Approximate Analytical Solution Of Elastic Stress Around Tunnels And Within Slopes Under Supporting Forces And Its Application

It is essential to determine the stress field around tunnels and within slopes in the engineering design,and the stresses are calculated by using the classical analytical method and the widely used numerical method.Although many analytic works have been performed by utilizing the analytical method based on the complex variable method,its applicability is limited.Numerical methods are a powerful tool for this purpose,but the exact stress theoretical solution has not been obtained,and the modeling is time-consuming.Thus,the purpose of this thesis is to innovatively propose a general method for approximate analytical solution of the stress around tunnels or holes and within slopes,which can calculate the elastic stresses around multiple holes of complex shapes and slopes under various loading conditions,whose accuracy is enough high to approximate the analytical solution.Moreover,an effective method for calculating the stress field in the engineering design of tunnels and slopes under supporting forces is provided,and a research direction is further provided for the development of elastic theory.The main research work could be introduced as:(1)The approximate analytical solution system of elastic stress is improved,for an infinite and a half plane containing a convex polygonal hole under various loading conditions.The whole region surrounding a hole is taken as the union of a series of half-planes with each upper-surface coinciding with the associated side of the hole.The concept of the equivalent concentrated forces acting at the Gaussian points is proposed.Based on Flamant’s analytical solution for stresses in a half-plane,induced by a concentrated load acting on its upper surface,a direct iterative calculation scheme of the equivalent concentration forces acting upon the upper surface of the half-planes is established.An equivalent replacement method of the traction is proposed for eliminating the multi-value displacement of a multi-connected body caused by the nonzero resultant force of tractions acting along the side of the hole based on Kelvin’s analytical solution for stresses in an infinite plane,induced by a concentrated load acting within the plane.Aiming at improving the convergence of the hole including acute inner angles,an auxiliary line is proposed to draw a perpendicular to the line bisecting the acute inner angle(called a small angle ‘auxiliary surface’ method),resulting in effectively computing the stress field around the hole.Using the superposition principle of elastic stress,the stress calculation problem of concentrated or distributed forces acting within the plane is effectively solved.Results of example studies show that the present method can give values of the stresses within the regions extremely near to the corners of the hole,which are found to be essentially identical to the analytical solutions available.Values of stresses in the farther regions are simultaneously obtained,which are substantially validated by the finite element method.(2)The approximate analytical solution of the elastic stress around multiple holes in a plane of complex boundary is proposed.The problem of a plane with complex boundaries containing multiple holes can be divided into a series of individuals of an infinite plane containing a hole,and the “cutting criterion” is proposed to effectively solve the division problem of the cross holes and the openings.An effective iteration calculation scheme of the virtual concentrated forces acting upon the boundaries of the multiple holes is constructed based on the virtual surface force method.Moreover,the stress solution of the multiple solutions loaded by various loads upon their boundaries or within the plane is obtained based on the superposition principle.Example studies demonstrate that for the multiple holes of complex shapes arranged arbitrarily in a plane with arbitrary geometric boundaries,of which the approximate solution of the elastic stress with stable convergence can be obtained using the present method.According to the engineering characteristics of tunnels or underground cavern groups,an approximate analytical solution of elastic stress around underground tunnel-group under supporting loads is proposed.The initial earth stress and the release stresses due to excavation can be incorporated.More investigations,using this method,are performed into the influence of key parameters such as supporting force,buried depth,and spacing on the stress distribution around the shallow-buried single tunnel,double tunnels,and connected tunnels under an inclined ground surface.(3)Approximate analytical solution of elastic stress within slope under supporting forces and the optimization method of slope reinforcement are proposed.The problem of a slope can be divided into several sub-problems of an infinite plane containing a semi-infinite hole along its inclined surfaces and crest according to the division method of a slope.The elastic stress within the slope subjected to supporting forces,such as anchoring forces,is obtained based on Melan’s analytical solution for stresses in a halfplane,induced by a concentrated load acting within the half-plane combined with the principle of superposition.With the elastic stress field within the slope,the linear expression with the anchoring force coefficient as the state variable is established,and the linear programming problem with the sum of the values of supporting forces as the objective function is constructed.The linear programming method is used to solve the problem,resulting in the optimal value and distribution of supporting forces being obtained.Example studies demonstrate that the values of the stresses obtained by the present method agree well with those of the FEM in the whole region,the stress concentration near the slope toe and the accurate stress distribution near the region loaded by supporting forces can be simultaneously obtained.With this method,contour plots of stresses within a slope inclined at various angles are presented,which can be applied directly in practical engineering.Furthermore,with the present method,the influence of surcharge and supporting force on the stress field within the multi-stage slope is further performed.(4)The stress field around a slope with a tunnel group under various loading conditions and the interaction mechanism between them is studied.The stress field around the slope with a tunnel group can be considered as the summation of those around individual problems,which can be obtained by using the approximate analytical solution of the elastic stress around multiple holes.With the present method,the influence of a slope excavation on the stress field around adjacent existing tunnels and of slope angle on the stress distribution around the existing tunnels and upon its boundary are analyzed.Meanwhile,the influence of the new tunnel excavation on the stress field within the slope containing existing tunnels and of the new tunnel with different spacing on the stress distribution upon the boundary of the existing tunnel and the inclined surface of the slope are studied.Moreover,the influence of the new connected tunnel of complex shapes on the stress field within the existing slope is studied.(5)With the approximate analytical solution of the elastic stress for multiple holes in a plane,the stress calculation and stability analysis on three typical practical projects,such as a group of underground caverns in a mountain,a compressed gas energy storage cavern in an abandoned mine,and a group of underground caverns in a hydropower station,are carried out.The influence of cavern excavation on the stress field around the existing cavern and of shallow buried cavern with large span excavation on the stress field within the slope is studied,and the effect of buried depth,cavern shape,and high pressure on the stress field around the compressed gas energy storage cavern in an abandoned mine and on its stability is analyzed,and the stress field around underground caverns in a hydropower station under different excavation steps is studied.As a result,the present method can be used to calculate the stress field around cavern groups and within slopes in underground engineering,slope engineering,and other fields,providing a new and effective tool for stress analysis and design reinforcement of practical engineering.