This paper presents a one dimensional nonlinear stress-strain model called ARCS (Axis Rotation and Cubic Spline) capable of reproducing any user-input modulus reduction and damping curve. Unlike many previous nonlinear models, the ARCS model does not utilize Masing's rules, nor does it require a specific functional form for the backbone curve such as a hyperbola. Rather, the model matches the desired modulus reduction curve by fitting cubic splines to the implied stress-strain curve, and matches the damping curve by utilizing a coordinate transformation technique in which one axis lies along the secant shear modulus line with the other axis in the orthogonal direction for a particular unload-reload cycle. Damping is easily controlled in the transformed coordinate space. An inverse coordinate transformation returns the desired stress. The integration algorithm is independent of strain step size, meaning that the returned stress for a large strain increment is identical to the stress that would be returned by subdividing the strain increment into smaller increments. Small-strain damping may be modeled hysteretically, avoiding the need for supplemental viscous damping. The model is shown to match the results of laboratory cyclic simple shear tests involving deliberately irregular stain histories. The performance of the model is illustrated in a set of ground response simulations where its predictions are compared with those of existing models. The ARCS model does not explicitly account for rate effects, cyclic degradation, or pore pressure generation.However, the equations can potentially be adapted in more advanced constitutive models to capture these effects. Such implementations are reserved for future publications.
Several building codes, such as the National Building Code of Canada, recommend that an effective stress ground response analysis be performed if a liquefiable stratum is identified within a soil profile. Although, constitutive models for total stress ground response analysis have been well verified against earthquake recordings, existing models for effective stress ground response analysis have yet to be thoroughly validated. This article investigates the predictions of five pore pressure models derived for effective stress ground response analysis. First, a dataset of five downhole arrays and two centrifuge experiments in which a potential of liquefaction was identified is presented. The profiles and ground-motion recordings are selected to represent a broad range of soil properties, ground-motion intensities, and excess-pore pressure generation levels. The differences between predictions of the effective stress models against commonly used 1D ground response total stress equivalent-linear and nonlinear analyses are evaluated. The predicted and measured motions are compared in terms of spectral response and amplification factor. The pore pressure response of all models is evaluated as a function of shear strain and found to agree well with published correlations representing the expected behavior of liquefiable soils. Although, the models show the ability to capture liquefaction triggering, the results indicate that for the selected dataset, total stress simulations were found to be, at least, as precise and accurate as the effective stress simulations. Therefore, simplified models for effective stress ground analysis should be used with caution by practicing engineers to predict surface spectra but can be used confidently to assess the potential for liquefaction triggering.
This paper presents one-dimensional ground response simulations of centrifuge models involving soft clay deposits subjected to ground motions of varying intensity. Total stress ground response simulations were performed using equivalent-linear (EL) and nonlinear (NL) methods. Shear strains higher than 10% were mobilized during large ground motions, therefore undrained shear strength of the clay is an important parameter for the simulations. Testing shows that the Bay Mud materials used in centrifuge modeling have monotonic shear strengths that increase by 13% per log cycle of shear strain rate. Comparison of simulation results to observations reveals the importance of incorporating shear strength into the development of stress-strain backbone curves, with appropriate consideration of rate-adjustments to shear strength and stiffness. NL ground response simulations provide a good match to observed pseudo-spectral accelerations only when rate-adjusted shear strengths are properly accounted for, otherwise the NL simulations have significant under-prediction bias at oscillator periods less
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