脆性岩石力学模型与流固耦合机理研究
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摘要
随着岩体工程不断向深部发展,其所处的地质和应力环境变得更为复杂,高地应力和高渗透压力条件下岩体力学问题的研究已经提上日程,如何更准确地模拟岩体的力学响应已成为地下工程的关键问题之一。鉴于此,针对锦屏Ⅱ水电站深埋引水隧洞开挖过程中遇到的两类问题：高地应力下围岩的破坏和高水压力下的突(涌)水灾害,开展了大理岩力学模型和高渗透压下的流固耦合机理研究。本文主要研究工作与成果如下：
(1)进行了两种大理岩(T2y6和T2b)和一种砂岩的峰前和峰后循环加卸载试验,用于研究脆性岩石材料经历塑性变形时的弹塑性耦合特性、后继屈服特性和剪胀特性。针对围压对岩石变形和强度的影响,提出了考虑围压影响的塑性内变量,基于该内变量可以考虑不同应力路径下岩石的屈服过程。根据循环加卸载试验结果和定义的塑性内变量,系统地研究了弹性参数、强度参数以及剪胀参数的演化过程。
(2)从加载速率角度研究了加荷和卸荷条件下所得强度的关系。提出用屈服接近速率(YAR)来表征加荷和卸荷状态下应力接近屈服状态的快慢,继而分析了加载和卸载条件下的屈服接近速率,并通过弹塑性细胞自动机EPCA2D的模拟试验和大理岩的实验室卸围压试验证明：卸载应力点在弹性范围内时,当卸荷速率为常规轴向加载速率的0.2-0.3倍时,卸荷和加载路径下的强度相当,即应力路径对强度没有影响。
(3)根据T2y6和T2b大理岩以及砂岩的峰前和峰后循环加卸载试验的结果,提出了弹塑性耦合力学模型。这一模型同时考虑了岩石材料的弹塑性耦合特性、硬化-软化特性、剪胀特性以及应力状态对屈服过程的影响。对室内三轴压缩试验和加拿大Mine-By试验洞破坏区的模拟结果表明,所建力学模型可以较好地反映脆性岩石的主要力学特性以及高地应力条件下岩体开挖后的损伤破坏特征。更为重要的是,所提力学模型对卸围压应力路径下岩石的变形和强度特性也能较好地反映。
(4)结合作者提出的弹塑性耦合力学模型,给出了连续介质条件下流固耦合分析的基本方程,建立了弹塑性条件下流固耦合分析的基本框架。针对现有文献对流固耦合方程中的流体连续性方程的形式存在的争议,采用两种思路推导了连续性方程,得到的连续性方程是等价的,同时将该方程与其他学者通过土体单元的质量守恒得到的连续性方程进行了对比,证明是一致的,从而得到了正确的连续性方程的形式。
(5)分析了有效应力系数的物理机理及其主要影响因素,在此基础上,提出了等效孔隙连通率的概念,以此表征岩土类孔隙介质的结构和孔隙之间的连通性,基于连续介质力学和张量分析的基本原理,建立了有效应力系数张量演化的普适性理论模型,该模型在各向同性和异性条件下都是适用的。基于煤和砂岩弹性阶段的有效应力测试结果,以及大理岩和砂岩塑性条件下的有效应力测试结果,获得了弹塑性条件下岩石有效应力系数演化的规律,计算结果与试验结果吻合较好,表明本文所建立的有效应力系数普适模型和分析方法是可行的；推导了Darcy流和非Darcy流统一渗流方程,并根据层流的粘性剪应力和紊流引起的附加剪应力的比例关系,提出了非Darcy流的判据。
(6)结合智能反演理论,将所建立的弹塑性耦合力学模型用于辅助洞2#试验洞开挖过程的模拟分析,研究了隧洞开挖过程中,围岩变形、损伤区和应力的演化规律,较好地给出了破坏区的位置和范围。根据所建立的流固耦合模型,考虑高渗透压下的非Darcy流效应,对锦屏Ⅱ水电站引水隧洞的开挖过程进行了流固耦合分析。探讨了隧洞周围的高压水对隧洞安全性的影响。根据流固耦合分析的结果,对突(涌)水的预防和治理提出了相应的建议。
As the geotechnical engineering around the world becames deeper, where the geological and stress environment has become more complex, the study of rock mechanics under the condition of high stress and high seepage pressure has been put on the agenda. In particular, how to simulate the mechanical response of rock has been one of the key issues. The failure of surrounding rock mass under high geo-stress and the occurrence of water burst under high seepage pressure are the two main problems met during the construction of diversion tunnel in Jinping II hydroelectric station. In order to solve these problems, the mechanical model and fluid-solid coupling mechanism under high seepage pressure of marble are both studied here. In sum, the main work and conclusion including:
1. In order to study the elato-plastic character, subsequent yield character and dilation of brittle rocks, cyclic-loading experiments, both before and after the peak strength of two kinds of marble (T2y6 and T2b) and a kind of sandstone, are carried out. A plastic internal variable is defined, which takes the influence of confining pressure on yield process into consideration. Based on the results of cyclic-loading experiments and the plastic internal variable, the evolution process of elastic, strength and dilation parameters with plastic strain is studied.
2. The relation of strength under unloading and loading conditions is studied with respect to the rate of loading. Yield approach rate (YAR) is proposed to denote the stress varying rate under loading and unloading conditions. Then, the characters of YAR under loading and unloading conditions are analyzed. The simulation by EPCA2D (Elasto-Plastic Cellular Automaton) and the unloading tests of marble indicate that if the initial unloading stress is in the elastic state, the strength under loading and unloading conditions is equal when the unloading rate is 0.2-0.3 of the loading rate.
3. Based on the results of experiments on two kinds of marble (T2y6 and T2b) and a kind of sandstone, an elasto-plastic coupling mechanical model is proposed. The model takes the variety of elastic parameters, strength parameters and dilation parameter into consideration and can reflect the influence of stress state on the yield process. Simulation results of the traxial compression experiments and excavation process in Mine-by tunnel show that the mechanical model proposed here can capture the deformation and yield characters of brittle rock under different stress path. Especially, the deformation and yield characters in confining pressure unloading tests are also well described by the model.
4. Combined with the elasto-plastic coupling mechanical model, the basic frame of fluid-solid coupling analyze under plastic condition is established. As different researchers disputed on the continuum equation of fluid, two methods are used to derive the continuum equation. The continuum equations deduced form the two methods are found to be equivalent. In addition, the equations are compared to the continuum equation derived by other researchers based on mass conservation law, and they are found to be coincident. Then, the right form of fluid continuum equation is proved.
5. Physical mechanism and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed to denote the meso-scaled structure of these materials. Then a general expression describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pore is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Based on the effective stress tests of coal and sandstone under elastic deformation, and the effective stress tests of marbles and sandstone under plastic deformation, the evolution law of effective stress coefficient with strain is obtained. The simulation results agree very well with the test results.
Unified equation of Darcy flow and non-Darcy flow is deduced. Then, the criterion of non-Darcy flow is put forward based on the contrast relationship of bond shear stress in laminar flow and additional shear stress in turbulent flow.
6. Finally, with intelligent inversion theory, the elato-plastic coupling constitute model is used to simulate the excavation process of the 2# experiment tunnel in the assisted tunnel of Jinping II diversion tunnel. Evolution process of deformation, disturbed zone and stress are got according to the excavation step. The position and extent of failure zone is in good agreement with the field.
Using the fluid-solid coupling method proposed here, the excavation process of the JinpingⅡdiversion tunnel is simulated which takes the high fluid pressure into consideration. The result shows that the high fluid and seepage pressure has effect on the stability of the wall rock. Based on the simulation results, suggestions are raised for the prevention and management of water burst.
(1)进行了两种大理岩(T2y6和T2b)和一种砂岩的峰前和峰后循环加卸载试验,用于研究脆性岩石材料经历塑性变形时的弹塑性耦合特性、后继屈服特性和剪胀特性。针对围压对岩石变形和强度的影响,提出了考虑围压影响的塑性内变量,基于该内变量可以考虑不同应力路径下岩石的屈服过程。根据循环加卸载试验结果和定义的塑性内变量,系统地研究了弹性参数、强度参数以及剪胀参数的演化过程。
(2)从加载速率角度研究了加荷和卸荷条件下所得强度的关系。提出用屈服接近速率(YAR)来表征加荷和卸荷状态下应力接近屈服状态的快慢,继而分析了加载和卸载条件下的屈服接近速率,并通过弹塑性细胞自动机EPCA2D的模拟试验和大理岩的实验室卸围压试验证明：卸载应力点在弹性范围内时,当卸荷速率为常规轴向加载速率的0.2-0.3倍时,卸荷和加载路径下的强度相当,即应力路径对强度没有影响。
(3)根据T2y6和T2b大理岩以及砂岩的峰前和峰后循环加卸载试验的结果,提出了弹塑性耦合力学模型。这一模型同时考虑了岩石材料的弹塑性耦合特性、硬化-软化特性、剪胀特性以及应力状态对屈服过程的影响。对室内三轴压缩试验和加拿大Mine-By试验洞破坏区的模拟结果表明,所建力学模型可以较好地反映脆性岩石的主要力学特性以及高地应力条件下岩体开挖后的损伤破坏特征。更为重要的是,所提力学模型对卸围压应力路径下岩石的变形和强度特性也能较好地反映。
(4)结合作者提出的弹塑性耦合力学模型,给出了连续介质条件下流固耦合分析的基本方程,建立了弹塑性条件下流固耦合分析的基本框架。针对现有文献对流固耦合方程中的流体连续性方程的形式存在的争议,采用两种思路推导了连续性方程,得到的连续性方程是等价的,同时将该方程与其他学者通过土体单元的质量守恒得到的连续性方程进行了对比,证明是一致的,从而得到了正确的连续性方程的形式。
(5)分析了有效应力系数的物理机理及其主要影响因素,在此基础上,提出了等效孔隙连通率的概念,以此表征岩土类孔隙介质的结构和孔隙之间的连通性,基于连续介质力学和张量分析的基本原理,建立了有效应力系数张量演化的普适性理论模型,该模型在各向同性和异性条件下都是适用的。基于煤和砂岩弹性阶段的有效应力测试结果,以及大理岩和砂岩塑性条件下的有效应力测试结果,获得了弹塑性条件下岩石有效应力系数演化的规律,计算结果与试验结果吻合较好,表明本文所建立的有效应力系数普适模型和分析方法是可行的；推导了Darcy流和非Darcy流统一渗流方程,并根据层流的粘性剪应力和紊流引起的附加剪应力的比例关系,提出了非Darcy流的判据。
(6)结合智能反演理论,将所建立的弹塑性耦合力学模型用于辅助洞2#试验洞开挖过程的模拟分析,研究了隧洞开挖过程中,围岩变形、损伤区和应力的演化规律,较好地给出了破坏区的位置和范围。根据所建立的流固耦合模型,考虑高渗透压下的非Darcy流效应,对锦屏Ⅱ水电站引水隧洞的开挖过程进行了流固耦合分析。探讨了隧洞周围的高压水对隧洞安全性的影响。根据流固耦合分析的结果,对突(涌)水的预防和治理提出了相应的建议。
As the geotechnical engineering around the world becames deeper, where the geological and stress environment has become more complex, the study of rock mechanics under the condition of high stress and high seepage pressure has been put on the agenda. In particular, how to simulate the mechanical response of rock has been one of the key issues. The failure of surrounding rock mass under high geo-stress and the occurrence of water burst under high seepage pressure are the two main problems met during the construction of diversion tunnel in Jinping II hydroelectric station. In order to solve these problems, the mechanical model and fluid-solid coupling mechanism under high seepage pressure of marble are both studied here. In sum, the main work and conclusion including:
1. In order to study the elato-plastic character, subsequent yield character and dilation of brittle rocks, cyclic-loading experiments, both before and after the peak strength of two kinds of marble (T2y6 and T2b) and a kind of sandstone, are carried out. A plastic internal variable is defined, which takes the influence of confining pressure on yield process into consideration. Based on the results of cyclic-loading experiments and the plastic internal variable, the evolution process of elastic, strength and dilation parameters with plastic strain is studied.
2. The relation of strength under unloading and loading conditions is studied with respect to the rate of loading. Yield approach rate (YAR) is proposed to denote the stress varying rate under loading and unloading conditions. Then, the characters of YAR under loading and unloading conditions are analyzed. The simulation by EPCA2D (Elasto-Plastic Cellular Automaton) and the unloading tests of marble indicate that if the initial unloading stress is in the elastic state, the strength under loading and unloading conditions is equal when the unloading rate is 0.2-0.3 of the loading rate.
3. Based on the results of experiments on two kinds of marble (T2y6 and T2b) and a kind of sandstone, an elasto-plastic coupling mechanical model is proposed. The model takes the variety of elastic parameters, strength parameters and dilation parameter into consideration and can reflect the influence of stress state on the yield process. Simulation results of the traxial compression experiments and excavation process in Mine-by tunnel show that the mechanical model proposed here can capture the deformation and yield characters of brittle rock under different stress path. Especially, the deformation and yield characters in confining pressure unloading tests are also well described by the model.
4. Combined with the elasto-plastic coupling mechanical model, the basic frame of fluid-solid coupling analyze under plastic condition is established. As different researchers disputed on the continuum equation of fluid, two methods are used to derive the continuum equation. The continuum equations deduced form the two methods are found to be equivalent. In addition, the equations are compared to the continuum equation derived by other researchers based on mass conservation law, and they are found to be coincident. Then, the right form of fluid continuum equation is proved.
5. Physical mechanism and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed to denote the meso-scaled structure of these materials. Then a general expression describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pore is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Based on the effective stress tests of coal and sandstone under elastic deformation, and the effective stress tests of marbles and sandstone under plastic deformation, the evolution law of effective stress coefficient with strain is obtained. The simulation results agree very well with the test results.
Unified equation of Darcy flow and non-Darcy flow is deduced. Then, the criterion of non-Darcy flow is put forward based on the contrast relationship of bond shear stress in laminar flow and additional shear stress in turbulent flow.
6. Finally, with intelligent inversion theory, the elato-plastic coupling constitute model is used to simulate the excavation process of the 2# experiment tunnel in the assisted tunnel of Jinping II diversion tunnel. Evolution process of deformation, disturbed zone and stress are got according to the excavation step. The position and extent of failure zone is in good agreement with the field.
Using the fluid-solid coupling method proposed here, the excavation process of the JinpingⅡdiversion tunnel is simulated which takes the high fluid pressure into consideration. The result shows that the high fluid and seepage pressure has effect on the stability of the wall rock. Based on the simulation results, suggestions are raised for the prevention and management of water burst.
引文
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