In this paper, two complex critical-state models are implemented in a displacement finite element code. The two models are used for structured clays and sands, and are characterized by multiple yield surfaces, plastic yielding within the yield surface, and complex kinematic and isotropic hardening laws. The consistent tangent operators - which lead to a quadratic convergence when used in a fully implicit algorithm - are difficult to derive or may even not exist. The stress integration scheme used in this paper is based on the explicit Euler method with automatic substepping and error control. This scheme employs the classical elastoplastic stiffness matrix and requires only the first derivatives of the yield function and plastic potential. This explicit scheme is used to integrate the two complex critical-state models - the sub/super-loading surfaces model (SSLSM) and the kinematic hardening structure model (KHSM). Various boundary-value problems are then analysed. The results for the two models are compared with each other, as well with those from standard Cam-clay models. Accuracy and efficiency of the scheme used for the complex models are also investigated.
International Journal for Numerical and Analytical Methods in Geomechanics Vol. 29, no. 12, p. 1209-1229