均质弹性条件下多洞平面问题解析算法及其应用研究

The scholars in the world have been trying to find an effective analytic algorithm of multiple hole problems usually meet in engineering designs. Though some studies on circular or elliptic holes had been achieved under specific conditions, no efforts were made to any multiple hole problems that is most significant for engineering designs. The author has made further studies on any multiple hole problems, using complex variable function method and Schwarz alternating method. After solving a series of technological difficulties, the author obtains an effective analytic algorithm, and acquires stress field and displacement field with high accuracy, which can be conducted for arbitrary many iterations according to practical accuracy requirements. In addition, th solution of stress and displacement fields, even for multiple holes of complex shapes and smaller distances. Further, the author made preliminary studies on viscoelastic displacement solution for any double holes. In terms of the obtained displacement solution of any multiple holes, this paper studies displacement back-analysis for the excavations of two tunnels, and find that the back-analysis method is accurate. Additionally, the author presents the mathematical prove of inversion uniqueness for ground stresses, elastic modulus and Poisson ratio. The author believes that the accurate analytic algorithm provided in this paper will presents an effective way to stress and displacement analysis for any multiple hole problems, optimal arrangement of multiple holes, hole shape optimization of multiple holes, etc..