Research

The majority of the problems in soil mechanics are of two types: stability problems and elasticity problems. The stability problems involve finding the load that the soil mass can withstand at its ultimate failure. For the design of a structure, a suitable factor of safety is applied against the ultimate failure of the soil mass to ensure the serviceability requirements at the working load condition. In this thesis, the resistance is to be offered by the support systems of tunnels, i.e., tunnel lining against the stresses acting on it at the ultimate failure of the surrounding soil. Out of the methods available, the stability problems undertaken in this thesis have been solved based on the lower bound theorem of limit analysis.

The limit analysis relies on some assumptions: (i) the material behaves perfectly plastic; (ii) the normality condition of the plastic strain and the convexity of the yield surface hold true (associated flow rule); (iii) the change in geometry of the material is insignificant at failure. In the lower bound theorem of limit analysis, the magnitude of the collapse load is determined from a statically admissible stress field satisfying the equilibrium and stress boundary conditions without the violation of the yield criterion. The computed collapse load is either smaller or, at most, equal to the true collapse load’s magnitude. For a continuum like soil, these conditions are to be satisfied at infinite locations in the domain. It makes the computation of analytical solutions difficult when the problem or the loading conditions or both are complicated. Therefore, the continuous lower bound formulation is made discrete by discretizing the soil domain using the finite element approach. The search for the greatest lower bound eventually leads to a constrained optimization problem.