Based on complex conformal mapping and Duhamel’s integral method the steady and transient dynamic stress distribution around an elliptical cavity subjected to plane P-wave was obtained. The influence of incident angle(θ0), axial ratio(k) and normalized wave length (t0) on the dynamic stress concentration factor (DSCF) was evaluated. Further, the finite element method (FEM) software LS-DYNA was utilized to validate the analytical solution. The results indicated that the maximum compression DSCF increased with θ0, except θ0=0, and decreased with k. When θ0=0 the maximum tensile DSCF increase with the decrease of k. The position of maximum compression and tensile DSCF varied with incident θ0. Under the transient incident condition DSCF was affected by normalized wave length t0, with the increasing of t0 the DSCF gone up then down finally gone closed to the static stress concentration factor. Further, the stress state around the elliptical cavity under transient impact loading was compared with the experimental results of elastic stress distribution and plastic failure and got a good agreement, and possible dynamic failure modes of elliptical cavity were discussed.

The complex boundary of the elliptical inclusion rendered it difficult to solve the problem of wave scattering. In this study, the steady-state response was analyzed using the wave function expansion method. Subsequently, the Ricker wavelet was employed as the transient disturbance and Fourier transform was used to determine the distribution of transient dynamic stress concentration around the elliptical inclusion. The effects of wave number, elliptical axial ratio and difference in material properties on the distribution of the dynamic stress concentration around the elliptical inclusion were evaluated. The numerical results revealed that the dynamic stress concentration always appeared at both ends of the major axis and minor axis of the elliptical inclusion, and the difference in material properties between the inclusion and medium influenced the variations in the dynamic stress concentration factor with the wave number and elliptical axial ratio.

Fatigue tests under high static pre-stress loads can provide meaningful results to better understand the time-dependent failure characteristics of rock and rock-like materials. However, fatigue tests under high static pre-stress loads are rarely reported in precious literatures. In this study, the rock specimens were loaded with a high static pre-stress representing 70% and 80% of the UCS, and cyclic fatigue loads with a low amplitude (i.e., 5%, 7.5% and 10% of the UCS) were applied. The results demonstrate that the fatigue life decreased as the static pre-stress level or amplitude of fatigue loads increased for all rock types, and the high static pre-stress affected the fatigue life greatly when the static pre-stress was larger than the damage stress of rocks in uniaxial compression test. The accumulative fatigue damage exhibited three stages during the fatigue failure process: crack initiation, uniform velocity, and acceleration, and so the fatigue modulus showed an “S-type” change trend. The lateral strain and volumetric strain had a much higher sensitivity to the cyclic loading and could be used to predict fatigue failure characteristics, and it was found that volumetric strain “ε” _“v” = 0 is a threshold for microcracks coalescence and is an important value for estimating the fatigue life.