Optimal Support Solution for a Soft Rock Roadway Based on the Drucker–Prager Yield Criteria

Through theoretical calculation, the stress and deformation of surrounding rock can be analyzed, providing guidance for the support design and optimization of soft rock roadways. In this paper, theoretical solutions for both the optimal support pressure and the allowable maximum displacement of surrounding rock are derived from the Drucker–Prager (DP) yield criteria and the steady creep criterion expressed by the third invariant of deviator stress. The DP criterion with different parameters is compared and analyzed with an engineering example. Then, based on the calculation results the effects of long-term strength, cohesion, and internal friction angle of soft rock on the maximum plastic zone radius and allowable maximum displacement of roadway are discussed. The results show that the optimal support solution of soft rock roadways based on the DP criteria can not only reasonably reflect the intermediate principal stress but can also be used to compare and discuss the influence of different DP criteria on the calculation results. The higher the long-term strength of the rock surrounding a roadway is, the smaller the optimal support force is and the larger the allowable maximum displacement is. When the calculated long-term strength of soft rock can ensure that the deformation of the roadway does not exceed the allowable maximum displacement, the roadway can maintain long-term stability without support. With an increase in the cohesion or internal friction angle of soft rock, the radius of the plastic zone decreases gradually and the allowable maximum displacement is reduced by degrees. The use of grouting and other means to improve the strength of surrounding rock can effectively reduce the roadway deformation and save support costs. This new theoretical solution can consider different intermediate principal stress effects and different DP strength criteria, enabling the parameters to become easier to determine. It has a wider range of applications, and the calculation results better demonstrate the strength potential of the surrounding rock.