Investigation Of Shallow Tunnel Stability Using Upper Bound Solution Of Limit Analysis

Shallow tunnel surrounding rock pressure calculation and stability analysis has great effect on tunnel design, construction and theory investigation. The traditional solutions of limit equilibrium and slip line methods have difficulties in solving such problems. When tunnel surrounding rock failure is simulated, finite element method has to perform large numbers of iterative calculation, which are time-consuming and would arise convergent problem. Compared to the above solutions, upper bound solution of limit analysis is an effective way. The rigid blocks upper bound solution can obtain results with little iterative calculation for specific problems. Finite element upper bound solution of limit analysis takes advantage of finite element method and has no need to assuming failure mechanism beforehand. Therefore, it is suitable for complicated boundary conditions. Based on the two upper bound solutions, the shallow tunnel surrounding rock stability under different parameters were calculated and analyzed. The main contents are detailed as following:(1) The main characteristics and applicability of traditional rigid blocks upper bound solution were discussed. And the method of constructing failure mechanism and its corresponding velocity field were also proposed. The failure mechanism of surrounding rock pressure of rectangular tunnel and shallow tunnel face stability were constructed, and the tunnel stability was analyzed using the compiled program.(2) Based on the fundamental theory of finite element upper bound solution with linear program, the calculation process was proposed and the two dimensional computer program of finite element upper bound was compiled, which can be used for tunnel stability analysis. And the complicated stability problem can also be performed with adjusting mesh and constrain condition. The bearing capacity of strip footing was calculated and compared with the existing exact solution to verify the compiled program. In addition, the impact of calculation accuracy of the dense and form of the mesh and the number of plastic multiplier were discussed.(3) Using finite element upper bound solution, the calculation chart of circular tunnel surround rock stability factor for undrained ground was obtained. And calculation chart of tunnel support pressure factor Nγ, Ns, Nc were also obtained for circular tunnel with various calculating parameters. The results were all compared with the existing data in literature.(4) The strength reduction method was introduced to finite element upper bound solution. And corresponding calculation process was proposed. The safety factor of shallow tunnel stability was obtained by numerical examples.(5) By using finite element upper bound solution, the failure mechanism and influence factors of shallow tunnel was discussed. And its characteristics and changing regulations for different parameters were summarized.(6) The surrounding rock pressure of rectangular tunnel and tunnel face support pressure factor Nγand Ns with different parameters were obtained using finite element upper bound solution. And the results were compared with rigid blocks upper bound solution.(7) For parallel and incline tunnel, the stability of surrounding rock and the characteristics, range and changing regulations of the failure mechanisms were analyzed and discussed. And the results were compared with shallow tunnel of level surface.(8) Based on the case study of failure of surrounding rock and support structure of Yun Yangshan tunnel in mild clay ground, the characteristics and range of failure mechanism was analyzed, so as to verify the validity and practicability of finite element upper bound solution.