梁的纯弯段视为由水泥砂浆、粗骨料及两者间的黏结带所组成的复合材料。采用既考虑应变率强化效应又计及损伤弱化效应的动态本构模型反映细观单元的损伤退化。通过自编的以位移控制的有限元程序对全级配混凝土梁在不同预静载作用下的破坏机制进行了数值模拟,给出了相应的应力一应变曲线和动弯拉强度。计算结果显示：全级配混凝土梁的动弯拉强度随着预静载的增加而上升。     

Effects of the constitutive relationship on seismic response of soils. Part II. The site amplification study

This paper is the first part of the general paper dealing with effects of constitutive modeling of cyclic stress–strain behavior of soils on site amplification. The paper concentrates on modeling of pseudo-static cyclic soil behavior in small to medium strain range. In order to fit the small strain data accurately, the chosen analytical stress–strain relationship should satisfy the specific small strain condition formulated for soils using the small strain data from the pseudo-static cyclic tests. Analysis of conventional relationships, in particular the Ramberg–Osgood (R–O) relationship, indicated that a failure to satisfy this condition lead to low accuracy of prediction of both tangent stiffness and damping ratio at small and medium strains. The logarithmic function originally proposed to describe static monotonic stress–strain behavior is applied to fit experimental cyclic backbone curves. Constructed to satisfy the formulated small strain condition for soils, this function has proven to be free from the limitations of the R–O and other relationships. When applied in combination with the Masing rules to predict damping ratios, it gives a good prediction in the small to medium strain range, where the Masing hypothesis is supported by experimental evidence.     

Simulating stiffness degradation and damping in soils via a simple visco-elastic–plastic model

Stiffness degradation and damping represent some of the most well-known aspects of cyclic soil behavior. While standard equivalent linear approaches reproduce these features by (separately) prescribing stiffness reduction and damping curves, in this paper a multiaxial, 3D, viscoelastic – plastic model is developed for the simultaneous simulation of both cyclic curves over a wide cyclic shear strain range.The proposed constitutive relationship is based on two parallel resisting/dissipative mechanisms, purely frictional (elastic–plastic) and viscous. The frictional mechanism is formulated as a bounding surface plasticity model with vanishing elastic domain, including pressure-sensitive failure locus and non-associative plastic flow – which are essential for effective stress analysis. At the same time, the use of the parallel viscous mechanism is shown to be especially beneficial to improve the simulation of the overall dissipative performance.In order to enable model calibration from stiffness degradation ($G/G_{\mathit{max}}$) and damping curves, the constitutive equations are purposely kept as simple as possible with a low number of material parameters. Although the model performance is here explored with reference to pure shear cyclic tests, the 3D, multiaxial formulation is appropriate for general loading conditions.     

岩石蠕变扩容与损伤变量本构关系

首先介绍了在不同压力组合下关于油母页岩的蠕变实验.实验表明,在瞬时扩容后,蠕变过程中的依赖时间的扩容持续增长.在引入反映岩石扩容程度时的损伤变量后,建立了损伤演化方程和本构方程以描述蠕变扩容的变化规律.最后,数值模拟了体应变与时间关系,与实验结果基本一致.