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An adaptive substepping explicit integration scheme is proposed for a subloading surface plasticity (SSP) model for unsaturated soils. The SSP model is referred to as the modified σ Θ model, the constitutive laws of which are established in the space of Bishop's effective stress ( σ ) and effective degree of saturation (Θ ). The modified σ Θ model includes a convex subloading surface in the p-q plane and a nonconvex subloading surface in the p- Θ plane. The convex/nonconvex subloading surface in the model may cause problems of incorrect loading-unloading decisions during the stress update. A Double Cosine loading-unloading decision method (DC method) is revised and embedded into the explicit integration scheme for the modified σ Θ model. The local error of the effective degree of saturation ( Θ ) is introduced in the error control for each substep. The performance of the DC method for the modified σ Θ model is discussed. The importance of involving the effective saturation ( Θ ) in the error control is also demonstrated via numerical examples.

Explicit integration scheme of a subloading surface plasticity model for unsaturated soils