Nonlinear Calculation Method for Safe Thickness of Foundation Pit Bottom Plate Against Upwelling under the Action of Confined Water

Determining the critical thickness for preventing upwelling of foundation pit base slabs under confined water pressure is a pivotal concern for ensuring the safety of foundation pit construction.Given the nonlinear nature of foundation pit base slab upwelling,a novel calculation method for assessing the critical thickness to mitigate this risk has been introduced.By simplifying the waterproof soil layer of the foundation pit base slab under confined water pressure into a fixed-end beam mechanical model subjected to uniform load with preload, and drawing on catastrophe theory, principles of mechanical equilibrium, and energy balance, a catastrophe model for foundation pit base slab upwelling under confined water pressure is formulated. This model derives the necessary and sufficient conditions for upwelling of the waterproof soil layer, along with a nonlinear formula for calculating the critical safe thickness. The critical thickness is then solved using an iterative approach with Matlab programming, and the interplay between the critical thickness and various influencing factors is analyzed. The research findings reveal a negative correlation between the elastic modulus E of the foundation pit base slab and its critical thickness, whereas a positive correlation is observed between the critical thickness and factors such as the confined water head in the foundation pit, the length L of the soil beam,the excavation depth D of the foundation pit.To validate the effectiveness of this method, two foundation pit cases are examined.The research outcomes offer theoretical guidance for the design and on-site construction of foundation pits under confined water pressure.