Carlo Callari

An analysis of strong discontinuities in a saturated poro-plastic solid

We present in this paper an analysis of strong discontinuities in fully saturated porous media in the infinitesimal range. In particular, we describe the incorporation of the local effects of surfaces of discontinuity in the displacement field, and thus the singular distributions of the associated strains, from a local constitutive level to the large-scale problem characterizing the quasi-static equilibrium of the solid. The characterization of the flow of the fluid through the porous space is accomplished in this context by means of a localized (singular) distribution of the fluid content, that is, involving a regular fluid mass distribution per unit volume and a fluid mass per unit area of the discontinuity surfaces in the small scale of the material. This framework is shown to be consistent with a local continuum model of coupled poro-plasticity, with the localized fluid content arising from the dilatancy associated with the strong discontinuities. More generally, complete stress–displacement–fluid content relations are obtained along the discontinuities, thus identifying the localized dissipative mechanisms characteristic of localized failures of porous materials. The proposed framework also involves the coupled equation of conservation of fluid mass and seepage through the porous solid via Darcys law, and considers a continuous pressure field with discontinuous gradients, thus leading to discontinuous fluid flow vectors across the strong discontinuities. All these developments are then examined in detail for the model problem of a saturated shear layer of a dilatant material. Enhanced finite element methods are developed in this framework for this particular problem. The finite elements accommodate the different localized fields described above at the element level. Several representative numerical simulations are presented illustrating the performance of the proposed numerical methods. Copyright

Finite element methods for the analysis of strong discontinuities in coupled poro-plastic media

This paper presents the formulation of finite element methods for the numerical resolution of strong discontinuities in poro-plastic solids. Fully coupled infinitesimal conditions are considered. These solutions are characterized by a discontinuous displacement field, with the associated singular strains, and a singular distribution of the fluid content. Here, singular distributions refer to Dirac delta functions. The singular component of the fluid content distribution models the fluid accumulated per unit area of the discontinuity surface, and it is directly related with the dilatancy characterizing singular inelastic strains localized along such a surface. It further accounts for a discontinuous fluid flow vector, given by Darcys law in terms of a continuous pore pressure field. All these considerations are incorporated in the proposed finite element methods through a local enhancement of the finite element interpolations as these discontinuities appear. The local character of these interpolations lead after the static condensation of the enhanced fields to a large-scale problem exhibiting the same structure as common finite element models of the global poro-plastic problem, but incorporating now crucially the localized dissipative effects characteristic of the localized failures. Several numerical simulations are presented to evaluate the performance of the proposed methods.

A FINITE-STRAIN CAM-CLAY MODEL IN THE FRAMEWORK OF MULTIPLICATIVE ELASTO-PLASTICITY

Abstract The present work discusses a finite-strain plasticity model for soft clays. To motivate such a model, the infinitesimal-strain assumption is shown to be inadequate for the constitutive description of soft clays. Hence, assuming the multiplicative elasto-plastic decomposition of the deformation gradient, a finite-strain Cam-clay model is presented. In particular, with respect to the original Cam-clay formulation, this model improves the description of the isotropic compression behaviour as well as of the elastic shearing response. The constitutive laws are discussed and their implications are pointed out. The physical meaning of the model parameters is carefully addressed. Finally, the ability to properly match some experimental results available in the literature is assessed.

A probabilistic method for the seismic assessment of existing concrete gravity dams

This work presents a probabilistic seismic assessment method able to manage the physical complexity of the dam–foundation–reservoir system and the uncertainties regarding structural data and external actions. The seismic response of the structure is estimated from a reduced number of dynamic time-history analyses, performed employing a finite element discretisation of dam body, reservoir water and foundation rock mass. The system fragility curves are then obtained via a standard Monte Carlo simulation procedure. The methodology has been applied to the case of Kasho Dam, a concrete gravity dam located in Japan, which experienced in 2000 the Western Tottori earthquake with no damage at dam body. The assessment has been carried out with respect to an operational limit state, for which several ‘critical’ failure mechanisms have been identified and numerically evaluated, both in terms of demand definition and capacity evaluation.

The Role of Probabilistic Methods in Evaluating the Seismic Risk of Concrete Dams

A recent research on seismic assessment of concrete dams is illustrated in this chapter, including a brief comparison with other available approaches to the subject. The work of the authors has been focused on development and validation of a probabilistic methodology taking into account the uncertainties affecting structural data and external actions as well as the physical complexity of the dam-foundation-reservoir system. The seismic response of such a system is estimated from a reduced number of dynamic finite element analyses and the corresponding fragility curves are obtained via a Monte Carlo simulation procedure. The main results of the application of the proposed methodology to the case of an existing concrete gravity dam are finally summarized.

Computational Modeling of Backward Erosion Piping

This work presents a short account of some recent advances in the numerical simulation of backward erosion piping, accomplished in the framework of a collaborative research between Italian and French research groups. After a brief review of the state of the art in engineering practice and research, we outline the key points of a novel approach and show some of the results obtained in an extensive validation work.

A Numerical Approach for the Analysis of Piping Erosion in Hydraulic Works

A method recently proposed for the computational modeling of backward erosion piping is applied for the numerical back-analysis of some pioneering experimental tests on physical models of cofferdams performed by Marsland (1953).