A New Semi-Analytical Method for the Calculation of Multi-Crack Stress-Intensity Factors under Hydro-Mechanical Coupling

Calculating the hydro-mechanical coupling stress-intensity factor (SIF) is an important basis for conducting safety evaluations in geotechnical engineering. The current methods used to calculate hydro-mechanical coupling multi-crack SIFs have difficulties concerning their complicated solution processes and unsuitable stress field expressions. In this paper, a new semi-analytical method is proposed based on a new hydro-mechanical coupling stress function and the extended reciprocal theorem of the work integral formula to calculate hydro-mechanical coupling multi-crack SIFs, which can be verified by comparison with the results available in the literature. The new semi-analytical method is applicable to an arbitrary number of cracks under arbitrary hydro-mechanical coupling loading and facilitates a more effective representation of the water pressure effect on the stress field. Moreover, the influence of the integral path and loading conditions is also discussed, and the results revealed an integral path radius of r2 < 0.75 mm when the crack spacing b is 1.5 mm. When σy and Ph are constant at 15 MPa, the SIFs are almost the same for different σy/Ph, while the maximum circumferential stresses at r = 0.25 mm are 15.79 MPa, 20.83 MPa, and 25.78 MPa.