岩石断裂失稳破坏与冲击地压的分叉和混沌特征研究
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摘要
不同应力状态下岩石材料的失稳断裂破坏一直是岩石力学与工程研究的重点。本文在对岩石进行平面应变、常规三轴和声发射实验及煤岩CT实验的基础上,采用非线性分叉理论、混沌理论对岩石在断裂失稳过程中的局部化分叉与混沌特征以及冲击地压的混沌特性进行了研究。本文的主要研究成果如下:
1.根据许多岩石工程处于平面应变状态的实际情况,自行研制了岩石平面应变仪,进行了岩石平面应变实验,并将平面应变实验结果和常规三轴实验结果进行了比较。结果表明,不同应力状态下岩石的失稳断裂表现出不同的本构特性,简单地将常规三轴实验结果应用到处于平面应变状态的实际工程将导致很大的误差甚至得到错误的结论。
2.为研究岩石材料弹性模量的应力敏感性,进行了不同围压和不同应力水平下岩石的加卸荷循环实验。实验结果分析表明,岩石材料的弹性模量表现出较强的压硬性特点,同时与塑性变形耦合,表现出强烈的非线性性质。
3.处于平面应变和常规三轴条件下的岩石在中低围压(<40MPa)下均表现为剪切局部化破坏的特征。对破坏后试件剪切面倾角的测量结果显示,在常规三轴情况下,剪切面倾角有随围压增加而降低的趋势;而平面应变情况下试件倾角表现出相对的稳定性,不随围压的变化而变化。
4.根据岩石的平面应变和常规三轴实验结果,建立了不同应力状态下岩石非关联弹塑性本构模型,应用变形分叉理论的声张量法推导了不同应力状态下的分叉条件。对不同应力条件下岩石分叉的计算结果和实验结果的分析表明,常规三轴条件下,岩石的分叉发生在材料的应变软化即峰值应力出现之后,而平面应变条件下,岩石的分叉发生在应变硬化区,即峰值应力出现之前。
5.在煤岩CT实验的基础上,通过研究煤岩CT数在不同应力水平时的变化,建立了煤岩CT数演化的混沌模型。对该模型的分析表明,煤岩在断裂失稳过程具有混沌分叉的特点。
6.在岩石声发射实验基础上,根据混沌理论的非线性时间序列分析方法,对岩石的声发射参数时间序列进行了相空间重构、关联维分析和最大Lyapunov指数的计算。结果表明,岩石声发射时间序列具有混沌特性,描述不同围压下岩石声发射参数演化的最小因子数大于16,说明岩石变形失稳断裂过程是一个极其复杂的非线性动力系统。
7.在煤岩CT数混沌模型和声发射时间序列混沌分析的基础上,结合损伤力学和耗散结构理论初步提出了混沌损伤的概念,认为岩石变形失稳断裂过程是一个混沌损伤的过程。
8.结合对煤矿冲击地压发生条件和影响因素的分析,引入单滑块单状态本构模型、双状态本构模型和双滑块模型对煤矿冲击地压的发生机理从非线性动力学的角度进行了研究,分析了不同模型的动力学演化行为,探讨了模型的适用条件。
Instability and failure of rocks during different loading conditions are always important concerns in rock mechanics and engineering. On the basis of an extensive experimental program of conventional triaxial compression, plain strain and CT tests, the formation and orientation of a localization band in the sandstone, the chaotic characteristics of rock fracturing, the CT evolution of the coal rock and rockbursts occurring at deep coal mines were studied using discontinuous bifurcation theories and chaos theories. The results could be summarized as follows:
1. A new plain strain apparatus for testing mild rocks were designed and built and a series of plain strain tests on sandstone have been performed. The comparison of plain strain experimental results of sandstone to that under conventional triaxial compression shows that the constitutive responses of rocks differ greatly for various loading conditions. Questionable predictions may arise when data obtained from axi-symmetric tests are applied to two dimensional problems.
2. The unloading-reloading cycles in triaxial tests at different confining pressures have been undertaken to investigate the stress-dependent elasticity of sandstone. The analysis of experimental results show that the elasticity of sandstone is not only stress sensitive but also coupled to the plasticity, manifesting strong nonlinearity.
3. All sandstone specimens in our test program failed by a single plane called a shear band when subjected to confining pressures lower than 40MPa regardless of loading conditions. The measurements of shear band inclinations of failed specimens indicate that the orientations are decreasing with increasing confining pressures under conventional triaxial compression, while that of specimens subjected to plain strain conditions seem unaffected by varying confining pressures.
4. The onset and orientation of a localization band formed in sandstone was studied theoretically within the framework of equilibrium bifurcation theory. Corresponding elastoplasitc constitutive models with nonlinear yield and potential functions were developed from plain strain and conventional triaxial compression experiments. The inclinations of shear bands and the bifurcation points were predicted using so-called acoustic tensor method. Comparison of computation results with experimental results indicates that the initiation of a shear band predicted by the three dimensional model occurs closely after the peak axial stress, while the two dimensional model predicts bifurcation will happen within the strain hardening region, i.e. prior to the peak stress.
5. A model characterizing the CT evolution of coal rocks during uniaxial loading was developed on the basis of CT test on coal rock. Dynamical analysis of the model shows the model behaves chaotically, implying there possibly exists chaotic characteristics in the process of coal rock fracturing.
6. The acoustic emission time series obtained from conventional triaxial testing on sandstone at different confining pressures was analyzed by use of nonlinear time series techniques including the phase space reconstruction, the correlation dimension analysis and the evaluation of the largest Lyapunov exponent. The analysis concludes that the acoustic emission time series is a chaotic one, and the smallest dimensions of the embedding spaces is 16, indicating the instability process of rocks could be a complex nonlinear dynamical system.
7. On the basis of the previous analyses of CT evolution model for coal rock and acoustic emission time series of sandstone in connection with damage mechanics and dissipation structure theories, a new definition on damage of rocks is first presented, which is called chaotic damage, and it is thought that damages in rocks during loading may develop in a chaotic way.
8. The single state variable model, two state variables model, corresponding to a single degree of freedom elastic system, and the two degrees of freedom elastic system are introduced to model the rockbursts occurring frequently at many deep coal mines based on the investigation into the conditions triggering rockbursts. The models’dynamical behaviors and their applicability are discussed in detail.
1.根据许多岩石工程处于平面应变状态的实际情况,自行研制了岩石平面应变仪,进行了岩石平面应变实验,并将平面应变实验结果和常规三轴实验结果进行了比较。结果表明,不同应力状态下岩石的失稳断裂表现出不同的本构特性,简单地将常规三轴实验结果应用到处于平面应变状态的实际工程将导致很大的误差甚至得到错误的结论。
2.为研究岩石材料弹性模量的应力敏感性,进行了不同围压和不同应力水平下岩石的加卸荷循环实验。实验结果分析表明,岩石材料的弹性模量表现出较强的压硬性特点,同时与塑性变形耦合,表现出强烈的非线性性质。
3.处于平面应变和常规三轴条件下的岩石在中低围压(<40MPa)下均表现为剪切局部化破坏的特征。对破坏后试件剪切面倾角的测量结果显示,在常规三轴情况下,剪切面倾角有随围压增加而降低的趋势;而平面应变情况下试件倾角表现出相对的稳定性,不随围压的变化而变化。
4.根据岩石的平面应变和常规三轴实验结果,建立了不同应力状态下岩石非关联弹塑性本构模型,应用变形分叉理论的声张量法推导了不同应力状态下的分叉条件。对不同应力条件下岩石分叉的计算结果和实验结果的分析表明,常规三轴条件下,岩石的分叉发生在材料的应变软化即峰值应力出现之后,而平面应变条件下,岩石的分叉发生在应变硬化区,即峰值应力出现之前。
5.在煤岩CT实验的基础上,通过研究煤岩CT数在不同应力水平时的变化,建立了煤岩CT数演化的混沌模型。对该模型的分析表明,煤岩在断裂失稳过程具有混沌分叉的特点。
6.在岩石声发射实验基础上,根据混沌理论的非线性时间序列分析方法,对岩石的声发射参数时间序列进行了相空间重构、关联维分析和最大Lyapunov指数的计算。结果表明,岩石声发射时间序列具有混沌特性,描述不同围压下岩石声发射参数演化的最小因子数大于16,说明岩石变形失稳断裂过程是一个极其复杂的非线性动力系统。
7.在煤岩CT数混沌模型和声发射时间序列混沌分析的基础上,结合损伤力学和耗散结构理论初步提出了混沌损伤的概念,认为岩石变形失稳断裂过程是一个混沌损伤的过程。
8.结合对煤矿冲击地压发生条件和影响因素的分析,引入单滑块单状态本构模型、双状态本构模型和双滑块模型对煤矿冲击地压的发生机理从非线性动力学的角度进行了研究,分析了不同模型的动力学演化行为,探讨了模型的适用条件。
Instability and failure of rocks during different loading conditions are always important concerns in rock mechanics and engineering. On the basis of an extensive experimental program of conventional triaxial compression, plain strain and CT tests, the formation and orientation of a localization band in the sandstone, the chaotic characteristics of rock fracturing, the CT evolution of the coal rock and rockbursts occurring at deep coal mines were studied using discontinuous bifurcation theories and chaos theories. The results could be summarized as follows:
1. A new plain strain apparatus for testing mild rocks were designed and built and a series of plain strain tests on sandstone have been performed. The comparison of plain strain experimental results of sandstone to that under conventional triaxial compression shows that the constitutive responses of rocks differ greatly for various loading conditions. Questionable predictions may arise when data obtained from axi-symmetric tests are applied to two dimensional problems.
2. The unloading-reloading cycles in triaxial tests at different confining pressures have been undertaken to investigate the stress-dependent elasticity of sandstone. The analysis of experimental results show that the elasticity of sandstone is not only stress sensitive but also coupled to the plasticity, manifesting strong nonlinearity.
3. All sandstone specimens in our test program failed by a single plane called a shear band when subjected to confining pressures lower than 40MPa regardless of loading conditions. The measurements of shear band inclinations of failed specimens indicate that the orientations are decreasing with increasing confining pressures under conventional triaxial compression, while that of specimens subjected to plain strain conditions seem unaffected by varying confining pressures.
4. The onset and orientation of a localization band formed in sandstone was studied theoretically within the framework of equilibrium bifurcation theory. Corresponding elastoplasitc constitutive models with nonlinear yield and potential functions were developed from plain strain and conventional triaxial compression experiments. The inclinations of shear bands and the bifurcation points were predicted using so-called acoustic tensor method. Comparison of computation results with experimental results indicates that the initiation of a shear band predicted by the three dimensional model occurs closely after the peak axial stress, while the two dimensional model predicts bifurcation will happen within the strain hardening region, i.e. prior to the peak stress.
5. A model characterizing the CT evolution of coal rocks during uniaxial loading was developed on the basis of CT test on coal rock. Dynamical analysis of the model shows the model behaves chaotically, implying there possibly exists chaotic characteristics in the process of coal rock fracturing.
6. The acoustic emission time series obtained from conventional triaxial testing on sandstone at different confining pressures was analyzed by use of nonlinear time series techniques including the phase space reconstruction, the correlation dimension analysis and the evaluation of the largest Lyapunov exponent. The analysis concludes that the acoustic emission time series is a chaotic one, and the smallest dimensions of the embedding spaces is 16, indicating the instability process of rocks could be a complex nonlinear dynamical system.
7. On the basis of the previous analyses of CT evolution model for coal rock and acoustic emission time series of sandstone in connection with damage mechanics and dissipation structure theories, a new definition on damage of rocks is first presented, which is called chaotic damage, and it is thought that damages in rocks during loading may develop in a chaotic way.
8. The single state variable model, two state variables model, corresponding to a single degree of freedom elastic system, and the two degrees of freedom elastic system are introduced to model the rockbursts occurring frequently at many deep coal mines based on the investigation into the conditions triggering rockbursts. The models’dynamical behaviors and their applicability are discussed in detail.
引文
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