摘要
岩石类材料内部微观裂隙在载荷作用下的扩展贯通，导致材料内部形成剧烈变形的局部化带，材料力学性能与整体承载能力下降，局部化带内的剧烈变形进一步发展导致材料的最终破坏。为了防止裂隙岩体的变形破坏，需采用各种锚杆(索)进行加固。由于材料的损伤局部化失稳与锚固机理极其复杂，目前仍有许多问题尚未彻底解决。本文紧密围绕材料的损伤局部化失稳与锚固机理研究中存在的主要问题，在岩石类材料损伤局部化分叉分析、应变软化模型与局部化带的特征点的对应关系、裂隙岩体的锚固止裂机理、不同形式的权函数对裂纹应力应变场的影响、非线性非局部应变梯度模型的探讨等方面进行了比较深入而系统的分析研究。论文的主要研究内容包括以下几个方面：
1．岩石类材料在弹塑性变形过程中由于大量微观缺陷的出现而伴有显著的体积扩容与刚度的不同程度下降等非线性特征，在材料的分叉与失稳分析中，必须同时考虑弹塑性和损伤两种非线性变形特征。本文在岩石类材料的各向同性损伤假定下，在弹塑性模型的不连续局部化分叉方法中引入了损伤变量与损伤加卸载函数，考虑岩石损伤过程中的刚度退化和体积扩容所引起的泊松比增大等变化特征，通过理论推导得出了岩石类材料损伤失稳时的最大硬化模量和此时的局部化方向角，探讨了最大硬化模量与局部化方向角对岩石类材料的损伤程度和初始泊松比的依存关系，并分别在平面应力与平面应变两种条件下，对单轴拉伸压缩试件的分叉失稳问题进行了对比分析。
2．由于试验过程中试样的力学参数及应变软化阶段特性和外载荷加载时的差异，其变形过程中应力应变状态并不相同，并且试样的变形破坏过程难于观测。本文将材料的各向同性损伤与经典的Mohr-Coulomb屈服准则相关联，将材料的各向同性损伤转化为材料粘聚力和内摩擦角的降低，确定了材料的损伤临界面。应用数值模拟手段对平面应变条件下不同初始条件时试样变形过程中特征点的应力位移变化值进行监测，分析了试样分叉与局部化带形成过程中轴向应力位移曲线、轴向-侧向位移对比曲线、剪切带网络特征及其随损伤程度、围压、泊松比变化的规律，并进一步应用非关联流动准则考虑损伤的Mohr-Coulomb理论，推导出试样的局部化方位角在不同的变形特征点随围压和损伤程度的变化规律，并与数值模拟所得到的量侧值进行了对比分析。
3．针对工程岩体中常见的Ⅰ-Ⅱ复合裂纹，采用数值模拟手段对岩体中不同倾角的一条裂纹与两条共线裂纹的扩展机制进行了研究，从应变的角度根据裂纹尖端附近塑性区最短距离断裂准则得到了不同倾角裂纹的破裂方向、裂纹尖端的塑性区最短距离及破坏后岩桥之间的有效距离。依据预应力锚索的锚固段与自由段的受力机制不同，应用等效应变法和等效降温法施加预应力对岩体中单一锚索加固和群锚加固机理进行了有限元分析，给出了预应力锚索的锚固段与岩体的受力与变形特征，指出了应用预应力锚索加固时应该注意的问题，并结合研究了预应力锚索对裂隙岩体的锚固止裂效应，对比分析了不同倾角的两条共线裂纹的在不同锚固条件下的扩展机制。
4．分析了非局部理论中不同形式的权函数的性质及其选取原则，给出了其影响域及其随内部长度因子变化的规律。为了消除裂纹尖端附近应力应变场的奇异性问题，应用采用不同形式权函数的非局部理论分析了Ⅰ-Ⅱ型复合裂纹尖端的应力应变场的分布影响，并与裂纹尖端附近不同方向上的局部应变进行了对比，进而探讨了基于不同权函数的非局部理论与应力强度因子K_Ⅰ与K_Ⅱ值对于裂纹尖端非局部各个应力应变分量的影响。
5．考虑线性软化模型不能反映材料软化变形复杂性的不足，选取高斯正态分布函数作为非局部理论的权函数，同时采用指数型应力衰减模式考虑软化的非线性特征，进一步地将这种非线性非局部理论与采用Laplace算子考虑塑性应变梯度效应的塑性梯度理论相结合，建议了一种非线性非局部应变梯度模型，通过对各向同性均质杆拉伸过程的分析，确定了指数型非线性软化模型的塑性应变分布，并与线性软化模型的解答进行了对比。
The localized band with intense deformation is caused by the development and coalescence of micro-cracks in loaded rock-like geomaterials. The process of deformation of rock-like geomaterials is companied by degradation of mechanical behaviors and whole loaded capability. The farther development of intense deformation caused structural whole failure:To prevent the deformation and failure, the pre-stress anchor cable is used to reinforce jointed rock mass. However the mechanics of Instability and Reinforcement with Damage Localization is very complex and there are some issues that have not been well solved in engineering practice. An intensive study is required for consideration on mechanics of instability and reinforcement with damage localization of rock-like geomaterials. Therefore the analysis of damage bifurcation and instability of rock-like geomaterials, the relationship between strain softening model and characteristic point of localized band, mechanism of reinforcement on crack prevention of jointed rock mass, effect of non-local models with different types of functions on stress-strain field at crack tip, the bifurcation and instability of plastic softening model and its finite element implementation are mainly concerned in this dissertation. The main research and results involved in the dissertation includes the following parts.
1. The process of deformation of rock-like geomaterials is accompanied with nonlinear features of obvious stiffness degradation and volumetric dilatancy. In analyzes of bifurcation and instability of materials the two nonlinear deformation features of elasto-plasticity and damage should be taken into consideration simultaneously. Therefore, under the condition of isotropic damage, in this paper the damage variation and damage loaded-unioaded function are taken into consideration in the analysis of discontinuous bifurcation of elastic-plastic model. The variation characteristics such as stiffness degradation and initial Poisson's ratio increasing are taken into account, then the critical hardening modulus and localized orientation angle of materials with consideration of damage degradation and volumetric dilatancy are set up through theoretical derivation. The relationship of localized orientation angle and critical hardening modulus depended on degree of damage and initial Poisson's ratio of rock is explored. Comparative analyzes are conducted to study the bifurcation of uniaxial compression-tension samples under the conditions of plane stress and plane strain.
2. The relations of stress-strain is different in the process of deformation owing to the differences of mechanical parameters, the characteristic of the strain softening phase and load under experimental conditions. And the fracture process of samples is not easy to observe. In the paper the damage critical curved surface is derived considering the related effect of isotropic damage and degradation of cohesion and internal friction angle of Mohr-Coulomb strength law. The characteristics of axial stress-displacement curve, axial-lateral displacement curve, networks of shear bands and the change with degree of damage, confining pressure, poisson's ratio are investigated numerically by monitoring the stress-displacement values in the process of deformation of samples under plane strain and different initial conditions. Furthermore, the law of the localized orientation of samples in different deformation characteristic point with the change of confining pressure and degree of damage is derived by non-associative damage Mohr-Coulomb yield law. The localized orientation is Compared with that obtained by numerical simulation.
3. The fracture orientation of crack of different angle, the mini-plastic zone displacement near crack tip, the effective displacement of rock-bridge between con-liner close cracks tips after fracture are derived by the rule of mini-plastic zone displacement near crack tip from strain viewpoint. A new method of equivalent pre-stress is suggested to simulate the mechanism on reinforcement of pre-stress anchor cable by finite element method. The mechanism and distortional character of consolidated segment and rock mass under single anchor cable and multi anchor cables is analyzed. Some attentions is indicated when reinforcement by pre-stress anchor cable. The mechanism of reinforcement of pre stress anchor cable on crack prevention of jointed rock mass is studied by the fracture rule of mini-plastic zone displacement. The extending mechanism of con-linear cracks of different angle is analyzed under different consolidation condition.
4. The essential characteristics together with optimum selection of weighted functions is analysed in the non-local theory. Therefore, the influence area of the weighted functions and its dependency on internal length scale are examined for a number of commonly used types of weighted functions. To eliminate the singular of stress and strain field near crack tip, the stress and strain field in the neighborhood of the tip ofⅠ-Ⅱmixed mode crack are analyzed in compare with local strain of different orientation near crack tip by using the non-local theories based on different types of weighted functions. Furthermore, the effects of non-local theory of different types of the weighted functions and the stress intensity factor K_Ⅰand K_Ⅱon the all components of stresses and strains at the crack tip are investigated.
5. Considering deficiency of linear softening model which cannot reproduce distortion complexity of geo-material, a nonlinear and non-local model of plastic-strain gradient is presented by incorporating the nonlinear and non-local theory with the theory of plastic strain gradient. A nonlinear and non-local model is proposed by using an exponential pattern of strain softening and weighted by Gaussian distribution function while the effect of plastic strain gradient is taken into account. The mechanical characteristics of isotropic bar under uniaxial tension are examined by the proposed model and analysis results of the proposed model are compared with those of the linear-softening model.
引文
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