Review
Poisson's ratio values for rocks

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Abstract

Compared to other basic mechanical properties of rocks, Poisson's ratio is an elastic constant of which the significance is generally underrated. Yet, in rock mechanics, there is a considerable number of diverse areas which require a prior knowledge or estimation of the value of Poisson's ratio. This paper examines the values and applications of Poisson's ratio in rock mechanics. Following an historical account of the initial controversy, whether it was a material constant or not, the effects of Poisson's ratio in the elastic deformation of materials, intact rocks, and rock masses are briefly reviewed. Also, the reported values of Poisson's ratio for some elements, materials, and minerals are compiled while typical ranges of values are presented for some rocks and granular soils. Finally, Poisson's ratio classifications are recommended for isotropic intact rocks.

Introduction

ISRM Commission on Terminology, Symbols and Graphic Representations defines Poisson's ratio as “the ratio of the shortening in the transverse direction to the elongation in the direction of applied force in a body under tension below the proportional limit” [1]. It is a surprising fact that this definition leaves much to be desired, i.e. it is mechanically inaccurate and unsatisfactory. To begin with, unless the initial dimension of the body parallel to loading is equal to its lateral dimension, the definition should involve strains not the dimensional changes such as shortening or elongation. Then, there is the question of missing negative sign before the ratio. Besides, the uniaxial loading may be not only tensile but compressive as well. Yet, the ISRM definition has not been corrected for about 30 years.

The importance of this mechanical property has not been appreciated as much as it deserves since the values of Poisson's ratio reported for rocks vary in a narrow range. Although the use of approximate or typical values in most rock mechanics applications does not create significant problems, Poisson's ratio plays an undeniably important role in the elastic deformation of rocks and rock masses subjected to static or dynamic stresses. Furthermore, its effects emerge in a wide variety of rock engineering applications, ranging from basic laboratory tests on intact rocks to field measurements for in situ stresses or deformability of rock masses. Therefore, information on various aspects of Poisson's ratio can be beneficial for rock engineering.

This paper aims to review the values of Poisson's ratio for rocks. First, some historical information on Poisson's ratio is summarized, and its importance in mechanics is emphasized. Then, its significance in rock mechanics is reviewed by particular references to minerals, intact rocks, jointed rock masses, and rock engineering applications. Also, recommendations are given for classification of intact rocks based on their Poisson's ratio.

Section snippets

Historical background

Thomas Young (1773–1829) drew the attention of his readers to a phenomenon in his Course of Lectures which was published in 1807. He noted that, during the experiments on tension and compression of bars, longitudinal deformations were always accompanied by some change in the lateral dimensions [2].

Siméon Denis Poisson (1781–1840), in his famous memoir [3], which was published in the year Young died but had been read to the Paris Academy on the 14th of April 1828 [4], made a proposal about an

Poisson's ratio in mechanics

Before emphasizing the significance of Poisson's ratio in mechanics, an accurate definition of this interesting property should be made. There are numerous definitions of Poisson's ratio in the literature and many lack completeness. Poisson's ratio, simply, is the negative of the ratio of transverse strain to the axial strain in an elastic material subjected to a uniaxial stress. In mechanics of deformable bodies, the tendency of a material to expand or shrink in a direction perpendicular to a

Poisson's ratio in rock mechanics

Since Poisson's ratio is a mechanical property that plays a role in the deformation of elastic materials, it is utilized in rock engineering problems associated with the deformation of rocks, e.g. it is a required computational input for the numerical stress analyses. In the related literature [33], [34], though very seldom, negative values or values greater than 0.5 are reported for Poisson's ratio of some rock types. Those few cases, probably, are associated with highly anisotropic rocks;

Recommendations for classification

During the preparation of this review, it was noticed that there was not any Poisson's ratio classification for rocks although a number of classifications existed about some mechanical, physical and index properties of intact rocks. For example; those involving the uniaxial compressive strength (σci) [95], [96], [97], [98], [99], [100], [101], Young's modulus (E) [99], cohesion (c) [102], unit weight (γ) [103], point load strength index (Is(50)) [104], [105], slake durability index (Id) [106],

Conclusions

Poisson's ratio is an interesting mechanical property of elastic solids. Its significance in mechanics and rock engineering applications is much greater than that is implied by the narrow range of values it usually assumes. The data compiled in the paper can be used in engineering applications which require an estimation of Poisson's ratio. Also, the classifications recommended for Poisson's ratio of rocks are simple and easy to remember, and they can be utilized for qualitative grouping of

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