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Two-dimensional finite element model was created in this work to investigate the stress distribution within rock-like samples with offset open non-persistent joints under uniaxial loading. The results of this study have explained the fracture mechanisms observed in tests on rock-like material with open non-persistent offset joints (Mughieda and Alzo 'ubi, Geotech Geol Eng J 22:545-562, 2004). Finite element code SAP2000 was used to study the stresses distribution within the specimens. Fournoded isoperimetric plain strain element with two degrees of freedom per node, and the three-noded constant strain triangular element with two degree of freedom per node were used in the present study. The results of the present study showed that the tensile stress in the bridge area caused coalescence for specimens with overlapped preexisting cracks (joints) while the coalescence of the secondary cracks, due to shear stress, caused the failure of specimens with non-overlapping cracks.

Crack coalescence in rock masses was studied by performing a series of biaxial compresion tests on specimens made of rock-like material. Specimens of size 63.5 · 27.9 · 20.3 cm, made of 72% silica sand, 16% cement (Type I) and 12% water by weight were tested. The joint inclination angle was maintained at 45°, while the offset angle i.e. angle between the plane of the joint and the line that connects the two inner tips of the joints, was changed from 0°to 90°with an increment of 15°. Three levels of lateral stress were used; 0.35 MPa, 0.7 MPa and 1.5 MPa on each sample. HP data acquisition system was used to record the data for each sample. In each sample, four LVDTs were fixed to measure the axial and lateral displacement along the sample. The failure mechanisms were monitored by eye inspection and a magnifier to detect crack initiation and propagation. For each test, the failure surfaces were investigated to determine the characteristics of each surface. Wing cracks initiated at the tip of the joint for the low confining stress applied, while at higher confining stresses wing cracks also initiated at the middle of the joint. Secondary cracks initiated at the tip of the joint due to shear stress. Three modes of failure took place due to coalescence of the secondary and wing cracks. The bridge inclination was the main variable that controlled the mode of failure. For bridge inclination of 0°, the coalescence occured due to shear failure and for bridge inclination of 90°the coalescence occurred due to tensile failure while for the other bridge inclinations coalescence occured due to mixed tensile and shear failure.

The stability of the landfill is an environmental issue. The collapse of the landfill causes environmental pollution and influences human life. In the present study, the crack on the cover of the landfill was simulated. Rankine’s theory and the Phantom Node Method were used for the simulation length of the crack and the mechanism of the crack propagation in the nonlinear extended finite element method (NXFEM). Artificial Neural Networks (ANNs) based on Levenberg-Marquardt Algorithm and Abalone Rings Data Set mode were used to predict displacement in critical points of the model. The vibration mechanism of the landfill was changed in each model. During applying seismic load on the model, the optimized thickness of the clay cover on the landfill was discussed. The thickness of the landfill cover controls the seismic response of the landfill. The numerical simulation shows differential displacement of the landfill impacts on the crack propagation and the need for the appropriate design of the cover thickness of the landfill.

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