Study on plastic zone expansion of surrounding rock in rectangular roadway based on D-P criterion

Accurately characterizing plastic zone evolution is essential for the support design and stability control of underground roadways. Rectangular sections are widely adopted in coal mines, but most existing plastic zone models are established for circular roadways using the Mohr-Coulomb criterion, while few studies have systematically considered the intermediate principal stress for rectangular roadways. To fill this gap, an analytical solution for the plastic zone boundary of rectangular roadway surrounding rock under 3D non-uniform in-situ stress is derived based on the plane complex variable function theory and Drucker-Prager (D-P) yield criterion. Parameter analyses are conducted to reveal the effects of lateral pressure coefficient, intermediate principal stress coefficient, rock cohesion and internal friction angle, and calculation differences among different D-P criteria are quantified. The results indicate that the lateral pressure coefficient governs plastic zone morphology, which transforms successively into butterfly, dumbbell and cross shapes as the coefficient rises from 0.2 to 1.6. The maximum plastic zone radius presents a U-shaped trend with the increase of intermediate principal stress coefficient, and declines monotonically with growing cohesion and internal friction angle. The calculated radius follows the order: DP3 (inscribed circle) > DP1 (inner corner circumscribed circle) > DP4 (plane strain matching circle) > DP2 (Mohr-Coulomb equivalent area circle). DP1 and DP4 are recommended for practical engineering due to good safety and economic performance. This work improves the theoretical framework for surrounding rock failure analysis and provides references for the support design of deep rectangular roadways.