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Liquefaction Mitigation Using Stone Columns with Non-Darcy Flow Theory

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Abstract

One effective technique for mitigating the earthquake-induced liquefaction potential is the installation of stone columns. The permeability coefficients of stone columns are high enough to cause a high seepage velocity or expedited drainage. Under such conditions, the fluid flow law in porous media is not linear. Nevertheless, this nonlinear behavior in stone columns has not been evaluated in dynamic numerical analyses. This study proposes a dynamic finite element method that integrates nonlinear fluid flow law to evaluate the response of liquefiable ground improved by stone columns during seismic events. The impact of non-Darcy flow on the excess pore pressure and stress path compared to conventional Darcy law has been investigated numerically in stone columns. Furthermore, the effects of different permeability coefficients and stone column depths have been studied under near and far field strong ground motions. The results indicate that the non-Darcy flow increases the excess pore water pressure as high as 100% in comparison to the Darcy flow.

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Data Availability

The numerical results that support the findings of this study are available from the corresponding author, R. Taslimian, upon reasonable request.

Abbreviations

SC:

Stone column

EPP:

Excess pore pressure

NF:

Near field

FF:

Far field

PGA:

Peak ground acceleration

PPI:

Pore pressure increment

\(PP_{D}\) :

Pore pressure (PP) using Darcy flow

\(PP_{ND}\) :

Pore pressure (PP) using non-Darcy flow

S:

Non-Darcy coefficient

\(\dot{w}\) :

Average relative velocity of fluid

\(\nabla p\) :

Pressure gradient resulting from fluid flow

\(\rho_{f}\) :

Density of pore fluid

g:

Gravitational acceleration

\(k\) :

Coefficient of permeability

\(n\) :

Porosity of porous media

\(D_{50}\) :

Average diameter of grains

\(k_{ji}\) :

Permeability tensor

\(\delta_{ji}\) :

Kronecker delta

\(p\) :

Pore fluid pressure

\(N_{ }^{u}\) :

Shape functions for solid phase

\(N_{ }^{w}\) :

Shape functions for fluid phase

B:

Strain matrix

\(D_{e}\) :

Elastic constitutive matrix

\(C\) :

Artificial damping matrix or Rayleigh damping applied to the solid phase

\(f_{b}\) :

Body forces on soil mixture

\(f_{b}^{\prime}\) :

Body forces on fluid

\(f_{\sigma }\) :

External stresses

\(f_{p}\) :

External pressures

\(i\) :

Hydraulic gradient

\(p_{1}\) :

Actual perimeter of SC

D:

SC diameter

\(p_{2}\) :

Perimeter of simulated plane strip

L:

Length of equivalent plain strip or spacing of SCs

\(k_{eq}\) :

Equivalent permeability

\(T\) :

Time period

Dr :

Relative density

\(\mathop P_{0}^{\prime }\) :

Initial mean effective stress

\(\mathop p^{\prime }\) :

Mean effective stress

\(q\) :

Deviatoric stress

\({\mathbb{M}}\) :

Mass matrix

\({\mathbb{C}}\) :

Damping matrix

\({\mathbb{f}}\) :

External load vector

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Acknowledgements

The authors would like to acknowledge the assistance provided by Ms. Parisa Delalat during this research. Moreover, they gratefully acknowledge the contributions of Professor Andrew H.C. Chan for providing the computer program (DIANA-SWANDYNE II—GLADYS-2E) and for the invaluable guidance.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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  1. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Rohollah Taslimian

  2. Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran

    Ali Noorzad

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Taslimian, R., Noorzad, A. Liquefaction Mitigation Using Stone Columns with Non-Darcy Flow Theory. Geotech Geol Eng (2024). https://doi.org/10.1007/s10706-024-02785-6

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