Underground coal mining activities are prone to cause movement and breakage in geological strata and also lead to mining subsidence and even ground fissures. Along the direction working panel advancing, ground fissures may occur in roof in front and/or behind working panel. However, the investigations of previous similarity tests in lab only emphasize on the region behind working panel. By improving strata material property in construction and mounting artificial pressure devices, two physical simulation tests were conducted and successfully investigated the simulated results. Then, the mechanical model of “cantilever beam and elastic foundation beam” was proposed to calculate the stress distribution and the crack initiation angle in overlying strata and it well explains the mechanisms of ground fissures generation and propagation. Results show that, the maximum internal force in roof always occurred in front of working panel. However, because the void space in gob due to excavation is large enough to cause the bend and rotation of roof strata, compare to the triaxially compressed region in front of working panel, the roof always broke off at some positions above gob since the stress concentration resulting from such bend and rotation of strata could easily reach the limit strength of strata rocks. Also, the length of cantilever beam changed dynamically as respect to the panel advancing and the breakage intervals. Thus, the breakage position where the internal force first reached the limit tensile strength is not fixed and there will be two different kinds of relative positions between the crack initiation point and the working panel. The crack initiation direction is always perpendicular to the internal force, and the crack propagation direction is affected by the initiation angle, overburden-separation degree and the position of the hydraulic shields. If there is no overburden-separation or less, the roofs will break off as a composite beam and the propagation direction will be roughly along the central line between the initial broken point and the support position. Otherwise, the roof strata will bend with the support shields moving forward, then the fracture angle will be close to the initiation angle and the fault surface will be stepped.

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Contact problems are among the most difficult issues in mathematics and are of crucial practical importance in engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional contact problems with small deformation in elastostatics. Only the boundaries of the contact system are discretized into surface elements by the scaled boundary finite-element method. The dimension of the contact system is reduced by one. The frictional contact conditions are formulated as B-differentiable equations. The B-differentiable Newton method is used to solve the governing equation of 3D frictional contact problems. The convergence of the B-differentiable Newton method is proven by the theory of mathematical programming. The two-block contact problem and the multiblock contact problem verify the effectiveness of the proposed method for 3D frictional contact problems. The arch-dam transverse joint contact problem shows that the proposed method can solve practical engineering problems. Numerical examples show that the proposed method is a feasible and effective solution for frictional contact problems.

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