Bearing Capacity and Settlement Response of Ordinary and Geosynthetic Encased Granular Columns in Soft Clay Soils: Analysis and Design Charts

Abstract

This paper discusses the bearing capacity and settlement response of granular columns with and without geosynthetic encasement using the currently available design procedure. The design procedure is modified to include the influence of the geosynthetic encasement. The key parameters influencing the load bearing capacity and settlement are studied through comprehensive parametric analyses. The results portray the advantage of geosynthetic encased granular columns in enhancing the bearing capacity and reducing the settlements compared to granular columns without encasement. Different installation patterns of granular columns were considered in this investigation. The maximum bearing capacity improvement and settlement reduction are observed with granular columns installed in triangular plan arrangement. The hexagonal pattern results in the lowest area replacement ratio and also the lowest improvement factors. It is shown that with geosynthetic encasement, the performance with hexagonal pattern could be improved to match with other more efficient patterns like square and triangular. Some selected results are validated through detailed finite element results. A quick assessment of the settlement improvement with geosynthetic encapsulated granular columns is possible with the design charts presented.

Appendix

Section A: Design of OGCs as per IS 15284 Part 1 (2003) [35]

Detailed calculations for estimating the bearing capacity and settlement reduction factors are given in this section. The foundation soil is assumed to be 10 m thick having an undrained cohesive strength of 5 kPa. The K_o of the soil was assumed to be 0.50. The granular columns are assumed to be of 600 mm diameter and aggregate having friction angle of 36°. The columns are assumed to be provided at a c/c spacing of 1.2 m in triangular pattern. The geosynthetic is assumed to have tensile modulus of 500 kN/m at 5% strain. The settlement is assumed to be limited to 5% of soil thickness. The saturated unit weight of soil is assumed to be 20 kN/m³, and the water table is at ground level.

Step-1 Capacity Based on Bulging of the Ordinary Granular column

Initial effective radial stress $\sigma_{r0}$ = $K_{0} \sigma_{v0}$ = 0.5 $\times$ 10 $\times$ 2 $\times 0.6 = 6 \;{\text{kPa}}$

Limiting radial stress $\sigma_{rL}$ = $\left( {\sigma_{r0} + 4C_{u} } \right)$ = $\left( {6 + 4 \times 5} \right) = 26 \;{\text{kPa}}$

The limiting axial stress in the column $\sigma_{v} = \sigma_{rL} \times K_{{p_{\text{col}} }} = 26 \times 3.85 = 100.14 \;{\text{kPa}}$

Safe load on the stone column Q₁ (with factor of safety of 2) $= \frac{{\left( {\sigma_{v} \frac{\pi }{4} D^{2} } \right)}}{2} = \frac{{\left( {100.14 \times 0.7854 \times 0.6^{2} } \right)}}{2} = 14.16 \;{\text{kN}}$

Step-2 Capacity Based on Surcharge Effect

The safe bearing pressure of the soil with a factor of safety of 2.5, $q_{\text{safe}} = C_{u} N_{c} /2.5$

$$ q_{\text{safe}} = \frac{{\left( {5 \times 5.14} \right)}}{2.5} = 10.28 \;{\text{kPa}} $$

The increase in mean radial stress due to surcharge

$$ \Delta \sigma_{r0} = \frac{{q_{\text{safe}} }}{3}\left( {1 + 2K_{0} } \right) = \left( {\frac{10.28}{3}} \right)\left( {1 + \left( {2 \times 0.5} \right)} \right) = 6.85 \;{\text{kPa}}. $$

The increase in the safe load of the stone column Q₂ $= \left( {\frac{{Kp_{\text{col}} \Delta \sigma_{r0} A_{s} }}{2}} \right) = \left( {\frac{3.85 \times 6.85 \times 0.283}{2}} \right) = 3.73 \;{\text{kN}}.$

Step-3 Capacity Based on Bearing Support Provided by the Intervening Soil

Effective area of unit cell area for triangular pattern = $0.866\;{\text{S}}^{2}$.

Area of the intervening soil $A_{g} = 0.866\;{\text{S}}^{2} - \frac{{\pi D^{2} }}{4} = 0.866\left( {2 \times 0.6} \right)^{2} - 0.283 = 0.964 \;{\text{m}}^{2}$.

Safe load taken by the intervening soil Q₃ = $q_{\text{safe}} A_{g} = 10.28 \times 0.964 = 9.91 \;{\text{kN}}$ for triangular pattern.

Overall safe load on each unit cell = $\left( {Q_{1} + Q_{2} + Q_{3} } \right) = 27.80$.

Section B: Modification to IS 15284 Part 1 (2003) [35]

The additional confinement $\Delta \sigma_{3}$ offered by the geosynthetic encasement is quantified by the equation proposed by Henkel and Gilbert [56].

$$ \Delta \sigma_{3} = \frac{2M}{d}\left( {\frac{{1 - \sqrt {1 - \varepsilon_{a} } }}{{1 - \varepsilon_{a} }}} \right) = \frac{2 \times 500}{0.6}\left( {\frac{{1 - \sqrt {1 - 0.05} }}{1 - 0.05}} \right) = 44.42 \;{\text{kPa}} $$

.

This additional confinement is summed up with the modified limiting radial stress $\sigma_{rL*} = \left( {\sigma_{r0} + 4C_{u} + \Delta \sigma_{3} } \right) = 6 + 20 + 44.42 = 70.42 \;{\text{kPa}}$.

The modified limiting axial stress in the column $\sigma_{v*} = \sigma_{rL*} \times K_{{p_{\text{col}} }} = 70.42 \times 3.85 = 271.1 \;{\text{kPa}}.$

Now, the safe load on the geosynthetic encased stone column Q_1* (with factor of safety of 2) $= \frac{{\left( {\sigma_{v*} \frac{\pi }{4} D^{2} } \right)}}{2} = \frac{{\left( {271.1 \times 0.7854 \times 0.6^{2} } \right)}}{2} = 38.33 \;{\text{kN}}$.

Overall safe load that can be applied on each unit cell area = $\left( {Q_{1*} + Q_{2} + Q_{3} } \right) = 51.97\;{\text{kN}}$.

Section C: Settlement of the Soft Clay Treated with OGC and EGC based on IS 15284 Part 1 (2003) [35]

The settlement of the granular column-treated ground is estimated using the stress concentration ratio (n) and the area replacement ratio a_s. The stress concentration ratio is obtained as per the equation indicated below,

The stress concentration ratio for OGC,

$$ n = \frac{{\sigma_{s} }}{{\sigma_{g} }} = \left( {\frac{{{{\left( {\sigma_{v} + \left( {\Delta \sigma_{r0} \times K_{{p_{\text{col}} }} } \right)} \right)} \mathord{\left/ {\vphantom {{\left( {\sigma_{v} + \left( {\Delta \sigma_{r0} \times K_{{p_{\text{col}} }} } \right)} \right)} {2.5}}} \right. \kern-0pt} {2.5}}}}{{q_{\text{safe}} }}} \right) = \left( {\frac{{\left( {100.14 + \left( {6.85 \times 3.85} \right)} \right)/2.5}}{10.28}} \right) = 4.92 $$

Similarly, stress concentration factor for ${\text{EGC }} = \left( {\frac{{\left( {272.1 + \left( {6.85 \times 3.85} \right)} \right)/2.5}}{10.28}} \right) = \, 11.57$

Area replacement ratio = 0.7854 × 0.6²/(0.866 × 1.2²) = 0.227.

Then the settlement reduction ratio is computed from the calculated stress concentration ratio (n) and area replacement ratio (a_s) as per [32].

$$ {\text{For }}\;{\text{OGC}}, \beta = \frac{{S_{t} }}{S} = \frac{1}{{1 + \left( {n - 1} \right)a_{s} }} = \frac{1}{{1 + \left( {4.92 - 1} \right)0.227}} = 0.53 $$

For EGC, $\beta = \frac{{S_{t} }}{S} = \frac{1}{{1 + \left( {n - 1} \right)a_{s} }} = \frac{1}{{1 + \left( {11.57 - 1} \right)0.227}} = 0.29$,

The settlement of the treated soil is 53% of the total settlement of the untreated soil in the case of OGC and 29% in the case of EGC.

The corresponding improvement factors (1/$\beta$) as per (42) are 1.89 and 3.45, respectively, for OGC and EGC.