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Analytical model for consolidation and bearing capacity of soft soil stabilized by combined PVD-deep cement mixing columns

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Abstract

Soil improvement can be enhanced significantly when combining the two well-known methods, i.e., prefabricated vertical drains (PVDs) and deep cement mixing (DCM) columns. While this approach has been proved to be effective through recent site studies, there is a lack of rigorous theoretical methods to model the coupled effects of PVDs and DCM columns on soil behavior. This paper hence aims to propose a novel analytical solution for consolidation of soft ground stabilized by the combined PVDs-DCM columns. The solution is developed with radial drainage, in which the effects of smear zone, well resistance, and nonlinear behavior of permeability and compressibility during the consolidation process are simultaneously considered. The proposed solution is verified by comparing itself with field data and previous theoretical solutions. The results indicate promising outcomes from the proposed model considering its good agreements with field data and other solutions. Subsequently, key parameters affecting the performance of composite PVDs-DCM foundation are investigated using the proposed solution. The results show that the effects of the compression modulus and cross-section area of DCM columns on consolidation rate are prevalent over their hydraulic conductivity. The discharge capacity of PVDs significantly affects the short-term bearing capacity of the DCM columns. The study offers significant values to industry applications via the newly proposed model and parametric assessment.

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Data Availability

The data presented in the paper are presented in the main text. The results were understood from figures, tables which mentioned in this article.

Abbreviations

a s :

area improvement ratio (\({a}_{s}={A}_{col}\text{/}A\))

A :

area of influent zone (unit cell) (m)

A s :

area of soil in influent zone (unit cell) (m)

A col :

cross-section area of DCM column (m)

A DCM :

area of DCM zone in influent zone (m)

A w :

area of PVD in influent zone (m)

$$b=\frac{{r}_{e}}{{r}_{sm}}$$
C c :

compression index

c col :

is cohesion of column material

C k :

a constant used to reflect the decrease in permeability as the void ratio changes during consolidation

c u :

undrained shear strength of the clay

C r :

recompression index

D col :

diameter of DCM column

DCM:

deep cement mixing

$$d=\frac{{r}_{s}}{{r}_{D}}$$
d e :

diameter of unit cell (m)

d sm :

diameter of the smear zone (m)

d w :

diameter of the drain (m)

e o , e :

void ratio

e o :

initial void ratio

E s :

compression modulus of soil (kPa)

E col :

compression modulus of DCM column (kPa)

E w :

compression modulus of PVD (kPa)

F :

factor

FEM :

finite element method

$$f=\frac{{r}_{e}}{{r}_{D}}$$
H :

thickness of soft clay layer (m)

h 1 and h 2 :

thickness of upper and lower clay layer (m)

k col :

coefficient of permeability of DCM column (m/s)

k h :

coefficient of permeability in radial direction (m/s)

k s :

coefficient of permeability in smear zone (m/s)

k w :

coefficient of permeability of drain (m/s)

k wo :

initial value of kw (m/s)

n :

drain spacing ratio, (\(n=\frac{{r}_{e}}{{r}_{w}}\))

n s :

stress concentration factor, \({n}_{s}={\sigma }_{col}\text{/}{\sigma }_{s}\)

OCR :

overconsolidation ratio.

q r :

water flow in unit cell (m.3/s)

q w :

discharge capacity of drain (m.3/year)

r :

radius (m)

r e :

radius of the unit cell (m)

r sm :

radius of the smear zone (m)

r w :

radius of the drain (m)

r D :

radius of the DCM zone in unit cell (m)

S c :

final consolidation settlement (m).

s :

smear ratio (\(s=\frac{{d}_{sm}}{{d}_{w}}\))

PVD:

prefabricated vertical drain

P ( t) :

external load with time (kPa)

Q ult ,col :

ultimate bearing capacity of DCM column in short term (kN)

Q ult , col ( t ) :

ultimate bearing capacity of DCM column according to time (kN)

u :

excess pore water pressure (kPa)

\({\overline{u} }_{r}\) :

average excess pore water pressure in unit cell (kPa)

\({u}_{o}\) :

initial excess pore water pressure (kPa)

\({\overline{u} }_{w}\) :

average excess pore water pressure at drain (kPa)

\(\overline{U },{\overline{U} }_{1},{\overline{U} }_{2}\) :

degree of radial consolidation (%)

z :

depth (m)

$$\alpha :=\frac{{k}_{h}}{{k}_{sm}}$$
$$\beta :=\frac{{k}_{h}}{{k}_{col}}$$
\({\varepsilon }_{v}\) :

vertical strain at any depth

\({\gamma }_{sat}\) :

unit weight of saturated soil (kN/m.3)

\({\gamma }_{w}\) :

unit weight of water (kN/m.3)

\({\sigma }_{v}\) :

total stress (kPa)

\({\sigma }_{h}\) :

lateral pressure (kPa)

\({\sigma }_{vo}^{^{\prime}}\) :

initial vertical effective stress of soil (kPa)

\({\tilde{\sigma }}_{vo}^{^{\prime}}\) :

average value of initial vertical effective stress of composite foundation (kPa)

\({\tilde{\sigma }}_{s}^{^{\prime}}\),\({\sigma }_{v}^{^{\prime}}\) :

vertical effective stress of soil (kPa)

\({\tilde{\sigma }}_{vo}^{^{\prime}}\) :

average value of vertical effective stress of composite foundation (kPa)

\(\Delta {\sigma }_{v}\) :

total of external load (kPa)

$$\lambda :\text{ } = \frac{{E}_{s}}{\overline{E} }$$

References

  • Asaoka A (1978) Observational procedure for settlement prediction. Soils Found 18(4):87–101

    Article  Google Scholar 

  • Bergado DT, Anderson LR, Miura N, Balasubramaniam AS (1996) Soft ground improvement, in lowland and other environments. ASCE, New York, p 427p

    Google Scholar 

  • Chai J-C, Carter JP (2011) Deformation analysis in soft ground improvement. Springer, Netherlands, p 258

    Book  Google Scholar 

  • Chai J-C, Shen S-L, Miura N, Bergado D-T (2001) Simple method of modeling PVD improved subsoil. J Geotech Geoenviron Eng, ASCE 127(11):965–972

    Article  Google Scholar 

  • Chai J-C, Shrestha S, Hino T, Ding W-Q, Kamo Y, Carter J (2015) 2D and 3D analyses of an embankment on clay improved by soil–cement columns. Comput Geotech 68:28–37

    Article  Google Scholar 

  • Chai JC, Miura N, Kirekawa T, Hino T (2009) Settlement prediction for soft ground improved by columns. Proc Inst Civil Eng–Ground Improv 163(2):109–119

  • Deng YB, Liu GB, Lu MM, Xie KH (2014) Consolidation behavior of soft deposits considering the variation of prefabricated vertical drain discharge capacity. Comput Geotech 62:310–316

    Article  Google Scholar 

  • Feng W-Q, Yin J-H (2017) A new simplified Hypothesis B method for calculating the consolidation settlement of ground improved by vertical drains. Int J Numer Anal Meth Geomech 42(2):295–311

    Article  Google Scholar 

  • Guo W et al (2018) An observational method for consolidation analysis of the PVD-improved subsoil. Geotext Geomembr 46(5):625–633

    Article  Google Scholar 

  • Hansbo S (1981) Consolidation of fine-grained soils by prefabricated drains. Proc, 10th Int Conf Soil Mech Found Eng 3:677–682

    Google Scholar 

  • Horpibulsuk S, Chinkulkijniwat A, Cholphatsorn A, Suebsuk J, Liu MD (2012) Consolidation behavior of soil–cement column improved ground. Comput Geotech 43:37–50

    Article  Google Scholar 

  • Hu Y-Y, Zhou W-H, Cai Y-Q (2014) Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading. Can Geotech J 51(2):144–157

    Article  Google Scholar 

  • Indraratna B, Zhong R, Fox P, Rujikiatkamjorn C (2017) Large strain vacuum-assisted consolidation with non-darcian radial flow incorporating varying permeability and compressibility. J Geotech Geoenviron Eng, ASCE 143(1):04016088

    Article  Google Scholar 

  • Jiang Y, Han J, Zheng G (2013) Numerical analysis of consolidation of soft soils fully-penetrated by deep-mixed columns. KSCE J Civ Eng 17(1):96–105

    Article  Google Scholar 

  • Kim YT, Nguyen BP, Yun DH (2018) Effect of artesian pressure on consolidation behavior of drainage-installed marine clay deposit. ASCE’s J Mater Civil Eng 30(8):04018156

    Article  Google Scholar 

  • Kim YT, Nguyen BP, Yun DH (2018b) Analysis of consolidation behavior of PVD-improved ground considering a varied discharge capacity. Eng Comput 35(3):1183–1202

    Article  Google Scholar 

  • Kivelo M (1988) Stabilization of embankments on soft soil with lime/cement columns. Doctoral Thesis, Royal Institute of Technology

  • Lai YP, Duangchan T, Lorenzo G, Bergado DT (2006) Full-scale reinforced embankment on deep jet mixing improved ground. Proc Inst Civ Eng Ground Improv 10(4):153–164

    Article  Google Scholar 

  • Leo CJ (2004) Equal strain consolidation by vertical drains. J Geotech Geoenviron Eng 130(3):316–327

    Article  Google Scholar 

  • Li P, Li L, Lu M (2020) Semi-analytical solution to one-dimensional consolidation of viscoelastic saturated soils subject to an inner point sink. Eng Comput 37(5):1787–1804

    Article  Google Scholar 

  • Liu K-W, Rowe RK (2015) Numerical modelling of prefabricated vertical drains and surcharge on reinforced floating column-supported embankment behaviour. Geotext Geomembr 43:493–505

    Article  Google Scholar 

  • Liu SY, Han J, Zhang DW, Hong ZSA (2008) Combined DJM-PVD method for soft ground improvement. Geosynth Int 15(1):43–54

    Article  Google Scholar 

  • Lorenzo GA, Bergado DT (2003) New consolidation equation for soil cement pile improved ground. Can Geotech J 40(2):265–275

    Article  Google Scholar 

  • Lu MM, Jing HW, Zhou A, Xie KH (2018) Analytical models for consolidation of combined composite ground improved by impervious columns and vertical drains. Int J Numer Anal Meth Geomech 2018:1–18

    Google Scholar 

  • Nguyen B-P (2021) Nonlinear analytical modeling of vertical drain-installed soft soil considering a varied discharge capacity. Geotech Geol Eng. https://doi.org/10.1007/s10706-020-01477-1

    Article  Google Scholar 

  • Nguyen TT, Indraratna B (2019) Micro-CT scanning to examine soil clogging behavior of natural fiber drains. ASCE J Geotech Geoenviron Eng 145(9):04019037

    Article  Google Scholar 

  • Nguyen B-P, Kim Y-T (2019a) An analytical solution for consolidation of PVD-installed deposit considering nonlinear distribution of hydraulic conductivity and compressibility. Eng Comput 36(2):707–730

    Article  Google Scholar 

  • Nguyen B-P, Kim Y-T (2019b) Radial consolidation of PVD-installed normally consolidated soil with discharge capacity reduction using large-strain theory. Geotext Geomembr 47(2):243–254

    Article  Google Scholar 

  • Nguyen B-P, Do T-H, Kim Y-T (2020) Large-strain analysis of vertical drain-improved soft deposit consolidation considering smear zone, well resistance, and creep effects. Comput Geotech 123C:103602

    Article  Google Scholar 

  • Nguyen B-P, Pradhan AMS, Nguyen TH, Doan N-P, Nguyen V-Q, Huynh T-C (2021) Large-strain consolidation analysis of PVD-installed soft soil considering the discharge capacity variation according to depth and time. Eng Comput 38(4):1652–1676

    Article  Google Scholar 

  • Nguyen TT, Indraratna B (2021) Rail track degradation under mud pumping evaluated through site and laboratory investigations. Int J Rail Transp 1–28. https://doi.org/10.1080/23248378.2021.1878947

  • Nguyen TN, Shukla S, Nguyen D, Lam L, H-Dang P, Nguyen P (2019) A new discrete method for solution to consolidation problem of ground with vertical drains subjected to surcharge and vacuum loadings. Eng Comput 37(4):1213–1236

  • Nguyen B-P, Nguyen TT, Nguyen THY, Tran TD (2022) Performance of composite PVD–SC column foundation under embankment through plane-strain numerical analysis. Int J Geomech 22(9):04022155–1–15.

  • Ni P, Mangalathu S, Mei G, Zhao Y (2017) Permeable piles: an alternative to improve the performance of driven piles. Comput Geotech 84:78–87

    Article  Google Scholar 

  • Pongsivasathit S, Chai JC, Ding WQ (2013) Consolidation settlement of floating-column-improved soft clayey deposit. Proc Inst Civil Eng-Ground Improv 166(1):44–58

    Article  Google Scholar 

  • Shi M, Pang F, Zhang B (2005) Behaviors of pile-supported embankments in highway engineering. J Southeast Univ (english Edition) 21(4):495–499

    Google Scholar 

  • Sun Y, Cheng J, Li Y, Chen Q, Zhang W, Shao G (2020) Model test of the combined subgrade treatment by hydraulic sand fills and soil-cement mixing piles. Bull Eng Geol Env 79:2907–2918. https://doi.org/10.1007/s10064-020-01735-9

    Article  Google Scholar 

  • Tavenas F, Tremblay M, Larouche G, Leroieil S (1986) In-situ measurement of permeability in soft clays. ASCE Spec Conf Use in-Situ Tests Geotech Eng, NewYork 1986:1034–1048

    Google Scholar 

  • Tran-Nguyen H-H, Luong BT, Nguyen KDT (2022) Investigation of the hydraulic conductivity of soilcrete specimens made by soft clays and medium clays mixed with cement. Geotech Geol Eng. https://doi.org/10.1007/s10706-022-02323-2

    Article  Google Scholar 

  • Wang XS, Jiao JJ (2004) Analysis of soil consolidation by vertical drains with double porosity model. Int J Numer Anal Meth Geomech 28(14):1385–1400

    Article  Google Scholar 

  • Wang ZF, Shen SL, Yin ZY, Xu Y-S (2015) Rapid field evaluation of the strength of cement-stabilized clayey soil. Bull Eng Geol Env 74:991–999. https://doi.org/10.1007/s10064-014-0643-3

    Article  Google Scholar 

  • Wijerathna M, Liyanapathirana DS, Leo C (2016) Consolidation behaviour of deep cement mixed column improved ground during breakage of soil-cement structure. Aust Geomech J 51(2):35–42

    Google Scholar 

  • Wu H-N, Shen S-L, Ma L, Yin Z-Y, Horpibulsuk S (2015) Evaluation of the strength increase of marine clay under staged embankment loading: a case study. Mar Georesour Geotechnol 33(6):532–541

    Article  Google Scholar 

  • Xu C, Ye GB, Jiang ZS, Zhou QZ (2006) Research on mechanism of combined improvement of soft soils based on field monitoring. Chin J Geotech Eng 28(7):918–921 (in Chinese)

    Google Scholar 

  • Xu BH, Indraratna B, Rujikiatkamjorn C et al (2022) Nonlinear consolidation analysis of multilayered soil with coupled vertical-radial drainage using the spectral method. Acta Geotech. https://doi.org/10.1007/s11440-022-01679-2

    Article  Google Scholar 

  • Ye GB, Zhang Z, Xing HF, Huang MS, Xu C (2012) Consolidation of a composite foundation with soil-cement columns and prefabricated vertical drains. Bull Eng Geol Env 71(1):87–98

    Article  Google Scholar 

  • Ye GB, Zhang Z, Han J, Xing HF, Huang MS, Xiang PL (2013) Performance evaluation of an embankment on soft soil improved by deep mixed columns and prefabricated vertical drains. J Perform Constr Facil (ASCE) 27(5):614–623

    Article  Google Scholar 

  • Ye G, Shu H, Zhang Z, Kang S, Zhang S, Wang Q (2021) Solidification and field assessment of soft soil stabilized by a waste-based binder using deep mixing method. Bull Eng Geol Env 80:5061–5074. https://doi.org/10.1007/s10064-021-02193-7

    Article  Google Scholar 

  • Yoshikuni H, Nakanodo H (1974) Consolidation of soils by vertical drains with finite permeability. Jpn Soc Soil Mech Found Eng 14(2):35–46

    Article  Google Scholar 

  • Yuan W, Zhang W, Dai B, Wang Y (2019) Application of the particle finite element method for large deformation consolidation analysis. Eng Comput 36(9):3138–3163

    Article  Google Scholar 

  • Zhang DW, Liu SY, Han WJ, Du GY (2013) A combined dry jet mixing-prefabricated vertical drain method for soft ground improvement: a case study. Mar Georesour Geotechnol 31:332–347

    Article  Google Scholar 

  • Zhang Z, Ye G, Xing H (2015a) Consolidation analysis of soft soil improved with short deep mixed columns and long prefabricated vertical drains (PVDs). Geosynth Int 22(5):1–14

    Article  Google Scholar 

  • Zhang N, Shen S-L, Wu H-N, Chai J-C, Xu Y-S, Yin Z-Y (2015b) Evaluation of effect of basal reinforcement under embankments loading on soft marine deposits. Geotext Geomembr 43(6):506–514

    Article  Google Scholar 

  • Zhang DW, Liu SY, Hong ZS (2006) Consolidation calculating method of soft ground improved by DJM‐PVD combined method. In: Ground Modification and Seismic Mitigation. Proc GeoShanghai Int Conf [C]. Shanghai, China: ASCE Geotech Spec Publ (GSP 152), 29–36

  • Zhou W-H, Lok T-H, Zhao L-S, Mei G-X, Li X-B (2017) Analytical solutions to the axisymmetric consolidation of a multi-layer soil system under surcharge combined with vacuum preloading. Geotext Geomembr 45(5):487–498

    Article  Google Scholar 

  • Zhu G, Yin JH (2004) Consolidation analysis of soil with vertical and horizontal drainage under ramp loading considering smear effects. Geotext Geomembr 22:63–74

    Article  Google Scholar 

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Acknowledgements

The support of this research by the Industrial University of Ho Chi Minh City is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Civil Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City, 700000, Vietnam

    Ba-Phu Nguyen

  2. School of Civil and Environmental Engineering, ARC-DECRA/UTS Chancellor’s Fellow, University of Technology Sydney, Ultimo, Australia

    Thanh T. Nguyen

  3. Smart Computing in Civil Engineering Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Tan Nguyen

  4. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, 700000, Vietnam

    Tan Nguyen

  5. School of Civil Engineering, Tianjin University, Tianjin, China

    Wei Guo

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  1. Ba-Phu Nguyen
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Nguyen, BP., Nguyen, T.T., Nguyen, T. et al. Analytical model for consolidation and bearing capacity of soft soil stabilized by combined PVD-deep cement mixing columns. Bull Eng Geol Environ 82, 286 (2023). https://doi.org/10.1007/s10064-023-03287-0

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