Semi-analytical solutions for the consolidation of unsaturated composite ground with floating permeable columns under equal strain condition

This study focuses on the mathematical interpretation and consolidation behavior of unsaturated composite ground with floating permeable columns (FPC). By combining the axisymmetric consolidation model with the equal strain assumption, the consolidation problem of unsaturated composite ground with FPC is transformed into a one-dimensional consolidation problem of an equivalent double-layer ground. The consolidation governing equations of the reinforced zone and the underlying stratum are derived respectively. The Laplace transformation and Gauss elimination method are used to obtain solutions for the average excess pore pressure and settlement in the Laplace transform domain. The semi-analytical solutions for the consolidation of composite ground in the time domain are obtained by implementing the Crump numerical method for the inverse Laplace transformation. A comparison with the existing literature and numerical simulation results from Finite Element Methods (FEM) confirms the correctness of the proposed semi-analytical solutions. Based on these solutions, the consolidation behavior of an unsaturated composite ground with FPC under instantaneous loading is investigated. The results indicate that the penetration ratio of the permeable column is the most significant factor affecting the consolidation of composite ground. Furthermore, the consolidation rate and settlement of the composite ground also highly depend on the unsaturated soil in the underlying stratum.