Extended Summary

Quasi-brittle materials such as concrete very often fail during tension (or compression) due to localization. Micro-cracks, whose development at the beginning is almost homogeneous, start to concentrate in a region inside the material as the peak load is approached and the failure occurs with a sudden propagation of one or more macro-cracks. With the increase of diffuse cracking there is also a decrease in the stiffness of the material. In damage models this reduction of stiffness is expressed through a damage variable1. On the other hand, experimental results have shown that for low and intermediate stress levels, the permeability (water2,3 or gas4) of concrete has significant change, and increases drastically when the load is very close to the ultimate strength of the material. From a microscopic point of view the width of the cracks is relatively small up to the peak load5, but increases radically in the shoftening regime, causing a tremendous change in the permeability. It is difficult to derive a proper relationship relating the variable of permeability of the material to mechanical quantity. Here we employ a lattice analysis for this purpose. The lattice which is described in this paper was used6 in the past for the study of failure o