Summary of the poissons ratio debate 1990 2003 cseg recorder. An experimental investigation of shale mechanical properties. Compared to other basic mechanical properties of rocks, poisson s ratio is an elastic constant of which the significance is generally underrated. Conventional materials contract laterally when stretched and poisson s rati. Consider a large rectangular plate under uniform temperature increase. Two to three meters of rock with a poisson s ratio greater than 0. Determination of poissons ratio for rocks by static and. Poisson s ratio poisson s ratio when a force is applied to a body, at right angles to the force, a certain amount of lateral transverse expansion or contraction takes place. While our clients data reflected very low modulus, the reported poissons ratio. Stress is a concept which is fundamental to rock mechanics principles and applications. The deformation modulus is youngs modulus e for a rock mass erm or a soil mass. Introduction to poissons ratio mechanics of materials duration. Correlation between poissons ratio and porosity in porous materials article pdf available in journal of materials science 414.
Results of measurements and calculations are given in table 1. Sh min importance of static youngs modulus and poisson s ratio for hydrofracture design static moduli are often used in wellbore stability and insitu stress applications to evaluate the possibility of breakouts, elevated pore pressure, and tectonic stress. At low effective stresses open cracks will lower the poisson s ratio significantly, while at high effective stress the majority of cracks are closed and poisson s ratio is primarily influenced by the rock matrix and will tend to increase. Following an historical account of the initial controversy, whether it was a material constant or not. However the result from modeling shows an added value to strain due poissons ratio. How such materialswhich have a negative poisson s ratio can be created with specific properties, the implications of these unusual properties, and recent advances are discussed. Applied rock mechanics training course petroskills arm. In the petroleum engineering industry, geomechanics is used to predict important parameters, such as insitu rock stress, modulus of elasticity, leakoff coefficient and poisson s ratio. The proposed the yield strength criterion f is not only related to friction angle and cohesion of jointed rock masses at the visual angle but also related to the intersection angle between the visual angle and the.
Poissons name survives in poissons integral, poissons distribution in statistics, poissons constant in electricityand poissons ratio. Basic mechanics of soils university of the west of. Drilling operations and well design, second edition, keeps petroleum and drilling engineers centrally focused on the basic fundamentals surrounding geomechanics, while also keeping them uptospeed on the latest issues and practical problems. Some properties, such as tension parallel to the grain, and all properties.
In addition, the calculated logging values should be calibrated with experimental measurements of rock mechanics. Limits of poissons ratio in isotropic solid stack exchange. Poissons ratio of dry rock versus poisson ratio of rock solid at 10 mpa. Drilling operations and well design covers the fundamentals of solid mechanics and petroleum rock mechanics and their application to oil and gasrelated drilling operations and well design. Solid mechanics part i kelly158 the material symmetry inherent in the orthotropic material reduces the number of. The dynamic elastic constants can be derived with appropriate equations, using sonic log compressional and shear travel time along with density log data. Poisson s ratio is defined as the negative of the ratio of the lateral strain to the axial strain for a uniaxial stress state. In order to promote public education and public safety, equal justice for all, a better informed citizenry, the rule of law, world trade and world peace, this legal document is hereby made available on a noncommercial basis, as it is the right of all humans to. Characterization of geologic materials abdul shakoor.
A constitutive model for jointed rock mass, which can consider the persistence ratio in different visual angle, is proposed. In all fairness it must be stated that in recent years the underlying assumptions for using poissons ratio in rock mechanics have been questioned and the. Most materials have poisson s ratio values ranging between 0. In general, the stresses on another plane will be different. Youngs modulus, and poissons ratio, play an important role in wellbore stability. Anisotropic modulus of elasticity and poissons ratio. Typical values of modulus of elasticity of some common are given in the table below. United states through a comparison of rock mechanics laboratoryreported youngs modulus and poissons ratio values likely a consequence of the too often misunderstood and missapplied brittleness concept.
Poissons ratio, denotit an named efter simeon poisson, is the signed ratio o transverse streen tae axial streen. Jan 16, 2018 for the love of physics walter lewin may 16, 2011 duration. Its an empirical relationship, based on the data shown, and is perhaps useful in the barnett or wherever the data are from, we arent told. The poisson s ratio at 600 mpa approximates the values for quartz single crystal 0. Poissons ratio is a measure of the poisson effect, that describes the expansion or contraction of a material in directions perpendicular to the direction of loading. Static and dynamic elastic properties, the cause of the. It is common practice to choose a net effective stress that is thought to result in identical rock properties. During triaxial compression, you can estimate poisson s ratio by measuring lateral expansion of the specimen while measuring vertical compression of course. The static poisson ratios of rocks increase with the pressure both under simple and under hydrostatic compression. Rock physics aims to characterize rock properties based on the behavior of seismic waves propagating through them.
Where evaluation of elastic settlement is critical to the design of the foundation or. In mechanics, poissons ratio is the negative of the ratio of transverse strain to lateral or axial strain. Compared to other basic mechanical properties of rocks, poissons ratio is an elastic constant of which the significance is generally underrated. For elastic and isotropic materials, the elastic constants are interrelated. Now, to actually answer your original question, we need to formulate poisson s ratio in terms of the quantities g and k. Elastic properties of rock poissons ratio often is used to express the plasticity of. The relationship between void ratio and effective vertical stress, p, is shown on. In order to promote public education and public safety, equal justice for all, a better informed citizenry, the rule of law, world trade and world peace, this legal document is hereby made available on a noncommercial basis, as it is the right of all humans to know and speak the laws that govern them. Tools for seismic analysis in porous media, cambridge. The effect of water on rock mechanical properties has been studied for many. The effect of poissons ratio on fracture height onepetro.
Pdf correlation between poissons ratio and porosity in. Aug 03, 2016 material scientists fascination with negative poisson s ratio nanowerk spotlight poisson s ratio describes the fundamental elasticity of any solid. An elastic constant that is a measure of the compressibility of material perpendicular to applied stress, or the ratio of latitudinal to longitudinal strain. Since poissons 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. Poissons ratio measures the ratio of lateral strain to axial strain at linearly elastic region. An introduction to engineering properties of soil and rock. Most car mechanics are aware that it is hard to pull a rubber hose e.
Bentley abstract poissons ratio is determined by two independent factors, i. Poissons ratio 42 modulus of rigidity 43 strength properties 43. Jan 01, 2007 read poisson s ratio values for rocks, international journal of rock mechanics and mining sciences on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Elastic properties youngs modulus, shear modulus, bulk modulus, and poissons ratio see stress strain relationships in rocks for calculations of these properties. The effect of poissons ratio on rock properties onepetro. Static and dynamic elastic properties, the cause of the difference and conversion methods case study.
The drained poissons ratios were, on average, 40 % or lower than the. It means that when a material is loaded within elastic limit than the ratio of lateral strain to the longitudinal strain gives us a constant called poissons ratio. Poissons ratio poissons ratio when a force is applied to a body, at right angles to the force, a certain amount of lateral transverse expansion or contraction takes place. Rocks, like most materials, are subject to poissons effect while under stress.
It is named after simeon poisson and denoted by the greek letter nu, it is the ratio of the amount of transversal expansion to the amount of axial compression for small values of these changes. First, the factors that determine the magnitude of a dynamic poisson ratio. Poisson s ratio can be made either greater or less than 14 or can be made negative as shown in fig. Rather than go through the pages of algebra to do so, i will direct you to a table at the bottom of this page. Young s modulus and poisson s ratio are measured directly in uniaxial compression or extension tests, i. Rock testing introduction rock mechanics is a field of applied science and has been recognized as a discipline in engineering since the last four decades.
These properties are represented as the average mechanical properties of the species. Poisson s ratio and shear modulus can be determined by dynamic. It is named after simeon poisson and denoted by the greek. Rock mechanics laboratory testing for youngs modulus and poissons. Determine the new diameter of a cylinder as a result of an applied axial load using poisson s ratio.
The poisson s ratio becomes positive only when p 400 mpa. The material for which the data is given in an anisotropic material, therefore i need to calculate modulus of elasticity and poisson s ration is x,y. Crains petrophysical handbook elastic constants mech. Standard test method for dynamic youngs modulus, shear. 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. It is a study on the mechanical properties and behaviors of rock under loading mechanics, sets of established principles expressing rock mass response to load, and a logical methodology for applying these notions and techniques. In addition to a comprehensive manual, software is provided for the student to perform wellbore stability calculations. Advances in negative poissons ratio materials lakes. Design manual engineering properties of soil and rock. The former is influenced by the constituent mineral composition. If a tensile load is applied to a material, the material will elongate on the axis of the load perpendicular to the tensile stress plane. Study on the constitutive model for jointed rock mass.
Thus, it points out the importance of poisson s ratio in the understanding of some of the questions in rock mechanics. Poissons ratio and thermal expansion comsol multiphysics. The average value of poissons ratio for steels is 0. Poissons ratio and auxetic properties of natural rocks ji. It is defined as the ratio of lateral strain to the longitudinal strain within elastic limit. Gercek 2007 found that the value of poissons ratio for the rock mass was larger than the value for the intact rock in majority of the cases and concluded that the poissons ratio for the rock mass is about 20% higher than that of the intact rock. Crains petrophysical handbook calculating mechanical. Standard test method for dynamic youngs modulus, shear modulus, and poissons ratio by impulse excitation of vibration1 this standard is issued under the. The harder the rock, the less does the poisson ratio. Inelastic properties fracture gradient and formation strength. Increased moisture content increases the static poisson ratio. Poissons ratio values for rocks request pdf researchgate. The value of poisson s ratio is the negative of the ratio of transverse strain to axial strain.
The higher poissons ratio of the rock solid is, the higher is poissons ratio of the rock. Measuring the static poissons ratio is cumbersome and few values exist in the literature and there is a great temptation to use the abundant dynamic poissons ratio values available. An introduction to two of the most important properties of materials, including rocks. This response gives rise to the poisson ratio effect. Appendix 2 lists the laboratory mechanical properties of rocks. Thus, it points out the importance of poissons ratio in the understanding of some of the questions in rock mechanics. The value of poissons ratio in saturated soils and rocks stressed under undrained conditions. For most rocks, the value of poissons ratio ranges in between 0. Poissons ratio longitudinal strain and lateral strain in mechanics, poissons ratio is the negative of the ratio of transverse strain to lateral or axial strain. Poissons ratio of dry rock versus poisson ratio of rock solid at 100 mpa. It compiles data scattered in many papers and books published around the world. The value of poissons ratio is the negative of the ratio of transverse strain to axial strain. Dec, 2016 my book rock mechanics an introduction, is an attempt to cover some important topics like stereographic projections, rock mass classification, intact rock tests, and some applications, in a. This paper examines the values and applications of poisson s ratio in rock mechanics.
This video explains the complete definition of poissons ratio with the help of an example, stretching of rubber strip. The volume of materials that have poissons ratios less than 0. The value of poissons ratio in saturated soils and rocks stressed. Modern developments relate to seismology, continuum mechanics, discontinuum mechanics, and transport phenomena. You can also measure poisson s ratio from pressuremeter measurements or dilatometer measurements in the field, as well as by measuring both pwave and swave velocity. This requires consideration of how the composition of a rock dictates its stressstrain relationship and thus seismic response. In ither words, is the amoont o transversal expansion dividit bi the amoont o axial compression, for smaw values o thir chynges. Poissons ratio definition and meaning collins english. This elastic constant is named for simeon poisson 1781 to 1840, a french mathematician. I looked in all my geomechanics text books and none addressed this. 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. In youngs modulus the longitudinal strain is called poissons ratio.
Many of the mechanical properties of wood tabulated in this chapter were derived from extensive sampling and analysis procedures. Definition of poissons ratio strength of materials. Sh min importance of static youngs modulus and poissons ratio for hydrofracture design static moduli are often used in wellbore stability and insitu stress applications to evaluate the possibility of breakouts, elevated pore pressure, and tectonic stress. The figure shows an example of a negative poisson s ratio structure with mechanical isotropy in. Rock mechanical properties, such as compressive strength. These three cases show the importance of cracks pores of low aspect ratios in poissons ratio determination berryman, pride and wang, 2002. Introduction to poisson s ratio mechanics of materials duration. Influence of water saturation on the mechanical behaviour. Hookes law for an axial member undergoing tensile loading. Wood handbookchapter 4mechanical properties of wood.
To visualise the stresses on all the possible planes, a graph called the mohr circle is drawn by plotting a normal stress, shear stress point for a plane at every possible angle. System uscs details of which can be found in most soil mechanics books. This volume is devoted to static and dynamic constants of rock. Poissons ratio longitudinal strain and lateral strain. The poissons ratio, is the ratio of transverse strain, to axial strain, where an axial force has been applied. Poissons ratio longitudinal strain and lateral strain byjus. If i understand the notation, this is the same as writing b 7. In applied rock mechanics, students are provided with basic theory, laboratory demonstrations, handson exercises, and computer modeling demonstrations. Poissons ratio values for rocks poissons ratio values for rocks gercek, h. The greater the moisture content, the greater is the influence of load on the poisson ratio. Essentially poissons ratio is one measure of a rocks strength that is another critical rock property related to.
The strain should be simply the value of thermal expansion multiply by value of temperature increase. For small values of these changes, is the amount of transversal expansion divided by the amount of axial compression. The practical application of rock mechanics is emphasized. D587819 standard guides for using rock mass classification systems for engineering purposes rock mass erosion resistance abutment unified rock classification system slope stabilization rock chamber excavation. In sample j6, auxetic properties occur in a wide range of confining pressure from 0. Rock physics basics need for static moduli 2c 2b s hmin p b 2c 1. More specifically, it examines the role of formation, strength of rock materials, and wellbore mechanics, along with the impact of. Estimation of the rock mechanical properties using. In this paper the authors address two problems encountered in the application of poissons ratio. Poissons ratio values for rocks article in international journal of rock mechanics and mining sciences 441. Characterization of rock mechanical properties using lab tests. Hi, i have some experimental data and i am interested to use this data to calculated modulus of elasticiy youngs modulus and poisson s ratio.
Estimation of the rock mechanical properties using conventional log data in north rumaila field 28 ijcpe vol. Meaning, pronunciation, translations and examples log in dictionary. Applies block theory to rock slopes and underground excavations, and covers the q theory of rock classification, the empirical criterion of joint shear strength, rock bolting, properties of weak rocks, statistical frequency of jointing, an empirical criterion of rock strength, and design of underground supports. Gas zones, where the sonic compressional data has not been corrected for gas, will show abnormally low poisson s ratio. Values of normal stress and shear stress must relate to a particular plane within an element of soil. Standard guides for using rock mass classification systems. Deformation mechanisms, negative poissons ratio materials. Thus, static poisson s ratio from core should be used with caution in geomechanics applications. Although the slides have been modified in part to add context, they.
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