| 层状煤岩介质的基本解 |
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| 引用本文： | 张劲,牟善波,张士诚.层状煤岩介质的基本解[J].地质学报,2008,82(10):1450-1453. |
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| 作者姓名： | 张劲 牟善波 张士诚 |
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| 作者单位： | 中国石油大学(北京),北京,102249 |
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| 基金项目： | 国家重点基础研究发展规划“973”项目“中国煤层气成藏机制及经济开采基础研究”(编号2002CB117009)、国家科技重大专项“大型油气田及煤层气勘探开发”（编号2008zx050001406）和中国石油2006年风险基金(石油大学02)资助成果。 |
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| 摘 要： | 煤岩的水力压裂实际上就是半无限大分层均匀介质的断裂问题，要利用有限元法或边界元法模拟裂缝扩展，就必须找出半无限空间的基本解。本文从三维弹性力学最基本的平衡方程和本构关系出发，推导出状态传递微分方程。在求解状态传递微分方程时，对指数矩阵进行分解，避免了直接解法导致状态变量的发散。引入了半无限体的无穷边界条件，推导出半无限层表面的位移与应力关系式。根据状态传递方程，可得出层状煤岩任意点的应力和位移的值。此结果可直接退化到经典的半无限域经典的Mindlin解。
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| 关 键 词： | 传递矩阵 积分变换 基本解 Mindlin解 |
| 收稿时间： | 5/7/2008 12:00:00 AM |
| 修稿时间： | 2008/9/16 0:00:00 |
A Fundamental Solution for Semi Infinite Layered Coal |
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| ZHANG Jin,MOU Shanbo and ZHANG Shicheng.A Fundamental Solution for Semi Infinite Layered Coal[J].Acta Geologica Sinica,2008,82(10):1450-1453. |
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| Authors: | ZHANG Jin MOU Shanbo and ZHANG Shicheng |
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| Institution: | China University of Petroleum, Beijing, 102249;China University of Petroleum, Beijing, 102249;China University of Petroleum, Beijing, 102249 |
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| Abstract: | The crack propagation of hydraulic fracturing of coal is actually a fracturing problem of semi-infinite layered media.It is necessary to discover a fundamental solution for layered coal,if the crack propagation of hydraulic fracturing is simulated by finite element or bunduary element method.A transfer matrix differential equation is derived from the three-dimensional equilibrium equations and constitutive equations of a homogeneous,isotropic linear elastic body.The exponential matrix is discomposed in order to avoid non-convergence in solving directly the transfer matrix differential equations.The relations between the displacements and the stresses on the surface of semi-infinite body are obtained in introducing the infinite boundary conditions.The displacements and stresses in an arbitrary point of the semi-infinite body are easily deduced by using the transfer matrix equation.The results derived here can be degenerated to the classic Mindline's solution in a semi-infinite body. |
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| Keywords: | transfer matrix integrate transform fundamental solution |
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