K. Krabbenhoft

Lower Bound Limit Analysis Of Slabs With Nonlinear Yield Criteria

A finite element formulation of the limit analysis of perfectly plastic slabs is given. An element with linear moment fields for which equilibrium is satisfied exactly is used in connection with an optimization algorithm taking into account the full nonlinearity of the yield criteria. Both load and material optimization problems are formulated and by means of the duality theory of linear programming the displacements are extracted from the dual variables. Numerical examples demonstrating the capabilities of the method and the effects of using a more refined representation of the yield criteria are given.

Computation of Effective Cement Paste Diffusivities from Microtomographic Images

A computational framework for extracting effective diffusivities from microtomographic images is presented. As an example of the capabilities of this framework, the effective diffusivity of a cement paste whose microstructure has been digitized to a resolution of 1 μm is derived. Besides presenting a consistent homogenization procedure, the importance of statistical testing is also highlighted. Indeed, for the problem at hand, it appears that statistical testing and subsequent interpretation of the results in terms of statistical quantities is a necessity for obtaining quantitative information on the property of interest.

Bearing Capacity of Strip Footings in Cohesionless Soil Subject to Eccentric and Inclined Loads

AbstractLower-bound calculations based on the FEM are used to determine the bearing capacity of a strip foundation subjected to an inclined, eccentric load on cohesionless soil with varying surcharges and with friction angles of 25, 30, and 35°. The soil is assumed to be perfectly plastic following the Mohr-Coulomb failure criterion. The results are reported as graphs showing the bearing capacity as a function of the friction angle, eccentricity, inclination, and surcharge. These results have been compared, and for smaller eccentricities, except in the case of no surcharge, the lower-bound values are the greater, the discrepancy increasing with growing surcharge. Positive load inclinations have a negative effect for smaller eccentricities but may have a beneficial effect on the bearing capacity for greater eccentricities. Negative load inclinations have the opposite effect, and especially for small friction angles and great surcharges, other values are considerably greater than the lower-bound values.

Effects of pCO2 on the Removal of Fluoride from Wastewater by Calcite

AbstractFree-drift batch reactor experiments using calcite (limestone, CaCO3) were used to study fluoride removal through precipitation as fluorite (CaF2) from solutions with concentrations reflective of an industrially contaminated site. The influence of CO2 partial pressure (pCO2), stirring rate, and fluoride concentration were investigated in this paper. Equilibrium modeling shows that in wastewaters with high fluoride concentrations (∼2,000  mg/L), the flux of CO2(g) to CO2(aq) could not keep up with the consumption of CO2(aq), resulting in an initial disequilibrium with experimental pH reaching equilibrium quickly, while fluoride removal lagged. Increasing stirring rate significantly decreased the extent of disequilibrium and the time at which the CaCO3-fluoride-CO2 system attained equilibrium due to the increased rate of transport of dissolved CO2 to the CaCO3 surface, and simultaneously the rate of transport of the dissolved CaCO3 to the bulk solution. Optimal fluoride removal occurs at pCO2∼10−0.5...

Double porosity models for the description of water infiltration in wood

In this paper some of the possibilities of applying double porosity and permeability models to the problem of water infiltration in wood are explored. It is shown that the double porosity model can capture a number of commonly reported anomalies including two-stage infiltration/sorption and apparent sample length dependent transfer parameters. Starting with the double porosity model, several extensions are discussed and the type of principal behaviour possible with the models is elaborated on. Finally, a set of highly anomalous experimental results is fitted to within a reasonable accuracy by a double permeability model.

An Indirect Approach for Correlation of Permeability and Diffusion Coefficients

Diffusion tests in porous media are quite sensitive and long lasting procedures compared to permeability tests, which are usually more reliable and of shorter duration. Both diffusion and advection phenomena are dependent on the tortuosity of the material tested. A relevant question is to know whether it is possible to correlate permeability tortuosity p and diffusion tortuosity d. Several diffusion and permeability tests have been performed on non-uniform sand specimens having different grain size distribution. For each specimen, both the permeability and diffusion coefficients have been measured and two tortuosity factors (permeability and diffusion) have been back calculated. A theoretical model has been proposed to estimate d from p for a non-uniform granular material. The maximum particle diameter dmax is used to determine the maximum hydraulic diameter dh-max using the Hydraulic Radius Theory (HRT) for a 3D arrangement of spheres of same diameter dmax. Then, a filling factor  is applied to dh-max in order to capture the fact that smaller grains tend to fill the voids present in between the bigger particles. The filling factor is based on the coefficient of uniformity Cu. Relatively good results are obtained so that this model allows estimating the diffusion properties from a simple permeability test rapidly and at a fraction of the diffusion test cost.

Formulation of non-standard dissipative behavior of geomaterials

Abstract.In this paper, fundamental mathematical concepts for modeling the dissipative behavior of geomaterials are recalled. These concepts are illustrated on two basic models and applied to derive a new form of the evolution law of the modified Cam-clay model. The aim is to discuss the mathematical structure of the constitutive relationships and its consequences on the structural level. It is recalled that non-differentiable potentials provide an appropriate means of modeling rate-independent behavior. The Cam-clay model is revisited and a standard version is presented. It is seen that this standard version is non-dissipative, which at the same time explains why a non-standard version is needed. The partial normality is exploited and an implicit variational formulation of the modified Cam-clay model is derived. As a result, the solution of boundary-value problems can be replaced by seeking stationary points of a functional.

Discretization Errors of Random Fields in Finite Element Analysis

The mechanical properties of natural materials such as rocks and soils vary spatially. This randomness is usually modelled by random field theory so that the material properties can be specified at each point in space. When these point-wise material properties are mapped onto a finite element mesh, discretization errors are inevitable. In this study, the discretization errors are studied and suggestions for element sizes in relation with spatial correlation lengths are given.

Parallel preconditioned conjugate gradient method for large sparse and highly ill-conditioned systems arising in computational geomechanics

The efficiency of parallel preconditioned conjugate gradient PCG algorithm for solving large sparse linear systems arising from application of interior point methods to conic optimisation problems in the context of nonlinear finite element limit analysis FELA for computational geomechanics is studied. For large 3D problems, the use of direct solvers in general becomes prohibitively expensive owing to exponentially growing memory requirements and computational time. And the so-called saddle-point systems resulting from use of optimisation framework is not an exemption. On the other hand, although preconditioned iterative methods have moderate storage requirements and therefore can be applied to much larger problems than direct methods, they usually exhibit high number of iterations to reach convergence. In the present paper, we show that this problem can be effectively tackled using efficient variants of sparse approximate inverse preconditioners along with an elaborate parallel implementation on multicore CPUs and significant improvements can be achieved by parallel implementation on graphic processing unit GPU. Furthermore, the efficiency of our proposed implementation is verified by the presented numerical results.

Interface Modelling in Computational Limit Analysis

In many geotechnical stability problems it is important to account for interface conditions between two or more adjoining bodies, e.g. retaining walls and footings with no-tension contact between soil and structure. These interfaces can be considered as discontinuities in stress and velocity fields developed in the system undergoing plastic collapse. Discontinuous variable fields are routinely employed in FE lower and upper bound limit analyses to improve the performance of lower order elements used to obtain rigorous bounds on the collapse factor. Traditionally, stress and velocity discontinuities have been implemented as a set of special equalities on the stress and velocity variables of adjacent nodes across inter-element boundaries. The major drawback of this approach is that the velocity discontinuities are restricted only to materials with Tresca or Mohr-Coulomb yield criteria. Recently, however, it was shown that velocity discontinuities can be represented by a patch of regular elements of zero thickness. This development opens the way for a discontinuous upper bound formulation to be used with general yield criteria in both two- and three-dimensions. By also treating stress discontinuities as a patch of zero thickness elements in a lower bound formulation, lower and upper bound FE methods can be used effectively to solve stability problems involving a wide variety of materials and interface conditions.