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1

On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil

Chwała Marcin

Studia Geotechnica et Mechanica

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2020

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Vol. 42, nr 2

125--136

EN

This paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.

2

Spatially-averaged oscillatory flow over a rough bed

Coleman S. E., Nikora V. I., Schlicke T.

Acta Geophysica

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2008

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Vol. 56, no. 3

698-733

EN

A rigorous framework involving flow decomposition and averaging is presented, within which the mechanics of rough-(e.g., rippled-) bed oscillatory flows can be better interpreted and understood. Spatiallyaveraged equations for conservation of fluid mass and momentum are developed for analyses of rapidly-changing bed conditions, e.g., for growing ripples. Where repeated observations of the changing bed conditions are available, the ensemble and spatially-averaged versions of these equations can be used for more detailed analyses of the flow dynamics. The double-averaged (in space and phase or time) equations of mass and momentum conservation are shown to be appropriate for analyses of flows over fixed rough beds and equilibrium ripples. The value of the present framework is highlighted herein by its application to PIV-measured oscillatory-flow velocities, stresses and vorticities over growing and equilibrium wave-induced intermediate-depth orbital-vortex ripples. In particular, discussions are provided regarding the mechanisms by which gravity-induced and pressure-gradient-induced momentum is transferred to the bed, with the analysis framework naturally and explicitly including the combination of the full range of fluid stresses and boundary form and skin friction drag that is important in defining the flow mechanics.

3

Double-averaged velocity profiles over fixed dune shapes

McLean S. R., Nikora V. I., Coleman S. E.

Acta Geophysica

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2008

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Vol. 56, no. 3

669-697

EN

Spatially averaged profiles of time averaged velocity, using integrals over thin horizontal slabs (Cartesian double average), are employed in characterizing the flow over fixed dune shapes. For comparison the spatial averaging method of Smith and McLean (1977) that averages along lines at constant distance from the local bed elevation is also investigated. The Cartesian double averaged profiles of the inverse of the velocity shear are nearly constant below the crest elevation, but increase rapidly above the crest level. This results in velocity profiles that increase linearly with distance from the bed below the crest. Above the crest it can be argued that the velocity increases logarithmically, but a power law profile can also be argued. Spatially averaged eddy viscosity profiles are calculated by multiplying the average Reynolds stress by the inverse shear. The resulting profile is more complex than the uniform flow counterpart.

4

Reliability of rigid piles subjected to lateral loads. a revised approach

Puła W., Różański A., Shahrour I.

Prace Naukowe Instytutu Geotechniki i Hydrotechniki Politechniki Wrocławskiej. Konferencje

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2005

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Vol. 75, nr 41

463-472

EN

In this paper the reliability of laterally loaded rigid piles in case of piles capacity is considered. A revised approach utilising the response surface method is proposed and compared with the solution presented in earlier papers. In both cases the problems were limited to non-cohesive soils only. However the expansion of the new approach on cohesive soils is going to be a near future studies. Additionally the influence of spatial averaging is also analysed in this paper.

PL

W pracy przedstawiono nową metodę oceny miar niezawodności dla przypadku nośności bocznej sztywnego pala obciążonego siłami poprzecznymi. Nowe podejście oparte na metodzie powierzchni odpowiedzi zestawiono z wcześniejszym stosującym obliczenia symboliczne w programie MATHEMATICA. Obie metody dały prawie identyczne rezultaty. Nowa metoda jest jednak prostsza pod względem obliczeń numerycznych, a ponadto daje możliwość uogólnienia na przypadek gruntów spoistych. Innym nowym elementem jest analiza niezawodności z uwzględnieniem uśrednień przestrzennych.