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We analyze the distribution of grains in solid cubes of ice in terms of deterministic and stochastic 3d fractal models. We argue that the fractal dimension D or the Hurst exponent H optimally describe the void distribution in the snow sample and can be used as a parameter to describe the mechanical properties of snow at different scales.

An energy-based criterion is introduced in order to investigate the nonlinear dynamic response of RC beams subject to rapid and unexpected damages. Since only static pushover analysis is necessary, the structural behavior of the damaged members can be evaluated with a new simplified procedure. It is firstly applied to the case of elastic–perfectly plastic continuous beam, when one of the supports is quickly removed. In such a situation, the proposed procedure gives satisfactory results if compared to those of a more rigorous dynamic analysis. By means of a nonlinear static analysis, which encompasses also the post-peak response, the energy-based approach is also applied to concrete beams. More specifically, it is used to predict the bearing capacities of reinforced concrete beams, having different steel rebars, when they suddenly lose a single support.

The apparent shear strength of rock discontinuities is lower than that of small scale samples. At the same time, the sliding behavior is characterized, in situ, by marked instabilities. Numerical algorithms permit to calculate contact forces at any point, and to describe the stick-slip transition. On the other hand, the critical aspects are not captured by classical theories. Multiscale simulations show that the contact domain between rough surfaces is a lacunar set. This explains the size-dependence of the apparent friction coefficient. By applying an increasing tangential force, the regime of partial-slip comes into play. However, the continuous and smooth transition to fullsliding predicted by the Cattaneo-Mindlin theory is not occurring in real situations. We implement a numerical renormalization group technique, taking into account the redistribution of stress consequent to partial-slip. This permits the critical value of the tangential force to be found. The critical force is less than the one predicted by Coulomb’s theory, and depends on the specimen size and on the topology of the interface.