calculation of maximum and minimum plastic zone radius around circular tunnels; new emprical relation

 this paper discusses the calculation of plastic zone radius around the circular tunnel which were based on the hoek-brown failure criterion. the importance of plastic zone radius calculation for different stress ratio can be illustrated by knowing that for each stress ratio, the shape of failure zone will get changed. the calculation of plastic zone radius was done for five stress ratio with numerical modeling by defining the factor of d. the maximum and minimum of plastic zone radius were determined for each stress ratio and after that by fitting the curve to the data, the emprical relations were obtained. new emprical relations are the results of this paper which can be used for calculation of maximum and minimum plastic zone radius in different condition.