In terms of stress wave theory and complex function

analytical solution for the interaction between blasting seismic wave and arbitrary shape underground chambers is deduced. The detail process is that through the conformal mapping method

the arbitrary shape hole in physical plane can be mapped into unit circle in mapped plane; the problem is translated into solving the interaction between blasting seismic wave and unit circle chambers. Taking the interaction between blasting seismic wave and an arch tunnel with vertical sidewalls for example

the distribution of stress and vibration velocity of rock mass is presented and analyzed under the acting of the incident blasting seismic wave with different frequencies and incident angles

and then the critical particle vibration velocity is decided basing on the tensile strength of rock mass.