脆性岩石破裂演化过程的三维细胞自动机模拟

在三维条件下定义了实体细胞自动机的基本组件,综合运用弹塑性理论、细胞自动机自组织演化理论、统计原理以及岩石力学理论等,建立了模拟岩石三维破裂过程的张量型细胞自动机模型,并开发了相应的数值模拟软件EPCA3D。利用EPCA3D对脆性岩石进行单轴压缩破裂过程模拟,通过破裂模式、岩样内部破裂情况、全应力-应变曲线和声发射曲线等的分析,揭示岩石破裂的机制。结果表明,EPCA3D能够较好地模拟非均质岩石在载荷作用下微裂纹的萌生、扩展和贯通的全过程。利用该模拟系统,采用应力-应变线性组合的加载控制方式,研究了不同围压对岩石全应力-应变曲线的影响。研究结果表明：对于脆性非均质岩石,低围压下容易表现为II类行为,且强度较低;高围压下容易表现为I类变形行为,且强度较高。     

三维应力状态下粗粒料强度特性试验研究

粗粒料所处的应力状态具有随时间和空间而变的特点,往往处于较复杂的三维应力状态下。通过粗粒料大型真三轴各向等压固结等比例加载试验,研究了不同中主应力系数条件下粗粒料的强度特性。试验结果表明：中主应力对粗粒料的强度有重要影响,三维应力状态下,粗粒料的强度比常规三轴应力状态下有较大提高,大小主应力之差与大主应变关系曲线也更加陡峭;中主应力系数b从0增大到0.25时,破坏时大小主应力之差增加了39%～50%;摩尔–库仑强度参数咬合力c和内摩擦角? 均随着中主应力系数b的增大而增大,其中咬合力c的增长较为显著,特别是b从0增大到0.25时;相同小主应力条件下,b = 0时,破坏偏应力与球应力之比最小,b = 0.25时,破坏应力比达到最大值,随着b的增大破坏应力比又有所减小;相同中主应力系数条件下,随着小主应力的增大,破坏应力比逐渐减小。     

考虑中间主应力Hoek-Brown强度准则及其适用性

为考虑中间主应力对岩石极限破坏强度作用,在广义Hoek-Brown强度准则幂率项中添加定量表征中间主应力项,构建新的三维Hoek-Brown强度准则。该准则在主应力空间是通过3个角点外接Hoek-Brown准则包络面的曲六面体,在 空间包络线是幂律型曲线。通过与Hoek-Brown准则、Drucker-Prager准则和Mogi准则分别对4组真三轴压缩强度试验数据的拟合对比分析,探讨其反映中间主应力效应的适用性。结果表明,修正的Hoek-Brown强度准则拟合试验数据效果总体最好,Mogi准则次之,Hoek-Brown准则和Drucker-Prager准则较差。从而修正的Hoek-Brown强度准则最适用于粗面岩、大理岩和花岗岩等硬脆性岩石的真三轴强度预测及中间主应力影响规律描述。     

中主应力对硬岩破裂机制的影响

采用数值方法模拟硬岩的三轴压缩试验,应用4个本构模型,即Mohr-Coulomb模型、Drucker-Prager模型、应变软化模型及考虑变形模量劣化的应变软化模型,研究中主应力对均质及非均质硬岩破裂机制的影响。结果表明：不论是均质还是非均质岩体,中主应力对采用Drucker-Prager模型的岩体强度影响较大,而对采用其他本构模型的岩体强度影响不大;当非均质岩体采用Mohr-Coulomb模型或Drucker-Prager模型时,中主应力对岩体破坏过程影响不大,但对其破坏模式有较大影响;当非均质岩体采用应变软化模型时,中主应力对岩体破坏过程及其模式均有较大影响。针对工程算例,采用不同的本构模型获得的均质或非均质岩体强度相差很大,除Drucker-Prager模型外,同一本构模型的均质岩体强度远大于非均质岩体。实际工程岩体对中主应力的响应是不同的,故在地下结构设计过程中应根据岩体特性选择合理的本构模型以保证工程安全。     

The Various Stress Paths Causing Deformation and Failure in Rocks

The rock deformation and failure tests are performed along various stress paths under true triaxial stress state. The experimental results have shown that the change of three principal stresses (the increase of the maximum principal stress, the decrease of the minimum principal stress, the decrease of the confining pressure and the increase or decrease of the intermediate principal stress ) can lead to deformation and failure in rocks. The strength, the deformability and the failure precursors of rocks are related with stress paths. Based on the results of the study, the problems of the stress path in rock engineering are discussed.     

岩体变形和破坏的各种应力途径

在真三轴应力状态下进行了各种应力途径的岩石变形和破坏实验。实验表明,三个主应力的变化(最大主应力的增加,最小主应力的减小,围压的减小以及中间主应力的增加或减小)都能引起岩石变形和破坏。而且岩石的强度、延性和脆性、体积变化和破坏前兆等都与应力途径有关。据根试验结果探讨了岩体工程中的应力途径问题。     

不同卸荷速率下岩石强度特性研究

卸荷条件下的岩石强度特性研究对于分析开挖作用下岩石工程的安全性具有极为重要的意义。卸荷试验中影响岩石强度的因素很多,包括岩性、卸荷点的位置、卸荷应力路径和卸荷速率等,以锦屏大理岩为对象,重点研究卸荷速率对强度的影响。提出用屈服接近速率来统一表征加荷和卸荷下的应力增加或减小的速率,通过比较加荷和卸荷条件下的屈服接近速率表明,当围压卸荷速率为常规试验轴向应力加荷速率的0.2～0.3倍时,两种应力路径下接近破坏时的屈服接近速率相当。通过2D弹塑性细胞自动机的数值试验和大理岩的室内卸围压试验来验证理论分析的结果,表明:围压卸荷速率越大,岩样的强度就越高;当卸荷速率为常规轴向加荷速率的0.2～0.3倍时,卸荷和加荷路径下的强度相当。从而得出结论:对于各种卸荷应力路径,如果卸荷点处于弹性范围内,当接近破坏时的屈服接近速率一定时,应力路径对强度的影响不明显。     

双向加载煤岩变形与声发射特性颗粒流研究

为了明确煤岩双向应力状态下的强度和损伤特性,通过煤岩的单轴试验测得其力学参数,然后利用颗粒流和fish程序结合试验结果获得煤岩细观力学参数,进行了煤岩双向加载下的强度、变形和损伤声发射特征的研究。获得以下主要结论:双向加载煤岩变形破坏过程中,中间主应力对屈服阶段影响最显著,而对峰后软化阶段基本没有影响,这与三向加载下围压对峰后软化阶段的影响不同,从而表明双向加载条件下煤岩峰后基本不存在脆性-延性转化的特征。双向加载下煤岩的体变经历线性体缩、非线性扩容和线性扩容阶段,中间主应力对非线性扩容阶段影响显著,而对其他两个阶段基本没有影响。煤岩损伤破坏过程中,在弹性阶段声发射呈线性增加趋势但增速较小,屈服阶段声发射进入非线性快速增加阶段,在峰值附近增速最快,峰后初期达到最大强度,随后声发射强度急剧减小。声发射最大强度有一定的滞后效应,随着中间主应力的增大,最大声发射强度的滞后效应相对减弱,且随着中间主应力的增大,声发射最大强度持续时间段明显延长。     

非均质共面断续节理岩体拉伸剪切破裂机制研究

工程开挖面附近卸荷扰动区的岩体,受结构面和拉应力共同影响作用,其变形和破坏具有拉剪复合特征。为研究节理岩体的拉剪力学特性,基于颗粒离散元法针对共面断续节理岩体开展了系列数值模拟研究。通过假设粒间接触的力学参数服从Weibull分布表征岩体的非均质性,探讨了非均质性、均质度、法向拉应力和节理连通率对节理岩体拉剪强度和破坏模式的影响。研究表明:拉剪应力条件下非均质性节理岩体主要沿阶梯型破裂面破坏,剪应力-水平位移曲线可以分为线性变形阶段、非线性变形阶段、峰值及峰后阶段;随均质度提高,节理岩体的剪切强度逐渐增加且提升幅度逐渐减弱,趋于均质岩体,岩体中微裂纹由弥散型分布向破裂面集中;节理岩体峰值剪切强度和法向拉应力的大小呈非线性负相关关系;岩体剪切强度随节理连通率增加而显著降低。     

考虑统计损伤模型的非均质节理岩体拉剪破坏机制研究

拉剪应力状态极易导致岩体破坏乃至失稳,为研究节理岩体拉剪破坏规律,开展了拉剪荷载下共面非贯通节理岩体变形破坏的理论与数值计算研究。通过自定义考虑岩石统计损伤演化的Mohr-Coulomb和最大拉应力准则模型,编写力学参数服从Weibull分布的fish函数,研究了拉剪条件下非均质节理岩体的破坏模式及破坏规律,讨论了岩石均质度、法向拉应力及剪切速率对岩体破坏模式及其力学性质的影响。结果表明,(1) 拉剪应力状态下节理岩体的破坏模式以张拉破坏为主,加载初期破坏位置分布散乱,随着加载和损伤演化逐渐形成带状破裂面,岩体宏观力学性质明显降低;(2) 非均质性对岩体破坏影响显著,主要表现为均质度的增加,岩体由弥散型破坏向集中型破坏转变,破裂面起伏度增大,同时岩体的宏观力学性质增强并最终趋向于均质岩体;(3) 低应力水平下拉应力增大不改变节理岩体以拉张破坏为主的破裂模式,但剪切破坏比例明显减少,同时岩体抗剪强度降低,破裂面的粗糙度增大;(4) 剪切速率对岩体力学性质的影响显著,静态加载范围内岩体抗剪强度随剪切速率的增大而增大,且增幅越来越小。     

单孔岩样水压致裂的数值分析

水压致裂是改变岩体结构的一种天然行为和人为手段。采用F－RFPA2D软件,对水压致裂过程、裂缝扩展形态及注水孔形状和大小、应力条件和岩样强度等影响因素进行了研究。将开始出现声发射的水压称为微裂压力,将声发射急剧增多、裂缝非稳定扩展直至岩样破坏的水压称为破裂压力。岩样尺寸一定时,微裂压力和破裂压力随内孔面积增加而降低,方形孔岩样的微裂压力和破裂压力均小于同面积的圆形孔。微裂压力和破裂压力随围压或岩样强度增加而增加,且其差值随岩样强度增加而增加,理论破裂压力与模拟值趋势基本一致。方形孔的宏观裂纹起裂位置多在角点附近,而圆形孔比较随机。无围压时,宏观裂纹的延伸方向随机;有围压时,宏观裂纹扩展方向大致与主应力方向一致,且沿较大主应力方向的宏观裂纹扩展至岩样破坏,较小主应力方向宏观裂纹不完全发育。研究结果对水压致裂试验和工程实践有一定参考意义。     

A new rock mass failure criterion for biaxial loading conditions

To simulate brittle rocks, a mixture of glastone, sand and water was used as a model material. Thin galvanized sheets of thickness 0.254 mm were used to create joints in blocks made out of the model material. To investigate the failure modes and strength, both the intact material blocks as well as jointed model material blocks of size 35.6 × 17.8 × 2.5 cm having different joint geometry configurations were subjected to uniaxial and biaxial compressive loadings. A new intact rock failure criterion is proposed at the 3-D level. This criterion is validated for biaxial loading through laboratory experimental results obtained on intact model material blocks. Results obtained from both the intact and jointed model material blocks are used to develop a strongly non-linear new rock mass failure criterion for biaxial loading. In this failure criterion, the fracture tensor component is used to incorporate the directional effect of fracture geometry system on jointed block strength. The failure criterion shows the important role, the intermediate principal stress plays on rock mass strength.     

Digital Image Based Approach for Three-Dimensional Mechanical Analysis of Heterogeneous Rocks

Summary This paper presents a digital image based approach for three-dimensional (3-D) numerical simulation and failure analysis of rocks by taking into account the actual 3-D heterogeneity. Digital image techniques are adopted to extract two-dimensional (2-D) material heterogeneity from material surface images. The 2-D image mesostructures are further extrapolated to 3-D cuboid mesostructures by assuming the material surface as a representation of the inner material heterogeneity within a very small depth. The iterative milling and scanning system is set up to generate the 3-D rock mesostructures. A Hong Kong granite specimen is used as an example to demonstrate the procedure of 3-D mesostructure establishment. The mechanical responses and failure process under the conventional Brazilian tensile test condition are examined through numerical analyses. The stress distribution, crack propagation process and failure model of heterogeneous material cases are simulated with a finite difference software. The numerical results indicate that material heterogeneity plays an important role in determining the failure behavior of rocks under external loading.     

岩石试样的强度准则及内摩擦系数

岩石是一种非均质材料并含有各种缺陷,利用岩样的应力应交全程曲线可以确定理想强度,在排除岩样缺陷后讨论峰值强度与围压的关系,即强度准则。通过岩样剪切破坏后保持轴向变形恒定降低围压试验,可以确定岩样由摩擦力维持的承载能力随围压的变化关系。比较峰值强度和残余强度随围压变化关系的异同,可以研究岩样屈服过程中内摩擦系数的变化情况,以及内摩擦力对岩样变形特性的影响。粉砂岩试样在峰值应方时内摩擦系数已经达到最大值,峰后只是粘结力或者说是材料强度的降低过程,围压对变形没有明显影响。大理岩试样屈服过程中内摩擦系数不断增加,而内摩擦力的增加量与围压有关,高围压时只有材料强度完全丧失之后,由内摩擦力达到岩样的承载极限。内摩擦力系数随屈服过程增大,是岩石由脆性转交为廷性的根本原因。      

Three-Dimensional Numerical Investigations of the Failure Mechanism of a Rock Disc with a Central or Eccentric Hole

The diametrical compression of a circular disc (Brazilian test) or cylinder with a small eccentric hole is a simple but important test to determine the tensile strength of rocks. This paper studies the failure mechanism of circular disc with an eccentric hole by a 3D numerical model (RFPA3D). A feature of the code RFPA3D is that it can numerically simulate the evolution of cracks in three-dimensional space, as well as the heterogeneity of the rock mass. First, numerically simulated Brazilian tests are compared with experimental results. Special attention is given to the effect of the thickness to radius ratio on the failure modes and the peak stress of specimens. The effects of the compressive strength to tensile strength ratio (C/T), the loading arc angle (2α), and the homogeneity index (m) are also studied in the numerical simulations. Secondly, the failure process of a rock disc with a central hole is studied. The effects of the ratio of the internal hole radius (r) to the radius of the rock disc (R) on the failure mode and the peak stress are investigated. Thirdly, the influence of the vertical and horizontal eccentricity of an internal hole on the initiation and propagation of cracks inside a specimen are simulated. The effect of the radius of the eccentric hole and the homogeneity index (m) are also investigated.     

真三轴试验中的端部摩擦效应分析

端部摩擦效应是三轴试验的常见问题之一。相对于常规三轴试验,由于在茂木式真三轴试验中方形试样4个端部需设置两对端部垫块,从而导致端部摩擦问题更加突出。运用FLAC3D,针对Mohr-Coulomb材料,即无中间主应力影响材料,模拟真三轴加载过程中端部摩擦对试样强度和变形行为的影响。计算结果表明,端部摩擦也可以产生虚假中间主应力效应,即使对于无中间主应力效应材料,中间主应力也会导致最大破坏主应力的增加,且摩擦系数越大,这种趋势则越明显。分析了端部摩擦产生这种趋势的原因,指出了真三轴试验中减小端部摩擦的重要性。     

不同密度粗粒料强度特性的大型真三轴试验

干密度对粗粒料的强度特性有重要影响,特别是三维应力状态下影响更为显著。通过不同密度粗粒料大型真三轴等小主应力等中主应力系数（b=0.25）加载试验和大三轴试验研究了干密度对粗粒料强度特性的影响。结果表明,大型真三轴试验的应力曲线基本呈爬升型,高于和陡于大三轴应力曲线,表现出较强的硬化性;粗粒料强度基本随初始干密度的增大或小主应力的增大呈线性增大;大型真三轴试验强度比大三轴试验强度增大20%～97%,且小主应力越小,强度增大幅度越大;令粗粒料黏聚力为0,则内摩擦角随初始干密度的增大基本呈线性增大,随小主应力的增大而减小;破坏应力比随初始干密度的增大呈线性增大,随小主应力的增大而呈线性减小,大型真三轴试验的破坏应力比小于大三轴试验的破坏应力比。     

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.     

三维应力作用下岩体层面效应分析

为得到层状岩体在真三轴压缩情况下的强度变形特征,利用数值分析方法建立计算模型,得到不同结构面倾角? 下试样的应力和变形响应,结果表明,(1) 加载初期,结构面倾角? = 0°和? = 90°试样对应的初始弹性模量最大;随着试样变形的增大,对应的弹性模量以? = 90°、60°、0°的顺序逐渐减小;? = 90°和? = 0°试样发生破坏的脆性特征比较明显;(2) 随着围压? 3 = σ2的增大,压缩强度? 1不断增大;围压对强度极值发生的位置影响不大;(3) 最小主应力与结构面走向平行情况下,随着中间主应力? 2的增大,试样压缩强度呈现先增大后减小的趋势;随着最小主应力? 3的增大,? 1逐渐增大;当? 3较小时,二者符合线性关系;随着? 3的增大,二者的关系逐渐呈现非线性特征;并且结构面滑移破坏型试样的非线性特征更加明显;(4) 最小主应力与结构面走向垂直的情况下层状岩体的压缩强度与中间主应力和最小主应力的关系均呈现显著的线性特征。     

Numerical analysis of the shape effect on the tensile strength evaluation of axisymmetric specimens

This paper analyses the shape effect on the tensile strength of axisymmetric rock specimens by an improved adaptive dynamic relaxation method. It is shown that the present approach is convenient and efficient. Numerical results for spheroidal specimens with different shapes reveal the variation of stress distributions along the loading axes and suggest that loading along the shorter principal axis is preferable in strength tests. Furthermore, an empirical formula based on the failure criterion of maximum tensile stress is proposed to evaluate the tensile strength of specimen materials.