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Nonlinear Analytical Modeling of Vertical Drain-Installed Soft Soil Considering a Varied Discharge Capacity

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Abstract

Discharge capacity is one of the important factors affecting the consolidation behavior of vertical drains (VDs). Both previous experimental tests and field behavior indicated that the discharge capacity of VDs usually decreased with an increase in effective stress. The aim of this study is to develop a nonlinear analytical solution for consolidation analysis of VD-installed soft deposits considering a reduction of discharge capacity, in which a nonlinear distribution of VD’s discharge capacity with depth is adopted. To verify this work, the proposed solution is compared with previous solutions. The analyzed results show that at a given time and depth, the consolidation rate in the case of discharge capacity with a nonlinear distribution is lower than that of a linear and constant distribution. The proposed solution is then applied to a real embankment on the VD-installed thick soft ground in Busan New Port. It is shown that the proposed solution using the nonlinear distribution of VD discharge capacity provides a good agreement with the field data.

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Abbreviations

A, A 1, A 2 :

Constants

C c :

Compression index

Ch :

Coefficient of horizontal consolidation (m2/s)

\(\bar{C}_{h}\) :

Average coefficient of horizontal consolidation (m2/s)

d e :

Diameter of unit cell (m)

d s :

Diameter of the smear zone (m)

d w :

Diameter of the drain (m)

e :

Void ratio

e o :

Initial void ratio

H :

Thickness of soft clay layer (m)

H 1 and H 2 :

Thickness of soft clay layer (m)

k h :

Coefficient of permeability in radial direction (m/s)

\(\bar{k}_{h}\) :

Average 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)

m v :

Coefficient of volume compressibility (MPa−1)

n :

Drain spacing ratio, (\(n = \frac{{r_{e} }}{{r_{w} }}\))

q r :

Water flow in unit cell

q w :

Discharge capacity of drain (m3/year)

q wo :

Initial value of qw (m3/year)

q wz :

Value of qw at depth z (m3/year)

r :

Radius (m)

r e :

Radius of the unit cell

r s :

Radius of the smear zone

r w :

Radius of the drain

s :

Smear ratio (\(s = \frac{{d_{s} }}{{d_{w} }}\))

T h :

Time factor in horizontal direction (dimensionless)

u :

Excess pore water pressure (kPa)

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

Average excess pore water pressure in unit cell (kPa)

\(u_{o}\) :

Initial excess pore water pressure (kPa)

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

Average excess pore water pressure at drain (kPa)

U r :

Degree of radial consolidation (%)

z :

Depth (m)

V :

Volume of the soil mass (m3)

\(\varepsilon_{v}\) :

Vertical strain at any depth

\(\gamma_{sat}\) :

Unit weight of saturated soil (kPa/m3)

\(\gamma_{w}\) :

Unit weight of water (kPa/m3)

\(\sigma\) :

Total stress (kPa)

\(\mu\) :

Factor used considering effects of smear zone and well resistance

\(\bar{\mu }\) :

Average value of \(\mu\) with depth

\(\bar{\mu }_{H}\) :

Value of \(\bar{\mu }\) in Hansbo’s solution

\(\bar{\mu }_{D}\) :

Value of \(\bar{\mu }\) in Deng et al. (2013) solution

References

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

    Google Scholar 

  • Bo MW (2004) Discharge capacity of prefabricated vertical drain and their field measurements. Geotext Geomembr 22:37–48

    Article  Google Scholar 

  • Bo MW, Arulrajah A, Nikraz H (2007) Preloading and prefabricated vertical drains design for foreshore land reclamation projects: a case study. Ground Improv 11(2):67–76

    Article  Google Scholar 

  • Bo MW, Arulrajah A, Horpibulsuk S, Chinkulkijniwat A, Leong M (2016) Laboratory measurements of factors affecting discharge capacity of prefabricated vertical drain materials. Soils Found 56(1):129–137

    Article  Google Scholar 

  • Busan Port Authority (2016) Construction design report of west container terminal phase 2–5, Busan (in Korean)

  • Chai JC, Miura N (1999) Investigation of factors affecting vertical drain behavior. J Geotech Geoenviron Eng ASCE 125(3):216–226

    Article  Google Scholar 

  • Chai JC, Miura N, Sakajo S, Bergado DT (1995) Behavior of vertical drain installed subsoil under embankment loading. Soils Found Tokyo 35(4):49–61

    Article  Google Scholar 

  • Chai JC, Shen SL, Miura N, Bergado DT (2001) Simple method of modeling VD installed subsoil. J Geotech Geoenviron Eng ASCE 127(11):965–972

    Article  Google Scholar 

  • Chai J-C, Miura N, Nomura T (2004) Effect of hydraulic radius on long-term discharge capacity of geosynthetics drains. J Geotext Geomembr 22:3–16

    Article  Google Scholar 

  • Chu J, Bo MW, Choa V (2006) Improvement of ultra-soft soil using prefabricated vertical drains. Geotext Geomembr 24:339–348

    Article  Google Scholar 

  • Chung SG, Kweon HJ, Jang WY (2014) Observational method for field performance of prefabricated vertical drains. Geotext Geomembr 42(4):405–416

    Article  Google Scholar 

  • Deng YB, Xie KH, Lu MM, Tao HB, Liu GB (2013) Consolidation by prefabricated vertical drains considering the time dependent well resistance. Geotext Geomembr 36:20–26

    Article  Google Scholar 

  • 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 

  • Hansbo S (1981) Consolidation of fine-grained soils by prefabricated drains. In: AA Balkema (ed)10th ICSMFE, Anonymous. Rotterdam-Boston, pp 677–682

  • Hansbo S (1983) Discussion. In: Proceedings of the 8th European conference on soil mechanics and foundation engineering, Helsinki, Vol. 3, Spec. Session 2, pp 1148–1149

  • Hird CC, Pyrah IC, Russell D (1992) Finite element modelling of vertical drains beneath embankments on soft ground. Géotechnique 42(3):499–511

    Article  Google Scholar 

  • Hyundai Engineering and Construction (2018) Report on survey management of Busan New Port Western container terminal (Phase 2–5) extension construction, Busan (in Korean)

  • Indraratna B, Redana IW (1997) Plane train modeling of smear effects associated with vertical drains. J Geotech Geoenviron Eng ASCE 123(5):474–478

    Article  Google Scholar 

  • Indraratna B, Redana IW (2000) Numerical modeling of vertical drains with smear and well resistance installed in soft clay. Can Geotech 37:132–145

    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 

  • Jang Y-S, Kim B, Lee J-W (2015) Evaluation of discharge capacity of geosynthetic drains for potential use in tunnels. Geotext Geomembr 43(3):228–239

    Article  Google Scholar 

  • Kim YT, Lee SR (1997) An equivalent model and back-analysis technique for modelling in situ consolidation behavior of drainage-installed soft deposits. Comput Geotech 20(2):125–142

    Article  Google Scholar 

  • Kim R, Hong SJ, Lee MJ, Lee W (2011) Time dependent well resistance factor of VD. Mar Georesour Geotechnol 29(2):131–144

    Article  Google Scholar 

  • Kim YT, Nguyen BP, Yun DH (2018a) Effect of artesian pressure on consolidation behavior of drainage-installed marine clay deposit. ASCE’s J Mater Civ 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(4):1183–1202

    Article  Google Scholar 

  • Lam LG, Bergado DTH (2015) VD improvement of soft Bangkok clay with and without vacuum preloading using analytical and numerical analyses. Geotext Geomembr 43(6):547–557

    Article  Google Scholar 

  • Li AL, Rowe RK (2001) Combined effects of reinforcement and prefabricated vertical drains on embankment performance. Can Geotech J 38(1):1266–1282

    Article  Google Scholar 

  • Miura N, Chai JC (2000) Discharge capacity of prefabricated vertical drains confined in clay. Geosynth Int 7(2):119–135

    Article  Google Scholar 

  • Nguyen TT, Indraratna B (2016) Hydraulic behaviour of parallel fibres under longitudinal flow: a numerical treatment. Can Geotech J 53(7):1081–1092

    Article  Google Scholar 

  • Nguyen TT, Indraratna B (2017) Experimental and numerical investigations into hydraulic behaviour of coir fibre drain”. Canadian Geotech J. https://doi.org/10.1139/cgj-2016-0182

    Article  Google Scholar 

  • Nguyen B-P, Kim YT (2019a) An analytical solution for consolidation of VD-installed deposit considering nonlinear distribution of hydraulic conductivity and compressibility. Eng Comput. https://doi.org/10.1108/EC-04-2018-0196

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nguyen B-P, Yun D-H, Kim Y-T (2018) An equivalent plane strain model of VD-installed soft deposit. Comput Geotech 103:32–42

    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 123:103602

    Article  Google Scholar 

  • Rixne JJ, Kraemer SR, Smith AD (1986) ‘Prefabricated vertical drains.’ Engrg Guidelines, FWHA/RD-86/168, vol I, Federal Highway Administration, Washington, D.C

  • Rowe RK, Taechakumthorn C (2008) Combined effect of VDs and reinforcement on embankments over rate-sensitive soils. Geotext Geomembr 26:239–249

    Article  Google Scholar 

  • Sekiguchi H, Shibata T, Fujimoto A, Yamaguchi H (1986) A macro-element approach to analyzing the plane strain behavior of soft foundation with vertical drains. In: Proceedings of the 31st symposium of the Japanese geochemical society, pp 111–116 (in Japanese)

  • Sengul T, Edil T, Ozaydin K (2016) Laboratory determination of smear and transition zones due to prefabricated vertical drain installation. Mar Georesour Geotechnol 35(7):895–904

    Article  Google Scholar 

  • Shen SL, Chai JC, Hong ZS, Cai FX (2005) Analysis of field performance of embankments on soft clay deposit with and without VD-improvement. Geotext Geomembr 23:463–485

    Article  Google Scholar 

  • Suzuki K, Yasuhara K (2007) Increase in undrained shear strength of clay with respect to rate of consolidation. Soils Found 47(2):303–318

    Article  Google Scholar 

  • Tran-Nguyen HH, Edil TB, Schneider JA (2010) Effect of deformation of prefabricated vertical drains on discharge capacity. Geosynth Int 17(6):431–442

    Article  Google Scholar 

  • Tripathi KK, Nagesha MS (2010) Discharge capacity requirement of prefabricated vertical drains. Geotext Geomembr 28:128–132

    Article  Google Scholar 

  • Zhu G, Yin J-H (2005) Solution charts for the consolidation of double soil layers. Can Geotech J 42(3):949–956

    Article  Google Scholar 

Download references

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, 12 Nguyen Van Bao, Go Vap, Ho Chi Minh City, 700000, Vietnam

    Ba-Phu Nguyen

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Nguyen, BP. Nonlinear Analytical Modeling of Vertical Drain-Installed Soft Soil Considering a Varied Discharge Capacity. Geotech Geol Eng 39, 119–134 (2021). https://doi.org/10.1007/s10706-020-01477-1

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