Applications of numerical limit analysis (NLA) to stability problems of rock and soil masses

This work presents formulations and results obtained with computer implementations of an alternative to the more standard techniques for the determination of the state of collapse of geotechnical structures in rock or soil masses. Examples of normally available and used techniques for those purposes are limit equilibrium based procedures and elasto-plastic finite elements. As an alternative to these techniques, the present paper describes Numerical Limit Analysis (NLA). The fundamentals for limit analysis, summarized in the so-called bound theorems, have been known for decades. Analytical solutions obtained with limit analysis are however limited in scope and are seldom used in the engineering practice. NLA on the other hand, by solving the limit analysis equations through numerical methods are general and applicable to a wide range of problems. The paper presents a discussion on available alternatives for the formulation of NLA specialized for the determination of collapse load factors of geotechnical structures in/on rock (fractured or not) and soil masses. Rock masses in particular are modelled as standard continua, Cosserat equivalent continua and true discontinua formed by discrete blocks. Finite elements are used for the solution of NLA equations of standard continua and Cosserat continua. The paper presents derivation of the pertinent equations, the numerical formulations used and details of their numerical implementation in computer programs. Attempt was made to validate all the implementations through existing analytical solutions. The obtained results permit to state that NLA is a promising and very often advantageous numerical technique to establish collapse states of geotechnical structures in rock and soil masses.