Analytical Analysis For Lined-Tunnel In Anisotropic Rock Mass

Due to the directional arrangement of rock particles and the existence of structural planes throughout the rock mass,the most of rock masses in nature have anisotropic material properties.According to the needs of water conservancy,transportation,mineral resources,national defense and other engineering constructions,tunnels of various shapes will inevitably be excavated in anisotropic rock mass.Tunnel excavation and lining support construction can disturb the in-situ stress distributions in original rock mass,and cause great stress concentration near the surrounding rock and lining.Large stress concentration seriously threatens the safety and stability of the tunnel.Different cross sections of lined tunnel induce different stress and displacement distributions.Therefore,exploring the mechanics solution for arbitrary shaped lined tunnel in anisotropic rock mass will have important guiding significance.The correct mechanics solution of lined tunnel cannot be separated from the accurate determinations of in-situ stresses and parameters for macro-scope anisotropic rock mass.However,the objective existence of inaccurate parameters in underground engineering problems has puzzled the development of rock mechanics for a long time.Until the parameter identification method of displacement back analysis is proposed,it is possible to realize the above process.Therefore,it will be of great practical significance to study the parameter identification of displacement back analysis in anisotropic rock mass.In another widely used anisotropic material wood and composite plates,due to the presence of fibers,the mechanical properties along the direction of fibers and perpendicular fibers are completely different.When opening holes in such anisotropic plates,under the action of external forces,there will be intense stress concentration near the holes,and failure may start from the hole edge in serious cases.Excellent hole shape can minimize the stress concentration and ensure the safety and stability of hole structure.Therefore,shape optimization of the hole in anisotropic plate will provide an important guide for the efficient utilization of anisotropic plate.To sum up,this study carries out the analytical solutions based on the complex variable method of linear elastic anisotropic medium for arbitrary shaped lined tunnel in anisotropic rock mass,parameter identification of displacement back analysis in anisotropic rock mass and shape optimization of the hole in anisotropic plate.Because the analytical method is mainly used in research process,the conclusions have strong theoretical guiding significance.Research contents are as follows:(1)Based on the complex variable method for arbitrary shaped holes in linear elastic anisotropic and isotropic media,the hydraulic lined tunnel with arbitrary shapes in anisotropic rock mass is deduced and calculated by conformal mapping and power series solution process.Two important contact patterns,pure-bond and full-slip contact conditions between lining and surrounding rock mass are considered in analysis.Besides,the support delay effect in lined tunnel construction and the water pressure effect during hydraulic tunnel operation are also taken into consideration in analytical process.Using the obtained analytical method,the analytical solutions for hydraulic lined tunnels with inverted U-shape in orthotropic rock mass(pure-bond contact)and horse hoof shape in transversely isotropic rock mass(full-slip contact)are carried out,respectively.The analytical solutions can satisfy the theoretical setting of boundary and continuity conditions with high accuracy,and is in good agreement with the numerical outcomes simulated by ANSYS finite element software.By analytical algorithm,the influences of the structural plane orientation,the degree of anisotropy of the excavation surface,the water pressure and two different contact conditions on the stress and displacement distributions in lining and surrounding rock mass are explored.(2)By combining the forward process of solving the displacements for lining-free tunnel with the differential evolution method(DE),an analytical inverse method for parameters identification of displacement back analysis in anisotropic rock mass is obtained.The problem of excavating a horse hoof-shaped tunnel on anisotropic plane of transversely isotropic rock mass is studied.The independent parameters in this model are introduced and the sensitivity information of parameters is calculated.According to the relative displacements "measured" by measuring lines that are arranged in tunnel cross section,all parameter combinations are back analyzed.The identification conclusions on uniqueness and accuracy of each parameter combination are summarized.The arrangement and number of measuring lines are also given.(3)By combining the forward process of solving the stresses for arbitrary shaped unreinforced holes with the mixed penalty function method,the algorithm for shape optimization of the hole in an orthotropic plate is obtained.Based on the criterion of minimizing the absolute value of the maximum tangential stress at the hole edge,the coefficients in conformal mapping function that describe the hole shape,are optimized.The optimal hole shapes under the pure shear and different compressive loads,different fiber orientations and different material anisotropies are obtained.The stress distributions around the holes,that have the minimum tangential stress concentration,are also obtained.