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位移不连续法及其在岩体工程中的应用
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摘要
自然界中的岩体存在着大量的诸如裂隙、节理、断层等等不连续面。这些不连续面的存在形成了它不同于其它均匀介质的复杂的力学特性。运用传统的有限单元法等数值方法,难以反映裂隙等不连续面及其扩展在岩体力学行为中所起到的关键性作用。
     位移不连续方法(displcement discontinuity method,简称DDM),作为一种间接边界元方法,由于其自身所具有的特点,决定了它比较适合用于研究含不连续面的弹性体问题。本文以裂隙岩体为研究对象,深入研究了位移不连续法这一数值方法,对其做了改进,扩大其应用范围,并将其用于解决岩体力学中的问题。主要有以下几点工作:
     1.提出了用位移不连续法模型解决含裂隙等不连续面的层状岩体问题的方法。采用Fourier变换以及Airy应力函数,从平面应变条件下的弹性力学基本方程出发,分别得到了传递矩阵和刚度矩阵,再把传递矩阵和刚度矩阵相结合,首次得到了具有任意有限层层状弹性半平面问题的均布位移不连续基本解。依此建立层状弹性半平面的位移不连续模型后,研究了岩体分层性对巷道开挖卸荷时顶部位移的影响。最后,还扩展讨论了复合半平面、边缘固定的层状体及粘弹性层状体的基本解的求解方法。
     2.考虑岩石本身的渗透性,在裂隙孔隙双重介质模型基础上,用位移不连续法研究了饱和裂隙岩体中的流固耦合问题。首先,从Biot方程出发,引入McNamee位移函数,通过双重变换,得到了饱和无限大孔弹性介质中的均布位移不连续基本解。以此方法推导裂隙孔隙体的位移不连续基本解,尚属首次。进而,建立了饱和裂隙孔隙岩体问题的位移不连续数值分析模型,研究了孔压对无限大平面中单裂隙的位移和应力场以及断裂应力强度因子值的影响。
     3.采用三维位移不连续方法研究了岩体内节理、断层等三维不连续面的特性和扩展规律。对压载条件下闭合不连续面上存在的摩擦滑动接触非线性问题,采用了一种直接缓和迭代的方法,并对受压长方体中单裂隙周边的位移和应力场进行了计算分析。接下来,考察了无限大岩体中断层的几何形态及断层破碎带的物理性质对地应力场的影响及其规律。研究当中考虑了断层破碎带本身的蠕变时效特性,计算表明,断层蠕变导致能量在断层尖灭处积聚,最终导致地震发生。最后,对四川龙门山断层带进行了模拟。
     4.为了理解岩体内不连续面的破坏条件及其发展过程,结合线弹性断裂力学做了进一步研究。首先介绍通过回归的近似得到与位移不连续量直接有关的断裂应力强度因子的方法,接下来介绍了一种能够直接得到应力强度因子值的特殊三维裂尖单元。在此基础上,假定裂纹前沿上点只能在其局部裂尖坐标系法平面内进行扩展,并采用最大周向应力扩展准则,首次采用三维位移不连续法编制了相应的程序MCP3D,模拟了复杂荷载下三维多裂纹准静态扩展过程,并验证了其有效性。
     5.将位移不连续法用于模拟冻融条件下的岩石微裂纹多轴疲劳扩展过程。先建立简化的物理模型,并引入节理本构关系,采用位移不连续法计算了冻融前后的位移和应力场。然后,引入有效应力强度因子幅这一概念,推广了经典的Paris疲劳演化公式。在此理论基础上,编制相应的计算程序,初步探索了冻融循环条件下无限大岩体中单个裂隙的疲劳扩展路径及规律,为今后更进一步的研究打下了基础。
In nature, a rock mass may contain large numbers of discontinuities or weaknesses at all scales, including cracks, joints and faults. The existance of the discontinuities gives rise to complex mechanical properties of fractured rock masses, which are much different from homogenous materials. It is difficult to understand the key role of these discontinuities and their propagation by using traditional finite element methods or other exiting numerical techniques.
     The displacement discontinuity method (DDM), a sort of indirect boundary element method, is proved to be an appropriate tool for use with fractured rock masses. Some improvement is made here to solve more problems in rock mechanics and rock engineering. In particular, the following questions have been investigated.
     1. The improved DDM is developed for rock mechanics problems in layered half-plane with discontinuities. Combined with the Fourier transform and the Airy stress function in elastic theory under conditions of plain strain, the uniform displacement discontinuity fundamental solutions are obtained by using the propagation matrix and stiff matrix methods for the first time. Next, a frame work using DDM for multi-layered elastic media in a half-plane is established. The displacement distribution of the tunnel roof in layered rock masses is presented, which shows that the layering feature of rock can not be ignored. At last, some other related fundamental solutions are discussed, for example, the compound plane.
     2. On the basis of the dual porosity media model and DDM, a frame work for handling saturated poroelastic media, where seepage and deformation are coupled, is put forward. Based on the Laplace-Fourier transform and the McNamee’s displacement functions, the general solution of the Biot’s consolidation functions for plane strain is easily obtained. Based on the continuity conditions of displacements and stresses, the unknowns are determined. Finally, the displacement discontinuity fundamental solutions for saturated poroelastic media are deduced through inverse Laplace-Fourier transform. After the discrete displacement discontinuity model is built, the problem of the single crack in an infinite plane is studied in detail. It is shown that the displacement discontinuity method, combined with the fractured porous media model, can reasonably simulate the coupling effects of ground water and rock masses.
     3. Three-dimensional problems of fractured rock masses are investigated using DDM. Friction between the surfaces of closed cracks under compression is considered by establishing a simple and efficient iterative algorithm based on contact resistance mitigation. The Mohr-coulomb rule is satisfied by iteration when the closed crack is in a sliding condition. The effect of fault structure on ground stress field is studied by using the displacement discontinuity method. The results indicate that the geometric configuration of the fault, mechanical property of the fault, and the loading condition are the main factors of ground stress distribution at the ends and vicinity of a fault. Considering the creep characteristics of the fault, it can be found that energy keeps on accumulating when the fault creeps, which will eventually bring on a structural earthquake. The displacement and stress fields of the Longmen fault zone are investigated.
     4. In order to understand the fracture process in rock masses, linear elastic fracture mechanics is applied. The stress intensity factories are obtained by an approximative regression method. A type of special crack tip element is introduced. Further, three-dimensional quasi-static crack propagation in fractured rock masses under complex loadings is investigated by using the DDM code MCP3D for the first time. Under the assumption that propagation occurs only in the perpendicular plane at each point in front of the crack, the maximum circumferential stress criterion for two-dimensional crack growth is used. Numerical examples of penny-shaped cracks subject to tension or compression in an infinite elastic media are analyzed. Comparison with both experimental and theoretical rerults shows that the code is accurate and effective.
     5. The rules of fatigue crack growth in brittle rocks under freeze-thaw cycles are investigated using DDM. A simplified physical model is proposed firist. If the water filling between both faces of the crack is totally frozen, the crack is modeled as a continuous filled joint and subjected to periodic frost heaving pressure on both faces of the crack. The frost heaving force can be determined by satisfying the compatible deformation condition. The maximum circumferential stress theory is used to predict the crack stability and the direction of propagation at each step.By introducing the effective stress intensity factor amplitude, the classic Paris’equation is extended to this case. Finally, the multi-axial fatigue propogation path of a single inclined microcrack is simultated, and the fatigue life is calculated.
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