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。     

基于Mohr-Coulomb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,损伤变量随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。     

基于Drucker-Prager准则的岩石弹塑性损伤本构模型研究

大多数岩石材料软化本构模型在硬化函数中引入塑性内变量来表示材料的硬化/软化性质,但并不能反映岩石微裂隙损伤对材料力学性能的影响及单轴拉伸和压缩所表现的初始屈服强度f0与屈服极限fu的差异。基于D-P准则同时考虑塑性软化及损伤软化,建立岩石类材料的弹塑性本构关系及其数值算法。塑性屈服函数采用Borja等的应力张量的硬化/软化函数,反映塑性内变量及应力状态对硬化函数的影响;由于岩石损伤软化是微裂隙扩展所导致的体积膨胀引起的,因此,提出用体积应变表征岩石损伤变量的演化,并用回映隐式积分算法编制了岩石的弹塑性损伤本构程序。对单轴压缩及拉伸荷载作用下的岩石材料试验进行数值模拟,结果表明,所提出的岩石弹塑性损伤本构模型可以较好地符合岩石材料的力学特性。     

峰后裂隙岩石非线性损伤特性与数值模拟研究

在地下洞室、隧道等工程中,裂隙岩石峰值强度后的损伤破坏特性及演化机制对控制围岩稳定至关重要,目前,对岩石峰后的损伤破坏特性研究不充分,认识不全面,易出现大体积塌方、大变形等工程事故。针对峰后裂隙岩石的力学性质,开展室内三轴试验,分析其非线性损伤破坏特性;假设岩石损伤满足Weibull分布规律,引入损伤变量,推导出峰后裂隙岩石非线性损伤破裂本构方程;将上述本构方程与能量耗散原理、应变能密度理论相结合,建立了峰后裂隙岩石的非线性损伤破坏准则;采用FISH语言开发了基于上述破坏准则的峰后岩石损伤破裂计算程序,用连续的方法模拟分析了峰后裂隙岩石的非连续损伤破裂过程,揭示了裂隙岩石峰后损伤破坏特性及其演化规律,并与裂隙岩石的三轴压缩试验结果进行了对比。结果表明:上述本构方程与判别准则能较好地模拟峰后裂隙岩石非线性损伤破裂过程。为有效控制围岩稳定提供一种新的理论分析手段。     

考虑初始损伤和蠕变损伤的岩石蠕变全过程本构模型

考虑到天然岩石存在不同程度初始损伤以及蠕变过程中岩石受载后裂隙扩展而导致的新损伤,对具有初始损伤的岩石蠕变特性进行全面描述。根据不闭合结构面应力与法向变形之间的关系,提出裂隙岩石塑性变形体元件,描述岩石蠕变过程中的瞬时塑性变形。引入初始损伤影响因子,建立具有初始损伤的岩石损伤变量演化方程,构建模拟岩石加速蠕变的蠕变损伤体元件。将裂隙岩石塑性变形体和蠕变损伤体与描述瞬时弹性变形和黏弹性变形的广义开尔文模型进行串联组合,形成能够反映具有初始损伤的岩石瞬时弹-塑性变形、稳定蠕变和加速蠕变的蠕变全过程本构模型,提出了进行少量蠕变试验既能解析模型参数的方法,在不同应力水平下模型理论曲线与蠕变试验曲线吻合。     

中低应变率下的岩石损伤本构模型研究

深部岩石的破碎与钻探中,岩石主要处在中低应变率的载荷作用下,而目前的研究还沿用中高应变率推导的动态损伤本构关系。从工程背景和试验角度分析了中低应变率下的岩石动力学特性,提出Maxwell体、Bingham体和损伤体的并联模型,借助拉普拉斯变换,引入基于岩石孔隙、裂隙劣化的损伤变量,导出了中低应变率下的岩石动态损伤本构模型。利用该模型对泥质砂岩和花岗岩在应变率为87 s-1、382 s-1、673 s-1时的应力-应变试验数据进行拟合,并将拟合结果与实测数值、原文献拟合曲线对比,结果表明该理论模型适用性较好。分析拟合参数可知,该动态损伤本构模型能够主动适应中低应变率两类情况,本构曲线和损伤变量的变化符合实际情况。     

基于3D-DIC的砂岩裂纹扩展及损伤监测试验研究

裂纹监测对岩石损伤演化的认识至关重要。为研究岩石裂纹扩展及损伤变形特性,开展了含不同倾角（0°～90°）预制裂隙的标准细黄砂岩样的单轴压缩试验。利用三维数字图像相关技术（3D-DIC）获取岩样三维空间坐标下的应变分布,并结合声发射从光学与声学的角度监测了裂纹的扩展演化。由此提出了一种裂纹主应变的计算方法,定量表征岩石劣化的损伤变量D值。最后,探讨了由声发射与损伤变量D值确定岩样特征强度的影响因素。结论如下：（1）裂纹主应变反映了岩样受荷过程中同源裂纹在时间上的变化速率与空间上的扩展趋势,能较好地表征岩石的开裂行为;（2）声发射适用于确定岩样的起裂应力,不适用于损伤应力的确定,损伤变量D值所确定的起裂应力滞后于声发射,但适用于损伤应力特征值的确定;（3）结合声发射与DIC技术确定的归一化起裂应力范围为0.63～0.94、归一化损伤应力的范围为0.83～0.99;（4）预有裂隙会影响岩石的材料力学性能。随着倾角的增加,岩石的起裂应力、损伤应力及峰值应力呈增长的趋势,由于难以形成局部应变场聚集,裂纹的萌生与起裂更加困难。结果表明,3D-DIC技术的利用可以提高对岩石开裂行为的理解,对岩石的损伤监测与判识更有重要的意义。     

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。     

渗流影响下岩石损伤和渐进破裂演化过程的数值试验研究

在FLAC-3D软件平台上,开发出岩石破裂过程的渗流-损伤耦合分析程序,对渗流-损伤耦合作用下岩石的裂纹萌生、扩展过程进行模拟研究。分析了在孔隙水压力作用下,含原生裂隙和弱化单元的非均质试件在单轴、三轴加载下的破坏过程,并与非渗流条件下试件在单轴、三轴压缩下的破坏过程相对比,通过动态显示损伤状态、渗流场,并分析应力应变关系、位移图等,对渗流影响下裂隙岩体的损伤和渐进破裂过程进行了研究。     

干燥及饱水状态下裂隙岩石冻融特征研究

岩体冻融风化作用主要受控于岩性、岩体结构、饱和状态及温变环境等因素。采取新疆寒区4种裂隙岩石进行温度变化下的冻融应变试验,得到了裂隙岩石在饱水及干燥冻融状态下的应变过程,即饱水状态下为8个阶段、干燥状态下为5个阶段;针对饱水裂隙岩石提出了冻融作用的胀缩率?,得到了不同岩性的?与冻融循环次数的拟合关系表达式,同时分析了在循环冻融过程中应变的变化规律,即裂隙岩石的冻胀阶段的微应变最大值都随循环次数的增加而增大。此外,通过在不同恒温下裂隙岩石冻融应变试验,分析了应变的变化规律,得到应变与不同恒温的拟合关系表达式;试验结果表明:裂隙岩石的?都随冻融次数的增加而增大,胀缩率的变化程度与不同岩样的孔隙率特征有关。饱水裂隙岩石在冻融过程中对温度具有较强的敏感性,损伤表现在温度损伤和冻胀损伤。     

交叉裂隙岩体裂纹扩展试验及混合有限-离散元数值模拟研究

对预制交叉裂隙岩石试样进行裂纹扩展试验,研究了裂纹萌生、扩展、聚合过程,分析了主裂隙和轴向载荷夹角及主次裂隙夹角对裂纹起裂应力和聚合应力的影响,并用混合有限元-离散元程序,即图形处理器并行化的3D Y-HFDEM代码对试验进行了仿真计算,实现了岩石破坏从连续介质向非连续介质的过渡,对裂纹类及损伤破坏模式进行了识别,捕捉到了试验中难以发现的现象。研究表明：随主裂隙与轴向载荷夹角增加,裂纹聚合区的拉伸裂纹数量增加;裂纹起裂和聚合应力与主裂隙与轴向载荷夹角成正比;主次裂隙夹角增加,岩石的破坏模式由拉伸破坏转为剪切破坏,交叉裂隙加剧岩石破碎程度;主裂隙尖端萌生扩展的拉伸-剪切混合裂缝引起的破坏在岩石破坏中占主导地位,是导致岩体失去承载能力的主控裂纹;混合有限元-离散元仿真软件GPGPU并行化的3D Y-HFDEM IDE在岩石裂纹扩展研究中具有优势,可以捕捉实验室难以发现的损伤断裂类型,可以作为岩石裂纹扩展研究的有力工具。     

Numerical Analysis of Blast-Induced Stress Waves in a Rock Mass with Anisotropic Continuum Damage Models Part 2: Stochastic Approach

Summary This paper reports the second part of the study carried out by the authors on the underground explosion-induced stress wave propagation and damage in a rock mass. In the accompanying paper reporting the first part of the study, equivalent material properties were used to model the effects of existing cracks and joints in the rock mass. The rock mass and its properties were treated as deterministic. In this paper, existing random cracks and joints are modeled as statistical initial damage of the rock mass. In numerical calculation, an anisotropic continuum damage model including both the statistical anisotropic initial damage and cumulative damage dependent on principal tensile strain and stochastic critical tensile strain is suggested to model rock mass behavior under explosion loads. The statistical estimation of stress wave propagation in the rock mass due to underground explosion is evaluated by Rosenblueth's point estimate method. The suggested models and statistical solution process are also programmed and linked to Autodyn3D as its user's subroutines. Numerical results are compared with the field test data and those presented in the accompanying paper obtained with equivalent material property approach.     

Numerical analysis of the failure process around a circular opening in rock

Damage and fracture propagation around underground excavations are important issues in rock engineering. The analysis of quasi-brittle materials can be performed using constitutive laws based upon damage mechanics. The finite element code RFPA2D (Rock Failure Process Analysis) based on damage mechanics was used to simulate a loading-type failure process around an underground excavation (model tunnel) in brittle rock. One of the features of RFPA2D is the capability of modeling heterogeneous materials. In the current model, the effect of the homogeneous index (m) of rock on the failure modes of a model tunnel in rock was studied. In addition, by recording the number of damaged elements and the associated amount of energy released, RFPA2D is able to simulate acoustic activities around circular openings in rock. The results of a numerical simulation of a model tunnel were in very good agreement with the experimental test using the acoustic emission technique. Finally, the influence of the lateral confining pressure on the failure mechanism of the rock around the model tunnel was also investigated by numerical simulations.     

The evolution of rock failure with discontinuities due to shear creep

A two-dimensional brittle creep model for rock provides insight into the initiation of shear fracture along weak discontinuities in rock. The model accounts for material heterogeneity and introduces the concept of a mesoscopic renormalization to capture the cooperative interaction between cracks in the transition from distributed to localized damage. A series of shear creep tests on rock with discontinuities were performed to simulate the initiation and propagation of crack along a pre-existing weakness under sustained shear stress and normal stress. The investigation showed that shear stress level and the normal stress level might have significant effect on the long-term behavior of rock with weak discontinuities. Moreover, a case study of rock slope instability was also investigated, where the numerically simulated instability failure of rock slope with discontinuities showed that both tensile and shear damage at the weakest elements are the trigger for the failure surface initiation in the rock slope. Once damage occurs, redistributed stress concentrations would then intensify fracture propagation and coalescence within these damage zones, leading to the progressive development of a failure surface. Moreover, failure surface extending is not only dominated by the properties and the position of discontinuities but also influenced remarkably by the complex interaction between existing discontinuities and fracture propagation. The results are of general interest because they can be applied to the investigation of time-dependent instability in rock masses, to the mitigation of associated rock hazards in rock engineering, and even to a better understanding of the physical phenomena governing the stability of rock slope.     

深部开采底板岩体卸荷损伤的强扰动危险性分析

为研究深部高应力岩体强烈的卸荷效应扰动底板破坏并诱发突水的危险性,根据卸荷力学理论,研究了深部开采卸荷对底板扰动破坏的影响,运用离散元软件计算了深部开采底板卸荷损伤的强扰动特征,基于三轴卸荷试验及损伤因子概念推导了卸荷量与损伤因子的关系,获得了底板岩体卸荷的扩展破坏条件,划分了底板卸荷扰动分区,分析了深部开采底板岩体卸荷损伤破坏的强扰动危险性。结果表明：随采深增加,底板卸荷起点及卸荷应力增加,卸荷量却降低,而深部开采较小的卸荷量便造成底板严重损伤破坏;岩体卸荷量越大,卸荷速率、位移量及渗透系数越高,越易致其扩展破坏;裂隙倾角及水平应力与垂直应力比值越小,越易满足底板岩体卸荷的扩展破坏条件。     

Composite damage constitutive model of jointed rock mass considering crack propagation length and joint friction effect

In order to study the damage constitutive model of rock mass with non-persistent joints in engineering practice, the assumption that the rock mesoscopic elements strength obeys the Weibull distribution function of random, the Drucker–Prager criterion is used as a representation method to describe the strength of the mesoscopic elements, and mesoscopic damage variable is deduced. Combined with the energy principle and the fracture damage theory, the macroscopic damage variable formula is deduced considering the crack propagation length and the friction effect of joint closure in the rock mass. Finally, based on the strain equivalent hypothesis of Lemaitre and considering the coupling of macro and micro defects, the composite damage variables are derived. A macro–meso composite damage constitutive model of rock mass with non-persistent joints is established based on the Drucker–Prager criterion. The theoretical constitutive curves of the model are in good agreement with the experimental constitutive curves of the non-persistent jointed rock masses. The considering effects of crack propagation length and joint closure friction effect are compared with those without considering the crack propagation length and joint closure friction effect, which finds that the former is superior to the latter, and the rationality and validity of the model is verified.     

超声波振动下非均匀岩石损伤过程数值模拟与试验

在振动载荷作用下,岩石内部细观缺陷的发展将导致其宏观力学性能的劣化。为了提高超声波振动碎岩效率,采用数值模拟与实验研究相结合的方法,对超声波振动下岩石内部的损伤过程进行分析;采用有限元与统计技术相结合的方法,建立岩石二维模型,引入损伤增量因子的概念,分析岩石非均匀性对岩石裂纹扩展过程的影响。研究结果表明:1)岩石材料在超声波振动下的损伤过程分为萌生、扩展、贯通3个阶段,随着非均匀系数的增加,岩石原始裂纹的扩展效率逐渐加快。2)损伤因子存在一个临界值,约为0.005 4:当某一时刻岩石的损伤因子低于0.005 4时,损伤增量因子与非均匀系数的响应关系不明显;当损伤因子高于0.005 4时,损伤增量因子随着非均匀系数的增大而急剧增大,此时岩石非均匀性对损伤因子的影响不容忽视。     

单轴压缩载荷作用下双裂隙扩展的CT扫描试验

由于精选后的陶瓷材料与岩石性质相似,因此选择陶瓷作为基本材料制作中部含2条圆币状裂隙的试件,进行单轴压缩荷载作用下的CT实时扫描试验,研究试件内双裂隙的扩展和损伤演化规律。采用3种不同区域划分方案,通过CT数、CT方差和CT图像的对比,分析上、下裂隙及岩桥区域不同的扩展状况。分析表明,上裂隙区域一直以压密为主,扩展很小,对试件破坏影响较小;下裂隙区域扩展剧烈,最终形成了宏观裂纹,对试件的破坏影响较大;当上下裂隙之间的中心距离等于4倍的裂隙半径时,裂隙的扩展过程将与裂隙自身参数有关,几乎看不出裂隙之间的相互作用。     

冻结红砂岩单轴损伤破坏CT实时试验研究

为探究冻结岩石的宏观力学特性及损伤演化机理,对20、?5、?10 ℃红砂岩进行单轴加载CT实时扫描,获得各扫描层的CT扫描图像。利用Matlab自编程序生成灰度直方图和二值图像,基于CT数H值正比于密度的关系定义岩样扫描层的安全区、损伤区、破坏区,结合温度效应、水的软化作用及冰的冻胀力对岩样的影响,定量地研究冻结岩石的损伤破坏演化规律。试验研究表明,(1) 温度由20 ℃降至?5、?10 ℃时未冻水含量减少而冻结冰含量增加,岩样强度增大、抗变形能力提高、整体稳定性提高,CT图像呈现出岩样裂纹尺寸发展减慢、损坏程度减弱的规律;(2) 不同温度下岩石单轴加载的损伤演化经历了裂隙萌生、闭合、延伸、汇集及形成宏观主裂纹的阶段,岩样变形增大发生破坏;(3) 由于端部效应,中间较两端扫描层的损伤程度高,外侧较内侧扫描层先发生损伤,损伤边缘化并向内部扩展。