Normalized Modulus Reduction and Material Damping Ratio Curves for Bay of Campeche Sand

Abstract

Predictive equations for estimating normalized shear modulus and material damping ratio of sand are presented in this paper. The equations are based on a modified hyperbolic model and a statistical analysis of existing isotropically consolidated resonant column and strain-controlled cyclic direct simple shear test results for 252 specimens obtained from the Bay of Campeche. Two independent modified hyperbolic relationships are fitted to model stiffness (G/Gmax)-strain using two parameters and material damping ratio-strain curves using four parameters. Variables used in the equation for normalized shear modulus are: confining pressure; shear-strain amplitude; a reference strain, defined as the shear strain at which the shear modulus has reduced to 0.5Gmax, and a curvature parameter which controls the rate of modulus reduction, such as the model suggested by Darendeli (2001). The equation for damping ratio D, is expressed in terms of the reference strain, defined as the shear strain for a 50% increase in material damping ratio (i.e. D/Dmax = 0.5), a curvature parameter which controls the rate of material damping ratio increase, the minimum material damping ratio Dmin, and the maximum material damping ratio Dmax, similar to the equation suggested by Gonzalez and Romo (2011). It is found that the Bay of Campeche sand exhibit more linear response and lower damping ratio than other sands reported in the literature. The uncertainties associated with the predictive equations are quantified. A case study is provided to illustrate an application of the predictive equations to seismic response analysis and the importance of considering confining stress. The predictive equations of normalized shear modulus reduction G/Gmax and Damping ratio curves are easy to apply in practice, and are useful in the analysis of granular strata and offshore structures subjected to earthquake loading when site specific laboratory testing is not available.

Dynamic Properties of Clay for Earthquake Response Analysis in the Bay of Campeche

“…Figure 15b shows the material damping ratio curves of calcareous clay and clayey carbonate mud for σ'm of 400 kPa and PI of 50 and compares them with previously published D- curves of non-calcareous clays developed for the corresponding mean effective confining pressure and PI by Vucetic and Dobry (1991), Darendeli (2001), Gonzalez andRomo (2011), andTaboada, et al (2017a).…”

“…The calculated D- curves developed for calcareous clay and clayey carbonate mud dissipate slightly more energy than the corresponding curve of Taboada, et al (2017a). They intersect at a cyclic shear strain of about  = 1.5 %, and beyond this , the calculated D- curves dissipate less energy than the curves of Taboada, et al (2017a).…”

“…The calculated modulus reduction curves G/Gmax- presented in figure 13a of calcareous clay and clayey carbonate mud with σ'm = 400 kPa and plasticity index PI = 50 are compared with previously published modulus reduction curves of non-calcareous clays developed for the corresponding mean effective confining pressure and plasticity index by Vucetic and Dobry (1991), Darendeli (2001), Gonzalez andRomo (2011), andTaboada, et al (2017a). Figure 15a shows that the calculated curves G/Gmax- of calcareous clay and clayey carbonate mud are more linear with a higher threshold cyclic shear strain than the curve of Taboada, et al (2017a). After the threshold strain is reached, the calculated curves degrade at a slightly higher rate than the curve of Taboada, et al, (2017a) and meet at a cyclic strain of 2 %, and after that they overlap and become only one curve.…”

“…Figure 15a shows that the calculated curves G/Gmax- of calcareous clay and clayey carbonate mud are more linear with a higher threshold cyclic shear strain than the curve of Taboada, et al (2017a). After the threshold strain is reached, the calculated curves degrade at a slightly higher rate than the curve of Taboada, et al, (2017a) and meet at a cyclic strain of 2 %, and after that they overlap and become only one curve.…”

“…The existing laboratory G/Gmax and D data used in this study are compiled from offshore geotechnical investigations performed in the Bay of Campeche between 2012 and 2015 that include isotropically consolidated resonant column and strain-controlled cyclic DSS test results for 225 specimens of clay (Taboada, et al, 2017a).…”