Stress distribution and failure characteristics around U-shaped caverns with different height-to-width ratios under biaxial compression

Understanding the stress distribution and failure characteristics around a U-shaped cavern is vital to the stability analysis of rock structures such as tunnels and roadways. In this study, the stress distribution around a U-shaped cavern with different height-to-width (h/w) ratios under biaxial compression was first analyzed based on the complex variable theory. Then, numerical simulations were conducted using PFC2D to study the failure process and energy evolution around a Ushaped cavern with different h/w ratios. Theoretical solution shows that the maximum stress concentration factor occurs at the bottom corner of the U-shaped cavern. With the h/w ratio increasing from 0.75 to 3.0, the stress concentration factor around the sidewall shows a declining trend, while the opposite trend is observed in the vault and floor. Numerical results show that when the maximum principal stress is parallel to the vertical direction, the thin slab buckling occurs in the sidewall of the cavern with low h/w ratios (h/w = 0.75 and 1.0), accompanied by the release of relatively high kinetic energy. Instead, the wedged-shaped slab spalling occurs in the sidewall of the cavern with high h/w ratios (h/w = 1.5, 2.0 and 3.0), which can be considered as a static process. Although the U-shaped cavern with low h/w ratios has higher integrity after failure, more stain energy is accumulated in the remaining surrounding rock, which is likely to cause rockbursts under a higher stress state or dynamic disturbance. When the maximum principal stress is horizontal, the rock slab separates from the cavern floor and presents a reverse trend with the increasing h/w ratio. The above results indicate that the h/w ratio and the direction of maximum principal stress should be considered comprehensively in the design of the support system of U-shaped caverns.