Study on the Minimum Safe Thickness of Overlying Rock Waterproof Layer in Karst Tunnels Under Different Water Pressures

In karst tunnel engineering, water-filled cavities located above the tunnel crown, under the combined effects of excavation disturbance and hydraulic pressure, are prone to triggering water and mud inrush disasters. The thickness of the water-resisting rock layer is therefore a key factor controlling the stability of the surrounding rock. To address the difficulty in accurately characterizing the mechanical behavior of the crown of horseshoe-shaped tunnels using conventional circular plate or beam models, this study innovatively develops an explicit analytical model for the minimum safe thickness of the water-resisting rock layer based on clamped elliptical thin plate theory and Kirchhoff plate theory, incorporating the influence of cross-sectional geometry. Parametric sensitivity analysis indicates that both karst water pressure and tunnel crown height significantly amplify the required minimum safe thickness, whereas an increase in the tensile strength of the surrounding rock effectively reduces the thickness demand. Specifically, when the karst water pressure increases from 2.5 MPa to 4.5 MPa, the minimum safe thickness rises from 7.5 m to 10.0 m, showing an approximately linear growth trend. The analytical model is further validated through numerical simulations under different “water pressure–thickness” conditions. The results demonstrate that at the calculated recommended thickness, the surrounding rock achieves stable convergence after excavation. High tensile stress and elevated pore pressure zones are mainly concentrated near the tunnel crown, without the formation of through-going tensile failure. Engineering application indicates that the proposed model can provide a quantitative basis for the design of water-resisting rock layer thickness and the assessment of water inrush risk in karst tunnels.