岩石变形特性与变形全过程统计损伤模拟方法研究
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摘要
岩石作为一种含有缺陷的典型脆性材料,在各种复杂应力状态下所体现的本构关系是一个复杂的基础理论问题。尤其在岩体工程的运营阶段,岩石的变形特性将直接影响工程的正常使用。为此,本文综合运用连续损伤理论、细观损伤力学与概率统计理论,在探讨岩石损伤模型的基础上,考虑各种荷载状态,并对损伤变量合理演化,得到模拟各种复杂应力状态的岩石损伤本构模型,进而在岩体工程中进行应用。
首先,在基于Lemaitre应变等价性理论的岩石损伤模型基础上,通过探讨岩石应变软化变形过程中损伤变量或损伤因子的变化规律,并结合岩石应变软化变形全过程特征及其损伤机理的研究,探讨了建立岩石损伤演化模型时考虑损伤阀值影响的必要性。在对现有岩石微元强度度量方法研究的基础上,提出了可考虑损伤阀值影响的新型岩石微元强度度量方法,并引进统计损伤理论,建立了可考虑损伤阀值影响的岩石统计损伤演化模型,该模型不仅能反映损伤阀值的影响,且能反映岩石损伤程度受应力状态影响和岩石损伤在不同应力状态下损伤起始点不同的特性。
其次,岩石的体积变化特征是岩石力学研究的重要内容之一。针对现有岩石损伤模型的局限性与不足,将应力作用下的岩石抽象为空隙、损伤与未损伤材料三部分,以空隙率反映岩石体积或空隙的变化,以损伤变量或损伤因子反映岩石力学性态的改变程度,通过对各部分材料的微观受力及其与宏观应力和应变的关系进行分析,建立出可反映岩石变形过程中体积或空隙变化特性的新型岩石损伤模型,进而建立出能反映岩石体积变化特征的统计损伤本构模型,并提出了其参数确定方法。在该本构模型的基础上,通过探讨岩石脆延特性及其相互转化的力学机理与特点,利用求解多元函数极值的分析方法,建立岩石脆延特性相互转化条件的确定方法,该方法能同时反映岩石所受荷载状态与本身力学性质对岩石脆延特性及其相互转化特征的综合影响,完善了岩石本构模型的研究内容。
再次,岩石应变软化变形破坏全过程模拟属于岩石力学研究的一个重要分支。在分析岩石应变软化变形全过程不同阶段变形特征基础上,针对现有岩石损伤模型难以反映岩石破坏后仍具残余强度特性的不足,假设受载岩石可抽象为损伤和未损伤两部分材料组成,其所受轴向荷载由这两部分材料共同承担,且损伤部分材料所受应力为残余强度,建立出可反映岩石破坏后仍具残余强度特征的新型损伤模型。然后,在此基础上建立出可反映岩石变形全过程特征的岩石统计损伤演化模型,进而建立出可模拟岩石应变软化变形全过程的损伤统计本构模型,并提出了其模型参数的确定方法。通过实例验证表明该模型能较好地反映岩石峰后残余强度阶段变形特征。
最后,为完善岩石变形模拟过程的研究内容,对岩石的动态变形过程模拟进行了研究。针对岩石动态变形特点,引进Kelvin模型的研究思路与方法,将岩石变形过程中的动态应力视为静态应力分量与动态应力分量的叠加,分别以粘性元件和非线性元件模拟岩石单元动态应力分量与静态应力分量,并建立出岩石动态应力的力学分析模型,在此研究基础上,利用粘性元件的力学特性和统计损伤理论分别建立出粘性元件和非线性元件变形过程模拟方法,进而得到岩石三轴动态变形过程模拟方法,并提出其模型的参数确定方法。通过实例分析与讨论,表明了该方法具有较强的合理性和可行性。
As rock is a typical brittle material containing flaws, its constitutive relation under complicated stress is a complicated basic theoretical question. Especially on the operation phase of rock engineering, the deformation characteristic will directly influence the normal use of engineering. Based on reasons above, the continuous damage theory, microscopic damage mechanics and the theory of probability have been integrated to reasonably evolve the damage variable on the basis of damage constitutive models of rock considering various loading conditions simulate damage constitutive models of rock under varied complex stress state and apply results to rock engineering.
In the first place, based on the damage constitutive model of rock under Lemaitre's hypothesis of strain equivalence, this paper discussed the necessity considering damage threshold to establish rock damage evolution model when exploring the law of damage variable or damage factor of strain softening deformation of rock, combined with the study of rock characteristics of strain softening deformation and mechanism of injury. On the existing rock micro-element strength measuring method, a new rock micro-element strength measuring method was put forward which could consider the impact of rock damage threshold. The statistical damage theory, and established the rock statistical damage evolution model which can weigh the impact of damage threshold of rock. This model can not only reflect the impact of damage threshold, but the damage degree by the influence of stress state and characteristics of varied damage starting point under varied stress states as well.
Secondly, the volume change characteristic is a major concern in rock mechanics. Due to limitations and shortcomings of the current damage constitutive models of rock, this paper divided rock under stress into three parts:void, damaged and undamaged material. By using void ratio to reflect the rock volume or void changes, damage variable (or damage factor) to reflect the variable feature of rock mechanics, relationship between micro and macro stress and strain analysis of all parts of material has been analyzed. Then the new rock damage model has been established, which rock deformation is able to indicate the volume or void changes in size or characteristics. And the statistical damage constitutive model was built which can show the volume change characteristic of rock. Also the method determining its parameters was given. Based on this constitutive model, the determination approach on conditions of transforming brittleness into ductility of rock was offered by exploring the rock brittle mechanical properties and mechanism of mutual transformation and characteristics and the use of extreme value analysis to solve multi-function approach. This method is capable to display simultaneously the loading state of rock and its own mechanical properties' influence on rock's brittleness and ductility and their mutual transformation characteristics and perfected the research content of rock's constitutive model.
Furthermore, the process simulation of rock deformation and destruction of strain softening is one of significant branches of rock mechanics research. in the analysis of various characteristics at different stages of the Strain softening of rock deformation process, due to the shortcomings that the existing rock damage model failed to indicate rock's residual strength properties after failure of rock, on the assumption that the loading rock is comprised of damaged and undamaged material and the axial load was shared by these two parts, the stress that damaged material bears is defined as residual strength, a new damage model was established showing rock's residual strength after failure. Then on the basis of this model, statistical damage evolution model of rock was built showing the whole deformation process and the statistical damage constitutive model was developed simulating the whole process of rock strain softening, the determination of the model parameters was given as well. The project case verified w that the model can better reflect the residual strength after the peak stage of rock deformation.
Finally, to improve the simulation of rock deformation research content, the dynamic deformation process of rock was simulated. According to the dynamic deformation characteristics of rock, the research methodology of Kelvin model was introduced. The dynamic stress during rock deformation was considered as the superposition of dynamic and static components of stress. By using viscous components and non-linear components to simulate dynamic and static stress components respectively, the mechanics analysis model for dynamic stress of rock was built. Based on this study, taking advantage of the mechanical properties of viscous components and statistical damage theory, the simulation of the deformation process of viscous and non-linear components was proposed and the simulation of rock triaxial dynamic deformation process was put forward, the determination of model parameter was included too. The analysis and discussion of project case justified the rationality and feasibility of this method.
首先,在基于Lemaitre应变等价性理论的岩石损伤模型基础上,通过探讨岩石应变软化变形过程中损伤变量或损伤因子的变化规律,并结合岩石应变软化变形全过程特征及其损伤机理的研究,探讨了建立岩石损伤演化模型时考虑损伤阀值影响的必要性。在对现有岩石微元强度度量方法研究的基础上,提出了可考虑损伤阀值影响的新型岩石微元强度度量方法,并引进统计损伤理论,建立了可考虑损伤阀值影响的岩石统计损伤演化模型,该模型不仅能反映损伤阀值的影响,且能反映岩石损伤程度受应力状态影响和岩石损伤在不同应力状态下损伤起始点不同的特性。
其次,岩石的体积变化特征是岩石力学研究的重要内容之一。针对现有岩石损伤模型的局限性与不足,将应力作用下的岩石抽象为空隙、损伤与未损伤材料三部分,以空隙率反映岩石体积或空隙的变化,以损伤变量或损伤因子反映岩石力学性态的改变程度,通过对各部分材料的微观受力及其与宏观应力和应变的关系进行分析,建立出可反映岩石变形过程中体积或空隙变化特性的新型岩石损伤模型,进而建立出能反映岩石体积变化特征的统计损伤本构模型,并提出了其参数确定方法。在该本构模型的基础上,通过探讨岩石脆延特性及其相互转化的力学机理与特点,利用求解多元函数极值的分析方法,建立岩石脆延特性相互转化条件的确定方法,该方法能同时反映岩石所受荷载状态与本身力学性质对岩石脆延特性及其相互转化特征的综合影响,完善了岩石本构模型的研究内容。
再次,岩石应变软化变形破坏全过程模拟属于岩石力学研究的一个重要分支。在分析岩石应变软化变形全过程不同阶段变形特征基础上,针对现有岩石损伤模型难以反映岩石破坏后仍具残余强度特性的不足,假设受载岩石可抽象为损伤和未损伤两部分材料组成,其所受轴向荷载由这两部分材料共同承担,且损伤部分材料所受应力为残余强度,建立出可反映岩石破坏后仍具残余强度特征的新型损伤模型。然后,在此基础上建立出可反映岩石变形全过程特征的岩石统计损伤演化模型,进而建立出可模拟岩石应变软化变形全过程的损伤统计本构模型,并提出了其模型参数的确定方法。通过实例验证表明该模型能较好地反映岩石峰后残余强度阶段变形特征。
最后,为完善岩石变形模拟过程的研究内容,对岩石的动态变形过程模拟进行了研究。针对岩石动态变形特点,引进Kelvin模型的研究思路与方法,将岩石变形过程中的动态应力视为静态应力分量与动态应力分量的叠加,分别以粘性元件和非线性元件模拟岩石单元动态应力分量与静态应力分量,并建立出岩石动态应力的力学分析模型,在此研究基础上,利用粘性元件的力学特性和统计损伤理论分别建立出粘性元件和非线性元件变形过程模拟方法,进而得到岩石三轴动态变形过程模拟方法,并提出其模型的参数确定方法。通过实例分析与讨论,表明了该方法具有较强的合理性和可行性。
As rock is a typical brittle material containing flaws, its constitutive relation under complicated stress is a complicated basic theoretical question. Especially on the operation phase of rock engineering, the deformation characteristic will directly influence the normal use of engineering. Based on reasons above, the continuous damage theory, microscopic damage mechanics and the theory of probability have been integrated to reasonably evolve the damage variable on the basis of damage constitutive models of rock considering various loading conditions simulate damage constitutive models of rock under varied complex stress state and apply results to rock engineering.
In the first place, based on the damage constitutive model of rock under Lemaitre's hypothesis of strain equivalence, this paper discussed the necessity considering damage threshold to establish rock damage evolution model when exploring the law of damage variable or damage factor of strain softening deformation of rock, combined with the study of rock characteristics of strain softening deformation and mechanism of injury. On the existing rock micro-element strength measuring method, a new rock micro-element strength measuring method was put forward which could consider the impact of rock damage threshold. The statistical damage theory, and established the rock statistical damage evolution model which can weigh the impact of damage threshold of rock. This model can not only reflect the impact of damage threshold, but the damage degree by the influence of stress state and characteristics of varied damage starting point under varied stress states as well.
Secondly, the volume change characteristic is a major concern in rock mechanics. Due to limitations and shortcomings of the current damage constitutive models of rock, this paper divided rock under stress into three parts:void, damaged and undamaged material. By using void ratio to reflect the rock volume or void changes, damage variable (or damage factor) to reflect the variable feature of rock mechanics, relationship between micro and macro stress and strain analysis of all parts of material has been analyzed. Then the new rock damage model has been established, which rock deformation is able to indicate the volume or void changes in size or characteristics. And the statistical damage constitutive model was built which can show the volume change characteristic of rock. Also the method determining its parameters was given. Based on this constitutive model, the determination approach on conditions of transforming brittleness into ductility of rock was offered by exploring the rock brittle mechanical properties and mechanism of mutual transformation and characteristics and the use of extreme value analysis to solve multi-function approach. This method is capable to display simultaneously the loading state of rock and its own mechanical properties' influence on rock's brittleness and ductility and their mutual transformation characteristics and perfected the research content of rock's constitutive model.
Furthermore, the process simulation of rock deformation and destruction of strain softening is one of significant branches of rock mechanics research. in the analysis of various characteristics at different stages of the Strain softening of rock deformation process, due to the shortcomings that the existing rock damage model failed to indicate rock's residual strength properties after failure of rock, on the assumption that the loading rock is comprised of damaged and undamaged material and the axial load was shared by these two parts, the stress that damaged material bears is defined as residual strength, a new damage model was established showing rock's residual strength after failure. Then on the basis of this model, statistical damage evolution model of rock was built showing the whole deformation process and the statistical damage constitutive model was developed simulating the whole process of rock strain softening, the determination of the model parameters was given as well. The project case verified w that the model can better reflect the residual strength after the peak stage of rock deformation.
Finally, to improve the simulation of rock deformation research content, the dynamic deformation process of rock was simulated. According to the dynamic deformation characteristics of rock, the research methodology of Kelvin model was introduced. The dynamic stress during rock deformation was considered as the superposition of dynamic and static components of stress. By using viscous components and non-linear components to simulate dynamic and static stress components respectively, the mechanics analysis model for dynamic stress of rock was built. Based on this study, taking advantage of the mechanical properties of viscous components and statistical damage theory, the simulation of the deformation process of viscous and non-linear components was proposed and the simulation of rock triaxial dynamic deformation process was put forward, the determination of model parameter was included too. The analysis and discussion of project case justified the rationality and feasibility of this method.
引文
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