ARCS: A one dimensional nonlinear soil model for ground response analysis

Abstract

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.

Shake‐table investigation of scoured RC pile‐group‐supported bridges in liquefiable and nonliquefiable soils

“…Adopted scaled real ground motions were originally recorded at WNT Station of 1999 Chi-chi Earthquake (magnitude, M = 7.62, source distance, R = 16.27 km) 50 and Port Island Station of 1995 Kobe Earthquake (M = 6.9, R = 3.31 km), 51 as indicatively shown in Figure 3. More specifically, the Chi-chi record contains more cycles of strong shaking than the Kobe record.…”

Integration of Viscoplastic Effects in Nonlinear Ground Response Analysis

“…Récemment, Yniesta et al (2017) ont présenté le modèle ARCS, qui est un modèle de contrainte-déformation non-linéaire unidimensionnelle capable de reproduire n"importe quelle courbe d"entrée d"amortissement ou de réduction du module de cisaillement. Cependant, ce modèle, ainsi que les autres modèles utilisés dans les analyses de réponse de dépôts, sont indépendants du taux de déformation.…”

“…Most previous models are unable to match both modulus reduction and damping curves which introduce a misfit of the desired behaviour. Yniesta et al (2017) proposed a one-dimensional nonlinear stress-strain model, called the ARCS model, able to reproduce any user-input modulus reduction and damping curve. However, soil behaviour is highly strain-rate dependent during monotonic and cyclic loading but none of the above modelsexplicitly include strain ratedependency.…”

“…Since the nonlinear ARCS model by Yniesta et al (2017) is able to reproduce any user-input modulus reduction and damping curve, its framework will constitute the basis of a new model that will include strain-rate dependency.…”

“…The formulation was based on the work of Liu and Gorman (1995) and provides a realistic damping by reducing the over-damping at both high and low frequencies. Yniesta et al (2017) proposed a one-dimensional nonlinear stress-strain model able to reproduce any user-input modulus reduction and damping curve that includes hysteretic damping even at small strains by departing from the Masing rules. This model, presented in this document, is based on the formulation from Yniesta et al (2017), and will be extensively presented in Chapter 3.…”