岩石（体）宏细观复合损伤理论与应用研究
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摘要
本文将反映岩石材料内部的损伤缺陷及变化机理的细观基准量,与反映岩石内部损伤累积到一定程度的宏观表现的宏观基准量联系起来,建立岩石宏细观复合损伤模型,研究单轴、三轴压应力作用下损伤岩石的应力应变曲线及特征点的相关性,从宏观和细观两方面研究分析岩石微裂纹变化发展的规律及其宏观特征,并结合宏、细观试验进行对比验证分析,进而分析岩体问题。基于宏细观损伤变量的关系和特征点的相关性,研究深埋圆形洞室围岩损伤问题。
本论文进行的主要工作为:
1)以细观损伤力学中描述宏观力学性能的裂纹密度作为连续损伤理论中损伤状态的描述参量,建立了单、双标量受压岩石宏细观损伤复合模型和应力应变与裂纹密度的变化关系。通过假设单元的状态处于破坏、损伤、无损三种状态,把宏观损伤统计理论与细观损伤理论结合起来,建立了可以反映岩石应力应变与裂纹密度关系的宏细观复合损伤模型。
2)分析了单轴受压岩石裂纹密度变化的扩展规律,探讨了裂纹密度f与应力、应变的变化关系及按Taylor法、广义自洽法、Taylor介质法确定岩体参数的差异和影响。分析了岩石特征点间的相关性,提出了确定岩石残余强度的方法,结合试验结果和资料,分析比较了岩石残余强度确定方法的差异。
3)推求了三轴受压条件下分别以单标量和双标量表示的岩石宏细观复合损伤模型,通过实例分析了三轴受压下岩石应力应变随微裂纹密度变化的规律;推导了由单轴抗压指标推求三轴受压下岩石应力应变曲线的计算公式。
4)针对上述工作进行了岩石的单轴、三轴受压试验验证,并与扫描电镜和CT试验的结果进行了对比计算分析。
5)提出了采用损伤模型表达岩体应力应变曲线参数的方法。讨论了岩体变形模量随围压的变化规律,提出了表示岩体的变形模量E与围压Δσ3关系的指数表达式,表征了裂隙密度参数随围压的增加呈指数关系减小的特征。
6)建立了岩体的裂隙密度参数与岩体的完整性系数或体积节理数的关系;分析比较了采用Taylor法、广义自洽法和Taylor介质法进行分析裂隙密度及其相互作用并用于确定岩体参数的差异。提出了通过地质调查统计法、岩体的完整性系数或弹性波方程法确定岩体裂纹密度的方法;
7)根据岩体的应力—应变曲线,把洞室围岩的变形划分为弹性区、塑性硬化损伤区和塑性软化损伤区和破裂区4种状态。根据岩体强度各特征点之间的关系,基于莫尔强度理论,推导建立了围岩分区半径、围岩形变压力和围岩变形损伤的计算公式。
The macro-and meso-damage composite model has been obtained through integrating the microcosmic datum quantum which reflecte the inner damage disfigurement and mechanism of its changing with the macrocosmic datum quantum which reflecte macro behave of rockmass inner damage piling up during a periord. The damage rock stress-strain curve under uniaxial and triaxial compression and the relationship of rock characteristics points have been analysed. The dissertation analyses the rock microcrack density expanding law and the influences on macro variable from macro-damage and meso-damage, The macro-tests and meso-tests of rock have been compared with calculating and analyzing, in turn the rock mass damage have been analyzed, Based on the relationship of macro-and meso-damage parameters and the correlations of rock characteristics points, the adjoining rock damage of deep circle cavern has been analysed.
The main thesis works are the following parts:
1) Using microcrack density which is used to discribing the macro-mechanics properties in meso-damage mechanics as the describe parameters of damage state on continuous damage theories, this dissertation makes the variation relation between double scalar quantity model and the crack density. Assuming that the element has three states,i.e. failure, damage and intactness, this dissertation unite the macro-damage statistical theory and meso-damage theory, establishes a macro-and meso-damage composite model.
2) This model can be used to describe the relation between the stress-strain of rock and the microcrack density. The dissertation analyses the rock microcrack density expanding law under uniaxial compressive test by examples, discusses the relations between the microcrack density and the stress - strain of rock, the differences and influences of the f being obtained by the Taylor method, the generalized self-consistent method and the Taylor medium method in the process of stress-strain. The relationship of rock characteristics points has being analysed. The method has been set up to determine the residual strength of rock with meso-damage theory;
3) This dissertation draws to the macro-and-meso damage composite model of rock, and the model is expressed with single scalar and double scalar under stiaxial compression. The rock stress-strain curve calculating formula under stiaxial compression is deduced with uniaxial anti-compression indicators.
4) According to the above work, the tests of rock uniaxial compression and triaxial compression have been completed, and the scanning electron microscopy test and CT results have been compared with calculated and analyzed. 5) The method of determining parameters is set up on the damage model to express
the rock stress-strain curve. The law is discussed of rock deformation modulus varying with surrounding pressure, and the formula being denoted with exponent formula is deduced about the relationship between the deformation of rock E and surrounding pressureΔσ3, and it expresses the character that the parameter of crack density decreases with the surrounding pressure increases.
6) Using meso-damage mechanics method it is to set up the relationship between the microcrack density parameters and rock integrality coefficients or volume joint quantities. By the Taylor method, the generalized self-consistent method and the Taylor medium method, this dissertation analyses and compares the differences in determining rockmass parameters on crack density and their reciprocities. The method to determine the crack density of rockmass has been introduced through the geological investigating statistical method, the intactness index of rock mass method or the elastic wave equation method.
7) Accouding to the rock stress-strain curves, the deformation of the rock surrounding cavern can be divided into the four states of the elastic zone and the plastic hardening damage zone and the plastic softening damage zone and the fracturing zone. Based on the relation among every characteristic points and the Mohr strength theory, the calculating formulas on damage have been established of rock surrounding cavern partition radius, the rock surrounding cavern pressure and the rock surrounding cavern deformation.
本论文进行的主要工作为:
1)以细观损伤力学中描述宏观力学性能的裂纹密度作为连续损伤理论中损伤状态的描述参量,建立了单、双标量受压岩石宏细观损伤复合模型和应力应变与裂纹密度的变化关系。通过假设单元的状态处于破坏、损伤、无损三种状态,把宏观损伤统计理论与细观损伤理论结合起来,建立了可以反映岩石应力应变与裂纹密度关系的宏细观复合损伤模型。
2)分析了单轴受压岩石裂纹密度变化的扩展规律,探讨了裂纹密度f与应力、应变的变化关系及按Taylor法、广义自洽法、Taylor介质法确定岩体参数的差异和影响。分析了岩石特征点间的相关性,提出了确定岩石残余强度的方法,结合试验结果和资料,分析比较了岩石残余强度确定方法的差异。
3)推求了三轴受压条件下分别以单标量和双标量表示的岩石宏细观复合损伤模型,通过实例分析了三轴受压下岩石应力应变随微裂纹密度变化的规律;推导了由单轴抗压指标推求三轴受压下岩石应力应变曲线的计算公式。
4)针对上述工作进行了岩石的单轴、三轴受压试验验证,并与扫描电镜和CT试验的结果进行了对比计算分析。
5)提出了采用损伤模型表达岩体应力应变曲线参数的方法。讨论了岩体变形模量随围压的变化规律,提出了表示岩体的变形模量E与围压Δσ3关系的指数表达式,表征了裂隙密度参数随围压的增加呈指数关系减小的特征。
6)建立了岩体的裂隙密度参数与岩体的完整性系数或体积节理数的关系;分析比较了采用Taylor法、广义自洽法和Taylor介质法进行分析裂隙密度及其相互作用并用于确定岩体参数的差异。提出了通过地质调查统计法、岩体的完整性系数或弹性波方程法确定岩体裂纹密度的方法;
7)根据岩体的应力—应变曲线,把洞室围岩的变形划分为弹性区、塑性硬化损伤区和塑性软化损伤区和破裂区4种状态。根据岩体强度各特征点之间的关系,基于莫尔强度理论,推导建立了围岩分区半径、围岩形变压力和围岩变形损伤的计算公式。
The macro-and meso-damage composite model has been obtained through integrating the microcosmic datum quantum which reflecte the inner damage disfigurement and mechanism of its changing with the macrocosmic datum quantum which reflecte macro behave of rockmass inner damage piling up during a periord. The damage rock stress-strain curve under uniaxial and triaxial compression and the relationship of rock characteristics points have been analysed. The dissertation analyses the rock microcrack density expanding law and the influences on macro variable from macro-damage and meso-damage, The macro-tests and meso-tests of rock have been compared with calculating and analyzing, in turn the rock mass damage have been analyzed, Based on the relationship of macro-and meso-damage parameters and the correlations of rock characteristics points, the adjoining rock damage of deep circle cavern has been analysed.
The main thesis works are the following parts:
1) Using microcrack density which is used to discribing the macro-mechanics properties in meso-damage mechanics as the describe parameters of damage state on continuous damage theories, this dissertation makes the variation relation between double scalar quantity model and the crack density. Assuming that the element has three states,i.e. failure, damage and intactness, this dissertation unite the macro-damage statistical theory and meso-damage theory, establishes a macro-and meso-damage composite model.
2) This model can be used to describe the relation between the stress-strain of rock and the microcrack density. The dissertation analyses the rock microcrack density expanding law under uniaxial compressive test by examples, discusses the relations between the microcrack density and the stress - strain of rock, the differences and influences of the f being obtained by the Taylor method, the generalized self-consistent method and the Taylor medium method in the process of stress-strain. The relationship of rock characteristics points has being analysed. The method has been set up to determine the residual strength of rock with meso-damage theory;
3) This dissertation draws to the macro-and-meso damage composite model of rock, and the model is expressed with single scalar and double scalar under stiaxial compression. The rock stress-strain curve calculating formula under stiaxial compression is deduced with uniaxial anti-compression indicators.
4) According to the above work, the tests of rock uniaxial compression and triaxial compression have been completed, and the scanning electron microscopy test and CT results have been compared with calculated and analyzed. 5) The method of determining parameters is set up on the damage model to express
the rock stress-strain curve. The law is discussed of rock deformation modulus varying with surrounding pressure, and the formula being denoted with exponent formula is deduced about the relationship between the deformation of rock E and surrounding pressureΔσ3, and it expresses the character that the parameter of crack density decreases with the surrounding pressure increases.
6) Using meso-damage mechanics method it is to set up the relationship between the microcrack density parameters and rock integrality coefficients or volume joint quantities. By the Taylor method, the generalized self-consistent method and the Taylor medium method, this dissertation analyses and compares the differences in determining rockmass parameters on crack density and their reciprocities. The method to determine the crack density of rockmass has been introduced through the geological investigating statistical method, the intactness index of rock mass method or the elastic wave equation method.
7) Accouding to the rock stress-strain curves, the deformation of the rock surrounding cavern can be divided into the four states of the elastic zone and the plastic hardening damage zone and the plastic softening damage zone and the fracturing zone. Based on the relation among every characteristic points and the Mohr strength theory, the calculating formulas on damage have been established of rock surrounding cavern partition radius, the rock surrounding cavern pressure and the rock surrounding cavern deformation.
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