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.

Seismic site response analyses are an important first step in the seismic evaluation of fixed offshore platforms in the Bay of Campeche. This analysis is used to estimate ground motions for the development of design response spectra, dynamic stresses, strains, and displacements within the soil profile and liquefaction hazard analyses. Seismic site response analyses of a clayey deposit located in the Bay of Campeche is performed using predicted dynamic soil properties, including the in-situ shear wave velocity based on empirical correlations developed for the Bay of Campeche clay, the shear modulus reduction curves and the material damping ratio curves based on equations also developed for the Bay of Campeche clay. The main objective of the study is to evaluate the effect of using predicted modulus reduction and material damping ratio curves on the design acceleration spectrum at the depth of maximum soil-pile interaction. Site response analyses is also performed using other generic modulus reduction and damping curves presented by Vucetic and Dobry (1991), and Darendeli (2001).The spectral acceleration amplitudes are underestimated when the curves of modulus reduction and material damping ratio of Vucetic and Dobry (1991) and Darendeli (2001) are used in the site response analyses, and overestimated when the curves proposed by Taboada et al., (2017) are used. It is found when comparing the results using laboratory curves that at the depth of maximum soil-pile interaction the maximum ground acceleration and the plateau of the design acceleration spectra are over estimated by 4% when the predicted modulus reduction and damping ratio curves are obtained using the equations developed by Taboada et al., (2017).Therefore, it is important to use predictive equations of modulus reduction and material damping ratio curves developed specifically for the Bay of Campeche clay when dynamic laboratory data is not available to generate these curves.

This study presents the influence of using predicted (calculated) normalized shear modulus (G/Gmax) and material damping ratio (D) curves on the design acceleration spectrum at the depth of maximum soil–pile interaction of a calcareous soil deposit in the Bay of Campeche.When comparing the predicted curves to the laboratory curves, it is concluded that due to limitations in the predicting models, the minimum confining pressure (σ’m) that must be used to get a good match with the laboratory curves is 150 kPa. After performing site response analyses for three shear wave velocity profiles and eight recorded acceleration time histories, the design acceleration spectrum was developed based on the envelope of the 24 calculated acceleration spectra. The acceleration amplitudes of the design spectrum in the short period range are slightly larger using the calculated curves than the laboratory curves. For periods longer than 0.27 seconds, the acceleration amplitudes of the design acceleration spectra are identical for practical purposes when both calculated and laboratory curves are used. Therefore, it is recommened to use the equations presented herein to calculate the curves of G/Gmax and D for calcareous soils in practice for preliminary and final seismic site response analyses. They can be especially useful in final evaluations of large or critical projects to calculate the curves when time and cost constraints make it impractical to perform direct experimental determinations of G/Gmax and D curves for each soil layer encountered in the soil deposit.

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Equations to calculate the modulus reduction curve (G/Gmax-γ) and material damping ratio curve (D-γ) of calcareous clay and clayey carbonate mud of the Bay of Campeche and Tabasco Coastline are developed. This was achieved using a database of 156 resonant column tests and 468 strain-controlled cyclic direct simple shear tests performed in clays with 10 % ≤ CaCO3 ≤90 %. The effects of carbonate content (CaCO3), mean effective confining pressure (σ′m), plasticity index (PI), and overconsolidation ratio (OCR) on the shape of the modulus reduction and material damping ratio curves are shown based on the available laboratory data and the equations developed to calculate these curves. It is shown that as CaCO3 increases, the normalized shear modulus (G/Gmax) curve tends to shift downward and the damping ratio (D) curve tends to shift upward; as σ′m and PI increase, the G/Gmax curve tends to shift upward and the damping ratio curve tends to shift downward; and the value of OCR has practically no effect on the position of the curves. The validation of the calculated values of G/Gmax and D shows the best predictions are found at low shear strains for G/Gmax and at large shear strains for D, falling within ± 25 % of the measured values, and shows that due to limitations in the model at large strains (γ > 1 %) for G/Gmax and at low strains (γ < 0.05 %) for D, the calculated values fall within ± 50 % of the measured values. The equations developed to calculate the curves of G/Gmax-γ and D-γ of calcareous clay and clayey carbonate mud are recommended for preliminary or perhaps even final seismic site response evaluations. However, considering the scatter of the data points around the curves, the equations should be used with caution, and parametric and sensitivity studies are strongly recommended to assess the importance of this scatter. In large critical projects, direct experimental determinations of G/Gmax and D for the soils of interest are suggested to be more appropriate.