# Design method for calculating settlement of stiffened deep mixed column-supported embankment over soft clay

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## Abstract

As a composite column, stiffened deep mixed (SDM) column is formed by inserting a precast concrete core pile into the center of a deep mixed (DM) column. The SDM columns have been successfully used to support highway and railway embankments and buildings over soft soil. However, there has been still a lack of feasible method to calculate the settlement SDM column-reinforced soft soil under an embankment load. This paper developed a theoretical solution to calculate the settlement of SDM column-supported embankment over soft soil. Based on the unit cell concept, the total settlement of the SDM column-reinforced soft soil consisted of three components, i.e., the compression of soil within the length of stiffened core pile, the compression of soil from the core pile base to the SDM column base, and the compression of soil below the SDM column base. The upward and downward penetrations of stiffened core pile were considered in the analysis. The analytical solution was verified by a comparison with the results computed by three-dimensional finite element analyses. A parametric study based on the derived solution was conducted to investigate the influence factors of modulus, length and diameter of DM column, length and diameter of core pile, and interface friction angle between DM column and core pile on the settlement of SDM column-reinforced soil, and some recommendations were proposed for its application in practice. The design charts for settlement calculation were developed for the ease of use in design. The design method was applied to two case histories of SDM column-supported embankments, and good agreements were found between the predicted settlements and the field measurements.

## Keywords

Embankment Settlement Soft clay Stiffened deep mixed column Theoretical analysis## List of symbols

*l*_{1},*l*_{2},*l*_{3}Original thicknesses of Region I, Region II, and Region III, respectively

- \(l_{1}^{{\prime }}\), \(l_{2}^{{\prime }}\), \(l_{3}^{{\prime }}\)
Thicknesses of Region I, Region II, and Region III when the unit cell is subjected to a surface pressure, respectively

- \(l_{0}\)
Depth of equal settlement plane

*D*,*d*Diameter of DM column and core pile, respectively

*D*_{e},*B*Equivalent diameter of influence zone and column spacing, respectively

- \(S_{\text{total}}\), \(S_{\text{I}}\), \(S_{\text{II}}\), \(S_{\text{III}}\)
Total settlement and the compression of Region I, Region II, and Region III, respectively

- \(\delta_{\text{up}}\), \(\delta_{\text{down}}\), \(\delta_{\text{core}}\)
Upward penetration and downward penetration of the core pile; the compression of the core pile, respectively

- \(S_{\text{su}}\), \(\delta_{1}\)
Compression of the surrounding soil and the compression of core pile above the neutral point, respectively

- \(S_{\text{sd}}\), \(\delta_{2}\)
Compression of the surrounding soil and the compression of core pile below the neutral point, respectively

- \(\Delta F\), \(\Delta z\)
Change in axial force at two adjacent depths and the distance between the two adjacent depths, respectively

- \(\tau_{0}\)
Negative friction at the elevation of core pile head

- \(\tau (z)\)
Skin friction stress at a depth of

*z**K*In situ coefficient of lateral earth pressure

- \(\varphi\), \(\varphi_{\text{i}}\)
Friction angle of DM column and the interface friction angle between the core pile and the DM column, respectively

*P*, \(\sigma_{\text{p}}\), \(\sigma_{\text{s}}\)Applied pressure on the whole area of the unit cell, the average vertical stress on the top of core pile and the equivalent surrounding soil, respectively

- \(m\), \(\alpha\)
Replacement ratio of SDM column and core pile area ratio in cross section of SDM column, respectively

- \(\lambda\), \(\gamma\)
Ratio used in derivation

- \(E_{\text{I}}^{\text{eq}}\), \(E_{{{\text{s}}{\rm I}}}\)
Equivalent constrained modulus of surrounding soil and DM column, the constrained modulus of subsoil in Region I, respectively

- \(\sigma_{\text{sz}}\), \(\sigma_{\text{pz}}\), \(\sigma_{{{\text{s}}l_{1} }}\), \(\sigma_{{{\text{p}}l_{1} }}\)
Vertical stress at certain depth

- \(A_{\text{e}}\), \(A_{\text{p}}\)
Areas of influence zone and core pile, respectively

- \(u_{\text{p}}\)
Perimeter of core pile

- \(p_{\text{c}}\), \(p_{\text{s}}\)
Upward penetration when a unit force is exerted on the top of core pile and downward penetration when a unit force exerted on the bottom of core pile, respectively

- \(l_{\text{GC}}\), \(E_{\text{GC}}\)
Thickness of gravel cushion and the constrained modulus of cushion, respectively

- \(\mu_{0}\)
Poisson’s ratio of DM column

*E*Constrained modulus of soil layer

- \(\mu\)
Poisson’s ratio of soil layer

*k*Coefficient of permeability

- \(\sigma_{1}\), \(\sigma_{2}\)
Vertical stress on the bottom of Region I and vertical stress on the bottom of Region II, respectively

- \(\eta\)
Coefficient of average superimposed stress

- \(n\)
Stress concentration ratio

- \(a\), \(b\), \(c\), \(u\), \(v\), \(s\)
Variations used in design method

## Notes

### Acknowledgements

The authors appreciate the financial support provided by the Natural Science Foundation of China (NSFC) (Grant Nos. 51508408, 41772281) and by the Fundamental Research Funds for the Central Universities (Grant No. 22120180106) for this research.

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