Coal bump refers to a sudden catastrophic failure of coal seam and usually causes serious damages to underground mining facilities and staff. Considering the combined coal-rock structure for coal bumps, failure process and acoustic emission (AE) characteristics of combined coal-sandstone samples under different loading rates were studied by uniaxial compression tests, and three basic failure modes and bump proneness for coal-rock structure were obtained. The following conclusions are drawn: (1) when loading rate was relatively low, plastic deformation of coal mass fully developed, while surface cracks of coal mass was not apparent and slip along the transfixion crack occurred in the postpeak stage; (2) with the increase in loading rate, surface tensile cracks developed into splitting cracks at the end of the prepeak stage and throughout the postpeak stage, and brittle failure finally happened due to the release of nonlinear step-shaped energy or one-time strain energy release of upper rock mass, resulting in the damage of internal bearing structure and weakening of bearing capacity; (3) the deformation and failure process of combined samples showed obvious phases, and corresponding AE energy release rate could be divided into periodic linear growth and transient growth, while the cumulative energy of AE events has multiple peak points and transient growth with the increase of loading rate; (4) it was demonstrated that two distinct frequency bands existed in AE events, which were about 50 kHz and 150 kHz, and the distribution of AE events near 50 kHz was larger and stronger, representing the main frequency range of cracks in coal mass. According to the damage characteristics and AE parameters for combined samples, an brittle model for coal-rock structure with mutation characteristics was proposed, and three basic failure modes for the combined structure with the increase of loading rate were progressive shear failure, splitting failure, and structural failure, respectively.
With consideration of pre-axial pressure and two-parameter elastic foundation (Pasternak), a new method was put forward for analysis of transverse free vibration of a finite-length Euler-Bernoulli beam resting on a variable Pasternak elastic foundation. Matrices and determinants corresponding to arbitrary boundary conditions were provided for engineers and researchers according to their own demand. In derivation process of new proposed method, Schwarz distribution was adopted for simplifying the partial derivative of Dirac function and compound trapezoidal integral formula was adopted for discretizing the shape function of beam. For the symmetrical boundary conditions, it was concluded that natural frequency of transverse free vibration obtained by FEM highly agreed with the new proposed method. In contrary, for the asymmetrical cases, the calculation results were different from each other. For solving the ordinary differential equation with nonlinear partial derivative terms of shape function, the key point of new proposed method was to establish stiffness equation set composed of obtained matrices, rather than a single equation on the basis of classical theory. This point should be treated as a great advantage. New proposed method can be generalized to solve more complicated problems, which were illustrated in conclusion and prospect.
The work introduces the so-called “true” deformations, i.e. for final deformations, three deformations of elongations and three components of shear deformations are taken as a measure of deformations. The so-called generalized stresses, referred to the units of the corresponding areas before the deformation of the body, and “true” stresses, referred to the units of the corresponding areas after the deformation of the body, are introduced into consideration. Based on the constructed relationships, an algorithm for solving the variational problem of the three-dimensional theory of elasticity is constructed, and a finite-element method for solving the problems of deforming elastoplastic structures is developed and implemented. The practical problem of deforming the pre-stressed kinetic energy storage has been solved.
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