Settlement Analysis of Non-homogeneous Single Granular Pile

Abstract

Stone columns or granular piles are frequently used for the stabilization of soft clays and silts and loose silty sands with large amount of fines. Granular piles/stone columns improve the performance of foundations on soft ground by reducing the settlement to an acceptable level and also by increasing the load carrying capacity. The columns of granular material also help to speed up consolidation effects in the soft ground. Consideration of granular piles often to be homogeneous may not be true always and may lead to errors in the predictions of response of granular pile reinforced ground. The consideration of non-homogeneity of granular pile in terms of its non-linear behaviour of deformation modulus for settlement analysis could represent its in situ behaviour closer and more realistic. Present analysis carried out study of non-homogeneous granular pile in homogeneous soil based on the continuum approach in terms of settlement influence factor, normalized axial load and mobilized stress distributions with depth and the percentage of applied load transferred to the base. This analysis is applicable for a range of linear to non-linear analysis of deformation modulus of granular pile from top to tip.

Appendix

$$\begin{aligned} \left\{ Y \right\} & = \left\{ {\begin{array}{*{20}c} {\frac{{4{\text{U}}\left( {P/E_{s} d^{2} } \right)(L/d)}}{{n\pi K_{gp0} }}} \\ 0 \\ 0 \\ - \\ 0 \\ \end{array} } \right\} \\ \left[ {I^{pD} } \right] & = \left[ {\begin{array}{*{20}c} {\left[ {{\text{U}} + {\text{V}}} \right]} & {\text{W}} & 0 & - & - & - & - & 0 & 0 & 0 \\ {\text{U}} & {\text{V}} & {\text{W}} & - & - & - & - & - & - & 0 \\ 0 & {\text{U}} & {\text{V}} & {\text{W}} & - & - & - & - & - & - \\ 0 & 0 & - & - & - & - & - & - & - & - \\ - & - & - & - & - & - & - & - & - & - \\ - & - & - & - & - & - & - & - & - & - \\ - & - & - & - & - & - & - & - & - & - \\ - & - & - & - & - & - & {\text{U}} & {\text{V}} & {\text{W}} & 0 \\ - & - & - & - & - & - & {F_{n - 2} } & {F_{n - 1} } & {F_{n} } & {F_{n + 1} } \\ - & - & - & - & - & - & - & {G_{n - 1} } & {G_{n} } & {G_{n + 1} } \\ \end{array} } \right] \\ \end{aligned}$$

where $\left[ {I^{pD} } \right]$ is a square matrix of size (n + 1) of pile displacement influence coefficients. {Y} is a column vector of size, (n + 1). U = (c₁ − c₂) × K_gp0/4, V = −c₂ × K_gp0/2, and W = (c₁ + c₂) × K_gp0/4 with.

$$c_{1} = \left[ {\frac{{2\left\{ {1 + \frac{{\alpha z_{1i}^{*} }}{{\left( {L/d} \right)}} + \delta \left( {\frac{{z_{1i}^{*} }}{{\left( {L/d} \right)}}} \right)^{2} } \right\}}}{{\Delta z_{1}^{*2} }}} \right],\;c_{2} = \frac{{\left( {\frac{\alpha }{L/d} + 2\delta \frac{{\Delta z_{1}^{*} }}{{\left( {L/d} \right)^{2} }}} \right)}}{{2\Delta z_{1}^{*} }}$$