Consolidation of unsaturated composite ground reinforced by permeable columns

Abstract In this paper, the governing equations and semi-analytical solutions are proposed to investigate the consolidation behavior of unsaturated composite ground with the permeable columns. Based on the stress and strain equilibrium conditions of composite ground and the strain–stress relations of unsaturated soils under the axisymmetric condition, a set of the basic equations are proposed for describing the strain–stress relations of soil element, air and water phases of unsaturated soils in the composite ground. Then, two consolidation equations for air and water phases are derived considering the continuity of pore volume change, and flow laws for air and water phases under the axisymmetric condition. Correspondingly, the semi-analytical solutions of the consolidation equations are proposed by using the Laplace and finite Hankel transforms. The proposed governing equations as well as the semi-analytical solutions are verified by checking against the existing ones for a special case in the literature. Finally, a parametric study is performed to investigate the consolidation behavior with different parameters for the permeable columns and surrounding unsaturated soils.

[1]  Yong-wei Tan,et al.  Semi-analytical solution to one-dimensional consolidation in unsaturated soils , 2008 .

[2]  De’an Sun,et al.  A semi-analytical solution to consolidation of unsaturated soils with the free drainage well , 2010 .

[3]  Buddhima Indraratna,et al.  Numerical modeling of vertical drains with smear and well resistance installed in soft clay , 2000 .

[4]  Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with symmetric semi-permeable drainage boundary , 2017 .

[5]  K. Deb,et al.  Rate of consolidation of stone column-improved ground considering change in permeability and compressibility during consolidation , 2017 .

[6]  H. Khabbaz,et al.  Analytical solution to axisymmetric consolidation in unsaturated soils with linearly depth-dependent initial conditions , 2016 .

[7]  Behzad Fatahi,et al.  Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading , 2015 .

[8]  Semi-analytical solutions to two-dimensional plane strain consolidation for unsaturated soil , 2018, Computers and Geotechnics.

[9]  Semi-Analytical Solution to One-Dimensional Consolidation for Unsaturated Soils with Exponentially Time-Growing Drainage Boundary Conditions , 2018 .

[10]  N. P. Balaam,et al.  Analysis of rigid rafts supported by granular piles , 1981 .

[11]  Mengmeng Lu,et al.  Analytical models for consolidation of combined composite ground improved by impervious columns and vertical drains , 2018 .

[12]  K. Terzaghi.  Theoretical Soil Mechanics , 1943 .

[13]  K. Deb,et al.  Rate of Consolidation of Stone Column–Improved Ground Considering Variable Permeability and Compressibility in Smear Zone , 2017 .

[14]  K. Xie,et al.  Consolidation Analysis of Composite Ground Improved by Granular Columns Considering Variation of Permeability Coefficient of Soil , 2006 .

[15]  Delwyn G. Fredlund,et al.  Constitutive relations for volume change in unsaturated soils , 1976 .

[16]  Delwyn G. Fredlund,et al.  One-dimensional consolidation theory: unsaturated soils , 1979 .

[17]  Jie Han,et al.  A Theoretical Solution for Consolidation Rates of Stone Column-Reinforced Foundations Accounting for Smear and Well Resistance Effects , 2002 .

[18]  De’an Sun,et al.  Analytical solution to one-dimensional consolidation in unsaturated soils under loading varying exponentially with time , 2010 .

[19]  Laing Barden,et al.  Consolidation of Compacted and Unsaturated Clays , 1965 .

[20]  Jie Han,et al.  SIMPLIFIED METHOD FOR CONSOLIDATION RATE OF STONE COLUMN REINFORCED FOUNDATIONS , 2001 .

[21]  Donovan Mujah,et al.  Numerical Modelling of the Consolidation Behavior of Peat Soil Improved by Sand Columns , 2016, Soil Mechanics and Foundation Engineering.

[22]  H. Khabbaz,et al.  Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method , 2014 .

[23]  De’an Sun,et al.  Analytical solution to one-dimensional consolidation in unsaturated soils , 2008 .

[24]  Kang-He Xie,et al.  Equal strain consolidation for stone columns reinforced foundation , 2009 .

[25]  G. Mei,et al.  Analytical Solutions to the Axisymmetrical Consolidation of Unsaturated Soils , 2018 .

[26]  Behzad Fatahi,et al.  A closed form analytical solution for two‐dimensional plane strain consolidation of unsaturated soil stratum , 2015 .

[27]  Eduardo Alonso,et al.  Consolidation of unsaturated soils including swelling and collapse behaviour , 1980 .

[28]  Exact solutions for one‐dimensional consolidation of single‐layer unsaturated soil , 2012 .

[29]  F. Durbin,et al.  Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method , 1974, Comput. J..

[30]  B. Fatahi,et al.  Analytical solution to axisymmetric consolidation of unsaturated soil stratum under equal strain condition incorporating smear effects , 2018, International Journal for Numerical and Analytical Methods in Geomechanics.

[31]  Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary , 2017 .

[32]  Wan‐Huan Zhou,et al.  One-Dimensional Consolidation of Unsaturated Soil Subjected to Time-Dependent Loading with Various Initial and Boundary Conditions , 2014 .

[33]  S. Hansbo.  Consolidation of fine-grained soils by prefabricated drains , 1981 .

[34]  Yongfu Xu,et al.  Semi‐analytical solutions of two‐dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary , 2019, International Journal for Numerical and Analytical Methods in Geomechanics.

[35]  De’an Sun,et al.  Hydromechanical behavior of unsaturated soil with different initial densities over a wide suction range , 2019 .

[36]  Antonio Gens,et al.  Interpretation of unsaturated soil behaviour in the stress – Saturation space, I: Volume change and water retention behaviour , 2012 .

[37]  Antonio Gens,et al.  Interpretation of unsaturated soil behaviour in the stress–saturation space , 2012 .

[38]  B. Fatahi,et al.  Axisymmetric Consolidation in Unsaturated Soil Deposit Subjected to Time-Dependent Loadings , 2017 .

[39]  Guocai Wang,et al.  Consolidation of Soft Clay Foundations Reinforced by Stone Columns under Time-Dependent Loadings , 2009 .

[40]  A. Garg,et al.  Generalized Analytical Solution for the Consolidation of Unsaturated Soil under Partially Permeable Boundary Conditions , 2017 .

[41]  A simple analytical solution to one‐dimensional consolidation for unsaturated soils , 2014 .

[42]  R D Barksdale,et al.  DESIGN AND CONSTRUCTION OF STONE COLUMNS VOLUME I , 1983 .

[43]  Ping Cao,et al.  Numerical Analysis of Fiber-Reinforced Soils Based on the Equivalent Additional Stress Concept , 2019, International Journal of Geomechanics.

[44]  Behzad Fatahi,et al.  Analytical solution for free strain consolidation of stone column-reinforced soft ground considering spatial variation of total stress and drain resistance , 2020 .

[45]  Yongfu Xu,et al.  Semi-analytical solutions to two-dimensional plane strain consolidation for unsaturated soils under time-dependent loading , 2019, Computers and Geotechnics.

[46]  Kenny S. Crump,et al.  Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation , 1976, J. ACM.

[47]  K. Xie,et al.  Consolidation theory for a composite foundation considering radial and vertical flows within the column and the variation of soil permeability within the disturbed soil zone. , 2010 .

[48]  I. N. Sneddon.  The use of integral transforms , 1972 .

[49]  Scott W. Sloan,et al.  Nonlinear consolidation of vertical drains with coupled radial-vertical flow considering well resistance , 2015 .

[50]  Behzad Fatahi,et al.  One-Dimensional Consolidation Analysis of Unsaturated Soils Subjected to Time-Dependent Loading , 2016 .