Simplified Model for Small-Strain Nonlinearity and Strength in 1D Seismic Site Response Analysis
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 142, Issue 9
Abstract
Commonly used simplified one-dimensional nonlinear seismic site response analyses employ constitutive models based on a variation of the hyperbolic model to represent the initial stress-strain backbone curve. Desirable features of the backbone curve include provision of (1) an initial shear modulus at zero shear strain, (2) a limiting shear stress at large shear strains, and (3) flexible control of the nonlinear behavior between those boundary conditions. Available hyperbolic models have combinations of two of these features. A new general quadratic/hyperbolic (GQ/H) model is developed from the bivariate quadratic equation to provide all desired features. Nonlinear behavior is controlled by a shear-strain-dependent curve-fitting function. The model’s unload-reload rules and coupling with pore-water pressure generation are also presented. Several total-stress site response analyses are presented to demonstrate the performance of the GQ/H model relative to a commonly used hyperbolic model in which the maximum shear stress cannot be defined. The analyses show the importance of properly representing the maximum shear stress in the constitutive model because it may lead to underestimation or overestimation of the computed site response.
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References
Ancheta, T. D., et al. (2014). “NGA-west2 database.” Earthquake Spectra, 30(3), 989–1005.
Baturay, M. B., and Stewart, J. P. (2003). “Uncertainty and bias in ground-motion estimates from ground response analyses.” Bull. Seismol. Soc. Am., 93(5), 2025–2042.
Borja, R., and Amies, A. (1994). “Multiaxial cyclic plasticity model for clays.” J. Geotech. Eng., 1051–1070.
Boulanger, R., Kamai, R., and Ziotopoulou, K. (2011). “Numerical modeling of liquefaction effects.” 4th IASPEI/IAEE Int. Symp., Univ. of California, Santa Barbara.
Chiu, P., Pradel, D. E., Kwok, A. O.-L., and Stewart, J. P. (2008). “Seismic response analyses for the silicon valley rapid transit project.” Geotechnical Earthquake Engineering and Soil Dynamics IV, ASCE, Sacramento, CA.
Darendeli, M. B. (2001). “Development of a new family of normalized modulus reduction and material damping curves.” Ph.D. thesis, Univ. of Texas, Austin, TX.
EPRI (Electric Power Research Institute). (1993). “Guidelines for determining design basis ground motions.”, Palo Alto, CA.
Gingery, J., and Elgamal, A. (2013). “Shear stress-strain curves based on the G/Gmax logic: A procedure for strength compatibility.” IACGE 2013, ASCE, Reston, VA, 721–729.
Green, R. A., Mitchell, J. K., and Polito, C. P. (2000). “An energy-based excess pore pressure generation model for cohesionless soils.” Proc., John Booker Memorial Symp., Balkema, Rotterdam, Netherlands.
Hardin, B. O., and Drnevich, V. P. (1972). “Shear modulus and damping in soils: Design equations and curves.” J. Soil Mech. Found. Eng. Div., 98(SM7), 667–692.
Hashash, Y. M. A., Dashti, S., Romero, M. I., Ghayoomi, M., and Musgrove, M. (2015). “Evaluation of 1-D seismic site response modeling of sand using centrifuge experiments.” Soil Dyn. Earthquake Eng., 78, 19–31.
Hashash, Y. M. A., and Park, D. (2001). “Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment.” Eng. Geol., 62(1–3), 185–206.
Hashash, Y. M. A., Phillips, C., and Groholski, D. R. (2010). “Recent advances in non-linear site response analysis.” 5th Int. Conf. in Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Missouri Univ. of Science and Technology, Rolla, MO.
Hayashi, H., Honda, M., Yamada, T., and Tatsuoka, F. (1994). “Modeling of nonlinear stress strain relations of sands for dynamic response analysis.” Proc., 10th Earthquake Engineering World Conf., Balkema, Rotterdam, Netherlands.
Kondner, R. L., and Zelasko, J. S. (1963). “Hyperbolic stress-strain formulation of sands.” 2nd pan American Conf. on Soil Mechanics and Foundation Engineering, Associação Brasileira de Mecânica dos Solos, São Paulo, Brazil.
Ladd, C. C. (1991). “Stability evaluation during staged construction.” J. Geotech. Eng., 540–615.
Masing, G. (1926). “Eigenspannungen und Verfestigung beim Messing.” 2nd Int. Congress on Applied Mechanics, Orell FüssliZurich, Switzerland.
Matasovic, N. (1993). “Seismic response of composite horizontally-layered soil deposits.” Ph.D. thesis, Univ. of California, Los Angeles.
Phillips, C., and Hashash, Y. M. A. (2009). “Damping formulation for nonlinear 1D site response analyses.” Soil Dyn. Earthquake Eng., 29(7), 1143–1158.
Ramberg, W., and Osgood, W. (1943). “Description of stress-strain curves by three parameters.”, National Advisory Committee for Aeronautics, Washington, DC.
Stewart, J. P., and Kwok, A. O. (2008). “Nonlinear seismic ground response analysis: Code usage protocols and verification against vertical array data.” Geotechnical Engineering and Soil Dynamics IV, D. Zeng, M. T. Manzari, and D. R. Hiltunen, eds., ASCE Geotechnical Special Publication, Sacramento, CA.
Vucetic, M., and Dobry, R. (1991). “Effect of soil plasticity on cyclic response.” J. Geotech. Eng., 89–107.
Yee, E., Stewart, J., and Tokimatsu, K. (2013). “Elastic and large-strain nonlinear seismic site response from analysis of vertical array recordings.” J. Geotech. Geoenviron. Eng., 1789–1801.
Zhang, J., Andrus, R. D., and Juang, C. H. (2005). “Normalized shear modulus and material damping ratio relationships.” J. Geotech. Geoenviron. Eng., 453–464.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 142 • Issue 9 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Apr 3, 2015
Accepted: Jan 8, 2016
Published online: May 19, 2016
Published in print: Sep 1, 2016
Discussion open until: Oct 19, 2016
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