A model for coupled mechanical and hydraulic behaviour of a rock joint

Constitutive laws for rock joints should be able to reproduce the fundamental mechanical behaviour of real joints, such as dilation under shear and strain softening due to surface asperity degradation. In this work, we extend the model of Plesha to include hydraulic behaviour. During shearing, the joint can experience dilation, leading to an initial increase in its permeability. Experiments have shown that the rate of increase of the permeability slows down as shearing proceeds, and, at later stages, the permeability could decrease again. The above behaviour is attributed to gouge production. The stress–strain relationship of the joint is formulated by appeal to classical theories of interface plasticity. It is shown that the parameters of the model can be estimated from the Barton–Bandis empirical coefficients; the Joint Roughness Coefficient (JRC) and the Joint Compresive strength (JSC). We further assume that gouge production is also related to the plastic work of the shear stresses, which enables the derivation of a relationship between the permeability of the joint and its mechanical aperture. The model is implemented in a finite element code (FRACON) developed by the authors for the simulation of the coupled thermal–hydraulic–mechanical behaviour of jointed rock masses. Typical laboratory experiments are simulated with the FRACON code in order to illustrate the trends predicted in the proposed model. © 1998 by John Wiley & Sons. Ltd.     

A viscoplastic model including anisotropic damage for the time dependent behaviour of rock

This paper presents a new constitutive model for the time dependent mechanical behaviour of rock which takes into account both viscoplastic behaviour and evolution of damage with respect to time. This model is built by associating a viscoplastic constitutive law to the damage theory. The main characteristics of this model are the account of a viscoplastic volumetric strain (i.e. contractancy and dilatancy) as well as the anisotropy of damage. The latter is described by a second rank tensor. Using this model, it is possible to predict delayed rupture by determining time to failure, in creep tests for example. The identification of the model parameters is based on experiments such as creep tests, relaxation tests and quasi‐static tests. The physical meaning of these parameters is discussed and comparisons with lab tests are presented. The ability of the model to reproduce the delayed failure observed in tertiary creep is demonstrated as well as the sensitivity of the mechanical response to the rate of loading. The model could be used to simulate the evolution of the excavated damage zone around underground openings. Copyright © 2005 John Wiley & Sons, Ltd.     

Analytical model for the mechanical behaviour of bolted rock joints subjected to shearing

Summary This study proposes a new analytical model for the prediction of the contribution of bolts to the shear strength of a rock joint. The main characteristics of this model are the accounts for the interaction of the axial and the shear forces mobilised in the bolt, as well as the large plastic displacements of the bolt occurring during the loading process. The complete curve of the bolt contribution as a function of the displacement along the joint can be computed, and the maximum bolt contribution is obtained by dissociating the bolt cohesion and the confinement effects. The comparison of the performances of this analytical model with test results shows its capacity to describe the observed phenomena. The effects of the most important parameters such as bolt inclination, mechanical properties of bolt material, rock strength and joint friction angle are clearly established and discussed.     

岩体结构面新型本构模型研究

对于涉及需要单独考虑岩体结构面的工程岩体结构分析,采用能反映岩体结构面主要力学特性的合理的本构模型是取得合理解答的关键问题之一。针对在经典连续介质力学理论框架内建立岩体结构面本构模型的缺点,基于岩体结构面的实际受力变形特性,采用直接法建立了一种新型岩体结构面本构模型。所建立的模型依据岩体结构面切向应力变形曲线及剪胀曲线的实际特征,将其分为峰前线性段、峰前非线性段以及峰后软化段,并分别给出了用于描述岩体结构面变形和强度等主要力学特性的数学模型,进而推导建立了结构面各变形阶段的增量型本构模型。最后,编写相关计算程序,采用所建立的新型本构模型以及被广泛采用的Plesha模型对经典的岩体结构面直剪试验成果进行拟合分析。结果表明,所建立的新型本构模型能更为合理的描述岩体结构面的主要力学特性,且模拟能力优于Plesha模型     

一种新的节理裂隙岩体弹塑性模型

提出一种节理裂隙岩体弹塑性模型,将结构划分为块体单元和缝单元,其中缝单元可以是实际节理裂隙,也可以是人为缝单元。以块体单元形心的刚体位移和块体的平均应变作为基本未知量。该模型能充分考虑节理裂隙材料和块体材料的本构关系,计算量不大,是一种位移不协调单元。该模型特别适合节理裂隙岩体的数值分析。     

A model for swelling rock in tunnelling

Summary In this paper, the phenomenon of swelling in tunnelling will be treated as a hydraulic-mechanical coupled process. This approach allows one to model the observed floor heaves realistically, i. e. without the prediction inevitable in the previous models of movements at the tunnel crown and walls. Furthermore, the development of heave and pressure over the course of time can be studied. The absence of deformations above the floor level is here interpreted as a consequence of the hydraulic boundary conditions. Besides the importance of seepage flow, the influence of rock strength is illustrated. Swelling rock is considered as an elastoplastic material. This allows one to predict the often large haaves of a tunnel floor as observed in situ. According to the numerical results, the area of practically relevant swelling strains extends as far as the plastic zone.     

基于Burgers模型的岩石非定常蠕变模型

伯格斯（Burgers）模型适合用来描述岩石第三期以前的蠕变曲线。为了描述整个蠕变过程,可以考虑力学参数的时间效应,用非定常黏壶替换Burgers模型中的定常黏壶,给出一种非定常Burgers模型,并推导出它的蠕变柔量,实验数据拟合表明该模型能较好地反映岩石的试验曲线     

A rock mass classification model for caving roofs

Summary Evaluation of the caving behaviour of longwall roof rocks has thus far been based on a pot-pourri of classification systems, which ignore basic caving criteria. The paper outlines a new classification model of roof strata namely cavability using fuzzy set methodology and linguistic variables to assign ratings for individual roof beds. A microcomputer program has been developed to evaluate the decision ratings for cavability and the model applied to ten longwall case-histories from Indian coalfields. The classification model has excellent potential for being used as a standard tool for the evaluation of caving behaviour of longwall roof rocks.     

软岩流变的一种新力学模型

软岩在低应力水平下表现为弹性和粘弹性;在较高的应力水平下表现为弹性、塑性和粘弹性;在高应力水平下表现为弹性、塑性、粘弹性和粘塑性。为了对其进行全面描述,首先,提出了两种非线性元件-蠕变体和裂隙塑性体,并将它们和描述衰减蠕变特性的开尔文体及描述瞬弹性的虎克体相结合,得到了一种新的复合流变力学模型。然后,通过其采用的软岩蠕变的分级增量循环加卸载试验证明,该模型可很好地描述软岩在不同应力水平下的蠕变特性特别是裂隙闭合阶段和加速蠕变阶段的特性,可在工程实际中推广应用。     

A double medium model for diffusion in fluid-bearing rock

The concept of a double porosity medium to model fluid flow in fractured rock has been applied to model diffusion in rock containing a small amount of a continuous fluid phase that surrounds small volume elements of the solid matrix. The model quantifies the relative role of diffusion in the fluid and solid phases of the rock. The fluid is the fast diffusion path, but the solid contains the volumetrically significant amount of the diffusing species. The double medium model consists of two coupled differential equations. One equation is the diffusion equation for the fluid concentration; it contains a source term for change in the average concentration of the diffusing species in the solid matrix. The second equation represents the assumption that the change in average concentration in a solid element is proportional to the difference between the average concentration in the solid and the concentration in the fluid times the solid-fluid partition coefficient. The double medium model is shown to apply to laboratory data on iron diffusion in fluid-bearing dunite and to measured oxygen isotope ratios at marble-metagranite contacts. In both examples, concentration profiles are calculated for diffusion taking place at constant temperature, where a boundary value changes suddenly and is subsequently held constant. Knowledge of solid diffusivities can set a lower bound to the length of time over which diffusion occurs, but only the product of effective fluid diffusivity and time is constrained for times longer than the characteristic solid diffusion time. The double medium results approach a local, grain-scale equilibrium model for times that are large relative to the time constant for solid diffusion.     

A model for the ductile yield of porous rock

A relatively simple yield model is developed for isotropic, porous rocks which yield in a ductile manner. The flow rule and yield function are derived using an adaptation of the work-balance approach of critical state soil mechanics. This adaptation allows for the dissipation of work by frictional and volume change mechanisms, including the dissipation of frictional work at sensibly constant plastic volumetric strain. The yield model uses two material parameters—a basic frictional parameter and a plastic volumetric strain adjustment parameter which is assumed to be constant for the yield locus corresponding to a particular specific volume. The model gives excellent fits to yield loci for two limestones, a chalk and gypsum plaster prepared at different initial void ratios.     

黏弹性节理岩体的位移不连续模型研究

选用三参数标准线性固体作为岩石本构,提出了一种考虑岩体黏弹性的位移不连续模型;根据一维黏弹性波的特征线法,推导了节理处质点速度、应力和应变递推公式。首先,基于分离式霍普金森压杆（SHPB）对砂层进行试验,得到其应力-应变关系,并换算出砂层节理的法向刚度;接着,通过一维强间断黏弹性波的波速公式、高频波衰减系数以及任一频率下的衰减系数,确定出数值算法中的三参数。最后,基于自制的摆锤装置,探讨了一维应力波在节理岩体中的传播规律,试验中以两根长1 000 mm、直径为68.50 m的岩杆作为入射和透射杆,以3 mm砂层模拟节理。试验和数值结果吻合度良好,进一步验证了该方法的可靠性。     

基于岩石统一能量屈服准则的硬岩损伤模型

为了更准确、便捷地确定深埋地下工程中硬岩的力学行为,开展了如下研究：根据损伤与塑性演化存在相似机制,假设损伤阈值与初始屈服采用相同的确定方法,将岩石统一能量屈服准则作为损伤阈值的判定准则;基于Rabotnov对损伤变量的定义和Lemaitre应变等效性假设,并考虑未损伤部分的应力-应变关系符合广义虎克定律,提出了简化形式的硬岩损伤本构方程;为了更好地表达硬岩从低围压到高围压条件下的脆-延转化特性,提出了改进的Mazars损伤演化方程;基于锦屏T2b大理岩常规三轴压缩试验结果,对损伤模型参数进行求解,并分别与基于Mazars损伤演化方程和Mohr-Coulomb准则为损伤阈值判定准则的损伤模型进行对比,结果表明：提出的损伤模型可更好地表达硬岩从低围压的脆性到高围压的延性转变过程,特别是对损伤阈值后岩石的损伤演化过程的模拟更为精确,对硬脆性岩石的工程计算有一定的借鉴意义。     

基于Burgers模型考虑损伤的非定常岩石蠕变模型

Burgers模型只能描述岩石蠕变的前两个阶段,为了描述蠕变全过程,考虑蠕变参数的时间效应及损伤带来的影响,采用非定常黏性元件取代Burgers模型中串联的定常黏性元件,使其能描述加速蠕变阶段。根据损伤变量的变化特征,假定了一个函数,经过Lemaitre应变等效原理,代入Kelvin模型可得到能描述蠕变衰减阶段的模型。试验数据拟合结果显示,改进的Burgers模型能很好地描述加速蠕变阶段,模型拟合曲线与试验曲线基本吻合,相关系数高,参数取值也在合理范围内;非定常Burgers模型更适合描述不同应力下的岩石蠕变特征曲线。     

描述岩石粘弹性固体性质的开尔文模型

大多数固体材料都具有弹性,但真实的固体却极少严格遵从弹性的虎克定律。这些固体材料的变形往往有对时间的依赖性,这种性质是流变学研究的内容。岩石是自然界最普遍的固体,它的力学性质在通常条件下可用虎克定律作精确的描述,而在漫长的地质过程中,岩石的流变特征就逐渐显现出来。地质作用越缓慢,岩石对变形时间的依赖性越明显。为精确描述岩石在地质过程的力学性质,流变学方法被引入地质学。笔者已经介绍过描述"牛顿流体"的马克斯威尔流变模型,文中介绍描述粘弹性固体的开尔文流变模型。和马克斯威尔模型一样,开尔文模型也是流变学的基本模型,它是由一个弹性元件和一个阻尼元件并联而成。文中给出开尔文模型的本构关系和地质应用的简介。     

循环加-卸载岩石本构模型研究

循环加-卸载岩石本构模型是预测压气储能洞室长期稳定性的关键,但目前还没有适用的本构模型,因此,提出了一种能够描述岩石循环加载和卸载的本构模型。鉴于岩石在循环作用下损伤不断累积,将基于Weibull分布的岩石损伤软化模型进行拓展,并用内变量疲劳本构模型描述每个循环的初始模量和卸载模量的变化,进而得到循环加-卸载作用下的岩石本构模型,然后将该模型与现有的试验结果进行对比。该模型物理意义明确,涉及的参数较少,且便于拟合。提出的循环加-卸载下岩石本构模型对试验数据拟合效果较好,能较准确地反映循环荷载上、下限值对应的轴向应变,也能反映出循环内部变形模量衰减的趋势。该模型的成功建立为循环加-卸载下岩石本构模型的研究提供了新思路。     

A new bounding surface model for thermal cyclic behaviour

To accurately predict soil volume changes under thermal cycles is of great importance for analysing the performance of many earth structures such as the energy pile and energy storage system. Most of the existing thermo‐mechanical models focus on soil behaviour under monotonic thermal loading only, and they are not able to capture soil volume changes under thermal cycles. In this study, a constitutive model is proposed to simulate volume changes of saturated soil subjected to cyclic heating and cooling. Two surfaces are defined and used: a bounding surface and a memory surface. The bounding surface and memory surface are mainly controlled by the preconsolidation pressure (a function of plastic volumetric strain) and the maximum stress experienced by the soil, respectively. Under thermal cycles, the distance of the two surfaces and plastic modulus increase with an accumulation of plastic strain. By adopting the double surface concept, a new elastoplastic model is derived from an existing single bounding surface thermo‐mechanical model. Comparisons between model predictions and experimental results reveal that the proposed model is able to capture soil volume changes under thermal cycles well. The plastic strain accumulates under thermal cycles, but at a decreasing rate, until stabilization. Copyright © 2017 John Wiley & Sons, Ltd.