Moving Collinear Cracks in a Prestressed Dry Sandy Medium Fracture Response under Traveling Punch Loads

Abstract

The dynamic fracture behaviour of two moving collinear Griffith cracks in an initially stressed dry sandy medium subjected to concentrated crack-face loading and moving punch pressure is investigated. A moving coordinate system transforms the transient problem into a steady state formulation, while the effects of initial stress and sandiness are incorporated into the governing equations. Fourier integral transforms are employed to obtain the characteristic equation and the transformed traction displacement relations. The crack face, symmetry, and outer surface conditions reduce the problem to coupled Cauchy type singular integral equations. For a sufficiently thick strip, an asymptotic kernel reduction is developed, and the resulting equations are solved analytically using the finite Hilbert transform. Closed form expressions are derived for the crack density functions, Mode I stress intensity factors at the inner and outer crack tips, and the crack opening displacement. Several limiting cases are recovered from the general formulation, providing analytical consistency checks. The results demonstrate the combined influence of crack speed, crack geometry, initial stress, sandiness, and moving punch loading on crack tip intensification and crack opening. The proposed analytical framework provides useful insights for fracture assessment and the design of transportation infrastructure, geotechnical systems, underground excavations, and other engineering structures involving dry sandy media subjected to moving loads.