有限矩形区域定流量点汇诱发孔隙弹性的解析解  

An analytical solution to poroelasticity induced by constant-flux point sinks within a finite rectangular domain

作　　者：李培超[1,2] 王克用[1] 张敏良[1] 

机构地区：[1]上海工程技术大学机械工程学院,上海201620 [2]普林斯顿大学土木与环境工程系08544普林斯顿

出　　处：《应用力学学报》2013年第6期855-858,951-952,共4页Chinese Journal of Applied Mechanics

基　　金：上海工程技术大学高水平项目培育专项基金(2012gp04);上海市教委科研创新重点项目(10ZZ124);上海市重点学科建设项目(P1401)

摘　　要：采用量纲为一的Biot固结模型给出了有限矩形区域内定流量点汇诱发的孔隙弹性问题的一个解析解。假设多孔介质为不可压缩、各向同性、线弹性,且被单相流体所饱和,孔隙压力场符合封闭边界条件,在此基础上,利用傅里叶变换和拉普拉斯变换及反演方法获得了孔隙弹性问题的精确解,体现为双重无穷项级数和的封闭形式;并利用现有文献解析解对其进行了验证,二者的一致性证明了该解析解的正确性。对压力场解析解的分析表明,定流量点汇所诱发的压力场并没有稳态解,压力的变化特征主要取决于其对应的边界条件。该解析解适用于验证有限矩形区域孔隙弹性问题的数值算法和程序,对工程应用具有一定的参考价值。An analytical solution to poroelasticity due to constant-flux point sinks is presented for the case of a finite rectangular region. In this study, the poroelastic theory follows the non-dimensional Biot' consolidation model. Porous media is assumed to be incompressible, isotropic, linear elastic and saturated by single-phase pore fluid, and boundaries of pore pressure field are closed. Under above assumptions, the exact solution is firstly obtained by using the method of Fourier and Laplace integral transforms and inversions. It is in terms of summations of infinite series and closed in the form. Secondly, it is compared against the exact solution avaibalble in the literature. The consistency between them validates the accuracy of the presented analytical solution. The analysis on the presented analytical solution reveals that the pore pressure field induced by a constant-flux point sink can not reach steady-state with time, and the characteristics of the pore pressure dependent upon the corresponding boundary conditions. The presented analytical solution is highly applicable to the calibrations of two-dimensional poroelasticity related numerical solutions, and useful for guiding the development of industrial norms and standards concerning geotechnical engineering. Meanwhile, it can also provide us in-depth insights into the mechanical behavior of fluid-solid interactions in finite two-dimensional porous materials.

关 键 词：有限矩形区域 孔隙弹性理论 定流量点汇 解析解 

分 类 号：O357.3[理学—流体力学]