Study on Stress and Displacement of Axisymmetric Circular Loess Tunnel Surrounding Rock Based on Joint Strength

The development of an effective evaluation method suitable for loess-tunnel excavation is necessary to avoid the collapse accidents caused by tunnel excavation and any secondary disasters. Although the Fenner formulas and the modified Fenner formulas are widely used in tunnel engineering, a defect still exists in these formulas because the Mohr-Coulomb (M-C) criterion exaggerates the tensile strength of the surrounding rock of the loess tunnel. A newly modified Fenner formula was derived based on joint strength to overcome this deficiency. First, the expressions of stress and the radius of the plastic zone of the surrounding rock of the loess tunnel and the expressions of radial displacement were derived based on the stress-equilibrium equation of the axisymmetric plane and the joint strength. Then, the difference in the modified Fenner formulas based on the two kinds of strength criteria for the loess tunnel were compared. The results showed that the radius of the plastic zone and the radial displacement of the loess tunnel determined by the modified Fenner formula based on joint strength were larger than those determined by the modified Fenner formula based on M-C strength. However, the plastic stress of the plastic zone determined by the modified Fenner formula based on joint strength was smaller. The comparative analysis reveals that the modified Fenner formula based on joint strength can evaluate the stress and plastic-displacement field of the surrounding rock of a loess tunnel more reasonably.