NTUA-SAND
Theoretical background
The NTUA-SAND model (Andrianopoulos et al 2010a, b, 2011) is a bounding surface, critical
state, plasticity model with a vanished elastic region, developed primarily for accurate
simulation of the rate-independent dynamic response of non-cohesive soils under small,
medium and large cyclic strain amplitudes. This is achieved using a single set of values for the
model constants, irrespective of initial stress and density conditions, as well as loading
direction. The model is equally efficient in simulating the monotonic response.
The NTUA-SAND model builds on the constitutive efforts of Manzari & Dafalias (1997) and
Papadimitriou & Bouckovalas (2002) and to ensure numerical stability the UDM employs the
modified-Euler integration scheme with automatic error control and sub-stepping (Sloan et al.
2001). Key constitutive ingredients of the NTUA-SAND model are:
a) the inter-dependence of the critical state, the bounding and the dilatancy (open cone)
surfaces (Fig. 1), that depict the deviatoric stress-ratios at critical state, peak strength and
phase transformation, on the basis of the state parameter ψ = e – e
cs
(with e the void ratio,
and e
cs
the void ratio at critical state at the same mean effective stress p, as per Been &
Jefferies 1985),
b) a (Ramberg-Osgood type) non-linear hysteretic formulation for the “elastic” strain rate, that
governs the response at small to medium cyclic shear strains (Fig. 2),
c) a discontinuously relocatable stress projection center r
ref
related to the “last” load reversal
point, which is used for mapping the current stress point on model surfaces (see Fig. 1)
and as a reference point for introducing non-linearity in the “elastic” strain rate, and finally
d) an empirical index of the directional effect of sand fabric evolution during shearing, which
scales the plastic modulus, and governs the rate of excess pore pressure build-up and
permanent strain accumulation under large cyclic shear strains potentially leading to
liquefaction and cyclic mobility (see Fig. 3)
Figure 1: Model surfaces and adopted mapping rule in the π-plane of the deviatoric stress ratio space,
based on a relocatable projection center r
ref
(from Andrianopoulos et al 2010b)
