Description of the nonlinear behaviour of materials and structures is often deterministic and the obtained results (ultimate loads, load-displacement response, patterns of cracking, etc.) are generally supposed to be correct. The purpose of this Paper is to show that these results can be debated and that the deterministic models are insufficient if a more accurate approach of safety is required. The Paper shows how a model on a probabilis- tic basis can improve the quality of the numerical simulation of the loading of concrete specimens.It shows also that a stochastic approach can give very important information on the problem of the localization of cracks in a heterogeneous material like concrete.

Under the shallow coal mining condition and based on the cracking and movement rules of the roof in different mining stages, the mechanical models of symmetrical pressure-arch, stepped pressure-arch, rotating-squeezed pressure-arch in the mining field were established. Then, the instability criterion of each pressure-arch structure was derived. Through the similarity material experiment and numerical simulation, the evolution characteristics of the composite pressure-arches in the near- and far-field were revealed. Results show that the stepped pressure-arch in broken blocks of the basic roof was formed when the horizontal principal stress was greater than the in-situ stress. The broken blocks’ sliding could induce roof cutting off and strong weighting load. The structural characteristics of the overlying strata were determined by the thickness of the bedrock. The upper broken rocks formed a symmetrical pressure-arch in the near- and a far-field pressure-arch formed in the mining field. The median periodic broken rocks formed the rotating-squeezed pressure-arch, bearing the load of the loose layers and protecting the mining panel. After all bedrocks breaking, the latter arch foot of the far-field pressure-arch was transferred to the compacted caving zone. This study can provide a theoretical reference for the similar mining engineering.

According to the damage evolution model of rock mass under stress-seepage coupling effect, the representative element theory is employed to describe the change law of rock mesostructure. Based on the theory of elasticity and Weibull distribution, the statistical damage constitutive model of rock mass and the finite element numerical algorithm are established, by adopting the COMSOL Multiphysics numerical software and MATLAB program. Besides, the validity of the statistical damage constitutive model of rock mass is verified by the triaxial compression test. Besides, the hydraulic fracturing processes of rock mass under equal and unequal in situ stresses are numerically simulated, and the mechanical behavior of rock mass during hydraulic fracturing in complex underground environment is also studied. Under the condition of equal in situ stress, the stress distribution of surrounding rock of circular hole is annular, which is similar to the elastic stress distribution of surrounding rock. Under the condition of unequal in situ stress, the stress distribution tends to be circular with the increase of lateral pressure coefficient, and the stress distribution along the diagonal decreases. The simulation results are in good agreement with the theoretical results, which indicates that the damage mechanical model and the numerical model have correlation and certain accuracy. By analyzing the size and direction of horizontal in situ stress, the shape and extension direction of cracks are judged, which provides an important theoretical basis for water inrush prediction and engineering protection.

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