Analysis and prediction of dynamic stress concentration in jointed coal using boundary element method

Dynamic stress concentrations around coal joints generated by mining-induced or seismic waves are a major precursor to dynamic disasters. To quantify and predict these stress amplifications, a boundary-element model (BEM) was developed for a single, planar coal joint subjected to planar P-wave loading. The model was verified against Universal Distinct Element Code (UDEC) simulations and digital image correlation (DIC) measurements. Parametric analyses were then performed to evaluate the influence of incident-wave frequency f, joint inclination angle θ, and joint length L_j. Results show that the maximum principal-stress concentration factor C_σ1m attains its peak when the wavelength-to-joint-length ratio L^∗=λ/L_j lies between 5 and 8, while the corresponding displacement-concentration factor C_uxm approaches an upper bound. Within the practical ranges f≤1000Hz, 10°≤θ≤60°, and L_j≤0.50m, C_σ1m is correlated with C_uxm (R²>0.99). An empirical expression that incorporates joint length, C_σ1m=(aC_uxm²+bC_uxm+c)L_j/L₂₀, where L₂₀=0.20m and a, b, and c are regression coefficients, was calibrated and shown to predict peak stresses with reasonable accuracy when L^∗>7. Because displacements are easier to monitor in situ than rapid stress transients, the proposed relationship provides a practical tool for estimating dynamic stress concentrations around coal joints, thereby facilitating early warning and support-design strategies in deep mining operations.