温度—水—应力下开挖扰动区裂隙花岗岩体流变过程研究及细胞自动机模拟
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摘要
随着水工隧洞、公路隧道、核废料地下处置、能源储备和资源开发等越来越向深部发展,而深部岩体所处的特殊环境,即高地应力、高地温和高岩溶水压,使得岩体的性质发生了巨大的变化,工程灾害也日趋增多,对深部围岩的长期稳定性造成了巨大的威胁。因此研究温度-水-应力(THM)等赋存环境下岩体的流变力学行为势在必行。这将不仅丰富和拓宽工程力学学科的研究内容,而且可以为实际岩石工程提供有意义的成果。本文围绕THM作用下裂隙岩体流变力学行为这一基本问题,以正在进行的国际合作项目DECOVALEX-THMC (Task B)为背景,采用不连续模型的细胞自动机方法对开挖扰动区裂隙花岗岩体流变行为开展了较为深入的基础和应用研究,主要工作如下:
(1)三维流变模型参数方面
基于一维应力状态,从三维蠕变方程出发,提出了三维粘弹组合模型参数的两种确定方法。并从理论上建立了广义Kelvin模型在两种常用假设下三维模型参数与一维模型相应量之间的变换表达式。提出了三维广义Maxwell模型参数的确定思路及方法,且证明了它的有效性。给出了鲍埃丁-汤姆森模型在两种常用假设下三维模型参数与一维模型参数之间的变换表达式。
(2)广义流变模型的等效性及其基本性质方面
利用拉氏变换以及蠕变柔量的定义,提出了求解广义Maxwell模型和Wiechert体蠕变柔量的方法及其具体表达式,在此基础上证明了4组常见广义流变模型的等效性,建立了广义Maxwell模型与Kelvin链相互转换的表达式。同时还得到了广义Maxwell模型和Kelvin链等广义流变模型的一个基本性质。该性质可作为这类广义流变模型描述现实材料粘弹性行为的一个实用判据。并用实例验证了本文蠕变柔量的求解方法和基本性质。
(3) THM作用下完整花岗岩及结构面流变模型方面
基于THM耦合作用下流变孔隙介质模型,根据花岗岩流变试验资料和DECOVALEX-THMC(Task B)项目特点,提出了简化的THM作用下花岗岩流变模型及其控制场方程。基于极限概念,导出了平面应变条件下THM作用的结构面流变模型,给出了考虑温度和水对结构面影响的方程。当采用节理单元模拟结构面的力学特性时,一般会存在五种独特的变形模式,初步实现了用带厚度Goodman节理单元来处理自身的这五种变形模式,推导了相应的本构关系,给出了其数值模拟的实现方法。由于节理单元的几何形态比较特殊,其物理量在整体和局部坐标系下的转换存在着自身特点,系统地推导了节理单元常见物理量的坐标转换关系。并证明了当从局部坐标系转换到整体坐标系时,无论Goodman节理单元是否带厚度,其刚度矩阵的坐标转换公式与Sharma and Desai薄层单元的刚度坐标转换公式在形式上并无差异。
(4)细胞自动机方面
根据细胞自动机的基本原理,结合粘性理论建立了二维细胞自动机蠕变模型,引入带厚度Goodman节理单元,开发了THM作用下裂隙岩体流变过程的细胞自动机数值分析系统VEPCA。并通过实例进行了验证,结果表明该程序是准确的、合理的。
(5) THM作用下开挖扰动区裂隙花岗岩体流变过程的数值模拟方面将自主开发的细胞自动机VEPCA应用于DECOVALEX项目的开挖扰动区BMT模拟研究,详细分析了从开挖回填直至100万年WB模型内应力和位移分布及其演化过程。将WB的VEPCA模拟分为弹性分析和流变分析两部分。在弹性分析部分,给出了使用GJE1型和GJE2型节理单元来模拟WB模型中裂隙的计算结果,对由模型所导出的嵌入问题(违背相容条件的)和具有张开位移的但同时在张开处还存在拉应力问题(与物理实际相悖的)进行了探讨,指出它们产生的原因,并给出其解决的办法。在流变分析部分,基于GJE2型弹性节理单元,考虑岩体的流变特性,建立了GJE3型流变节理单元,并将该流变节理单元用于WB模型中的裂隙模拟。获得的流变分析结果可为开挖扰动区的稳定性评价提供有益的参考。
With the construction of hydraulic tunnels, highway tunnels, nuclear waste repositories and the development of energy reserves and resource exploitation in deep underground, the long-term stability of deep engineerings is a challenge due to the special circumstances of surrounding rockmass, such as high geostress, high geotemperature, high hydraulic pressure and so on, which result in great changes of mechanic properties of the surrounding rockmass and increasing engineering disasters. Therefore, it is necessary to research the rheological behavior of rockmass in complicated circumstances, which can enrich the content of engineering mechanics and contribute to real rock engineering. On the background of the international DECOVALEX- THMC(Task B) project, Herein the basic problem concerning the rheological behavior of fractured rock mass under thermo-hydro-mechanical(THM) conditions is concerned. Concretely, THM rheological behavior of fractured granite in excavation disturbed zone(EDZ) is simulated by cellular automata with separating into THM rheological analysis of the intact rock and structural plane. The studying mainly covers the following aspects:
1. Based on the relation of the creep equations in 1-Dimension and 3-Dimension, two methods to determinate 3-Dimensional(3-D) viscoelastic model parameters are presented. Then the expressions describing the relation between the 3-D parameters and 1-D parameters of generalized Kelvin model are established on the basis of the methods. In addition, for the creep compliance of the generalized Maxwell model is expressed implicitly by the model parameters, in terms of the above methods, a new way to determinate the 3-D parameters of generalized Maxwell model is suggested and verified by the establishment of the expressions describing the relation between the 3-D parameters and 1-D parameters of Poynting-Thmson model.
2. It’s difficult to obtain the creep compliance of the generalized Maxwell model and Wiechert model due to their parallel connecting structure, but their detailed expressions are presented by Laplace transform and the definition of creep compliance, and the equivalence of the generalized Maxwell model and the Kelvin chain is achieved and the conversion relations of both model’s parameters are also derived. Moreover, a inherent property of generalized viscoelastic model obtained is the practical criterion when the rheological behavior of certain material is described by the kind of generalized viscoelastic model. The method to solve the creep compliance of the generalized Maxwell model and the inherent property of generalized viscoelastic model are proved by a couple of examples.
3. By using governing equations that describe the fully coupled THM behavior of the rheological porous media, a simplified model of intact granite is brought out according to the features of DECOVALEX-THMC(Task B) project and the creep tests of granite under THM conditions on literature. A plane strain creep joint model is derived under THM conditions on the basis of limit concept, and the equations to consider the effect of temperature and water pressure are also presented. When the creep joint model is applied to the structural plane in numerical simulation, five basic modes of deformation occur. A Goodman joint element with thickness considering the five deformation modes is presented. Due to the special shape of the Goodman joint element, almost all of the relations of mechanical parameters are derived in the global and local coordinates in light of the invariability of tensor, and it can be proved that the coordinate transform expression of the stiffness matrix of Goodman joint element with or without thickness is the similar with that of the thin-layer element introduced by Sharma and Desai.
4. According to the cellular automata(CA) theory and rheological theory, CA creep models such as elastic-viscoplastic model, elastic-viscoelastic-viscoplastic model and so forth, are built to solve the rheological problem. Then the VEPCA program developed in Visial C++ environment is to simulate the rheological behavior of fractured rock mass under THM conditions using rheological models of the intact granite and structural plane. Several examples have shown the reliability and rightness of the VEPCA program.
Finally, the VEPCA program is used to perform BMT (Benchmark test) simulation of THM processes in DECOVALEX-THMC(Task B) project. Detailed analyses of distribution and evolution of stresses and displacements in WB(Wall-Block) model are discussed during the whole history including the excavation, the pre-emplacement and post closure until the 1 million years. The analysis of WB model is divided into two parts: one is elastic analysis, the other is rheological analysis. Using the GJE1 joint element and GJE2 joint element, respectively, the elastic results are presented and compared in the problem of interpenetration and the problem of open with tensile stress. The clauses and the methods to solve these problems are also discussed. Using the GJE3 joint element which is based on the GJE2 joint element, the rheological results of WB are presented to evaluate the long-term stability of EDZ in underground disposal system.
(1)三维流变模型参数方面
基于一维应力状态,从三维蠕变方程出发,提出了三维粘弹组合模型参数的两种确定方法。并从理论上建立了广义Kelvin模型在两种常用假设下三维模型参数与一维模型相应量之间的变换表达式。提出了三维广义Maxwell模型参数的确定思路及方法,且证明了它的有效性。给出了鲍埃丁-汤姆森模型在两种常用假设下三维模型参数与一维模型参数之间的变换表达式。
(2)广义流变模型的等效性及其基本性质方面
利用拉氏变换以及蠕变柔量的定义,提出了求解广义Maxwell模型和Wiechert体蠕变柔量的方法及其具体表达式,在此基础上证明了4组常见广义流变模型的等效性,建立了广义Maxwell模型与Kelvin链相互转换的表达式。同时还得到了广义Maxwell模型和Kelvin链等广义流变模型的一个基本性质。该性质可作为这类广义流变模型描述现实材料粘弹性行为的一个实用判据。并用实例验证了本文蠕变柔量的求解方法和基本性质。
(3) THM作用下完整花岗岩及结构面流变模型方面
基于THM耦合作用下流变孔隙介质模型,根据花岗岩流变试验资料和DECOVALEX-THMC(Task B)项目特点,提出了简化的THM作用下花岗岩流变模型及其控制场方程。基于极限概念,导出了平面应变条件下THM作用的结构面流变模型,给出了考虑温度和水对结构面影响的方程。当采用节理单元模拟结构面的力学特性时,一般会存在五种独特的变形模式,初步实现了用带厚度Goodman节理单元来处理自身的这五种变形模式,推导了相应的本构关系,给出了其数值模拟的实现方法。由于节理单元的几何形态比较特殊,其物理量在整体和局部坐标系下的转换存在着自身特点,系统地推导了节理单元常见物理量的坐标转换关系。并证明了当从局部坐标系转换到整体坐标系时,无论Goodman节理单元是否带厚度,其刚度矩阵的坐标转换公式与Sharma and Desai薄层单元的刚度坐标转换公式在形式上并无差异。
(4)细胞自动机方面
根据细胞自动机的基本原理,结合粘性理论建立了二维细胞自动机蠕变模型,引入带厚度Goodman节理单元,开发了THM作用下裂隙岩体流变过程的细胞自动机数值分析系统VEPCA。并通过实例进行了验证,结果表明该程序是准确的、合理的。
(5) THM作用下开挖扰动区裂隙花岗岩体流变过程的数值模拟方面将自主开发的细胞自动机VEPCA应用于DECOVALEX项目的开挖扰动区BMT模拟研究,详细分析了从开挖回填直至100万年WB模型内应力和位移分布及其演化过程。将WB的VEPCA模拟分为弹性分析和流变分析两部分。在弹性分析部分,给出了使用GJE1型和GJE2型节理单元来模拟WB模型中裂隙的计算结果,对由模型所导出的嵌入问题(违背相容条件的)和具有张开位移的但同时在张开处还存在拉应力问题(与物理实际相悖的)进行了探讨,指出它们产生的原因,并给出其解决的办法。在流变分析部分,基于GJE2型弹性节理单元,考虑岩体的流变特性,建立了GJE3型流变节理单元,并将该流变节理单元用于WB模型中的裂隙模拟。获得的流变分析结果可为开挖扰动区的稳定性评价提供有益的参考。
With the construction of hydraulic tunnels, highway tunnels, nuclear waste repositories and the development of energy reserves and resource exploitation in deep underground, the long-term stability of deep engineerings is a challenge due to the special circumstances of surrounding rockmass, such as high geostress, high geotemperature, high hydraulic pressure and so on, which result in great changes of mechanic properties of the surrounding rockmass and increasing engineering disasters. Therefore, it is necessary to research the rheological behavior of rockmass in complicated circumstances, which can enrich the content of engineering mechanics and contribute to real rock engineering. On the background of the international DECOVALEX- THMC(Task B) project, Herein the basic problem concerning the rheological behavior of fractured rock mass under thermo-hydro-mechanical(THM) conditions is concerned. Concretely, THM rheological behavior of fractured granite in excavation disturbed zone(EDZ) is simulated by cellular automata with separating into THM rheological analysis of the intact rock and structural plane. The studying mainly covers the following aspects:
1. Based on the relation of the creep equations in 1-Dimension and 3-Dimension, two methods to determinate 3-Dimensional(3-D) viscoelastic model parameters are presented. Then the expressions describing the relation between the 3-D parameters and 1-D parameters of generalized Kelvin model are established on the basis of the methods. In addition, for the creep compliance of the generalized Maxwell model is expressed implicitly by the model parameters, in terms of the above methods, a new way to determinate the 3-D parameters of generalized Maxwell model is suggested and verified by the establishment of the expressions describing the relation between the 3-D parameters and 1-D parameters of Poynting-Thmson model.
2. It’s difficult to obtain the creep compliance of the generalized Maxwell model and Wiechert model due to their parallel connecting structure, but their detailed expressions are presented by Laplace transform and the definition of creep compliance, and the equivalence of the generalized Maxwell model and the Kelvin chain is achieved and the conversion relations of both model’s parameters are also derived. Moreover, a inherent property of generalized viscoelastic model obtained is the practical criterion when the rheological behavior of certain material is described by the kind of generalized viscoelastic model. The method to solve the creep compliance of the generalized Maxwell model and the inherent property of generalized viscoelastic model are proved by a couple of examples.
3. By using governing equations that describe the fully coupled THM behavior of the rheological porous media, a simplified model of intact granite is brought out according to the features of DECOVALEX-THMC(Task B) project and the creep tests of granite under THM conditions on literature. A plane strain creep joint model is derived under THM conditions on the basis of limit concept, and the equations to consider the effect of temperature and water pressure are also presented. When the creep joint model is applied to the structural plane in numerical simulation, five basic modes of deformation occur. A Goodman joint element with thickness considering the five deformation modes is presented. Due to the special shape of the Goodman joint element, almost all of the relations of mechanical parameters are derived in the global and local coordinates in light of the invariability of tensor, and it can be proved that the coordinate transform expression of the stiffness matrix of Goodman joint element with or without thickness is the similar with that of the thin-layer element introduced by Sharma and Desai.
4. According to the cellular automata(CA) theory and rheological theory, CA creep models such as elastic-viscoplastic model, elastic-viscoelastic-viscoplastic model and so forth, are built to solve the rheological problem. Then the VEPCA program developed in Visial C++ environment is to simulate the rheological behavior of fractured rock mass under THM conditions using rheological models of the intact granite and structural plane. Several examples have shown the reliability and rightness of the VEPCA program.
Finally, the VEPCA program is used to perform BMT (Benchmark test) simulation of THM processes in DECOVALEX-THMC(Task B) project. Detailed analyses of distribution and evolution of stresses and displacements in WB(Wall-Block) model are discussed during the whole history including the excavation, the pre-emplacement and post closure until the 1 million years. The analysis of WB model is divided into two parts: one is elastic analysis, the other is rheological analysis. Using the GJE1 joint element and GJE2 joint element, respectively, the elastic results are presented and compared in the problem of interpenetration and the problem of open with tensile stress. The clauses and the methods to solve these problems are also discussed. Using the GJE3 joint element which is based on the GJE2 joint element, the rheological results of WB are presented to evaluate the long-term stability of EDZ in underground disposal system.
引文
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