scispace - formally typeset
Search or ask a question
Proceedings ArticleDOI

Vertical Stress under Point Load on Cross-Anisotropic Elastic Half-Space with Reduced Parameter Material Model

TL;DR: In this article, the vertical stress distribution in a cross-anisotropic elastic soil deposit due to a point load was studied based upon the exact solution derived by Liao and Wang (1998) that uses Fourier and Hankel transforms to solve the governing differential equations of the displacement functions.
Abstract: Natural soil deposits commonly exhibit cross-anisotropy about a vertical axis due to their depositional environment. This paper presents a study of the vertical stress distribution in a cross-anisotropic elastic soil deposit due to a point load. The study is based upon the exact solution derived by Liao and Wang (1998) that uses Fourier and Hankel transforms to solve the governing differential equations of the displacement functions. The solution has been first modified to consider a reduced parameter elastic model for cross-anisotropy as proposed by Graham and Houlsby (1983). The vertical stress distribution in the soil has been studied for a vertical point load with a varying degrees of anisotropy.
References
More filters
Book
01 Jan 1892
TL;DR: Webb's work on elasticity as mentioned in this paper is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity.
Abstract: The present treatise is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity. He has unfortunately found himself unable to proceed with it, and I have therefore been obliged to take upon myself the whole of the work and the whole of the responsibility. I wish to acknowledge at the outset the debt that I owe to him as a teacher of the subject, as well as my obligation for many valuable suggestions chiefly with reference to the scope and plan of the work, and to express my regret that other engagements have prevented him from sharing more actively in its production. The division of the subject adopted is that originally made by Clebsch in his classical treatise, where a clear distinction is ill-awn between exact solutions for bodies all whose dimensions are finite and approximate solutions for bodies some of whose dimensions can be regarded as infinitesimal. The present volume contains the general mathematical theory of the elastic properties of the first class of bodies, and I propose to treat the second class in another volume. At Mr Webb's suggestion, the exposition of the theory is preceded by an historical sketch of its origin and development. Anything like an exhaustive history has been rendered unnecessary by the work of the late Dr Todhunter as edited by Prof Karl Pearson, but it is hoped that the brief account given will at once facilitate the comprehension of the theory and add to its interest. Readers of the historical work referred to will appreciate the difficulty of giving within a reasonable compass a complete account of all the valuable researches that have been made; and the aim of this book is rather to present a connected account of the theory in its present state, and an indication of the way in which that state has been attained, avoiding on the one hand merely analytical developments, and on the other purely technical details.

7,269 citations

MonographDOI
09 Jan 2020
TL;DR: The third edition of the reference book as discussed by the authors has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results, and highlights applications in unconventional reservoirs, including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates.
Abstract: Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

1,387 citations

Journal ArticleDOI
TL;DR: In this article, the authors examined the five elastic parameters needed to describe transverse isotropy, sometimes called crossanisotropy, and proposed reasonable assumptions with easily identifiable physical significance, which permit extrapolation from triaxial to more general stress conditions.
Abstract: Lightly overconsolidated natural clays are commonly anisotropic because of their mode of deposition. They exhibit substantial ranges of approximately linear, reversible (elastic) behaviour at stress levels which do not produce yielding of the particle structure of the clay. The Paper examines the five elastic parameters needed to describe transverse isotropy, sometimes called crossanisotropy. Only three parameters can be measured in triaxial tests, and reasonable assumptions, with easily identifiable physical significance, are proposed which permit extrapolation from triaxial to more general stress conditions. Convenient parameters are identified such as the bulk modulus K, shear modulus G, and a cross modulus J which expresses the relationships in a transversely isotropic soil between mean stress and shear strain and between shear stress and volumetric strain. A least squares solution is used to evaluate these parameters from 76mm diameter triaxial tests on Lake Agassiz clay from Winnipeg, Canada. The so...

380 citations

Journal ArticleDOI
TL;DR: In this article, the Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions of the displacements and stresses in a transversely isotropic elastic half-space.
Abstract: SUMMARY We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the e⁄ect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite di⁄erent for the displacement and stress calculated from isotropic solutions. ( 1998 John Wiley & Sons, Ltd.

85 citations

Journal ArticleDOI
TL;DR: In this paper, large cylindrical block samples were obtained from an excavation in reclaimed tidelands south of the San Francisco International Airport and tested in triaxial compression with vertical and horizontal material axes.
Abstract: Consolidated-undrained tests were performed on intact specimens of San Francisco Bay mud to study the anisotropic behavior of a normally consolidated clay. Large cylindrical block samples were obtained from an excavation in reclaimed tidelands south of the San Francisco International Airport. Evidence of soil fabric and its relation to the stratigraphy of the area were studied in preparation for the investigation of anisotropy. Cubical specimens were trimmed from the block samples and tested in triaxial compression with vertical and horizontal material axes. Consolidation characteristics, as well as stress-strain, pore pressure, and strength relations, were obtained along with lateral strains in two perpendicular directions. The experimental results were carefully evaluated and showed that the clay behaved as an orthotropic material, but for practical purposes could be characterized as being cross-anisotropic. The cross-anisotropic, elastic parameters were determined and related to the initial inclinations of the effective stress paths for vertical and horizontal specimens.

68 citations