基于有限变形理论的岩石变形与破坏问题研究
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摘要
随着大型水利水电工程，军事防护工程以及深部资源开发工程的飞速发展，岩石工程稳定与控制问题越发重要，特别是岩石非连续大变形问题的理论与计算成为学术界研究的焦点，本文基于有限变形理论和非连续变形分析方法（DDA），通过理论、数值模拟、试验三个方面对岩石的变形和破坏问题进行了深入的研究，主要工作进展如下：
(1)对矿山岩石力学中常见的露天开采边坡稳定性问题、巷道围岩位移场及稳定性问题，研究了有限变形理论框架下的解析解、半解析解，并和运用经典小变形理论得出的结果进行对比，指出度规张量的非线性和平均整旋角是造成两者差距的主要原因，且两者差距随变形量和平均整旋角的增大而增大。
(2)运用有限变形几何场理论，对现有的非连续变形分析方法进行了改进，改进后的DDA算法在计算中可以正确地将转动和变形分离，能够准确处理大位移、大变形、大转动问题，并通过实例证明了程序的普适性和准确性。运用改进后的DDA程序，分析了采矿工程中两个典型问题：(i)煤层瓦斯抽采中的“钻-割”增透，(ii)长壁开采过程中覆岩运动及载荷分布，为工程提供了参考依据。
(3)通过正交试验研究了多因素（温度、水、围压）作用下岩石的变形破坏特征，发现平均整旋角可以很好反映岩石的局部变形和破坏，提出了考虑平均整旋角影响的岩石本构方程。该模型和试验结果相符，可以较好地描述峰前压密、线性增强以及塑性屈服各个阶段。
(4)采用Burgers模型描述岩石蠕变行为，并得到了温度、饱水时间和围压共同影响下的稳态蠕变率方程。开发了计算岩石流变的非连续变形分析程序，计算了常温、干燥和高温、高湿状态下巷道围岩流变的位移场和应力场，计算表明程序能够很好模拟水、温度影响下岩石流变和应力释放过程。
该论文有图77幅，表22个，参考文献303篇。
As the rapid development of large-scale water resources and hydroelectricprojects，the military underground defensive engineering and exploitation of deepunderground resources, the stability and control problems of rock engineering becomemore and more important, especially, the theories and numerical methods ofdiscontinuous and large deformation problems of rock have become the focus ofacademic circles. Based on finite deformation theory and discontinuous deformationanalysis (DDA)， the deformation and failure problems of rock were studiedthoroughly by theoretical method, numerical method, and experiment. The mainprogresses are as follows:
(1) The analytical/semi-analytical solution of stability of slope in open pitmining, displacement field and stability the surrounding rock of tunnels were studiedbased on finite deformation theory. The comparison of the result obtained based onsmall strain theory and the one based on finite deformation theory shows that themean rotation angle and the nonlinear characteristics of metric tensor are the maincause of the difference. And the difference increases with the mean rotation angle anddeformation.
(2) The improvement of the present DDA was carried out based on finitedeformation geometric theory. The improved DDA code can separate the rotation anddeformation correctly and can handle the large displacement, large deformation andlarge rotation problems exactly. The universality and accuracy of the improved codewere validated by examples. Two typical problems of mining engineering:(i)“slotted-drilling” induced pressure relief and permeability improvement in coal seamgas extraction technology;(ii) movement and load distribution of overburden rockstratum during long wall mining; were also analyzed by employing the improved code.The numerical results provide basis for engineering.
(3) The characteristics of rock deformation and failure under the effects ofmulti-factors (temperature, water and confining pressure) were studied based onorthogonal design experiment. It can be concluded that the mean rotation angle canreflect the localization deformation and failure of rock well. With the consideration ofmean rotation angle, a constitutive equation was presented. It can be found that thisconstitutive model coincides with the experimental data and can describe the compaction stage, linear enhancement stage and the plastic yield stage well.
(4) The Burgers model was used to describe the creep behavior of rock; theevolution law equation of steady-state creep rate under the effects of temperature,saturated time and confining pressure was obtained. A DDA code that can computethe rheology problem was developed. The numerical analysis of dry-roomtemperature and high temperature, high humidity rock surrounding a tunnel was alsomade. It shows that the rheology behavior and the pressure relief process can be wellmodeled by using the developed DDA code.
The dissertation incudes77figures,22tables and cites303references.
(1)对矿山岩石力学中常见的露天开采边坡稳定性问题、巷道围岩位移场及稳定性问题，研究了有限变形理论框架下的解析解、半解析解，并和运用经典小变形理论得出的结果进行对比，指出度规张量的非线性和平均整旋角是造成两者差距的主要原因，且两者差距随变形量和平均整旋角的增大而增大。
(2)运用有限变形几何场理论，对现有的非连续变形分析方法进行了改进，改进后的DDA算法在计算中可以正确地将转动和变形分离，能够准确处理大位移、大变形、大转动问题，并通过实例证明了程序的普适性和准确性。运用改进后的DDA程序，分析了采矿工程中两个典型问题：(i)煤层瓦斯抽采中的“钻-割”增透，(ii)长壁开采过程中覆岩运动及载荷分布，为工程提供了参考依据。
(3)通过正交试验研究了多因素（温度、水、围压）作用下岩石的变形破坏特征，发现平均整旋角可以很好反映岩石的局部变形和破坏，提出了考虑平均整旋角影响的岩石本构方程。该模型和试验结果相符，可以较好地描述峰前压密、线性增强以及塑性屈服各个阶段。
(4)采用Burgers模型描述岩石蠕变行为，并得到了温度、饱水时间和围压共同影响下的稳态蠕变率方程。开发了计算岩石流变的非连续变形分析程序，计算了常温、干燥和高温、高湿状态下巷道围岩流变的位移场和应力场，计算表明程序能够很好模拟水、温度影响下岩石流变和应力释放过程。
该论文有图77幅，表22个，参考文献303篇。
As the rapid development of large-scale water resources and hydroelectricprojects，the military underground defensive engineering and exploitation of deepunderground resources, the stability and control problems of rock engineering becomemore and more important, especially, the theories and numerical methods ofdiscontinuous and large deformation problems of rock have become the focus ofacademic circles. Based on finite deformation theory and discontinuous deformationanalysis (DDA)， the deformation and failure problems of rock were studiedthoroughly by theoretical method, numerical method, and experiment. The mainprogresses are as follows:
(1) The analytical/semi-analytical solution of stability of slope in open pitmining, displacement field and stability the surrounding rock of tunnels were studiedbased on finite deformation theory. The comparison of the result obtained based onsmall strain theory and the one based on finite deformation theory shows that themean rotation angle and the nonlinear characteristics of metric tensor are the maincause of the difference. And the difference increases with the mean rotation angle anddeformation.
(2) The improvement of the present DDA was carried out based on finitedeformation geometric theory. The improved DDA code can separate the rotation anddeformation correctly and can handle the large displacement, large deformation andlarge rotation problems exactly. The universality and accuracy of the improved codewere validated by examples. Two typical problems of mining engineering:(i)“slotted-drilling” induced pressure relief and permeability improvement in coal seamgas extraction technology;(ii) movement and load distribution of overburden rockstratum during long wall mining; were also analyzed by employing the improved code.The numerical results provide basis for engineering.
(3) The characteristics of rock deformation and failure under the effects ofmulti-factors (temperature, water and confining pressure) were studied based onorthogonal design experiment. It can be concluded that the mean rotation angle canreflect the localization deformation and failure of rock well. With the consideration ofmean rotation angle, a constitutive equation was presented. It can be found that thisconstitutive model coincides with the experimental data and can describe the compaction stage, linear enhancement stage and the plastic yield stage well.
(4) The Burgers model was used to describe the creep behavior of rock; theevolution law equation of steady-state creep rate under the effects of temperature,saturated time and confining pressure was obtained. A DDA code that can computethe rheology problem was developed. The numerical analysis of dry-roomtemperature and high temperature, high humidity rock surrounding a tunnel was alsomade. It shows that the rheology behavior and the pressure relief process can be wellmodeled by using the developed DDA code.
The dissertation incudes77figures,22tables and cites303references.
引文
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