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... he full DRO policy for further details. ABSTRACT 4 Linear elastic-perfect plasticity using the Mohr-Coulomb yield surface is one of the most widely 5 used pressure-sensitive constitutive models in engineering practice. In the area of geotechnical 6 engineering a number of problems, such as cavity expansion, embankment stability and footing 7 bearing capacity, can be examined using this model together with the simplifying assumption of 8 plane-strain. This paper clarifies the situation regarding the direction of the intermediate principal 9 stress in such an analysis and reveals a unique relationship between hydrostatic pressure and the 10 principal stress ratio for Mohr-Coulomb and Tresca perfect plasticity under those plane-strain 11 conditions. The rational relationship and direction of the intermediate principal stress are illustrated 12 through both material point and finite-element simulations. The latter involves the analysis of a 13 rigid strip footing bearing onto a weightless soil and the finite deformation expansion of a cylindrical 14 cavity. 15 Keywords: Intermediate principal stress, Mohr-Coulomb, Tresca, elasto-plasticity, plane-strain 16 analysis, geomaterials. 17 √ 3 2 J 3 J 3/2 2 ∈ −π/6, π/6 . (2) 2 The deviatoric stress invariants are given by J 2 = tr([s] 2 )/2 and J 3 = tr([s] 3 )/3, where the traceless 46 deviatoric stress matrix [s] = [σ] − ξ[I]/ √ 3 and [I] is the third-order identity matrix. 47 The layout of the paper is as follows. Initially the M-C constitutive relations are presented, 48 including the isotropic linear stress-elastic strain law, yield criterion and plastic flow direction. The 49 next section restricts the M-C constitutive model to the case of plane-strain analysis and derives the 50 relationship between the hydrostatic stress, ξ, and the principal stress ratio, b. The limiting cases 51 of triaxial compression (b = 0; σ 2 = σ 1 ) and extension (b = 1; σ 2 = σ 3 ) are also considered. The 52 simplification of the M-C ξ versus b relationship for the Tresca constitutive model is given and the 53 rational relationship extended to account for inelastic straining in the out-of-plane direction induced 54 by the corners present in the yield envelopes. Following this, a simple material point investigation is 55 used to investigate the assumption that the out-of-plane stress is indeed the intermediate principal 56 stress. Three finite-element investigations using the M-C model are then presented: (i) a simple 57 two-element simulation, (ii) an analysis of a rigid strip footing bearing onto a weightless soil and (iii) 58 a finite deformation cavity expansion simulation. These simulations provide numerical verification 59 of the ξ-b relationship for the M-C model. Conclusions are drawn in the final section. 60 MOHR-COULOMB CONSTITUTIVE FORMULATION 61 The constitutive laws for (and the algorithmic treatment of) the isotropic linear elastic-perfectly 62 plastic M-C model are widely available in literature (for example, see the papers by Clausen et al. 63 (2006, 2007) and references cited therein). Here, to aid clarity, the basic equations required in the 64 later sections of this paper are reviewed briefly. 65