On incremental non‐linearity in granular media: phenomenological and multi‐scale views (Part I)

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto‐viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro‐mechanical models based on multi‐scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro‐mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non‐linear character of their behaviour. It is shown that both phenomenological and micro‐mechanical models exhibit an incremental non‐linearity. In addition, the multi‐scale approach reveals that the macroscopic incremental non‐linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.     

含天然气水合物沉积物损伤统计本构模型

水合物含量、有效围压是影响含天然气水合物沉积物力学性质的主要因素,在忽略其他次要因素（包括水合物种类、试样颗粒大小、试验条件等）的情况下,水合物含量和有效围压是决定试样弹性模量的两个关键参数。在分析等效弹性模量与水合物含量相互关系的基础上,考虑有效围压的影响,建立了弹性模量与有效围压的幂函数关系;同时采用Drucker-Prager破坏准则来表示含天然气水合物沉积物微元强度,并假设其微元强度服从Weibull分布,从而建立了含天然气水合物沉积物的损伤统计本构模型,与不同有效围压下的试验结果及已有研究成果相比较,表明了所建模型能够很好地模拟三轴剪切条件下含水合物沉积物试样的应力-应变关系特性。此研究成果可对含天然气水合物沉积物工程性状的数值模拟提供参考。     

渤海海冰动力学中的粘弹塑性本构模型

在粘塑性海冰本构模型的基础上,将Kelvin-Voigt粘弹性本构理论引入到海冰动力学中,进而建立了粘弹塑性海冰本构模型.该模型可较好地反映渤海海冰在小应变和小应变率条件下的粘弹性力学行为,同时还考虑了大应变率下的海冰粘塑性力学行为.对渤海辽东湾海冰进行了48h数值模拟.结果表明:粘弹塑性海冰本构方程较Hibler的粘塑性本构模型可更好地处理渤海的冰间相互作用,提高海冰数值模拟的计算精度.     

Nonlinear flexure and equivalent mechanical thickness of the lithosphere

The elastic flexural thickness of the lithosphere depends on plate curvature. As curvature increases, the elastic core of the plate is thinned from above (frictional yielding) and from below (plastic creep). Sometimes decoupling between crust and mantle elastic cores can also occur. The mechanical thickness of the lithosphere, on the other hand, is the thickness of the rheologically layered plate having a strength above a critical threshold. In order to estimate the mechanical thickness from a simple uniform-rheology plate model, we adopt a plastic work-hardening constitutive equation, which results in lower stresses in the regions of high strain, relative to the elastic model. It is, therefore, a better approximation to the actual rheology of the flexed lithosphere where there is no lower-crustal decoupling (e.g., in oceanic and in cold continental lithosphere). The equivalent mechanical thickness of the nonlinear plate can be directly obtained, if the curvature is known, from the estimated elastic flexural rigidity or thickness. Comparison with numerical integration of bending moment in rheologically layered lithosphere shows that equivalent mechanical thickness is a good estimation of mechanical thickness. Examination of both oceanic and continental data suggests that mechanical thickness is controlled by the 900 ± 100°C isotherm. This corresponds to a creep strength of the order of 10 MPa in upper mantle material.     

On the strength of transversely isotropic rocks

Accurate prediction of strength in rocks with distinct bedding planes requires knowledge of the bedding plane orientation relative to the load direction. Thermal softening adds complexity to the problem since it is known to have significant influence on the strength and strain localization properties of rocks. In this paper, we use a recently proposed thermoplastic constitutive model appropriate for rocks exhibiting transverse isotropy in both the elastic and plastic responses to predict their strength and strain localization properties. Recognizing that laboratory‐derived strengths can be influenced by material and geometric inhomogeneities of the rock samples, we consider both stress‐point and boundary‐value problem simulations of rock strength behavior. Both plane strain and 3D loading conditions are considered. Results of the simulations of the strength of a natural Tournemire shale and a synthetic transversely isotropic rock suggest that the mechanical model can reproduce the general U‐shaped variation of rock strength with bedding plane orientation quite well. We show that this variation could depend on many factors, including the stress loading condition (plane strain versus 3D), degree of anisotropy, temperature, shear‐induced dilation versus shear‐induced compaction, specimen imperfections, and boundary restraints.     

Comparative study on three-dimensional statistical damage constitutive modified model of rock based on power function and Weibull distribution

According to the characteristics of the microscopic unit strength of rock with random distribution, the power function distribution, and the Weibull distribution which is widely used in the past as the distribution function of the strength of the rock. Based on the theory of rock damage and statistical strength theory, two damage constitutive models established under three different confining pressures are modified. Then, the damage constitutive modified model of two kinds of distribution is verified and compared with the existing three axis test data. The results show that: (1) In the stage of elastic deformation of rock, the two theoretical damage constitutive model curves are in high agreement with the three axis test curve; (2) The rock at the plastic stage (hardening and softening), damage constitutive model established by Weibull probability distribution and experimental curve fits better than the damage constitutive model established by power function distribution. Especially in high confining pressure, damage constitutive model based on Weibull distribution can well describe the rock deformation from brittle to ductile transition process and power function is not; (3) In the residual strength in rock, damage variable D of damage constitutive model based on power function distribution appeared more than 1, which is deviation from the actual one and damage constitutive model based on Weibull distribution is not deviating. To summarize, using Weibull distribution statistical probability model to describe the microscopic unit strength of rock is more reasonable.     

干湿循环作用下砂岩力学特性及其本构模型的神经网络模拟

基于不同干湿循环作用下砂岩单轴压缩试验结果,分析了干湿循环效应对砂岩变形、强度、破坏特征等力学特性的影响规律,认为随着干湿循环次数的增加,弹性模量及峰值强度均有降低的趋势,降低幅度先大后小,而且会以某一具体值为临界值发展变化,就本次试验而言为干湿循环20次时的抗压强度和弹性模量值;砂岩的破坏特征亦会受到干湿循环试验次数的影响,干湿次数越少,脆性破坏越明显,反之则延性特征增强,即砂岩会呈现一种从脆性到延性转化的破坏规律。以应变和干湿试验次数为输入层,应力为输出层,构建了2-12-1的三层神经网络本构模型。通过样本的学习与检验,证明该模型能较好地描述干湿循环作用下砂岩的力学性能,验证了利用神经网络方法建立岩石本构模型的可行性与可靠性。基于预测结果,建立了完整的考虑干湿循环效应的砂岩力学特性变化规律的数学函数关系式。     

非均匀岩石介质单轴压缩强度及变形破裂规律的数值模拟

以有限差分法(FDM)为计算框架,利用Weibull分布描述细观单元弹性模量和单轴抗压强度的分布特征,采用弹塑性应变软化本构模型描述细观单元的力学响应,进而建立一种模拟非均匀岩石介质破裂的数值模型。采用该数值模型探讨了单轴压缩时细观均质度m及细观结构对数值试样宏观特性的影响。结果表明,（1）随着细观均质度提高,数值模型的非线性特征逐渐减弱,脆性逐渐增强;宏观峰值强度及弹性模量逐渐增大,峰值强度与lnm呈线性关系,而弹性模量与1/m为线性关系;数值试样表现出由塑性流动破坏至剪切破坏进而为张拉破坏的破坏模式;（2）当细观均质度一定时,细观结构或细观单元空间排列是决定岩石力学行为波动性的主要因素;应力–应变曲线峰前阶段对细观单元的空间排列不敏感,但峰值强度附近及峰后阶段对细观单元的空间排列比较敏感。     

层状岩体深埋长隧道锚杆支护优化设计

层状岩体是地下工程中经常遇到的一种岩体,力学性质具有明显的各向异性。选择合适的屈服准则和强度参数变化规律,结合各向异性弹性本构方程,获得横观各向同性弹塑性本构关系,利用该本构模型对共和隧道锚杆支护方案进行数值计算。首先考虑地应力、岩性的影响,从围岩的变形、破坏形式、塑性区及锚杆拉力的大小等方面改进、优化支护设计方案;其次从实际工程出发,考虑施工难度、工程造价等因素的影响,得到改进方案Ⅰ效果较理想,通过试验段现场监测确定改进方案I。本构模型对计算结果的影响很大,正确模型的计算结果可以为实际工程提供科学依据。     

一种新型粗糙节理面随机强度模型及其应用

天然岩体在长期地质作用下会生成各种节理裂隙等不连续面,而地下工程结构的稳定性一般取决于这些不连续面的强度。在众多因素中,表面形态对岩石节理面剪切强度具有决定性影响。为了系统研究岩石节理面剪切强度的确定方法,把岩石节理面概化为一系列高度不同的微长方体凸起组成的粗糙表面结构,且微长方体凸起有剪胀破坏和非剪胀破坏两种模式。综合微长方体凸起破坏规律,应用概率密度函数描述节理面表面起伏分布的影响,建立了粗糙节理面随机强度模型,推导了节理面剪切强度理论公式,提出了节理面强度的随机评价方法。基于随机强度模型和评价方法编制Matlab计算程序计算自然粗糙节理面的剪切强度,并将计算结果与试验结果进行比较分析。研究表明:粗糙节理面随机强度模型综合了粗糙节理面表面形态和法向应力对节理剪切强度的影响机制,理论计算值与试验数据吻合良好,可以较好的评价粗糙节理的峰值剪切强度和残余剪切强度。该随机模型可作为进一步深入研究的重要基础,分析结构面的连续剪切过程,建立更完善的节理面强度模型。     

基于Weibull分布的冻结砂岩损伤本构模型研究

冻结岩石的变形破坏特性是冻结法施工过程中的基础力学问题,在荷载作用下不同冻结温度岩石的力学特性和变形特征差异性较大,严重影响冻结壁的安全与稳定。因此,研究冻结岩石的损伤本构关系,对指导冻结法设计与施工具有重要意义。为分析荷载作用下冻结岩石变形破坏的全过程,采用Weibull分布描述岩石材料的非均质性,基于Drucker-Prager破坏准则,建立三轴应力状态下岩石损伤本构模型,结合冻结砂岩三轴压缩试验,重点分析本构关系中均质度系数m、平均强度F₀与冻结温度和围压的变化关系,对损伤本构方程进行修正,并基于此模型研究冻结砂岩的损伤演化规律。结果表明:在相同围压下,随着冻结温度的降低,砂岩峰值强度显著增大,峰值应变减小,压密阶段逐渐减弱,弹性变形阶段斜率增加,岩石脆性破坏特征明显。在相同冻结温度下,均质度系数m和平均强度F₀随围压升高无显著变化,而随着冻结温度的降低,m和F₀分别呈现指数增长和线性增长,说明随着冻结温度的降低,砂岩冻结越充分,内部自由水冻结成冰占比及冰体强度增长幅度越大,尤其在0~–10℃内提升效果显著,冻结作用提高了砂岩的均质性和平均强度。基于不同冻结温度砂岩的力学特性和变形规律,对不同冻结温度砂岩的损伤本构方程进行了修正。依据修正本构模型研究发现,损伤演化曲线能够很好地反映冻结砂岩压缩试验的压密、线弹性、屈服变形及应变软化各阶段的变形特征,验证了模型的合理性。研究结果为低温环境下岩石力学特性研究及地下冻结工程设计施工提供有益的参考。      

A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils

This paper presents a three‐dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled‐suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water‐retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water‐retention behaviour is studied using data obtained from controlled‐suction wetting–drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress–strain‐strength behaviour and the effect of void ratio on the water‐retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka–Nakai criterion. Model predictions of the stress–strain and water‐retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 John Wiley & Sons, Ltd.     

青藏冻结粉土与混凝土基础接触面本构关系研究

土冻结过程中,冰胶结作用使周围土体颗粒与建（构）筑物基础联成一体,这种胶结力称为土与基础间的冻结强度,通常采用冻土沿物体（例如基础材料）表面的剪切强度来度量。因而,冻土与基础接触面的应力-应变关系及其强度特征是确定冻土区基础工程承载力、抗拔性能和分析构筑物与冻土相互作用的基础和关键。为了更好地服务于工程实际,通过大量的冻结粉土与混凝土基础接触面剪切试验,总结了冻土接触面的基本力学特征和受力变形规律。根据获取的剪应力-位移曲线和冻结粉土接触面强度变化规律,利用标准本构模型建模方法,建立了冻结粉土接触面应力-位移-温度本构方程。该模型可以较好地描述不同温度冻结粉土接触面应力-位移变化规律,并为冻土区构筑物受力和变形数值计算提供基础。     

斜坡失稳的燕尾突变模型

文章对一个平面滑动型斜坡,考虑滑面介质有和上部岩体由不同力学性质的材料组成,上部岩体为弹性介质,滑带介质为应变软化介质。对应变软化介质,用W e ibu ll分布描述滑带介质的剪应力与应变关系,建立了斜坡系统的燕尾突变模型。通过分析,发现斜坡失稳与刚度比具有极大关联性。随着刚度比的增大,斜坡开始滑动时的0值降低不断降低,突跳时*值也随着降低。此时的临界值x*增大,突跳量x变小。当刚度比增加到一定程度后,会出现无突跳式的滑动。     

海冰韧脆转变特性的宏微观分析

冰荷载是寒区海洋工程结构物设计的控制荷载。海冰强度研究是确定冰荷载的基础。从宏微观结合的角度研究海冰强度特性,通过对海冰韧脆转变的微观机制分析,给出了微裂纹形成机制和扩同制;通过对Ｒｉｃｅ－Ｔｈｏｍｓｏｎ模型的分析,得出了韧－脆转变的判据;最后进行了韧脆转变区的强度计算。与实验结果相符。     

On double shearing in frictional materials

This paper evaluates the mechanical behaviour of yielding frictional geomaterials. The general Double Shearing model describes this behaviour. Non‐coaxiality of stress and plastic strain increments for plane strain conditions forms an important part of this model. The model is based on a micro‐mechanical and macro‐mechanical formulation. The stress–dilatancy theory in the model combines the mechanical behaviour on both scales. It is shown that the general Double Shearing formulation comprises other Double Shearing models. These models differ in the relation between the mobilized friction and dilatancy and in non‐coaxiality. In order to describe reversible and irreversible deformations the general Double Shearing model is extended with elasticity. The failure of soil masses is controlled by shear mechanisms. These shear mechanisms are determined by the conditions along the shear band. The shear stress ratio of a shear band depends on the orientation of the stress in the shear band. There is a difference between the peak strength and the residual strength in the shear band. While peak stress depends on strength properties only, the residual strength depends upon the yield conditions and the plastic deformation mechanisms and is generally considerably lower than the maximum strength. It is shown that non‐coaxial models give non‐unique solutions for the shear stress ratio on the shear band. The Double Shearing model is applied to various failure problems of soils such as the direct simple shear test, the biaxial test, infinite slopes, interfaces and for the calculation of the undrained shear strength. Copyright © 2006 John Wiley & Sons, Ltd.     

生物酶改良膨胀土的修正殷宗泽模型

以描述生物酶改良膨胀土的应力?应变关系为研究目的,提出基于生物酶掺量的修正殷宗泽模型。开展了一系列三轴排水剪切试验。对不同生物酶掺量下改良膨胀土的弹性形变演化规律进行了分析,同时研究了生物酶掺量与剪切压缩、剪切膨胀相关的屈服面形状的演化规律,以及与破坏线方程的演化规律。在此基础上分析了生物酶掺量对殷宗泽模型的参数影响规律。引入生物酶掺量作为修正殷宗泽模型的修正因子,最终对殷宗泽模型进行了修正。研究结果表明：生物酶能有效地提高改良膨胀土的力学性能,修正殷宗泽模型能够很好地描述生物酶改良膨胀土的土体本构关系。对比修正殷宗泽模型的理论计算值与试验值,两者具有很高的吻合度,且修正殷宗泽模型的参数确定方法与殷宗泽模型参数确定方法相同。     

Kinematic hardening plasticity formulation of small strain behaviour of soils

An objective of this paper is to demonstrate that the small strain model developed by the authors can be incorporated into the conventional kinematic hardening plasticity framework to predict pre‐failure defor mations. The constitutive model described in this paper is constituted by three elliptical yield surfaces in triaxial stress space. Two inner surfaces are rotated ellipses of the same shape, representing the boundaries of the linear elastic and small strain regions, while the third surface is the modified Cam clay large‐scale yield surface. Within the linear elastic region, the soil behaviour is elastic with cross‐coupling between the shear and volumetric stress–strain components. Within the small strain region, the soil behaviour is elasto‐plastic, described by the kinematic hardening rule with an infinite number of loading surfaces defined by the incremental energy criterion. Within the large‐scale yield surface, the soil behaviour is elasto‐plastic, described by kinematic and isotropic hardening of the small strain region boundary. Since the yield surfaces have different shapes, the uniqueness of the plastic loading condition imposes a restriction on the ratio between their semi‐diameters. The model requires 12 parameters, which can be determined from a single consolidated undrained triaxial compression test. Copyright © 2000 John Wiley & Sons, Ltd.     

基于正态分布的岩石损伤统计本构模型及其参数确定方法研究

根据岩石微元强度服从正态分布的特点,引进能合理描述岩石微元强度的参量,基于岩石三轴应力应变试验曲线建立了反映岩石破裂全过程的统计损伤本构模型。在此基础上,重点探讨了正态分布参数对岩石损伤本构模型的影响,据此对岩石统计损伤模型进行了合理修正,从而建立了反映岩石破裂全过程的三维统计损伤本构模型,与试验结果及现有研究结果进行比较显示了该模型的合理性,具有广泛的应用前景。     

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and time-dependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10?6 s?1 to 1×10?3 s?1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value (about 0.1 to 0.2), soon reaches its minimum (about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.