基于宏细观损伤耦合的非贯通裂隙岩体本构模型

针对非贯通裂隙岩体工程结构中的受荷岩体,提出受荷细观损伤与裂隙宏观损伤的概念。以完整岩石的初始损伤状态作为基准损伤状态,综合考虑裂隙宏观缺陷的存在、微裂纹细观缺陷在受荷下的损伤扩展以及宏细观缺陷在受荷过程中的耦合,基于Lemaitre应变等效假设,推导了考虑宏细观缺陷耦合的复合损伤变量,并给出同时考虑试件尺寸、裂隙几何与力学特性的宏观损伤变量的计算公式,从而建立了基于宏细观缺陷耦合的非贯通裂隙岩体在荷载作用下的损伤本构模型。用宏细观损伤耦合的本构模型来描述非贯通裂隙岩体在受荷过程中的细观损伤演化与宏观损伤行为,与非贯通裂隙岩体实际受荷情况符合较好。研究结果表明：（1）完整岩样和裂隙岩样的应力-应变行为在峰值强度之前差异较大,峰值强度以后差异逐渐减小,最后趋于一致,二者具有相近的残余强度;（2）裂隙岩体强度随裂隙贯通率的增加而增大,随裂隙倾角的变化具有明显的各向异性,同时还与裂隙面的内摩擦角有关;（3）裂隙倾角为90°时,裂隙岩样的峰值强度最高;张开型裂隙岩样的裂隙倾角为45°时,峰值强度最低;（4）非贯通裂隙岩体工程结构中的受荷岩体,其力学性能由受荷细观损伤与裂隙宏观损伤及其耦合效应所决定,基于宏细观损伤耦合的复合损伤变量可以较好地反映非贯通裂隙岩样的力学特性。     

双轴应力下非贯通节理岩体压缩损伤本构模型

针对目前节理岩体损伤变量定义中大多仅考虑节理长度、倾角等几何性质,而未考虑节理抗剪强度等力学性质的不足,基于断裂力学中的由于单个节理存在引起的附加应变能增量与损伤力学中的损伤应变能释放量相关联的观点,推导出了在双轴应力下含单条非贯通闭合节理岩体的损伤变量计算公式,并根据断裂力学理论对双轴压缩荷载下的单个节理尖端应力强度因子计算方法进行了研究,得出了应力强度因子KⅠ、KⅡ的计算公式;同时考虑多节理间的相互作用,给出了单组单排及单组多排非贯通节理尖端应力强度因子计算公式,由此建立了相应的节理岩体双轴压缩损伤本构模型,并利用该模型进行了相应的算例分析。结果表明：对含单条非贯通闭合节理的岩体而言,当节理倾角小于其内摩擦角时,岩体强度与完整岩石相同,岩体损伤为0,而后随着节理倾角增加,岩体强度、损伤随节理倾角的变化分别呈开口向上及向下的抛物线,当节理倾角约为60°时,岩体损伤最大,强度最低。随着节理长度增加,岩体损伤增加,而随着节理内摩擦角的增加,岩体损伤则减小;对含单组单排非贯通闭合节理的岩体而言,当节理总长度一定时,随着单条节理长度的减小及节理条数的增加,岩体损伤则逐渐减小,但其减小幅度与节理条数并不呈线性关系。     

单轴压缩荷载下非贯通闭合节理岩体损伤本构模型

目前损伤力学已被认为是研究节理岩体力学行为的有效工具,但是在目前的节理岩体损伤变量定义中大多仅考虑节理几何特征而未考虑节理内摩擦角等力学参数,这显然不能很好地反映节理岩体的力学特征。为此,拟推导出一个能够综合考虑节理几何及力学参数的损伤变量（张量）,并由此建立单轴压缩荷载下岩体损伤本构模型。首先,基于断裂力学的由于单个节理存在引起的附加应变能增量与损伤力学的损伤应变能释放量相关联的观点,推导出了含非贯通节理岩体的损伤变量计算公式;其次,根据断裂力学理论对单轴压缩荷载下的单个节理尖端应力强度因子计算方法进行了研究,得出了应力强度因子K_Ⅰ、K_Ⅱ的计算公式;同时考虑多节理间的相互作用给出了单组单排及多排非贯通节理应力强度因子计算公式。最后,利用该模型对含单条非贯通节理的岩体在单轴压缩荷载作用下的峰值强度及损伤变量进行了分析计算。结果表明,当节理倾角小于其内摩擦角时,岩体强度与完整岩石相同,岩体损伤为零,而后随着节理倾角增加,岩体强度、损伤随节理倾角的变化分别呈开口向上及向下的抛物线,当节理倾角约为60°时,岩体损伤最大,强度最低。随着节理长度增加,岩体损伤增加,而随着节理内摩擦角的增加,岩体损伤则减小。      

基于摩尔-库仑准则的断续节理岩体复合损伤本构模型

针对工程实际中断续节理裂隙岩体的损伤本构模型,假设岩石微元强度服从Weibull随机分布,以摩尔-库仑破坏准则作为描述微元强度的表示方法,推导出细观损伤变量。利用能量和断裂力学理论,综合考虑节理几何特征及力学特性,推导宏观损伤变量计算公式。基于Lemaitre应变等效假设,考虑宏细观缺陷耦合作用,推导出复合损伤变量,建立了基于摩尔-库仑准则的宏细观缺陷耦合作用的断续裂隙岩体损伤本构模型。研究结果表明：（1）采用摩尔-库仑准则作为描述微元强度的统计分布变量建立的损伤模型能够较好地反映岩石内部缺陷分布和变形特征,该模型真实地反映岩石微元强度受应力状态的影响。（2）该模型建立的理论曲线与断续节理岩体的试验曲线吻合较好。（3）节理裂隙岩体宏观损伤变量及峰值强度随节理倾角的变化规律与综合考虑宏细观耦合作用下的损伤变量及裂隙岩体峰值强度随节理倾角的变化规律基本一致。（4）宏细观耦合作用下的等效弹性模量与节理贯通率呈非线性负相关;在节理倾角一定的情况下,损伤变量与节理长度呈非线性正相关;在贯通率较小时,岩体的宏观损伤变量与内摩擦角的关系呈线性负相关变化,贯通率达到一定程度,线性关系变成非线性关系。     

SPH procedures for modeling multiple intersecting discontinuities in geomaterial

A methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic‐plastic constitutive model. Free‐sip, no‐slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system. The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd.     

非贯通节理岩体损伤变量计算方法研究

作为岩体组成部分的非贯通节理对岩体力学特性有着重要影响,然而几乎目前所有的岩体损伤变量计算方法都仅考虑节理几何参数对岩体力学特性的影响。对含单组非贯通节理的岩体力学特性进行研究,提出一个能够同时考虑节理几何及强度参数对岩体力学特性影响的新的岩体损伤变量计算方法。首先,采用弹性余能等效假设代替Lemaitre应变等效假设研究由节理引起的岩体各向异性损伤,并基于断裂力学中单个节理引起的附加应变能增量与损伤力学应变能释放量相关联的观点,推导出由单条节理引起的损伤变量计算公式。其次,根据断裂力学理论获得了单轴压缩下单条节理尖端应力强度因子（SIF）KⅠ、KⅡ的计算公式。最后,通过考虑节理间的相互作用给出了单组单排或多排节理尖端应力强度因子KⅠ、KⅡ的计算公式,得到了单组节理引起的岩体损伤变量计算公式,并与已有试验结果的对比分析证明了该公式的合理性。     

综合考虑宏微观复合损伤的节理岩体本构模型

针对目前节理岩体损伤本构模型中仅考虑节理等宏观缺陷造成的损伤,而没有考虑岩块中微裂纹等微观损伤的不足,提出了综合考虑宏微观损伤的节理岩体本构模型。其中微观损伤模型采用基于应变强度理论和岩石微元强度服从Weibull分布假定的统计损伤模型,把其应用于被节理切割而成的岩块。而宏观损伤模型主要基于连续介质力学原理,把节理对岩体性质的劣化作为损伤来考虑。在考虑节理传压及传剪系数的基础上,提出了综合考虑宏微观复合损伤的节理岩体本构模型。算例表明宏观节理的存在大大削弱了岩体的强度,降低了其刚度,增大了其柔性。所提出的模型能够较好地反映宏微观两类损伤对岩体应力-应变关系及强度的影响,较为合理。      

A three‐phase soil model for simulating stress wave propagation due to blast loading

A three‐phase soil model is proposed to simulate stress wave propagation in soil mass to blast loading. The soil is modelled as a three‐phase mass that includes the solid particles, water and air. It is considered as a structure that the solid particles form a skeleton and their voids are filled with water and air. The equation of state (EOS) of the soil is derived. The elastic–plastic theory is adopted to model the constitutive relation of the soil skeleton. The damage of the soil skeleton is also modelled. The Drucker–Prager strength model including the strain rate effect is used to describe the strength of the soil skeleton. The model is implemented into a hydrocode Autodyn. The recorded results obtained by explosion tests in soil are used to validate the proposed model. Copyright © 2004 John Wiley & Sons, Ltd.     

含顺层断续节理岩质边坡地震作用下的破坏模式与动力响应研究

基于二维颗粒流软件PFC2D的人工合成岩体技术（SRM）,研究了岩桥倾角和节理间距不同组合形式的含顺层断续节理岩质边坡在地震作用下的破坏模式与动力响应规律。研究结果显示：在地震动力作用下,含单潜在滑动面的顺层断续节理岩质边坡呈现出滑移-倾倒的混合破坏特征,含多潜在滑动面的顺层断续节理岩质边坡则主要发生倾倒破坏;由顺层断续节理以及岩桥交替连接所组成的潜在滑动面是控制边坡动力稳定性的关键因素。在地震动力作用下,最靠近坡脚的岩桥段首先萌生翼裂纹,使得拉应力得到释放,随后各节理相继萌生裂纹并扩展、贯通,最终导致坡体发生阶梯状整体失稳。裂纹扩展受顺层断续节理控制,萌生裂纹中以张拉裂纹为主,且裂纹数量与输入地震波的加速度曲线具有同步性。另一方面,节理面的存在对边坡动力响应产生明显影响,沿坡表以及沿水平方向上的峰值速度、峰值位移随着岩桥倾角的增大、节理间距的减小而增大,同时节理间距和岩桥倾角对于峰值加速度（PGA）放大系数的影响范围主要集中在坡表、坡肩;沿竖直方向上,峰值位移随着岩桥倾角、节理间距的增大而减小,PGA放大系数曲线随高程变化总体呈现U型分布特征。     

A Shear Model Accounting Scale Effect in Rock Joints Behavior

Understanding the scale effect on the mechanical behavior of a single rock joint is still very important in rock engineering. Rock joints can be classified into three different categories depending on their scale: the “micro scale” which is the scale of the asperities; the “meso scale” is the scale of the specimens tested in laboratory; and the “macro scale” which is the scale of the rock mass. The purpose of this paper is to propose an effective way to model rock joints at both the meso and macro scale. An original constitutive mechanical model, in which parameters are deduced from experimental results, has been developed. This model is then extended to simulate the discontinuities occurring at a larger size. At the macro scale, the constitutive modeling was carried out for both small and large relative displacements. Large displacements lead to substantial changes in dilation. For both cases, the peak shear stress vanishes for joints longer than 2 m.     

等效岩体技术在断续双节理岩石试件破裂机制细观分析中的应用

采用等效岩体技术,将岩体中的岩块和节理分别用颗粒体模型和光滑节理模型描述,从细观角度开展了人工预制含两条断续节理岩石试件力学特性及破裂机制的研究。同时,结合室内试验研究成果,通过计算与试验结果的对比分析,验证了等效岩体技术在断续节理岩体力学特性研究中的适宜性和可靠性。主要研究结果如下：（1）随着断续节理产状的不同,虽可将宏观破裂划分为剪切模式、翼型张拉模式和混合模式等3种类型,但从细观角度看,颗粒间张拉型微破裂均是引起各类宏观破裂模式的主要诱因。（2）在试样达到抗压强度前,破裂声发射事件次数较少,强度均较低,主要孕育于断续节理尖端处,并沿两断续节理尖端的连线在岩桥区域累积贯通。（3）在试样达到抗压强度后,破裂声发射事件次数迅速增加,且破裂强度有所提高。（4）各类试样中,声发射事件累积数和破裂强度之间均近似满足Doseresp生长函数关系。     

The stress-strain behaviour of rock material related to fracture under compression

Fracture is the main reason for the non-linear behaviour of hard rocks. The fracture mechanics of rock is studied in this article by analysis of the fracture process under compression. A constitutive model that describes the relationship between the macro deformation of rock and the micro fracture within rock is developed. The propagation of microcracks, the non-linearity of deformation, the loading-and-unloading hysteresis and the variation of the apparent Young's modulus and Poisson's ratio are studied using the developed model. The model simulations demonstrate that: (1) the fracture toughness, initial crack length, crack density, and Young's modulus are four crucially important parameters that affect the deformation behaviour of rock; (2) the elastic parameters (E and v) of the rock matrix should be measured in triaxial tests. If they are measured in uniaxial tests, the upper straight unloading portion of the stress-strain curve is suggested to be used for the purpose, unless the closure effect of open cracks will be included in the estimations. In addition (3), the slope of the reloading stress-strain curve is a measure of the damage in material.     

基于DIC的3D打印交叉节理试件破裂机制研究

为研究交叉节理的存在对岩体破裂机制的影响,采用3D打印技术制备了可模拟岩体交叉结构面的节理模型,通过相似材料浇筑形成含预制交叉节理的试件,并基于数字图像相关技术（DIC）分析了单轴压缩下试件裂纹起裂、扩展及破坏模式。研究结果表明：采用3D打印技术制作的闭合节理模型,可以有效替代传统的切割、插缝等方法形成的张开型节理裂隙。基于此展开的试验结果表明,交叉节理存在会显著降低试件强度,且随着交叉角度的增大,试件强度先升高后降低,在45o和60o之间达到最大值,峰值应变与强度呈现相反的变化规律;裂纹扩展过程可分为微裂隙闭合阶段、微破裂发展阶段、主节理起裂扩展阶段和次节理迅速延伸阶段,这与应力?应变曲线各阶段一一对应。研究还发现,在交叉节理岩体中,次节理对破裂的影响主要体现在峰后阶段,结合最大畸变能理论表明,其对主节理尖端应力分布影响较小,主节理对岩体的破坏起绝对控制作用,这对岩体工程有一定的指导意义。     

Numerical Simulation of the Process of Fracture of Echelon Rock Joints

The effect of joint overlap on the full failure behavior of a rock bridge in the shear-box test was numerically investigated by means of the particle flow code in two dimensions (PFC2D). Initially, the PFC2D was calibrated by use of data obtained from experimental laboratory tests to ensure the conformity of the simulated numerical model’s response. Furthermore, validation of the simulated models was cross-checked with the results from direct shear tests performed on non-persistent jointed physical models. By use of numerical direct shear tests, the failure process was visually observed and the failure patterns were seen to be in reasonable accordance with experimental results. Discrete element simulations demonstrated that macro shear fractures in rock bridges are because of microscopic tensile breakage of a large number of bonded discs. The failure pattern is mostly affected by joint overlap whereas the shear strength is closely related to the failure pattern. The results show that non-overlapping joints lost their loading capacity when nearly 50 % of total cracks developed within the rock bridge whereas the overlapping joints lost their loading capacity as soon as cracks initiated from the joint walls. Furthermore, progressive failure or stable crack growth was seen to develop for non-overlapped joints whereas brittle failure or unstable crack growth was seen to develop in overlapped joints.     

基于微裂隙变形与扩展的岩石冻融损伤本构模型研究

在冻融条件下岩石微裂隙中的水发生相变,体积膨胀,对微裂隙产生很大的冻胀力,当冻胀力超过岩石的抗拉强度时,微裂隙扩展。温度升高时,水又进入新的微裂隙,如此反复循环造成了岩石的损伤。据此,将岩石中的微裂隙等效为扁平状椭圆裂隙,基于断裂力学建立了单条微裂隙下裂隙扩展长度与冻胀力的关系,考虑岩石中微裂隙的分布,将岩石冻融条件下的应变分解为初始损伤应变、附加损伤应变和塑性应变,建立了弹塑性冻融损伤本构模型。最后,通过岩石冻融试验对该模型的合理性进行了验证,结果表明,该模型能够较好地模拟岩石在不同冻融次数下的应力-应变关系曲线。     

Micromechanical Model for Simulating the Fracture Process of Rock

Summary A micromechanical model is proposed to study the deformation and failure process of rock based on knowledge of heterogeneity of rock at the mesoscopic level. In this numerical model, the heterogeneity of rock at the mesoscopic level is considered by assuming the material properties in rock conform to the Weibull distribution. Elastic damage mechanics is used to describe the constitutive law of meso-level elements, the finite element method is employed as the basic stress analysis tool and the maximum tensile strain criterion as well as the Mohr-Coulomb criterion is utilized as the damage threshold. A simple method, similar to a smeared crack model, is used for tracing the crack propagation process and interaction of multiple cracks. Based on this model, a numerical simulation program named Rock Failure Process Analysis Code (RFPA) is developed. The influence of parameters that include the Weibull distribution parameters, constitutive parameters of meso-level elements and number of elements in the numerical model, are discussed in detail. It is shown that the homogeneity index is the most important factor to simulate material failure with this model. This model is able to capture the complete mechanical responses of rock, which includes the crack patterns associated with different loading stages and loading conditions, localization of deformation, stress redistribution and failure process. The numerical simulation of rock specimens under a variety of static loading conditions is presented, and the results compare well with experimental results.     

混凝土喷层支护节理岩体等效力学模型及其应用

考虑喷层在节理面局部的限剪和限裂作用,提出喷层支护节理岩体流变模型,在此基础上推导出喷层支护节理岩体的本构关系,建立了一种喷层支护节理岩体等效力学模型。采用该模型进行结构有限元计算,喷层、节理均不需要离散网格,进行等效模拟;当实际节理裂隙的数量与方向或喷层的厚度变化时,也不需要变化计算网格,从而可降低前处理工作量,为大型复杂结构的计算分析提供较大便利。最后,通过算例和实际工程验证了该模型的有效性--不仅具有离散模型便于模拟喷层真实作用机制的优点,而且具有等效模拟简单易行的优点,具有较好的工程应用前景。     

Modeling of wave propagation induced by underground explosion

A piecewise linear Drucker–Prager strength criterion and an isotropic continuum damage model with the damage scalar depending on an equivalent tensile strain are suggested to model rock mass behavior under blast loading. A rate-dependent constitutive relation is employed to model the energy dissipation caused by two sources, namely irreversible degradation of damage and permanent deformation caused by plasticity. The suggested model is incorporated with a commercially available software AUTODYN through its user’s subroutine function. Coupling of Euler and Lagrange processors are used to include all the materials under consideration such as explosive, air and rock mass, in the calculation. Using AUTODYN and the suggested model, shock wave propagation in rock mass induced by an underground explosion is simulated. Numerical results obtained agree favorably well with those obtained from an independently conducted field test. It demonstrates that the suggested model can be used to predict the damage area, plastic zone and ground motions generated by underground explosions.     

A rock damage constitutive model and damage energy dissipation rate analysis for characterising the crack closure effect

Due to the insufficiency of the previous damage constitutive model for rock, an improved damage mechanics model for rock is proposed with characterising the crack closure effect. Otherwise, the effective methods of determining the model parameters and crack closure coefficient are proposed. The results represent that the model can reflect the damage evolution of rocks in the deformation process in the crack closure stage and this improved model is more reasonable than the previous model. Crack closure coefficient also has great effect on distribution parameters. The calculation formula of damage energy dissipation rate considered that crack closure effect is derived and the relationships between damage energy dissipation rate and crack closure coefficient are analysed. Crack closure coefficient has great effect on damage dissipation energy rate. Damage energy dissipation rate increases with the decrease of crack closure coefficient and damage energy dissipation rate increases quickly in the post-peak stage.     

压剪应力状态下岩石复合型断裂判据的研究

考虑岩石闭合裂纹壁面间存在的摩擦力对裂纹尖端应力场的影响,应用最大周向应力理论得到压剪复合裂纹的断裂角。在此基础上,依据岩石裂纹尖端双向受力时的破坏特征,结合最大周向应力准则与修正的格里菲斯（Griffith）强度理论,建立了考虑摩擦效应的闭合裂纹失稳扩展的岩石压剪断裂判据。研究结果表明：断裂角受裂纹和荷载方向的夹角、裂纹壁面之间的摩擦系数、侧压力系数的影响;当压剪裂纹的断裂角是某个定值时,纯II型裂纹的断裂韧度与纯I型裂纹的断裂韧度的比值只与岩石裂纹表面的摩擦系数取值有关,而与其他岩石力学参数无关。此研究成果可为压剪应力作用下裂隙岩体的失稳破坏提供参考。