A nonlinear constitutive model for beam elements with cyclic degradation and damage assessment for advanced dynamic analyses of geotechnical problems. Part I: theoretical formulation

摘要

Dynamic soil-structure interaction (SSI) represents an interdisciplinary subject characterized by complex geometrical and material nonlinearities affecting both the soil and the structural components of the system under study. In the current practice, SSI problems are often solved using the so-called substructure method based on decomposing the superstructure-foundation-soil system into two subsystems whose response is determined independently. The direct method is a more general procedure to tackle SSI problems which is in principle capable of accounting for both soil and structural nonlinearities. Despite this generality, most of the current computational platforms are specialized either for structural applications or for geotechnical applications. Whereas the formers are capable to accurately reproduce the nonlinear response of the structural elements, they are usually poor in modeling soil nonlinear behaviour especially under earthquake loading. On the other hand, the latter do the reverse: they are advanced in modeling soil response but typically rough in reproducing the behaviour of the structural components of the system. Inevitably, all structures interact with the ground and therefore the need to model material and geometric nonlinearities maybe important both in the ground and structural elements. The variation of the stiffness mismatch between soil and structural elements during ground motions is one of the most influential parameters for the assessment of the kinematic component in SSI problems. The variation of the stiffness ratio is mainly governed by material nonlinearity that can develop in either the soil or the structural parts of the system. This paper presents a nonlinear constitutive model for beam elements that is compatible with performance-based earthquake engineering principles because it is capable to simulate the cyclic degradation of mechanical properties and to assess the damage suffered by the structural system. The proposed model is based on distributed plasticity and can be easily implemented in any computational platform allowing the use of an explicit solver. The article describes the theoretical aspects of the model. Validation and application of the model to the solution of a dynamic soil-structure interaction problem where the nonlinear behaviour of geomaterials is coupled with the inelasticity of structural elements, are presented in a companion paper (Andreotti and Lai in Bull Earthq Eng 2017).