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Mathematical and numerical analysis of a stratigraphic model

Véronique Gervais, Roland Masson (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness h , the L surface concentrations c i s in lithology i of the sediments at the top...

Mathematical and numerical analysis of a stratigraphic model

Véronique Gervais, Roland Masson (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness h, the L surface concentrations c i s in lithology i of the sediments at the...

Mathematical modelling of rock bolt reinforcement

Runt, David, Novotný, Jaroslav, Pruška, Jan (2017)

Programs and Algorithms of Numerical Mathematics

Rock bolts as construction elements are often used in underground civil engineering projects. This work deals with their numerical modelling. Aydan special finite elements for the description of rock bolts and hexahedral quadratic finite elements for the description of rock massif were used. A code for the computation of stiffness matrices and right hand sides of these elements was developed. The code was tested on several simple test examples and their results were compared with the analytical...

Mathematical modelling of rock bolt systems. I

Josef Malík (1998)

Applications of Mathematics

The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.

Mathematical modelling of rock bolt systems. II

Josef Malík (2000)

Applications of Mathematics

The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied.

Mechanical aspects of growth in soft tissues

D. Ambrosi, F. Guana (2004)

Bollettino dell'Unione Matematica Italiana

In the last years many efforts have been devoted to understand the stressmodulated growth of soft tissues. Recent theoretical achievements suggest that a component of the stress-growth coupling is tissue-independent and reads as an Eshelby-like tensor. In this paper we investigate the mathematical properties and the qualitative behavior predicted by equations that specialize that model under few simple assumptions. Equations strictly deduced from a dissipation principle are compared with heuristic...

Modelled behaviour of granular material during loading and unloading

Krejčí, Pavel, Siváková, Lenka, Chleboun, Jan (2019)

Programs and Algorithms of Numerical Mathematics

The main aim of this paper is to analyze numerically the model behaviour of a granular material during loading and unloading. The model was originally proposed by D. Kolymbas and afterward modified by E. Bauer. For our purposes the constitutive equation was transformed into a rate independent form by introducing a dimensionless time parameter. By this transformation we were able to derive explicit formulas for the strain-stress trajectories during loading-unloading cycles and compare the results...

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