Analytical Solution for the Synergistic Effect of Drilling Shaft Lining, Backfill Layer, and Weakly Cemented Formation Considering the Effect of Filter Cake

To reveal the mechanism of the load transfer of drilling shaft lining under the influence of filter cake, this study establishes a mechanical interaction model that integrates the surrounding rock, filter cake, backfill layer, and shaft lining system based on elastoplastic theory. The analytical solution of this system was derived; this was followed by the systematic examination of the impact of the key parameters (thickness of filter cake, elastic modulus of surrounding rock, cohesion, and internal friction angle) on stress field evolution and load distribution. The operational mechanisms of filter cake and load formation principles in drilling shaft linings were elucidated. The results show that the filter cake induces stress concentration in surrounding rock by delaying stress transmission, effectively mobilizing the bearing capacity of surrounding rock and improving the stress state of the lining. An increase in the elastic modulus of the surrounding rock enhances the load-bearing proportion of the surrounding rock, thereby reducing the load transferred to the backfill layer and shaft lining. Higher cohesion and a higher internal friction angle of the surrounding rock strengthen the bearing capacity of the surrounding rock, which decreases the load transmitted to the backfill layer and shaft lining. The increased stiffness of the backfill layer raises the load-bearing proportion of the backfill layer, while diminishing loads on both the shaft lining and surrounding rock. The above research provides a theoretical basis for promoting the application of drilling technology in deep, water-rich, and weakly cemented bedrock formations in western China.