Simplified modeling of cracking in concrete: Application in tunnel linings

• A model based on lumped damage mechanics of collapse of tunnel linings is proposed.
• The model is more efficient than the conventional approaches and quite accurate.
• A new kind of inelastic hinges is proposed to describe the quasi-brittle behavior.
• Crack opening displacement can be estimated in a simplified way.
• Experimental results were used to validate the proposed model.

This paper presents a formulation for the analysis of the inelastic behavior of pipes, tunnels and rings. This new framework is based on lumped damage mechanics and emphasizes on the mathematical description of concrete cracking; the approach can be extended to other brittle materials as well. Lumped damage mechanics combines the concept of plastic hinge with the ideas and procedures of fracture and continuum damage mechanics. The resulting models allow for the characterization of the damage state of the structure, it is even possible to quantify the crack opening displacements in a simplified way. Experimental and fracture mechanics results were used to validate the proposed method. The structural analyses can be carried out using very few elements (less than a dozen in most cases) while the conventional approaches require tens of thousands of them. Thus, even if the models can be implemented in conventional finite element programs, the computations can also be carried out with symbolic manipulators, general numerical analysis programs (Maple, Matlab, Mathematica, Mathcad, and so on) or even spreadsheet applications. This simplified approach can be used for design purposes, validation of finite element analysis or structural reliability assessment where thousands of analyses of a same structure are needed.