基于复变量微分法的岩石力学参数灵敏度分析

Sensitivity Analysis of Rock Mechanical Parameter Based on Complex-Variable-Differentiation Method

针对常规用差分方法计算费时费力的缺点,将复变量微分法应用于岩石力学参数灵敏度分析。复变量微分法以复变量Taylor级数展开为理论基础,直接建立复变量虚部与其一阶微分的关系。将该方法与有限元法相结合,可通过复变函数运算直接计算参数灵敏度。基于该方法编制了MATLAB计算程序,并应用于弹性问题及弹塑性岩石力学问题的参数灵敏度分析。实际算例表明该方法及程序有效,快速,且具备很高精度与普遍适用性,可为位移实际量测方案的修正和优化提供参考,从而为实施快速可靠的岩石力学参数反演计算奠定了良好的基础。

To avoid the inefficiency and poor precision of difference method in parameters sensitivity analysis,the complex-variable-differentiation method is used for rock mechanical parameters sensitivity analysis.The complex-variable-differentiation method is based on the Taylor series theory of complex variable,the relationship between the imaginary part of the complex-variable and its differentiation is established.The sensitivity of parameter can be obtained by function evaluation through combining this method with the finite element method. A MATLAB program for this combined method is designed to do parameters sensitivity analysis for elastic problems and elastic - plastic problems. The examples show that this method and program are effective with high precision and wide applicabihty, which can provide references for modifying and optimizing the scheme design of in - situ measurements, and also provide a solid foundation for rapid and reliable effective back analysis of rock mechanical parameters.