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Numerical investigation on zone of improvement for dynamic compaction of sandy ground with high groundwater table


This paper presents a numerical study of dynamic compaction (DC) on ground improvement in foundation with a high groundwater table, based on a dynamic fluid–solid coupled finite element method with a cap model. Firstly, an analysis of dry ground was carried out to evaluate the effective improvement range, with the proposal of a normalized formula capturing the improvement effect. Then, the parametric studies include the effect of groundwater table, the permeability coefficient, drop energy, and soil type have been carried out to not only find that the groundwater table has a dominant influence on soil improvement by DC but also clarify densification mechanisms of ground improvement by DC on the soil nearby groundwater table, which is through analyzing the contours of effective mean stress. Finally, a relative enhancement index, RD, based on a total of 52 calculations is derived to evaluate the depth of improvement below the groundwater table for different scenarios. These relationships provide a valuable reference for the evaluation of ground improvement by DC for a foundation with high groundwater table and the applicability of the proposed procedure is illustrated by comparing its prediction with three cases of DC in the field.

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Data availability

Data will be made available on reasonable request.


d :

Cohesion in p–q space


Effective mean stress

D″ and W″:

Volumetric hardening coefficients

η and κ :

Regression coefficients of Eq. 9

D r :

Relative density

p AP :

Atmospheric pressure

R :

Tamper radius

H :

Drop height

M :

Tamper mass

N :

Drop number

h :

Groundwater table

v :

Impact velocity

I r :

The relative degree of improvement

D r0 :

Initial relative density before DC

D r :

The increment of relative density


Dynamic compaction


The parameter that controls the shape of the cap

y max and x max :

The maximum depth and radius

y x max :

Depth of maximum radius

y max :

Maximum depth below crater level

y x max :

Depth of maximum radius below crater level

y cr :

Crater depth

d′ wat :

Depth of improvement corresponding to Ir for the foundation with high groundwater table

d′ dry :

Depth of improvement corresponding to Ir for dry soil

d wat :

Depth of improvement below groundwater table corresponding to Ir for the foundation with high groundwater table

d dry :

Depth of improvement below groundwater table corresponding to Ir for dry soil

x’ and y′:

Normalized depth and radius

x w :

Lateral extent at the groundwater table level


Elastic modulus

t :

Impact duration

v′ :

Poisson’s ratio

T :

Dimensionless time

R D = (d wat-h)/(d dry-h):

Normalized depth of improvement below the groundwater table

S :

Elastic constant


Constrained modulus

a 1 and b 1 :

Regression coefficients of Eq. 18

β :

Friction angle

Y 0, μ, and M :

Regression coefficients of Eq. 12


  1. Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J Acoust Soc Am 28(2):179–191

    MathSciNet  Article  Google Scholar 

  2. Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J Acoust Soc Am 28(2):168–178

    MathSciNet  Article  Google Scholar 

  3. Bo MW, Na YM, Arulrajah A, Chang MF (2009) Densification of granular soil by dynamic compaction. Proc Inst Civ Eng-Ground Improv 162(3):121–132

    Article  Google Scholar 

  4. Chen JW, Chen FC (2009) The effectiveness of dynamic compaction under various water levels. In: International conference on offshore mechanics and arctic engineering, vol 43475, pp 321-328

  5. Chen WF, Mizuno E (1990) Nonlinear analysis in soil mechanics: theory and implementation. Elsevier Science, Amsterdam, Netherland

    Google Scholar 

  6. Chow YK, Yong DM, Yong KY, Lee SL (1992) Dynamic compaction of loose sand deposits. Soils Found 32(4):93–106

    Article  Google Scholar 

  7. Chow YK, Yong DM, Yong KY, Lee SL (1992) Dynamic compaction analysis. J Geotech Eng 118(8):1141–1157

    Article  Google Scholar 

  8. Chow YK, Yong DM, Yong KY, Lee SL (1994) Dynamic compaction of loose granular soils: effect of print spacing. J Geotech Eng 120(7):1115–1133

    Article  Google Scholar 

  9. Feng TW, Chen KH, Su YT, Shi YC (2000) Laboratory investigation of efficiency of conical-based pounders for dynamic compaction. Géotechnique 50(6):667–674

    Article  Google Scholar 

  10. Feng SJ, Du FL, Chen HX, Mao JZ (2017) Centrifuge modeling of preloading consolidation and dynamic compaction in treating dredged soil. Eng Geol 226:161–171

    Article  Google Scholar 

  11. Feng SJ, Du FL, Shi ZM, Shui WH, Tan K (2015) Field study on the reinforcement of collapsible loess using dynamic compaction. Eng Geol 185:105–115

    Article  Google Scholar 

  12. Feng SJ, Shui WH, Gao LY, He LJ (2010) Field studies of the effectiveness of dynamic compaction in coastal reclamation areas. Bull Eng Geol Env 69(1):129–136

    Article  Google Scholar 

  13. Feng SJ, Shui WH, Tan K, Gao LY (2011) Field evaluation of dynamic compaction on granular deposits. J Perform Constr Facil 25(3):241–249

    Article  Google Scholar 

  14. Feng SJ, Tan K, Shui WH (2014) Dynamic compaction of ultra-high energy in combination with ground replacement in coastal reclamation areas. Mar Georesour Geotechnol 33(2):109–121

    Article  Google Scholar 

  15. Feng SJ, Tan K, Shui WH, Zhang Y (2013) Densification of desert sands by high energy dynamic compaction. Eng Geol 157:48–54

    Article  Google Scholar 

  16. Ghassemi A, Pak A, Shahir H (2009) Validity of Menard relation in dynamic compaction operations. Proc Inst Civ Eng-Ground Improvement 162(1):37–45

    Article  Google Scholar 

  17. Ghassemi A, Pak A, Shahir H (2010) Numerical study of the coupled hydro-mechanical effects in dynamic compaction of saturated granular soils. Comput Geotech 37(1–2):10–24

    Article  Google Scholar 

  18. Ghorbani J, Nazem M, Carter JP (2020) Dynamic compaction of clays: numerical study based on the mechanics of unsaturated soils. Int J Geomech 20(10):04020195

    Article  Google Scholar 

  19. Gu Q, Lee FH (2002) Ground response to dynamic compaction of dry sand. Géotechnique 52(7):481–493

    Article  Google Scholar 

  20. Han JT, Kim T, Cho W (2016) Centrifuge modeling of seismic response of normally consolidated deep silt deposit. Acta Geotech 11:71–81

    Article  Google Scholar 

  21. Helwany S (2007) Applied soil mechanics with ABAQUS applications. Wiley, Hoboken

    MATH  Book  Google Scholar 

  22. Jia M, Cheng J, Liu B, Ma G (2021) Model tests of the influence of ground water level on dynamic compaction. Bull Eng Geol Env 80(4):3065–3078

    Article  Google Scholar 

  23. Jia M, Liu B, Xue J et al (2021) Coupled three-dimensional discrete element–finite difference simulation of dynamic compaction. Acta Geotech 16:731–747

    Article  Google Scholar 

  24. Jia M, Liu B, Xue J, Ma G (2021) Coupled three-dimensional discrete element–finite difference simulation of dynamic compaction. Acta Geotech 16(3):731–747

    Article  Google Scholar 

  25. Jia M, Yang Y, Liu B, Wu S (2018) PFC/FLAC coupled simulation of dynamic compaction in granular soils. Granular Matter 20(4):1–15

    Article  Google Scholar 

  26. Jia M, Zhao T, Xie X, Chen X, Zhou J (2020) A novel experimental system for studying the sand liquefaction characteristics from macroscopic and microscopic points of view. Bull Eng Geol Env 79(4):2131–2139

    Article  Google Scholar 

  27. Kundu S, Viswanadham BVS (2020) Design and development of an in-flight actuator for modeling dynamic compaction in a geotechnical centrifuge. Geotech Test J 44(4)

  28. Lee FH, Gu Q (2004) Method for estimating dynamic compaction effect on sand. J Geotech Geoenviron Eng 130:139–152

    Article  Google Scholar 

  29. Lim YX (2017) Numerical study of cone penetration test in clays using Press-Replace Method. PhD Thesis, National University of Singapore

  30. Lim YX, Tan SA, Phoon KK (2019) Interpretation of horizontal permeability from piezocone dissipation tests in soft clays. Comput Geotech 107:189–200

    Article  Google Scholar 

  31. Liu J, Yuan J, Xiong H, Chen W (2008) Dynamic compaction treatment technology research of red clay soil embankment in southern mountains. J Cent South Univ Technol 15(2):50–57

    Article  Google Scholar 

  32. López-Querol S, Fernández-Merodo JA, Mira P, Pastor M (2008) Numerical modelling of dynamic consolidation on granular soils. Int J Numer Anal Meth Geomech 32(12):1431–1457

    MATH  Article  Google Scholar 

  33. Lukas RG (1995) Geotechnical engineering circular no. 1: dynamic compaction. FHWA-SA-95–037, Ground Engineering Consultants, Northbrook, Illinois, pp 13–15

  34. Mayne PW, Jones JJS, Dumas JC (1984) Ground response to dynamic compaction. J Geotech Eng 110(6):757–774

    Article  Google Scholar 

  35. Menard L, Broise Y (1975) Theoretical and practical aspect of dynamic consolidation. Géotechnique 25(1):3–18

    Article  Google Scholar 

  36. Merrifield CM, Davies MCR (2000) A study of low-energy dynamic compaction: field trials and centrifuge modeling. Géotechnique 50(6):675–681

    Article  Google Scholar 

  37. Miao L, Chen G, Hong Z (2006) Application of dynamic compaction in highway: a case study. Geotech Geol Eng 24(1):91–99

    Article  Google Scholar 

  38. Mostafa K (2010) Numerical modeling of dynamic compaction in cohesive soils. PhD Thesis, University of Akron

  39. Nashed R (2006) Liquefaction mitigation of silty soils using dynamic compaction. PhD Thesis, State University of New York at Buffalo.

  40. Navas P, Sanavia L, López-Querol S et al (2018) Explicit meshfree solution for large deformation dynamic problems in saturated porous media. Acta Geotech 13:227–242

    MATH  Google Scholar 

  41. Oshima A, Takada N (1997) Relation between distance of tamper impact points and depth of improvement by heavy tamping-Design procedure of the basis of ram momentum for sandy ground. Doboku Gakkai Ronbunshu 568(39):147–159

    Article  Google Scholar 

  42. Oshima A, Takada N, Tanaka Y (1996) Relation between compacted area and ram momentum by heavy tamping-density and strength increases due to single point tamping. Doboku Gakkai Ronbunshu 554(37):185–196

    Article  Google Scholar 

  43. Pan JL, Selby AR (2002) Simulation of dynamic compaction of loose granular soils. Adv Eng Softw 33(7–10):631–640

    Article  Google Scholar 

  44. Poran CJ, Rodriguez JA (1992) Finite element analysis of impact behavior of sand. Soils Found 32(4):68–80

    Article  Google Scholar 

  45. Satchithananthan U, Ullah SN, Lee FH, Gu H (2020) Axial sliding resistance of partially embedded offshore pipelines. Géotechnique, pp 1–18

  46. Shenthan T, Nashed R, Thevanayagam S, Martin GR (2004) Liquefaction mitigation in silty soils using composite stone columns and dynamic compaction. Earthq Eng Eng Vib 3(1):39–50

    Article  Google Scholar 

  47. Tan Y (2007). Deep dynamic compaction of liquefaction-potential granular backfill. In: 4th international conference on earthquake geotechnical engineering

  48. Thevanayagam S, Nashed R, Martin GR (2009) Dynamic compaction of saturated sands and silty sands: theory. Proc Inst Civ Eng-Ground Improvement 162(2):57–68

    Article  Google Scholar 

  49. Wang W (2016) Ground response Gand effective to dynamic compaction of saturated silty (sandy) soil. PhD Thesis, Shanghai Jiao Tong University

  50. Wang W, Chen JJ, Wang JH (2017) Estimation method for ground deformation of granular soils caused by dynamic compaction. Soil Dyn Earthq Eng 92:266–278

    Article  Google Scholar 

  51. Wang W, Feng Q, Yang C (2019) Investigation on the dynamic liquefaction responses of saturated granular soils due to dynamic compaction in coastal areas. Appl Ocean Res 89:273–283

    Article  Google Scholar 

  52. Welsh JP, Anderson RD, Barksdale RP, Satyapriya CK, Tumay MT, Wahls HE (1987) Soil improvement: a ten year update. In : Proceedings of a symposium sponsored by the committee on placement and improvement of soils of the geotechnical engineering division of ASCE, Geotechnical Special Publication no. 12, ASCE, Atlantic City, NJ, pp 67–75

  53. Ye F (2012). Elastic and elasto-plastic wave propagation in saturated soil and mixed-phase. PhD Thesis, National University of Singapore

  54. Ye F, Goh SH, Lee FH (2014) Dual-phase coupled u–U analysis of wave propagation in saturated porous media using a commercial code. Comput Geotech 55:316–329

    Article  Google Scholar 

  55. Yi JT (2009) Centrifuge and numerical modelling of sand compaction pile installation. PhD Thesis, National University of Singapore

  56. Yi JT, Goh SH, Lee FH, Randolph MF (2012) A numerical study of cone penetration in fine-grained soils allowing for consolidation effects. Géotechnique 62(8):707–719

    Article  Google Scholar 

  57. Yi JT, Zhang L, Ye FJ, Goh SH (2019) One-dimensional transient wave propagation in a dry overlying saturated ground. KSCE J Civ Eng 23(10):4297–4310

    Article  Google Scholar 

  58. Zadeh HK (2010) Finite element analysis and experimental study of metal powder compaction. PhD Thesis, Queen's University

  59. Zhang R, Sun Y, Song E (2019) Simulation of dynamic compaction and analysis of its efficiency with the material point method. Comput Geotech 116:103218

    Article  Google Scholar 

  60. Zhou Y, Cai Y, Yuan G et al (2021) Effect of tamping interval on consolidation of dredged slurry using vacuum preloading combined with dynamic consolidation. Acta Geotech 16:859–871

    Article  Google Scholar 

  61. Zhou J, Chao Y, Jia M, Huang M (2003) In-situ test study on soft soils improvement by the DCM combined with dewatering. Rock Soil Mech 24(3):376–380 ((in Chinese))

    Google Scholar 

  62. Zhou C, Jiang H, Yao Z, Li H, Yang C, Chen L, Geng X (2020) Evaluation of dynamic compaction to improve saturated foundation based on the fluid-solid coupled method with soil cap model. Comput Geotech 125:103686

    Article  Google Scholar 

  63. Zhou C, Yang C, Qi H, Yao K et al (2021) Evaluation on improvement zone of foundation after dynamic compaction. Appl Sci 11(5):2156

    Article  Google Scholar 

  64. Zhou J, Zhang J, Yao H (2005) Study on technique of low-energy dynamic consolidation method combined with dewatering used to treat soft roadbed. Rock Soil Mech 26:198 ((in Chinese))

    Google Scholar 

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This work was supported by Shandong Excellent Young Scientists Fund Program (Overseas) (2022HWYQ-016), Shandong Provincial Natural Science Foundation (ZR2021QE254; ZR2021ME103), Natural Science Foundation of Jiangsu Province (BK20220273), Guangdong Basic and Applied Basic Research Foundation (2021A1515110564) and the Foundation of Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University (KLE-TJGE-B2105).

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Correspondence to Kai Yao.

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Zhou, C., Yao, K., Rong, Y. et al. Numerical investigation on zone of improvement for dynamic compaction of sandy ground with high groundwater table. Acta Geotech. (2022).

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  • Dynamic compaction
  • Effective improvement range
  • Fluid–solid coupled analysis
  • High groundwater table