Approximate solution of plastic zone in surrounding rock under three-dimensional stress field based on Drucker-Prager strength criterion

This study proposes to address the stability of roadway surrounding rock under three-dimensional stress field based on the Drucker-Prager criterion and the theory of elastic-plastic mechanics. Specifically, we deduced the boundary equation of plastic zone of roadway surrounding rock under three-dimensional stress field by introducing the axial stress solution, and analyzed the shape and size of plastic zone of surrounding rock under different stress field conditions. We compared the effect of five Drucker-Prager yield criteria on the shape and size of plastic zone under variations of cohesion, internal friction angle, Poisson's ratio and roadway radius in roadway surrounding rock. We then analyzed its implications for engineering practice based on the evolution characteristics. Results show that ① Variations in horizontal stress exerts significant impact on the plastic zone morphology of roadway surrounding rock: too high or too low horizontal stress will lead to a butterfly-shaped expansion in the roadway surrounding rock. ② Variations in axial pressure has little effect on the plastic zone shape of roadway surrounding rock, yet exerts major influence on the plastic zone size of surrounding rock: under the same horizontal stress, different axial stress will lead to a bowl-shaped development in the plastic zone size of surrounding rock. With variations in the cohesion, internal friction angle and roadway radius, we observed consistency in the size variation of plastic zone in roadway surrounding rock under different Drucker-Prager criteria. Therefore, the choice of different Drucker-Prager criteria will affect the calculation results of plastic zone in surrounding rock of roadway.