Analytical solution of stress and displacement of double-arch tunnel without middle drift based on functions of complex variables
Due to the fact that the lining of the secondary tunnel overlaps on the arch waist of the lining of the front tunnel,the stress situation of the surrounding rock and lining is complex.Therefore,it is of important engineering significance to carry out stress and displacement analysis of the surrounding rock and lining.This study proposes a calculation method for stress and deformation analysis of the surrounding rock and lining in a double-arch tunnel without a middle drift,considering the deep burial conditions and the presence of the lining.The method utilizes the complex variable function theory and Schwarz alternating method.In the case of a double-arch tunnel without a middle drift,where the two tunnels intersect,the Cauchy integral method is employed to solve the problem.The boundary integral condition for the contact between the lining of a single tunnel and the surrounding rock is transformed into the subtraction between the complete boundary integral and the intersectional boundary integral when only a single tunnel exists.A similar treatment is applied to the calculation of the"additional surface force"in the Schwarz alternating method.Finally,the calculation method of intersectional boundary stress and displacement is given.A numerical example is provided to demonstrate the feasibility and accuracy of the method by comparing the analytical results with numerical simulation results.
double-arch tunnel without middle driftfunctions of complex variablesSchwarz alternating methodstress fielddisplacement field
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