Analytical Solution of Critical Filling Volume for Karst Bored Pile Reinforcement

The bored pile method is commonly used to ensure pile integrity in karst areas. However, due to insufficient reinforcement of karst voids and excessive lateral pressure in the pile hole, serious concrete loss accidents often occur. Previous studies have predominantly focused on the stability of cave roofs and the bearing performance of piles and have rarely studied the reinforcement of pile foundations passing through karst caves. In this work, we intend to provide a quantitative reference for karst bored pile reinforcement by determining the critical filling volume. Based on cylindrical cavity expansion theory combined with the Mohr–Coulomb failure criterion, the stress and displacement fields in the elastic–plastic zone of the karst backfill were established, and the calculation formula for critical filling volume was derived. The correctness and effectiveness of the proposed method were evidenced by consistent results from numerical manifold method simulations, theoretical calculations, and field measurements. In addition, the parametric analysis further reveals that a backfill with a higher elastic modulus, greater friction angle, and cohesion is more effective in reinforcing karst pile foundations. The stability of the karst backfill will be improved with a smaller depth of the karst roof, a lower cavern, and a larger safety factor.