岩石破裂过程数值模拟的格构细胞自动机方法研究
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摘要
随着深部采矿工程、地下结构工程的发展,我国将建造更多的深部采矿隧道、永久性地下结构硐室等;但是另一方面一些重大工程灾害如地下硐室的岩爆、采矿工程中的冲击地压等时有发生。岩石破坏机制的研究则是解决并进而控制以上重大工程灾害的基础,这就要求我们从微细观到宏观尺度上认知岩石破坏的规律。虽然众多学者利用不同的方法与理论对其进行过深入的研究,但是由于岩石破坏机制的复杂性,如何将岩石内部赋存的裂纹或缺陷的演化、相互作用与宏观变形和失效联系起来仍是亟待解决的课题。
本文针对这一课题,基于弹塑性损伤理论,综合了细胞自动机以及格构模型的优点,提出了一种格构细胞自动机模型,用于模拟岩石的破坏过程,研究岩石破坏的机理。主要工作如下:
1、在前人研究的基础上验证了细胞自动机模型用于固体力学分析的可行性,并基于力的平衡条件、变形协调条件以及本构方程,提出了可用于求解弹性平面桁架、塑性平面桁架、弹性平面刚架以及弹性平面问题的细胞自动机模型;
2、提出了用于模拟岩石破坏过程的格构细胞自动机模型,给出了模拟岩石破坏过程的基本思路以及模拟岩石非均质性、破坏过程声发射的具体方法;
3、利用格构细胞自动机模型模拟了单轴直接拉伸条件下岩石的破坏过程,研究了岩石的非均质性、几何形状(高径比)以及尺寸等对岩石拉伸断裂过程的影响;并利用该模型模拟了岩石试样在间接拉伸情况下(劈裂试样、三点弯曲试样)的破坏过程,数值模拟结果、试验结果与理论结果吻合较好;
4、利用细胞自动机模型模拟了单轴压缩条件下岩石的破坏过程,研究了岩石的非均质性、几何形状(高径比)以及尺寸等对岩石破坏过程和特性的影响;
5、利用该模型模拟了岩石试样中裂纹的扩展过程,研究了其扩展机理,首先模拟了单轴拉伸条件下I型裂纹扩展过程,研究了裂纹长度、非均质性等对裂纹扩展的影响,然后研究了单轴压缩条件下,含单个、两个预制裂纹的岩石试样的破坏过程以及扩展机理,分析两裂纹的不同几何位置、间距对裂纹相互作用的影响。
With the development of mining engineering in deep underground and underground structure engineering, more and more mining tunnels and permanent underground caves will be built. On the other hand, some engineering disasters such as rockburst, landslide and so on occur from time to time. The study on mechanisms of rock failure is the basis to solve, finally to control these disasters. It demands of us to understand the mechanisms of rock failure from macroscopic to microscopic scale. Though many scholars have adopted various theories and methods to deeply study the rock failure, because of the complexity of this problem how to connect the macroscopic deformation and failure of rock with the evolution of cracks and defects in rock is still an issue that needs to be solved.
In order to solve this issue, based on the elastic-plastic failure theory lattice cellular automata are presented to simulate the rock failure and study the mechanisms of rock failure and crack propagation, coalescence. Lattice cellular automata have the advantages of both cellular automata and lattice model. My work can be concluded as below,
1. Verify the feasibility to adopt cellular automata to solid mechanics analysis. And based on the equilibrium equations, geometrical equations and constitutive equations cellular automata that may be used to solve 2-D truss elastic problems, 2-D truss plastic problems, 2-D rigid framework elastic problems and 2-D continuum elastic problems are introduced or presented.
2. Lattice cellular automata are presented to simulate rock failure. And the basic thoughts to simulate rock failure, the methods to express the heterogeneity of rock and AE during rock failure are introduced in detail.
3. Lattice cellular automata are used to simulate the fracture process of rock samples in uniaxial direct tension. And the influences of heterogeneity, slenderness and size of rock samples on rock failure in direct tension are studied. The model is also used to simulate the fracture process under indirect tensile conditions such as splitting and three-point bend and so on. The simulated results are in good accordance with the experimental results.
4. Lattice cellular automata are used to simulate the failure process under uniaxial compression conditions. The influences of heterogeneity of rock, slenderness and size of rock samples on failure process of rock samples are studied.
5. The crack extension is also studied based on lattice cellular automata. Firstly the extension of I-type cracks is simulated. The influences of the length of cracks and heterogeneity are studied in uniaxial direct tension. Then in uniaxial compression the fracture processes of samples with one or two pre-existing cracks are simulated. And the influences of geometries and distance of two pre-existing cracks on interaction mechanisms of two pre-existing cracks are studied.
本文针对这一课题,基于弹塑性损伤理论,综合了细胞自动机以及格构模型的优点,提出了一种格构细胞自动机模型,用于模拟岩石的破坏过程,研究岩石破坏的机理。主要工作如下:
1、在前人研究的基础上验证了细胞自动机模型用于固体力学分析的可行性,并基于力的平衡条件、变形协调条件以及本构方程,提出了可用于求解弹性平面桁架、塑性平面桁架、弹性平面刚架以及弹性平面问题的细胞自动机模型;
2、提出了用于模拟岩石破坏过程的格构细胞自动机模型,给出了模拟岩石破坏过程的基本思路以及模拟岩石非均质性、破坏过程声发射的具体方法;
3、利用格构细胞自动机模型模拟了单轴直接拉伸条件下岩石的破坏过程,研究了岩石的非均质性、几何形状(高径比)以及尺寸等对岩石拉伸断裂过程的影响;并利用该模型模拟了岩石试样在间接拉伸情况下(劈裂试样、三点弯曲试样)的破坏过程,数值模拟结果、试验结果与理论结果吻合较好;
4、利用细胞自动机模型模拟了单轴压缩条件下岩石的破坏过程,研究了岩石的非均质性、几何形状(高径比)以及尺寸等对岩石破坏过程和特性的影响;
5、利用该模型模拟了岩石试样中裂纹的扩展过程,研究了其扩展机理,首先模拟了单轴拉伸条件下I型裂纹扩展过程,研究了裂纹长度、非均质性等对裂纹扩展的影响,然后研究了单轴压缩条件下,含单个、两个预制裂纹的岩石试样的破坏过程以及扩展机理,分析两裂纹的不同几何位置、间距对裂纹相互作用的影响。
With the development of mining engineering in deep underground and underground structure engineering, more and more mining tunnels and permanent underground caves will be built. On the other hand, some engineering disasters such as rockburst, landslide and so on occur from time to time. The study on mechanisms of rock failure is the basis to solve, finally to control these disasters. It demands of us to understand the mechanisms of rock failure from macroscopic to microscopic scale. Though many scholars have adopted various theories and methods to deeply study the rock failure, because of the complexity of this problem how to connect the macroscopic deformation and failure of rock with the evolution of cracks and defects in rock is still an issue that needs to be solved.
In order to solve this issue, based on the elastic-plastic failure theory lattice cellular automata are presented to simulate the rock failure and study the mechanisms of rock failure and crack propagation, coalescence. Lattice cellular automata have the advantages of both cellular automata and lattice model. My work can be concluded as below,
1. Verify the feasibility to adopt cellular automata to solid mechanics analysis. And based on the equilibrium equations, geometrical equations and constitutive equations cellular automata that may be used to solve 2-D truss elastic problems, 2-D truss plastic problems, 2-D rigid framework elastic problems and 2-D continuum elastic problems are introduced or presented.
2. Lattice cellular automata are presented to simulate rock failure. And the basic thoughts to simulate rock failure, the methods to express the heterogeneity of rock and AE during rock failure are introduced in detail.
3. Lattice cellular automata are used to simulate the fracture process of rock samples in uniaxial direct tension. And the influences of heterogeneity, slenderness and size of rock samples on rock failure in direct tension are studied. The model is also used to simulate the fracture process under indirect tensile conditions such as splitting and three-point bend and so on. The simulated results are in good accordance with the experimental results.
4. Lattice cellular automata are used to simulate the failure process under uniaxial compression conditions. The influences of heterogeneity of rock, slenderness and size of rock samples on failure process of rock samples are studied.
5. The crack extension is also studied based on lattice cellular automata. Firstly the extension of I-type cracks is simulated. The influences of the length of cracks and heterogeneity are studied in uniaxial direct tension. Then in uniaxial compression the fracture processes of samples with one or two pre-existing cracks are simulated. And the influences of geometries and distance of two pre-existing cracks on interaction mechanisms of two pre-existing cracks are studied.
引文
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