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Extended model of shear modulus reduction for cohesive soils

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Abstract

The shear modulus of a soil, G, shows a hyperbolic degradation curve relationship with increasing shear strain, γ. G is usually normalized against the small-strain modulus (Gmax) as G/Gmax vs γ (log). Factors that significantly influence G are shear strain amplitude, γ, soil plasticity index (PI) and effective pressure, σ′. Design curve charts of G/Gmax vs γ have been produced for seismic engineering purposes. Mathematical models have also been developed, using statistically analysed parameters to reflect the influence of γ, PI and σ′. Soil overconsolidation ratio (OCR) has a significantly lesser impact than the three mentioned factors. In this paper, mathematical fitting and shaping functions for PI and σ′ are developed to extend the shear modulus reduction model further. The requirement to calculate reference strain, γref, is removed, and only soil PI and σ′ are required. Cyclic triaxial experiments are conducted with reconstituted kaolin and bentonite in different mix proportions (to achieve varying PI) and at different effective stresses. The model equation matches well against both the established curves and experimental results and can facilitate preliminary prediction of shear stress–strain behaviour and Gmax with different cohesive soil types and at different depths below ground.

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Adapted from Vucetic and Dobry (1991) Fig. 6a [21]

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Abbreviations

B:

Bentonite

D:

Damping ratio, soil

E:

Elastic modulus, soil

e:

Void ratio, soil

Gmax :

Very small-strain shear modulus, soil

G:

Shear modulus, soil

G/Gmax :

Normalized shear modulus vs shear strain curve

K:

Kaolin

OCR:

Overconsolidation ratio, soil

PI:

Plasticity index, soil

UCS:

Unconfined compressive strength (quc)

σ′ :

Effective stress, soil

σ D :

Deviatoric stress, soil

α :

Power factor curvature parameter

ε :

Axial strain

γ :

Shear strain

γ 0 .7 :

Shear strain at G/Gmax = 0.7

ν :

Poisson ratio

f (σ′):

Fitting function (effective pressure)

f (PI):

Fitting function (plasticity index)

Z:

Curvature function (effective pressure)

atm:

Atmospheric pressure

References

  1. Darendeli MB (2001) Development of a new family of normalized modulus reduction and material damping curves. PhD thesis. University of Texas, Austin, TX, USA, 2001

  2. Diaz-Rodriguez JA, Lopez-Molina JA (2008) Strain Thresholds in Soil Dynamics. Presented at the 14WCEE, Beijing, China

  3. Hardin BO, Drnevich VP (1972) Shear modulus and damping in soils: design equations and curves. J Soil Mech Found Div 98(sm7):667–692

    Article  Google Scholar 

  4. Ishibashi I, Zhang X (1993) Unified dynamic shear moduli and damping ratios of sand and clay. Soils Found 33(1):182–191. https://doi.org/10.3208/sandf1972.33.182

    Article  Google Scholar 

  5. Iwasaki T, Tatsuoka F, Takagi Y (1978) Shear moduli of sands under cyclic torsional shear loading. Soils Found 18(1):39–56. https://doi.org/10.3208/sandf1972.18.39

    Article  Google Scholar 

  6. Kallioglu P, Tika Th, Pitilakis K (2008) Shear modulus and damping ratio of cohesive soils. J Earthq Eng 12(6):879–913. https://doi.org/10.1080/13632460801888525

    Article  Google Scholar 

  7. Karray M, Hussein MN (2017) Shear wave velocity as function of cone penetration resistance and grain size for holocene-age uncemented soils: a new perspective. Acta Geotech 12(5):1129–1158. https://doi.org/10.1007/s11440-016-0520-2

    Article  Google Scholar 

  8. Kishida T (2008) Seismic Site Effects for the Sacramento-San Joaquin Delta. Univ. of California, Davis, CA

  9. Kishida T (2017) Comparison and correction of modulus reduction models for clays and silts. J Geotech Geoenviron Eng 143(4):04016110. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001627

    Article  Google Scholar 

  10. Kishida T, Boulanger RW, Abrahamson NA, Wehling TM, Driller MW (2009) Regression models for dynamic properties of highly organic soils. J Geotech Geoenviron Eng 135(4):533–543. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:4(533)

    Article  Google Scholar 

  11. Kokusho T (1980) Cyclic triaxial test of dynamic soil properties for wide strain range. Soils Found 20(2):45–60. https://doi.org/10.3208/sandf1972.20.2_45

    Article  Google Scholar 

  12. Kokusho T, Yoshida Y, Esashi Y (1982) Dynamic properties of soft clay for wide strain range. Soils Found 22(4):1–18. https://doi.org/10.3208/sandf1972.22.4_1

    Article  Google Scholar 

  13. Kumar SS, Krishna AM (2021) Evaluation of monotonic and dynamic shear modulus of sand using on-sample transducers in cyclic triaxial apparatus. Acta Geotech 16(1):221–236. https://doi.org/10.1007/s11440-020-01035-2

    Article  Google Scholar 

  14. Kumar SS, Krishna AM, Dey A (2017) Evaluation of dynamic properties of sandy soil at high cyclic strains. Soil Dyn Earthq Eng 99:157–167. https://doi.org/10.1016/j.soildyn.2017.05.016

    Article  Google Scholar 

  15. Lanzo G, Vucetic M, Doroudian M (1997) Reduction of shear modulus at small strains in simple shear. J Geotech Geoenviron Eng 123(11):1035–1042. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:11(1035)

    Article  Google Scholar 

  16. Likitlersuang S, Teachavorasinskun S, Surarak C, Oh E, Balasubramaniam A (2013) Small strain stiffness and stiffness degradation curve of Bangkok clays. Soils Found 53(4):498–509. https://doi.org/10.1016/j.sandf.2013.06.003

    Article  Google Scholar 

  17. Marcuson WF III, Wahls HE (1972) Time effects on dynamic shear modulus of clays. J Soil Mech Found Div 98(SM12):1359–1373

    Article  Google Scholar 

  18. Tatsuoka F, Iwasaki T, Takagi Y (1978) Hysteretic damping of sands under cyclic loading and its relation to shear modulus. Soils Found 18(2):25–40. https://doi.org/10.3208/sandf1972.18.2_25

    Article  Google Scholar 

  19. Teachavorasinskun S, Thongchim P, Lukkunaprasit P (2002) Shear modulus and damping of soft bangkok clays. Can Geotech J 39(5):1201–1208. https://doi.org/10.1139/t02-048

    Article  Google Scholar 

  20. Vardanega PJ, Bolton MD (2013) Stiffness of clays and silts: normalizing shear modulus and shear strain. J Geotech Geoenviron Eng 139(9):1575–1589. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000887

    Article  Google Scholar 

  21. Vucetic M, Dobry R (1991) Effect of soil plasticity on cyclic response. J Geotech Eng 117(1):89–107. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:1(89)

    Article  Google Scholar 

  22. Wichtmann T, Triantafyllidis T (2018) Monotonic and cyclic tests on kaolin: a database for the development, calibration and verification of constitutive models for cohesive soils with focus to cyclic loading. Acta Geotech 13(5):1103–1128. https://doi.org/10.1007/s11440-017-0588-3

    Article  Google Scholar 

  23. Zhang J, Andrus RD, Juang CH (2005) Normalized shear modulus and material damping ratio relationships. J Geotech Geoenviron Eng 131(4):453–464. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:4(453)

    Article  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the following for their support and assistance: The University of Nottingham Malaysia, Faculty of Science and Engineering, Department of Civil Engineering. Soilpro Technical Services Sdn Bhd (Malaysia), from which experiments were conducted. www.mycurvefit.com for curve-fitting resources.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Nottingham Malaysia, Jalan Broga, 43500, Semenyih, Selangor, Malaysia

    John Kok Hee Wong & Soon Yee Wong

  2. Soilpro Technical Services Sdn Bhd, 16, Jalan TIB-1/17, Taman Industri Bolton, 68100, Batu Caves, Selangor, Malaysia

    Kim Yuen Wong

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Correspondence to John Kok Hee Wong.

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Wong, J.K.H., Wong, S.Y. & Wong, K.Y. Extended model of shear modulus reduction for cohesive soils. Acta Geotech. 17, 2347–2363 (2022). https://doi.org/10.1007/s11440-021-01398-0

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