岩体渗流与应力分析的数值方法研究
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摘要
岩体中普遍存在着断层、节理和裂隙等各种不连续面,这些不连续面往往对岩体的渗流和应力特性起着控制性作用。针对岩体的这一特点,学者们先后提出了多种数值仿真计算方法。归纳起来,这些方法无外乎基于两套体系：以有限元法、有限差分法为代表的基于连续介质力学的方法,以离散元法、块体元法、不连续变形分析方法为代表的基于非连续介质力学的方法。新近发展的无网格法和数值流形法则能同时考虑材料的连续和非连续变形能力。
以有限元法为代表的连续介质力学方法在岩土工程中应用得非常普遍。然而由于岩土工程本身的复杂性,其前处理工作费时耗力。本文在有限元法的框架下,为降低网格划分的难度,提出了几种新的或改进的数值方法：不连续有限元法、开挖模拟的动态有限单元法和改进的叠单元法。同时,由于基于非连续介质力学的方法能很好的描述岩体有别于其他材料的渗流和应力特性,本文基于块体单元法,对三维随机裂隙岩体的块体识别方法和渗流、应力及耦合特性进行了研究和探讨。
综合起来,论文主要开展了以下工作：
(1)提出了大坝／地基系统分析的不连续有限元法。该方法可以将复杂问题的网格划分工作分而治之,系统被分成大坝和地基两个网格独立的部分,通过建基面变形与两侧大坝、基础单元位移的几何相容方程、建基面的本构方程和系统整体的平衡方程来实现不连续网格的耦合。同时,将该方法推广到渗流分析领域,和应力应变分析方法组合成一套完整的计算方法。文中运用一个重力坝的算例说明了本套方法的正确性和有效性。
(2)针对复杂岩石边坡的开挖问题,借鉴数值流形方法的思路,提出了岩体开挖模拟的动态有限单元法。该方法在模拟岩体开挖时,建立的有限元网格中仅需考虑结构面的构造和复杂地形,而不用考虑复杂开挖面的形状,开挖面仅作为动态参数实时输入,这大幅度降低了前处理的难度。文中给出了该方法应用到小湾孔雀沟料场边坡的开挖仿真计算中,证明了本文方法的正确性和有有效性。
(3)借鉴坝体／地基系统的不连续有限元法和岩体开挖模拟的动态有限元法的思路,提出了改进的叠单元法,提高了其计算精度。并进一步将叠单元法推广到三维空间,提出了三维叠单元法,并运用该方法完成了对色尔古水电站地下厂房场区仅考虑自重作用的初始应力场的求解计算。通过和常规有限元结果的对比,说明了本文方法的精度较高。
(4)针对岩体中含有大小各异、数量巨大的裂隙,本文运用蒙特卡罗法完成了岩体中随机裂隙的计算机再现模拟；接着基于矢体的概念,提出了三维随机裂隙岩体的块体识别方法；假定岩块不透水、渗流仅通过裂隙面进行,利用达西定律和变分原理,建立了三维随机裂隙岩体渗流分析的块体单元法。最后通过两个算例分析来表明了本文方法的有效性。
(5)将断层、节理、裂隙等统称为裂隙,并视岩石裂隙为一种“充填介质”,进而将有填充物和无填充物的裂隙统一处理,推导了裂隙面的刚度系数、导水系数和法向应力之间的关系式。在此基础上,根据块体单元法的应力、渗流分析的基本原理,运用两场交叉迭代法,建立了三维裂隙岩体的渗流与应力耦合分析模型。通过沙沱重力坝的分析,验证了所提方法的准确性和有效性。
Faults, joints and fractures are widely distributed in rock masses. These discontinuous surfaces play a regulatory role on the seepage and stress characteristics of rock masses. Accordingly, some numerical simulation methods had been put forward over the past years. To sum up, these methods are based on two categories: continuum mechanics method and non-continuum mechanics method. The Finite Element Method (FEM) and the Finite Difference Method (FDM) are the representatives of continuum mechanics method. The Discrete Element Method (DEM), Block Element Method (BEM) and the Discontinuous Deformation Analysis Method (DDA) are the representatives of non-continuum mechanics method. The newest method such as Numerical Manifold Method (NMM) and Mesh-Free Method (MFM) can simulate both the continuum and non-continuum deformation.
The FEM based on continuum mechanics is widely used in the geotechnical engineering. Due to the complex character of the geotechnical engineering, the pre process is a time-consuming and painful job. In this thesis, based on the frame work of finite element method, three kinds of new numerical methods are presented:the discontinuous finite element method for the dam/foundation system, the dynamic finite element method for the excavation simulation, and the improved superposed element method.
The non-continuum mechanics can describe the seepage and stress characteristics of rock mass well. In this thesis, based on the Block Element Method, the automatic identification method for three dimensional random fracture network is put forward, then, the seepage, stress and coupling characteristics are studied and discussed.
In conclusion, the mainly innovation points of this thesis are as follows:
(1) The Discontinuous Finite Element Method (DFEM) for the dam/foundation system is presented. By using this method, the complex domain for the whole system can be divided into two unconcerned domains:the domain of dam and the domain of foundation. The elements connected to the base surface are coupled, using the geometric compatibility equation by the deformation of the dam and foundation connected to the base surface, constitutive equations of the base surface, and the equilibrium equations of the whole system. And the new method is extended into the seepage analysis field for the dam/foundation system too, which can make up as a whole numerical method with the stress analysis method. A gravity dam on complicated foundation is studied, and the results are in accordance with those from the general finite element method, the precision and validity of this method is proved.
(2) Refer to the Numerical Manifold Method, the dynamic finite element method for the excavation simulation of complex rock slope is presented. By using this new method, because there is no explicit excavated elements, and only the discontinuous surface and complex terrain should be taken into account, the excavated surface just be inputted as a real-time dynamic parameters, the difficulty of the pre process can be significantly deduced. The excavation simulation of peacock slope of Xiao Wan arch dam is studied, which proves the correctness and effectiveness of the method in the thesis.
(3) Base on the main ideas of discontinuous finite element method for the dam/foundation system and the dynamic finite element method for the excavation simulation, a renew Superposed Element Method (SEM) is presented, which can improve the calculative accuracy. Then, the new SEM is extended to three dimension space. Last, the initial gravity field around the underground powerhouse of SeErGu hydropower station is studied with the three dimensional SEM. And the results are in accordance with those from the finite element method, the precision of SEM is proved.
(4) Fractures in rock masses are randomly distributed, including the number and size. In this thesis, the Monte Carlo method is adopted to generate the stochastic fracture network first; second, on the base of the theory of directed body, the automatic identification method for three dimensional network with random fractures is realized; thirdly, based on the assumption that the intact rock is impervious and the water flows only along the fractures, the block element method for seepage analysis of three dimensional network with random fractures is established. Finally, two examples are studied to prove the precision and validity of this method.
(5) All the faults and joint are all treated as fractures and assumed as "filled medium", which enables to treat the rock fractures with or without fillings coincidently. The relationship between the stiffness coefficient, hydraulic conductivity coefficient and the normal effective stress is deduced. Based on the principle of the block element method, seepage-stress coupling model for three dimensional fracture rock mass is built by using the iterative algorithm. The ShaTuo gravity dam is studied to prove the precision and validity of this method.
以有限元法为代表的连续介质力学方法在岩土工程中应用得非常普遍。然而由于岩土工程本身的复杂性,其前处理工作费时耗力。本文在有限元法的框架下,为降低网格划分的难度,提出了几种新的或改进的数值方法：不连续有限元法、开挖模拟的动态有限单元法和改进的叠单元法。同时,由于基于非连续介质力学的方法能很好的描述岩体有别于其他材料的渗流和应力特性,本文基于块体单元法,对三维随机裂隙岩体的块体识别方法和渗流、应力及耦合特性进行了研究和探讨。
综合起来,论文主要开展了以下工作：
(1)提出了大坝／地基系统分析的不连续有限元法。该方法可以将复杂问题的网格划分工作分而治之,系统被分成大坝和地基两个网格独立的部分,通过建基面变形与两侧大坝、基础单元位移的几何相容方程、建基面的本构方程和系统整体的平衡方程来实现不连续网格的耦合。同时,将该方法推广到渗流分析领域,和应力应变分析方法组合成一套完整的计算方法。文中运用一个重力坝的算例说明了本套方法的正确性和有效性。
(2)针对复杂岩石边坡的开挖问题,借鉴数值流形方法的思路,提出了岩体开挖模拟的动态有限单元法。该方法在模拟岩体开挖时,建立的有限元网格中仅需考虑结构面的构造和复杂地形,而不用考虑复杂开挖面的形状,开挖面仅作为动态参数实时输入,这大幅度降低了前处理的难度。文中给出了该方法应用到小湾孔雀沟料场边坡的开挖仿真计算中,证明了本文方法的正确性和有有效性。
(3)借鉴坝体／地基系统的不连续有限元法和岩体开挖模拟的动态有限元法的思路,提出了改进的叠单元法,提高了其计算精度。并进一步将叠单元法推广到三维空间,提出了三维叠单元法,并运用该方法完成了对色尔古水电站地下厂房场区仅考虑自重作用的初始应力场的求解计算。通过和常规有限元结果的对比,说明了本文方法的精度较高。
(4)针对岩体中含有大小各异、数量巨大的裂隙,本文运用蒙特卡罗法完成了岩体中随机裂隙的计算机再现模拟；接着基于矢体的概念,提出了三维随机裂隙岩体的块体识别方法；假定岩块不透水、渗流仅通过裂隙面进行,利用达西定律和变分原理,建立了三维随机裂隙岩体渗流分析的块体单元法。最后通过两个算例分析来表明了本文方法的有效性。
(5)将断层、节理、裂隙等统称为裂隙,并视岩石裂隙为一种“充填介质”,进而将有填充物和无填充物的裂隙统一处理,推导了裂隙面的刚度系数、导水系数和法向应力之间的关系式。在此基础上,根据块体单元法的应力、渗流分析的基本原理,运用两场交叉迭代法,建立了三维裂隙岩体的渗流与应力耦合分析模型。通过沙沱重力坝的分析,验证了所提方法的准确性和有效性。
Faults, joints and fractures are widely distributed in rock masses. These discontinuous surfaces play a regulatory role on the seepage and stress characteristics of rock masses. Accordingly, some numerical simulation methods had been put forward over the past years. To sum up, these methods are based on two categories: continuum mechanics method and non-continuum mechanics method. The Finite Element Method (FEM) and the Finite Difference Method (FDM) are the representatives of continuum mechanics method. The Discrete Element Method (DEM), Block Element Method (BEM) and the Discontinuous Deformation Analysis Method (DDA) are the representatives of non-continuum mechanics method. The newest method such as Numerical Manifold Method (NMM) and Mesh-Free Method (MFM) can simulate both the continuum and non-continuum deformation.
The FEM based on continuum mechanics is widely used in the geotechnical engineering. Due to the complex character of the geotechnical engineering, the pre process is a time-consuming and painful job. In this thesis, based on the frame work of finite element method, three kinds of new numerical methods are presented:the discontinuous finite element method for the dam/foundation system, the dynamic finite element method for the excavation simulation, and the improved superposed element method.
The non-continuum mechanics can describe the seepage and stress characteristics of rock mass well. In this thesis, based on the Block Element Method, the automatic identification method for three dimensional random fracture network is put forward, then, the seepage, stress and coupling characteristics are studied and discussed.
In conclusion, the mainly innovation points of this thesis are as follows:
(1) The Discontinuous Finite Element Method (DFEM) for the dam/foundation system is presented. By using this method, the complex domain for the whole system can be divided into two unconcerned domains:the domain of dam and the domain of foundation. The elements connected to the base surface are coupled, using the geometric compatibility equation by the deformation of the dam and foundation connected to the base surface, constitutive equations of the base surface, and the equilibrium equations of the whole system. And the new method is extended into the seepage analysis field for the dam/foundation system too, which can make up as a whole numerical method with the stress analysis method. A gravity dam on complicated foundation is studied, and the results are in accordance with those from the general finite element method, the precision and validity of this method is proved.
(2) Refer to the Numerical Manifold Method, the dynamic finite element method for the excavation simulation of complex rock slope is presented. By using this new method, because there is no explicit excavated elements, and only the discontinuous surface and complex terrain should be taken into account, the excavated surface just be inputted as a real-time dynamic parameters, the difficulty of the pre process can be significantly deduced. The excavation simulation of peacock slope of Xiao Wan arch dam is studied, which proves the correctness and effectiveness of the method in the thesis.
(3) Base on the main ideas of discontinuous finite element method for the dam/foundation system and the dynamic finite element method for the excavation simulation, a renew Superposed Element Method (SEM) is presented, which can improve the calculative accuracy. Then, the new SEM is extended to three dimension space. Last, the initial gravity field around the underground powerhouse of SeErGu hydropower station is studied with the three dimensional SEM. And the results are in accordance with those from the finite element method, the precision of SEM is proved.
(4) Fractures in rock masses are randomly distributed, including the number and size. In this thesis, the Monte Carlo method is adopted to generate the stochastic fracture network first; second, on the base of the theory of directed body, the automatic identification method for three dimensional network with random fractures is realized; thirdly, based on the assumption that the intact rock is impervious and the water flows only along the fractures, the block element method for seepage analysis of three dimensional network with random fractures is established. Finally, two examples are studied to prove the precision and validity of this method.
(5) All the faults and joint are all treated as fractures and assumed as "filled medium", which enables to treat the rock fractures with or without fillings coincidently. The relationship between the stiffness coefficient, hydraulic conductivity coefficient and the normal effective stress is deduced. Based on the principle of the block element method, seepage-stress coupling model for three dimensional fracture rock mass is built by using the iterative algorithm. The ShaTuo gravity dam is studied to prove the precision and validity of this method.
引文
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