三维条件下的岩石破裂过程分析及其数值试验方法研究
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摘要
岩石破裂是一个复杂的非平衡、非线性的演化过程。研究岩土工程材料的破裂过程，对揭示材料破裂过程的宏观非线性力学行为，评价岩石以及岩石工程的安全状态，了解岩土工程结构的稳定性以及采取合理的支护措施，都具有重要的理论意义和工程价值。
岩石力学与工程问题本身就是三维的力学问题。除了少数的岩石力学问题可以简化为平面问题或者轴对称问题来进行处理外，二维模型的应用都是很有限的。由于岩石和岩体中非均匀性的存在，很容易产生不对称破坏。一旦涉及到不对称性的破坏，几乎所有的二维破坏问题都变成了三维破坏问题。
一方面，岩石介质是非透明材料，给岩石内部三维裂纹扩展和试件破坏观测带来非常大的困难。即使对于均质材料，经典断裂力学在三维破裂中遇到数学的困难，而对于极不均匀性的岩石介质的破裂问题还更难通过解析理论进行准确的描述。另一方面，在实验室的三轴试验中，因为试件制作以及加载条件的困难，往往采用伪三轴试验代替真三轴试验。数学理论上的复杂性、实验室试验和现场观测试验条件和技术的限制，都给岩石三维破裂过程的研究带来很大的困难。有限元方法仍然是解决这些问题的强有力的工具之一。以往数值模拟分析的目的往往是为了得到一个满意的初始应力场变形场或者最终受力结果，随着计算环境的改善和实际问题的客观要求的发展，岩石破裂过程分析正在转向整个结构和一个发展过程的全程模拟。
本文的研究工作可以总结为以下几个方面：
1、岩石三维破裂过程分析模型研究：采用Weibull等各种随机分布函数描述岩石材料的细观非均匀性，并通过Monte-Carlo方法实现单元力学属性的随机赋值。在考虑细观单元非均匀性的基础上，建立三维弹性损伤演化本构模型，通过非均匀介质变形过程中微破裂积累造成的力学性质弱化来反映岩石宏观变形非线性的本质特征。
2、分析系统开发：采用数值计算速度较快的Fortran语言在PowerStation平台开发RFPA~(3D)系统的应力分析模块，并在Linux Redhat 9.0平台下开发并行有限元计算模块，采用功能强大的Microsoft Visual C++语言开发RFPA~(3D)系统的独特的三维破坏分析模块，并利用Microsoft Visual C++语言开发RFPA~(3D)和RFPA~3D-Parallel系统方便友好高效的前后处理界面及其接口，采用SGL公司跨平台强大图形库模块OpenGL来实现软件模拟结果的图形图像的显示。
3、基本力学试验及其机理模拟分析：分析岩石不同非均匀性、压拉比和残余强度下的变形破坏行为，模拟分析试件尺寸效应、试件形状效应、加载端部刚度效应，以及不同的加载方式以及采用不同的破坏准则、细观单元不同的随机分布类型、不同的损伤模型对岩石破裂过程的影响，分析了围压效应和真三轴试验下的中间主应力效应。
4、断裂力学试验模拟：研究空间三维裂纹的萌生、扩展、相互作用和贯通的机理，以及裂纹角度、裂纹长度和裂纹深度对表面裂纹扩展和贯通的影响。模拟岩石在单轴压缩破坏、单轴拉伸断裂、剪切断裂以及复合断裂破坏过程，综合分析试验结果和声发射空间分布图像、数值试验图像以及这些图像与各自应力应变曲线之间的关系，研究岩石破裂过程中应力场、位移场和微破裂空间演化的基本规律以及非线性行为(包括自组织临界现象、分形和逾渗行为)。
5、高性能并行计算：编制大规模并行计算软件，通过物理实验和数值试验对比分析了含
Rock failure process is a complicated non-equilibrium nonlinear progressive process with the evolution of associated cracks initiation, propagation and coalesces. Due to the heterogeneities contained in the rocks, it is difficult to describe the structures and components accurately. In rock failure process study, the formation and interactions between all kinds of weakness on different scales are so intricate that more work is paid attention to stress field investigation and failure criterions of materials.
However, the investigation of fracture process is much more significant than stress field investigation. Since the first complete stress-strain curve was obtained by Cook in 1963, large numbers of rock failure experiments were undertaken to study the rock progressive failure process. The results showed that unstable point was found after the peak strength point in the complete stress-strain curve, and it explained that pillars or wall rocks had carrying capacity to some extent in mining engineering after their peak strength. The rocks or rock masses we encounter in mining engineering are not intact, and how to make most use of the residual strength of fractured rock masses to save support and excavation costs is much important than the acquirement of the peak strength of rock or rock masses.
The problems in rock mechanics and engineering are all of three dimensions to some extent. Rock and rock masses composing the earth's crust are under three-dimensional stress condition, and fracture formation in rocks, including crack propagation, interaction and coalescence shows three-dimensional features. In geophysical studies, the distribution of faults and seismic evens are all three-dimensional. Many rock mechanical problems, except plain strain problems and plain stress problems, such as crack propagation and crack interaction are related to many directions and cannot be simplified to two-dimensional problems. Few presentations can be found to explain the progressive failure of rock in three-dimension and related nonlinear behavior resulting from material heterogeneities.
On the one hand, it brings enormous difficulties to observe the three-dimensional fracture process in rocks, because of the non-transparency of rocks. Some transparent materials, such as PMMA or glass, used in experiments instead of rocks are homogeneous. Rocks belong to heterogeneous materials that contain micro cracks and flaws, and heterogeneity plays an important role in fracturing process. However, there are no proper approaches in mathematics to describe three-dimensional crack propagation even in homogenous material. On the other hand, artificial triaxial tests are undertaken in experimental investigations instead of triaxial tests, due to difficulties in rock sample preparation and the loading conditions. It has been approved theoretically and experimentally that the intermediate principal stress has great effects on rock failure process and the intermediate principal stress can not be considered in artificial triaxial tests.
Numerical test provides an utmost means to study the failure process of rock-like materials. Finite element method is a useful and effective tool among various numerical methods to analysis the rock mechanical problems. However, the traditional finite element method should adopt new techniques and other methods to meet the need of mesomechanics. The traditional numerical methods are applied to get a satisfactory initial stress, initial strain fields or the final stress state. With the improvement of computing environment and the practical demands in rock mechanics, rock failure process analysis is turning its steps to
岩石力学与工程问题本身就是三维的力学问题。除了少数的岩石力学问题可以简化为平面问题或者轴对称问题来进行处理外，二维模型的应用都是很有限的。由于岩石和岩体中非均匀性的存在，很容易产生不对称破坏。一旦涉及到不对称性的破坏，几乎所有的二维破坏问题都变成了三维破坏问题。
一方面，岩石介质是非透明材料，给岩石内部三维裂纹扩展和试件破坏观测带来非常大的困难。即使对于均质材料，经典断裂力学在三维破裂中遇到数学的困难，而对于极不均匀性的岩石介质的破裂问题还更难通过解析理论进行准确的描述。另一方面，在实验室的三轴试验中，因为试件制作以及加载条件的困难，往往采用伪三轴试验代替真三轴试验。数学理论上的复杂性、实验室试验和现场观测试验条件和技术的限制，都给岩石三维破裂过程的研究带来很大的困难。有限元方法仍然是解决这些问题的强有力的工具之一。以往数值模拟分析的目的往往是为了得到一个满意的初始应力场变形场或者最终受力结果，随着计算环境的改善和实际问题的客观要求的发展，岩石破裂过程分析正在转向整个结构和一个发展过程的全程模拟。
本文的研究工作可以总结为以下几个方面：
1、岩石三维破裂过程分析模型研究：采用Weibull等各种随机分布函数描述岩石材料的细观非均匀性，并通过Monte-Carlo方法实现单元力学属性的随机赋值。在考虑细观单元非均匀性的基础上，建立三维弹性损伤演化本构模型，通过非均匀介质变形过程中微破裂积累造成的力学性质弱化来反映岩石宏观变形非线性的本质特征。
2、分析系统开发：采用数值计算速度较快的Fortran语言在PowerStation平台开发RFPA~(3D)系统的应力分析模块，并在Linux Redhat 9.0平台下开发并行有限元计算模块，采用功能强大的Microsoft Visual C++语言开发RFPA~(3D)系统的独特的三维破坏分析模块，并利用Microsoft Visual C++语言开发RFPA~(3D)和RFPA~3D-Parallel系统方便友好高效的前后处理界面及其接口，采用SGL公司跨平台强大图形库模块OpenGL来实现软件模拟结果的图形图像的显示。
3、基本力学试验及其机理模拟分析：分析岩石不同非均匀性、压拉比和残余强度下的变形破坏行为，模拟分析试件尺寸效应、试件形状效应、加载端部刚度效应，以及不同的加载方式以及采用不同的破坏准则、细观单元不同的随机分布类型、不同的损伤模型对岩石破裂过程的影响，分析了围压效应和真三轴试验下的中间主应力效应。
4、断裂力学试验模拟：研究空间三维裂纹的萌生、扩展、相互作用和贯通的机理，以及裂纹角度、裂纹长度和裂纹深度对表面裂纹扩展和贯通的影响。模拟岩石在单轴压缩破坏、单轴拉伸断裂、剪切断裂以及复合断裂破坏过程，综合分析试验结果和声发射空间分布图像、数值试验图像以及这些图像与各自应力应变曲线之间的关系，研究岩石破裂过程中应力场、位移场和微破裂空间演化的基本规律以及非线性行为(包括自组织临界现象、分形和逾渗行为)。
5、高性能并行计算：编制大规模并行计算软件，通过物理实验和数值试验对比分析了含
Rock failure process is a complicated non-equilibrium nonlinear progressive process with the evolution of associated cracks initiation, propagation and coalesces. Due to the heterogeneities contained in the rocks, it is difficult to describe the structures and components accurately. In rock failure process study, the formation and interactions between all kinds of weakness on different scales are so intricate that more work is paid attention to stress field investigation and failure criterions of materials.
However, the investigation of fracture process is much more significant than stress field investigation. Since the first complete stress-strain curve was obtained by Cook in 1963, large numbers of rock failure experiments were undertaken to study the rock progressive failure process. The results showed that unstable point was found after the peak strength point in the complete stress-strain curve, and it explained that pillars or wall rocks had carrying capacity to some extent in mining engineering after their peak strength. The rocks or rock masses we encounter in mining engineering are not intact, and how to make most use of the residual strength of fractured rock masses to save support and excavation costs is much important than the acquirement of the peak strength of rock or rock masses.
The problems in rock mechanics and engineering are all of three dimensions to some extent. Rock and rock masses composing the earth's crust are under three-dimensional stress condition, and fracture formation in rocks, including crack propagation, interaction and coalescence shows three-dimensional features. In geophysical studies, the distribution of faults and seismic evens are all three-dimensional. Many rock mechanical problems, except plain strain problems and plain stress problems, such as crack propagation and crack interaction are related to many directions and cannot be simplified to two-dimensional problems. Few presentations can be found to explain the progressive failure of rock in three-dimension and related nonlinear behavior resulting from material heterogeneities.
On the one hand, it brings enormous difficulties to observe the three-dimensional fracture process in rocks, because of the non-transparency of rocks. Some transparent materials, such as PMMA or glass, used in experiments instead of rocks are homogeneous. Rocks belong to heterogeneous materials that contain micro cracks and flaws, and heterogeneity plays an important role in fracturing process. However, there are no proper approaches in mathematics to describe three-dimensional crack propagation even in homogenous material. On the other hand, artificial triaxial tests are undertaken in experimental investigations instead of triaxial tests, due to difficulties in rock sample preparation and the loading conditions. It has been approved theoretically and experimentally that the intermediate principal stress has great effects on rock failure process and the intermediate principal stress can not be considered in artificial triaxial tests.
Numerical test provides an utmost means to study the failure process of rock-like materials. Finite element method is a useful and effective tool among various numerical methods to analysis the rock mechanical problems. However, the traditional finite element method should adopt new techniques and other methods to meet the need of mesomechanics. The traditional numerical methods are applied to get a satisfactory initial stress, initial strain fields or the final stress state. With the improvement of computing environment and the practical demands in rock mechanics, rock failure process analysis is turning its steps to
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