Using state parameter to improve numerical prediction of a generalized plasticity constitutive model Somaye Sadeghian n , Manouchehr Latifi Namin School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran article info Article history: Received 30 September 2011 Received in revised form 29 June 2012 Accepted 30 June 2012 Available online 25 July 2012 Keywords: Constitutive model State parameter Centrifuge VELACS Generalized plasticity abstract Dilatancy, as a principal feature of sand behavior, is significantly affected by state of the sand. State of the soil is determined by density and mean principal effective stress. Constitutive models which fail to consider this state dependency of sand samples are unable to predict both dilative and contractive behavior of the soil using a unique set of model constants. In fact, state independent constitutive models have to redefine their model constants upon any changes in states of the soil. Several empirical correlations between internal parameters of constitutive models and several state variables have been proposed in literature. This study aims to investigate how implementing state parameter in a constitutive model can improve numerical predictions. Herein, some of the empirical correlations in literature are adopted in a generalized plasticity constitutive model. Afterwards some single element and multi element tests are simulated applying both state independent and modified state dependent constitutive models. Outcomes of the numerical simulations are used to assess the proposed modification. All in all, the results show that numerical analysis using state dependent constitutive model results in more accurate numerical predictions. Since, the proposed modifications make the constitutive model compatible with critical state theory and readjustment of constant parameters are no longer required. Simplicity is another advantage of the modified presented state dependent constitutive model inasmuch as no new material constant needs to be adopted. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction When sand is subjected to shear, two extreme classes of behavior are expected. In other words, sand shows contractive behavior while it is in loose state. In contrast, it shows dilative behavior in dense state (Castro, 1969; Poulos, 1981; Been and Jefferies, 1985; Sladen and Oswell, 1990; Been et al., 1991; Vaid and Sasitharan, 1992; Ishihara, 1993; Verdugo and Ishihara, 1996; Lashkari, 2009). Overlooking state dependency of granular mate- rial in analytical models of sand behavior results in quantitative inaccuracy, in particular for cyclic shearing (e.g. (Popescu and Prevost, 1995; Papadimitriou et al., 2001)). Indeed, state inde- pendent constitutive equations require a readjustment of the constant parameters to properly predict the effect of the initial state in analytical models. Therefore, to increase the accuracy of numerical studies and to simulate soil structures with a unique set of constant model parameters, shear behavior of sand should be defined as a direct function of some state parameters by implementing some state parameters in constitutive models’ equations (e.g. (Jefferies, 1993; Manzari and Dafalias, 1997; Gajo and Muir Wood, 1999; Li et al., 1999; Li and Dafalias, 2000)). Although some research has demonstrated that critical state line (CSL) are not unique (e.g. (Vaid and Chern, 1985; Vaid and Thomas, 1995; Vaid and Sivathayalan, 1996; Riemer and Seed, 1997; Mooney et al., 1998; Yoshimine et al., 1998; Li and Dafalias, 2002; Sadrekarimi and Olson, 2011)), this fact is not in the case in this study, and state parameters are defined with respect to a unique critical state line (CSL) or steady state line. This study aims to modify Pastor and Zienkiewics (Pastor and Zienkiewicz, 1986) constitutive model, which has been developed within the frame- work of generalized plasticity theory. Pastor and Zienkiewics (Pastor and Zienkiewicz, 1986) constitutive model, does not consider the effect of state parameter. Herein, some state para- meters are implemented in constitutive model equations by rendering the phase transformation ratio and the peak stress ratio a function of the state parameter. Several constitutive equations have been introduced in literatures which define phase transformation and peak stress ratios as a function of state parameters (i.e. (Manzari and Dafalias, 1997; Wan and Guo, 1998; Wang et al., 2002; Dafalias and Manzari, 2004)). In this study, some of these correlations are used. These modifications contribute to two worthwhile outcomes. Firstly, by means of a Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/cageo Computers & Geosciences 0098-3004/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cageo.2012.06.025 n Corresponding author. Tel.: þ98 21 44825591. E-mail address: so.sadeghian@gmail.com (S. Sadeghian). Computers & Geosciences 51 (2013) 255–268