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Rock Wing Cracks Model Under the Action of Hydraulic Pressure-Stress and Numerical Verification

ZHAO Yan-lin,WANG Wen-jun,ZHAO FU-jun,WAN Wen (Hunan Provincial Key Laboratory of Safe Mining Techniques of Coal Mines,School of Energy and Safty Enginerring, Hunan University of Science and Technology,Xiangtan,Hunan 411201,China)  
Considering the effect of hydraulic pressure on wing cracks and the connected part of main crack on the stress intensity factor at wing cracks tip,the compression-shear wing cracks model under the action of hydraulic pressure-stress is established firstly.With the equivalent crack length l_(eq) of wing crack is introduced,the stress intensity factor K_Ⅰat wing crack tip is assumed to be the sum of two terms;one is the component K_Ⅰ~((1)) for a single isolated straight wing crack of length,subjected to the externally applied stresses,the other is the component K_Ⅰ~((2)) due to the stresses induced by the presence of the equivalent main crack composed of the main crack and the equivalent crack length subjected to the same external stresses.According to different side pressure coefficients and hydraulic pressures in cracks,the FEM model of wing crack under the action of hydraulic pressure-stress is also established.The result shows that, under the action of high hydraulic pressure,with the wing crack propagation,the tensile stress regions increases gradually;the high hydraulic pressure and lateral tensile stress together leads to the wing cracks propagation in a unsteady way.A comparative analysis of theoretical model and finite element analysis shows that,except for the very short wing crack,compared with the finite element analysis results,considering hydraulic pressure,the stress intensity factor obtained from theoretical model is small.Without considering the model solution and FEM solution, the error is very small.So the relation curves between normalized SIF at wing cracks tip and equivalent cracks propagation length obtained from theoretical model is in good accordance with that from FEM model in both trend and magnitude.The wing cracks theoretical model provides some academic bases and references for studying hydraulic fracture and disaster mechanism of Karst water bursting in mine.
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