Elastic‒plastic analysis of rock surrounding a circular roadway considering plastic hardening and dilatancy characteristics

Excavation of deep roadways induces plastic failure of the surrounding rock, resulting in roof caving and uncoordinated large deformation, which seriously threatens support safety and production efficiency. A four-stage stress‒strain model of the elastic zone‒plastic zone‒softening zone‒fracture zone of the surrounding rock in a deep roadway is established to analyze the range of the roadway fracture zone. The model considers the unified strength criterion, the nonassociated flow rule, and the influence of the intermediate principal stress and dilatancy coefficient. From this model, closed solutions for the stress, strain and deformation of the surrounding rock are obtained. The results show that an increase in the value of the strength parameter b can reduce the tangential stress σ _θ on the surface of the roadway but increase the values of σ _θ and σ _r at the plastic-flow interface, and the peak value of σ _θ increases with increasing b value. The tangential strain ε _θ and radial strain ε _r decrease with increasing strength parameter b , and the radial displacement u _r decreases with increasing b but increases significantly with increasing initial internal friction angle φ ₀ and cohesion c ₀ . The dilatancy coefficient η _i is positively correlated with the b value and the dilatancy angle ψ _i , revealing that the surrounding rock with high dilatancy is more prone to volume expansion instability. The research results provide a theoretical basis and quantitative parameter support for stability evaluation and differential support design of deep roadways.