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Unsaturated soils are often encountered in civil engineering practice, such as compaction works in construction of roads, dams and other types of embankment. In unsaturated soil stress-strain behavior is complex and is influenced by many factors including externally applied stresses, soil type, structure, density, and suction. Therefore, constitutive models for soils should ideally represent the soil behavior over entire ranges of possible pore pressure and stress values. In the literature, there are different approaches differing upon the choice of the set of suitable variables describing the material behavior. This choice is a key point in unsaturated soils modeling. Possible pairs of suitable stress variables for use in unsaturated soil mechanics presented by Fredlund and Morgenstern (1977) with Three combinations Consist of and , and , and . The stress-state variables employed in early models are the net stress and the suction. It is the simplest and most practical choice in terms of stress path representation, but, it poses difficulties when trying to incorporate hydraulic hysteresis effects. This combination could fail to provide a straightforward transition between saturated and unsaturated states, i.e. for a null suction. On the other hand Terzaghi’s effective stress cannot be exactly recovered. Also these stress variables were also difficult to implement in existing finite element codes for saturated soils because most saturated soil relations are described in term of effective stress. The effective stress principle is probably the single most fundamental contribution in the field of soil mechanics. In the other hand, it is true to say that the principle of effective stress lies at the foundation of most modem soil mechanics theory and practice. Therefore, the choice of appropriate stress variables for unsaturated soils has often been an intensively debated issue, often in connection with the possibility of defining an effective stress measure. So far, many efforts have been made to the development of effective stress for unsaturated soils in the literature. This paper presents a comparison between the values of effective stress parameter of unsaturated granular soils obtained from relations proposed by Schrefler, Aitchison, Kohgo, Khalili-Khabbaz and Dangla-Coussy with special regard into the critical state concept. The principle is to re-plot experimental data obtained of both consolidated drained and constant water content tests in conventional stress–strain coordinates, stress variables being usually net stress and suction, into new effective stress coordinates. The critical state lines (CSL) at different suction values tend to converge remarkably towards a unique saturated line in the deviatoric stress versus mean effective stress coordinates. Therefor since critical state lines presented as independent of suction, comparison of soil properties in many cases becomes easier. The comparison results show that effective stress values determined from the relations proposed by Khalili-Khabbaz well best agrees with the values from the both type test results

Keywords: Effectve stress, unsaturated soil, critical state line, Validation, independent stress variables

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