Empirical Relationships Between the Elastic Settlement of Rigid Rectangular Foundations and the Settlement of the Respective Flexible Foundations

The problem of settlement of shallow foundations is among the most important ones in classical soil mechanics. And while for the settlement of flexible foundations elastic solutions are widely used, for rigid rectangular foundations where the actual contact pressure distribution is still unknown, the problem is approximated either analytically assuming a contact pressure distribution or semi‐empirically combining the theory of elasticity with experimental and/or numerical results. A third and often attractive choice is the use of simple empirical relationships or relevant tabulated values relating the elastic settlement of rigid foundations (ρ_R) with the settlement of the respective flexible foundations (e.g. at the center, ρ_Ce). Reviewing the relathionships of this third approach, the author revealed serious lack of consesous between the various sources; for example, according to the literature, ρ_R ranges between 68 and 125% of ρ_Ce, the time when it is well-known that ρ_R?<?ρ_Ce. In this paper, comparison of the settlement of 210 rigid foundation cases derived from 3D elastic finite element analysis, with the settlement of the respective flexible foundations derived from the theory of elasticity, led to simple empirical relationships between ρ_R and ρ_Ce as well as between ρ_R and ρ_Av (ρ_Av?=?average settlement of the flexible foundation) with coefficient of determination (R²) almost unity. The analysis showed that these relationships are largely independent of the aspect ratio of foundations and the thickness and Poisson’s ratio (ν) of the compressible medium, although separate relationships are given for ν?=?0.5, slightly increasing R². Finally, a correction factor for foundation rigidity is given exploting the known linear relationship that exists between the relative stiffness factor of foundations and settlement.

     

The Equivalent Modulus of Elasticity of Soil Mediums for Designing Shallow Foundations

Geotechnical and Geological Engineering - As known, in a Winkler type of analysis the soil medium underneath the foundation is violently replaced by a row of parallel springs having constant ks....     

Voronoi tessellation on the ellipsoidal earth for vector data

Voronoi tessellation, and its dual the Delaunay triangulation, provide a cohesive framework for the study and interpretation of phenomena of geographical space in two and three dimensions. The planar and spherical solutions introduce errors in the positional accuracy of both Voronoi vertices and Voronoi edges due to errors in distance computations and the path connecting two locations with planar lines or great circle arcs instead of geodesics. For most geospatial applications the introduction of the above errors is insignificant or tolerable. However, for applications where the accuracy is of utmost importance, the ellipsoidal model of the Earth must be used. Characteristically, the introduction of any positional error in the delimitation of maritime zones and boundaries results in increased maritime space for one state at the expense of another. This is a situation that may, among others, have a serious impact on the financial activities and the relations of the states concerned. In the context of previous work on maritime delimitation we show that the Voronoi diagram constitutes the ideal solution for the development of an automated methodology addressing the problem in its entirety. Due to lack of a vector methodology for the generation of Voronoi diagram on the ellipsoid, the aforementioned solution was constrained by the accuracy of existing approaches. In order to fill this gap, in this paper we deal with the inherent attributes of the ellipsoidal model of the Earth, e.g. the fact that geodesics are open lines, and we elaborate on a methodology for the generation of the Voronoi diagram on the ellipsoid for a set of points in vector format. The resulting Voronoi diagram consists of vertices with positional accuracy that is only bounded by the user needs and edges that are comprised of geodesics densified with vertices equidistant to their generators. Finally, we present the implementation of the proposed algorithm in the Python programming language and the results of two case studies, one on the formation of closest service areas and one on maritime boundaries delimitation, with the positional accuracy set to 1 cm.     

Stability of earth slopes. Part I: two‐dimensional analysis in closed‐form

A closed‐form solution (CFS) satisfying both equilibrium of moments and forces for the stability analysis of earth slopes in 2D is proposed. The sliding surface is assumed circular and treated as a rigid body, allowing the internal state of stress to be ignored. The proposed solution can be applied to both homogenous and non‐homogenous slopes of either simple or complex geometry, and can also deal with any kind of additional loading. The method is based on the fact that, all possible forces acting on the slope can be projected onto the failure surface where they are broken into driving and resisting ones. Comparison of the safety factors obtained by the proposed CFS and those obtained by traditional limit equilibrium methods, as applied to several test examples, indicates that the proposed method is more conservative, whereas moreover, it gives a more realistic point of view for the formation of tension crack in slopes. Copyright © 2012 John Wiley & Sons, Ltd.     

Choosing a Suitable Projection for Navigation in the Arctic

Navigation at sea is based on Electronic Chart Display and Information Systems (ECDIS) that allow for the use of a limited number of projections. As navigation in the Arctic region becomes a reality due to the progressive melting of the polar ice cap, a re-examination of the most suitable projections for navigation in the Arctic becomes timely. Several projections are proposed in the literature for this area. In our approach, the selection is based on an analytical study utilizing three criteria: the control of the magnitude of distortions within acceptable limits, the shape of great circles (GCs) and rhumb lines/loxodromes, and the shape of the graticule lines portrayed on the chart. The analysis carried out shows that to fulfill the set criteria, the arctic area should be divided into Arctic and sub-Arctic regions. More specifically, for the Arctic region the Azimuthal Polar Equidistant projection and the Azimuthal Polar Stereographic projection are the most suitable ones. For the sub-Arctic region, the Lambert Conformal Conic and the Conic Equidistant projection are considered more appropriate. All four projections proposed can be used for both the traditional nautical chart and the ECDIS, and both are considered as the starting point for further study of specific ECDIS requirements.     

Stability of earth slopes. Part II: three dimensional analysis in closed‐form

A closed‐form stability analysis of earth slopes performed in 3D is proposed. The sliding surface is assumed spherical and treated as a rigid body allowing the internal state of stress to be ignored. The proposed closed‐formed solution (CFS) can be applied to both homogenous and non‐homogenous slopes of either simple or complex geometry and can also deal with any kind of additional loading. Although it is recognized that the critical failure surface is often non‐spherical, the CFS methodology for spheres described herein provides an objective tool for the evaluation of the assumptions made by other limit equilibrium methods including the role of intercolumn forces. Copyright © 2012 John Wiley & Sons, Ltd.