Particle breakage occurs in granular materials with various engineering applications, such as when driving piles (especially where the strength of the particles is low) and in debris ‰ows (where the energy levels are high), and the in‰uence of this breakage on the mechanical behaviour of soils should be given proper consideration in a constitutive model for soils. Particle breakage results in an increase in the number ofˆne particles and broadens the grading of particle sizes, and the primary eŠect of broadening the grading is to lower the critical state line and other characteristics of the volumetric response in the compression plane. In our study, an existing constitutive model, the Severn-Trent sand model, in which the critical state line plays a central role as the locus of asymptotic states, has been extended to include the eŠects of particle breakage. Severn-Trent sand is a frictional hardening Mohr-Coulomb model described within a kinematic hardening, bounding surface framework. The central assumption is that strength is seen as a variable quantity, dependent on the current value of the state parameter (volumetric distance from the critical state line) which varies with changes in density and stress levels. If the critical state line falls as a result of broadening grading, the state parameter tends to increase and the soil feels looser.

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A simple and uniˆed constitutive model for soils, considering various eŠects such as the in‰uences of density, bonding, time dependent behavior and others, is presented in this paper. The elastoplastic behavior of over consolidated non-structured soils under a one-dimensional stress condition isˆrstly presented by introducing a state variable that represents the in‰uence of density (stage I). To describe the one-dimensional stress-strain behavior of structured soils, attention is focused on density and bonding as the main factors that aŠect the response of this type of soil, because it can be considered that soil a skeleton structure which is in a looser state than that of a normally consolidated soil is formed by bonding eŠects (stage II). Furthermore, a simple method is presented which allows for other soil characteristics to be considered, such as time and temperature dependency, and the eŠect of suction in unsaturated soils. Experimental observations show that the normally consolidated line (NCL) in the void ratio-stress relation (e.g., e-ln s curve) shifts depending on the change of strain rate, temperature, suction and others (stage III). The validation of the model at stages I and II is demonstrated by simulating one-dimensional consolidation tests for normally consolidated, over consolidated and natural clays. The applicability of the model at stage III is veriˆed not only by the simulations of time-dependent behavior of clays in one-dimensional element tests but also by the soil-water coupledˆnite element analysis of oedometer tests as a boundary value problem. The extension from one-dimensional models to three-dimensional models is easily achieved by deˆning the yield function using stress invariants instead of one-dimensional stress s' and by assuming an appropriate ‰ow rule in stress space. The details of the modeling in general three-dimensional stress conditions will be described in another paper (Nakai et al., 2011).

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Summary Several researchers have reported that the mean effective stress of unsaturated soils having a relatively high degree of saturation gradually decreases under fully undrained cyclic loading conditions, and such soils can be finally liquefied like saturated soils. This paper describes a series of simulations of fully undrained cyclic loading on unsaturated soils, conducted using an elastoplastic model for unsaturated soils. This model is a critical state soil model formulated using effective stress tensor for unsaturated soils, which incorporates the following concepts: (a) the volumetric movement of the state boundary surface containing the critical state line owing to the variation in the degree of saturation; (b) the soil water characteristic curve considering the effects of specific volume and hydraulic hysteresis; and (c) the subloading surface concept for considering the effect of density. Void air is assumed to be an ideal gas obeying Boyle's law. The proposed model is validated through comparisons with past results. The simulation results show that the proposed model properly describes the fully undrained cyclic behavior of unsaturated soils, such as liquefaction, compression, and an increase in the degree of saturation. Finally, the effects of the degree of saturation, void ratio, and confining pressure on the cyclic strength of unsaturated soils are described by the simulation results. The liquefaction resistance of unsaturated soils increases as the degree of saturation and the void ratio decrease, and as the confining pressure increases. Furthermore, the degree of saturation has a greater effect on the liquefaction resistance than the confining pressure and void ratio. Copyright © 2017 John Wiley & Sons, Ltd.

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