Development of Constitutive Models for Linear and Nonlinear Shear Modulus and Material Damping Ratio of Uncemented Soils
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 148, Issue 3
Abstract
The shear modulus () is the parameter commonly used to describe soil stiffness and to calculate shear deformations at small-to-moderate strains (). The material damping ratio () is the parameter commonly used along with to analyze the response of the geotechnical materials to dynamic shearing motions. The following four sets of empirical models are presented in this study: (1) small-strain shear modulus (), (2) nonlinear shear modulus () relationships, (3) small-strain material damping ratio (), and (4) nonlinear material damping ratio relationships (). The associated database included all traceable uncemented soil specimens tested in the Soil and Rock Dynamics Laboratory at The University of Texas at Austin using the combined resonant column and torsional shear (RCTS) equipment since the late 1980s. The effects of soil type, index properties, density, confining state, and strain level on the shear modulus and material damping ratio have been quantified through multivariable regression analyses performed in a staged manner. The staged outcomes provide options of models with user-preferred levels of complexity and corresponding accuracy. In conclusion, these empirical models for , relationships, , and relationships perform well in fitting the database and can be applied to predict the shear behavior of uncemented soils at small-to-moderate strains ().
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Andersen, K. H. 1983. Strength and deformation properties of clay subjected to cyclic loading.. Oslo, Norway: Norwegian Geotechnical Institute.
Anderson, D. G., and K. H. Stokoe II. 1978. Shear modulus: A time-dependent soil property. ASTM STP654. West Conshohocken, PA: ASTM.
Anderson, D. G., and R. D. Woods. 1975. “Comparison of field and laboratory shear modulus.” In Vol. 1 of Proc., ASCE Conf. on In Situ Measurement of Soil Properties, 69–92. Reston, VA: ASCE.
Andreasson, B. A. 1981. “Dynamic deformation characteristics of a soft clay.” In Vol. 1 of Proc., Int. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, 65–70. Rolla, MO: Univ. of Missouri-Rolla.
Borden, R. H., L. Shao, and A. Gupta. 1996. “Dynamic properties of piedmont residual soils.” J. Geotech. Eng. 122 (10): 813–821. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:10(813).
Darendeli, B. M. 2001. “Development of a new family of normalized modulus reduction and material damping curves.” Ph.D. dissertation, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Hardin, B. O. 1978. “The nature of stress-strain behavior of soils.” In Proc., Geotechnical Engineering Division Specialty Conf. on Earthquake Engineering and Soil Dynamics, 3–90. Reston, VA: ASCE.
Hardin, B. O., and W. L. Black. 1966. “Sand stiffness under various triaxial stresses.” J. Soil Mech. Found. Div. 92 (2): 27–42. https://doi.org/10.1061/JSFEAQ.0000865.
Hardin, B. O., and W. L. Black. 1968. “Vibration modulus of normally consolidated clay.” Supplement, J. Soil Mech. Found. Div. 94 (S2): 353–369. https://doi.org/10.1061/JSFEAQ.0001100.
Hardin, B. O., and V. P. Drnevich. 1972. “Shear modulus and damping in soils: Design equations and curves.” J. Geotech. Eng. 98 (7): 667–692. https://doi.org/10.1061/JSFEAQ.0001760.
Hwang, S. K. 1997. “Investigation of the dynamic properties of natural soils.” Ph.D. dissertation, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Isenhower, W. M. 1979. “Torsional simple shear/resonant column properties of San Francisco Bay Mud.” M.S. thesis, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Ishibashi, I., and X. J. Zhang. 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.
Ishihara, K. 1986. “Evaluation of soil properties for use in earthquake response analysis.” In Proc., Geomechanical Modelling in Engineering Practice, edited by R. Dingar and J. A. Studer, 241–275. Rotterdam, Netherlands: A.A. Balkema.
Iwasaki, T., F. Tatsuoka, and Y. Takagi. 1978. “Shear moduli of sands under cyclic torsional shear loading.” Soils Found. 18 (1): 39–56. https://doi.org/10.3208/sandf1972.18.39.
Kacar, O. 2014. “Building a framework for predicting the settlements of shallow foundations on granular soils using dynamically measured soil properties.” Ph.D. dissertation, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Keene, A. K. 2017. “Next-generation equipment and procedures for combined resonant column and torsional shear testing.” Ph.D. dissertation, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Kim, D. S. 1991. “Deformational characteristics of soils at small to intermediate strains from cyclic tests.” Ph.D. dissertation, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Kim, T. C., and M. Novak. 1981. “Dynamic properties of some cohesive soils of Ontario.” Can. Geotech. J. 18 (3): 371–389. https://doi.org/10.1139/t81-044.
Kokusho, T., Y. Yoshida, and Y. Esashi. 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.
Koutsoftas, D. C., and J. A. Fischer. 1980. “Dynamic properties of two marine clays.” J. Geotech. Eng. Div. 106 (6): 645–657. https://doi.org/10.1061/AJGEB6.0000977.
Laird, J. P. 1994. “Linear and nonlinear dynamic properties of soil at high confining pressures.” M.S. thesis, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Lee, M. K. W., and W. D. L. Finn. 1978. DESRA-2, dynamic effective stress response analysis of soil deposits with energy transmitting boundary including assessment of liquefaction potential.. Vancouver, BC, Canada: Univ. of British Columbia.
Lodde, P. F. 1982. “Shear moduli and material damping of San Francisco Bay Mud.” M.S. thesis, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Masing, G. 1926. “Eigenspannungen und Verfestgung Beim Masing.” In Proc., 2nd Int. Congress of Applied Mechanics, 332–335. Zurich, Switzerland: Orell Füssli.
Matesic, L., C.-C. Hsu, M. D’Elia, and M. Vucetic. 2010. “Development of database of cyclic soil properties from 94 tests on 47 soils.” In Proc., 4th Int. Conf, on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. Rolla, MO: Missouri Univ. of Science and Technology.
Menq, F. Y. 2003. “Dynamic properties of sandy and gravelly soils.” Ph.D. dissertation, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Ni, S. H. 1987. “Dynamic properties of sand under true triaxial stress states from resonant column/torsional shear tests.” Ph.D. dissertation, Dept. of Civil, Architectural, and Environmental Engineering, Univ. of Texas at Austin.
Oztoprak, S., and M. D. Bolton. 2013. “Stiffness of sands through a laboratory test database.” Géotechnique 63 (1): 54. https://doi.org/10.1680/geot.10.P.078.
Richart, F. E., Jr., J. R. Hall, and R. D. Woods Jr. 1970. Vibrations of soils and foundations. Englewood Cliffs, NJ: Prentice Hall.
Roblee, C., and B. Chiou. 2004. “A proposed geoindex model for design selection of non-linear properties for site response analysis.” In Proc., NSF/PEER Int. Workshop on Uncertainties in Nonlinear Soil Properties and their Impact on Modeling Dynamic Soil Response. Berkeley, CA: Univ. of California at Berkeley.
Rollins, K. M., M. D. Evans, N. B. Diehl, and W. D. Daily III. 1998. “Shear modulus and damping relationships for gravels.” J. Geotech. Geoenviron. Eng. 124(5): 396–405. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:5(396).
Romo, M. P., and A. Jaime. 1986. Dynamic characteristics of some clays of the Mexico Valley and seismic response of the ground. Mexico City, Mexico: Institute de Ingenieria, Mexico City.
Seed, H. B., and I. M. Idriss. 1970. Soil moduli and damping factors for dynamic response analyses. Report EERC 70–10. Berkeley, CA: Univ. of California.
Seed, H. B., R. T. Wong, I. M. Idriss, and K. Tokimatsu. 1986. “Moduli and damping factors for dynamic analyses of cohesionless soil.” J. Getech. Eng. 112 (GT11): 1016–1032. https://doi.org/10.1061/(ASCE)0733-9410(1986)112:11(1016).
Sun, J. I., R. Golesorkhi, and H. B. Seed. 1988. Dynamic moduli and damping ratios for cohesive soils. Rep. No. EERC 88-15. Berkeley, CA: Univ. of California.
Vucetic, M., and R. Dobry. 1988. “Degradation of marine clays under cyclic loading.” J. Geotech. Eng. 114 (2): 133–149. https://doi.org/10.1061/(ASCE)0733-9410(1988)114:2(133).
Vucetic, M., and R. Dobry. 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).
Vucetic, M., G. Lanzo, and M. Doroudian. 1998. “Damping at small strains in cyclic simple shear test.” J. Geotech. Geoenviron. Eng. 124 (7): 585–594. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:7(585).
Zen, K., Y. Umehara, and K. Hamada. 1978. “Laboratory tests and in situ seismic survey on vibratory shear modulus of clayey soils with various plasticities.” In Proc., 5th Japanese Earthquake Engineering Symp., 721–728. Tokyo: Japanese Society of Soil Mechanics and Foundation Engineering.
Zhang, J., R. D. Andrus, and C. H. Juang. 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).
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Feb 23, 2021
Accepted: Oct 14, 2021
Published online: Dec 21, 2021
Published in print: Mar 1, 2022
Discussion open until: May 21, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Ramesh Gangisetti, Sireesh Saride, Effect of Mean Particle Size and Uniformity on Modulus Degradation of Nonlinearly Graded Marine Sands, Journal of Geotechnical and Geoenvironmental Engineering, 10.1061/JGGEFK.GTENG-11625, 150, 5, (2024).
- Dong-Hwa Noh, Junghee Park, J. Carlos Santamarina, Tae-Hyuk Kwon, Multimode Free-Vibration Decay Column: Small-Strain Stiffness and Attenuation, Journal of Geotechnical and Geoenvironmental Engineering, 10.1061/JGGEFK.GTENG-10748, 149, 6, (2023).
- Amalesh Jana, Ali Dadashiserej, Benchen Zhang, Armin W. Stuedlein, T. Matthew Evans, Kenneth H. Stokoe, Brady R. Cox, Multidirectional Vibroseis Shaking and Controlled Blasting to Determine the Dynamic In Situ Response of a Low-Plasticity Silt Deposit, Journal of Geotechnical and Geoenvironmental Engineering, 10.1061/(ASCE)GT.1943-5606.0002924, 149, 3, (2023).
- Andrea Ciancimino, Renato Maria Cosentini, Sebastiano Foti, Giuseppe Lanzo, Alessandro Pagliaroli, Oronzo Pallara, The PoliTO–UniRoma1 database of cyclic and dynamic laboratory tests: assessment of empirical predictive models, Bulletin of Earthquake Engineering, 10.1007/s10518-022-01573-y, (2023).
- Pauline P. Kruiver, Manos Pefkos, Adrian Rodriguez-Marek, Xander Campman, Kira Ooms-Asshoff, Małgorzata Chmiel, Anaïs Lavoué, Peter J. Stafford, Jan van Elk, Capturing spatial variability in the regional Ground Motion Model of Groningen, the Netherlands, Netherlands Journal of Geosciences, 10.1017/njg.2022.13, 101, (2022).