An analytical model for 2D consolidation of unsaturated soil with semi‐permeable boundaries considering self‐weight stress and time‐dependent loading

Abstract This paper proposes an analytical solution for 2D (two‐dimensional) consolidation of unsaturated soil with impeded drainage boundaries by considering the combined effects of self‐weight stress of soil and time‐dependent loading. The governing equation of the 2D consolidation model was first formulated, followed by an analytical solution employing the methods of the Laplace transform technique and separation of variables. The solution is then degraded to validate the correctness against two classical lab tests and existing solutions. Subsequently, the proposed solution is further verified against finite element calculations. The results indicate that the self‐weight stress of soil acts as an additional load applied to the unsaturated soil, the larger the self‐weight stress, the greater the value of initial EPPs (excess pore pressures). Meanwhile, it can be easily found that the larger the value of self‐weight stress, the larger the consolidation settlement. Without accounting for the effect of self‐weight stress, the settlement of the soil will certainly be underestimated and the dissipation characteristics of EPPs will not be accurately captured. It can be also found that the ratio of k a / k w also significantly influenced the consolidation behavior.