ABSTRACT
This chapter presents the basic principles to be taken into account for the application of the stress–strain analysis methodology. The algorithms most commonly used in stress–strain analysis are the boundary elements, finite elements and finite difference elements algorithms. The finite element algorithm shares its name with the stress–strain calculation methodology, since when this methodology began being developed in the 1960s, there was only one algorithm to solve the equations, and therefore, the mathematical algorithm used kept this name. The finite element algorithm has another important disadvantage, namely, the way in which the models with intense yielding are solved. The distinct element algorithm is an evolution of the finite difference algorithm, which has been created to solve stress–strain calculation problems in a discontinuous medium with elasto-plastic behavior. Stress–strain calculation software programs are very powerful tools to accurately analyze the redistribution process of the stresses in the ground when an underground excavation is constructed.
