Rock mechanics 2012min07, 2012min39 topic of presentation rock mechanics challenges in ug construction and mining 2. A stress function, from which the kirsch equations can be derived, is developed here to account for the effect of hydraulic pressure on the cylindrical surface of the wellbore. Response of rocks to applied loads earth materials rocks soils fluids. Buy fundamentals and applications of rock mechanics book. More specifically, it examines the role of formation, strength of rock materials, and wellbore mechanics, along with the impact of insitu stress changes on wellbore and. List the strengths and limitation of each of the classification systems i schemes.
Geomechanical modeling of insitu stresses around a borehole. The kirsch equations are a set of closedform solutions, derived from the theory of. This is the field of linear elastic fracture mechanics lefm. This relationship was widely used in the early days of rock mechanics. In both equations 7 and 8, the moduli are in gpa and in equation 8, d is the rock density in gcm3. Rock mechanics and rock support magnus eriksson, jesper petersson peter danielsson, magnus leander. Fracture surface energy and elastic solutions of interest. Revisiting borehole stresses in anisotropic elastic media. Analytical solutions of the mechanical behaviour of rock with. Breakdown pressure an overview sciencedirect topics.
Layered composite materials can be treated as transverse isotropy in mechanics. Will the strength of the rock on the tunnel boundary be exceeded if. This rock is formed either inside the earth or on the surface. Kirsch 1989 accessible solutions from which the basic equations describing the strain distribution around a horizontal, vertical and inclined wellbore may be. More specifically, it examines the role of formation, strength of rock materials, and wellbore mechanics, along with the impact of. Budavari s ed 1986 rock mechanics in mining practice saimm jhb chapter 1, 3, 5 7 constitutive behaviour 7. Lectures on rock mechanicslectures on rock mechanics.
A pdf version of this document can be downloaded from. The compressive strength of rock is a function of the confining pressure. Confidence interval in kirsch equations semantic scholar. A statistical analysis of more than 200 tests reported in. These equations are virtually exclusively used in the petroleum in dustry. Soil is formed from rock due to erosion and weathering action. Sol mech course text feb10 solid mechanics at harvard. The general analytical solution of this problem is expressed in terms of the bessel functions. Stress concentration explained without math equations duration.
Igneous rock is the basic rock formed from the crystallization of molten magma. Basic numerical modelling which captures most relevant rock mass. Introduction to rock mechanics and geomechanical principals. Rock behavior is more complex than ideal materials. Several rock mass design curves developed by the rock mechanics group at the university of british columbia 6 are available, but they were not thought to be relevant to the. Simple analytical solutions for underground circular and elliptical. Methods of manual pole contouring are described by phillips 1971, hoek and. A complete summary of these equations and the stress transformation equations to use for inclined boreholes are listed in the publi cation by aadnoy and chenevert 1987. The use of diagrams, equations, and figures are encouraged in order to describe each of the cited classification schemes systems.
Borehole insitu stress stability analysis of rbs9 field. The importance of beam theory in structural mechanics stems from its widespread success in practical applications. The story of the analysis of stress concentrations begins in 1898 with ernst gustav kirsch s linear elastic solution for stresses around a hole in an infinite plate. Practical rock mechanics teaches from first principles and aids readers understanding of the concepts of stress and stress transformation and the practical application of rock mechanics theory.
Kirsch s solution contains the well known factorofthree stress concentration at the hole under uniaxial loading. When using the brazilian test to determine the indirect tensile strength of rock, it is usually. Engineering rock mechanics an introduction to the principles by j. Stress distribution around a circular hole kirsch equations.
We begin with the linear elastic solutions for stresses, strains, and displacements. Drilling mechanics and performance the drill rate that can be achieved with a specific bit is determined by the aggressiveness of its design, the weight on bit wob applied, the rotations per minute rpm and the rock strength. Further, because solid mechanics poses challenging mathematical and. The kirsch solution for the circumferential stress is.
Since the tunnel has neither a support pressure nor an internal pressure applied to it, the local stresses at the boundary have 3 r 0 and 1. Journal of rock mechanics and geotechnical engineering. Ppt geoscience and rock mechanics powerpoint presentation. Analytical stress functions applied to hydraulic fracturing. Lecture notes pdf s of these powerpoint slides will be made available for download via the course web page. The socalled kirsch equation is almost exclusively used to model fracture initiation in the oil industry. The criterion was derived from the results of research into the brittle failure of intact rock by hoek 3 and on model studies of jointed rock mass behaviour by brown 4.
Once the well bore wall is fractured, the equations break down. Rock mass values were calculated during mine visits and varied from an rmr high of 70% and a low of 16% in goldbearing fault gouge. Mainly, stress concentration about holes of simple shape, using results from elasticity theory, e. A stressdisplacement solution for a pressure tunnel with im scielo. Underground design forsmark layout d2 rock mechanics. As the confining pressure increases so does the strength. The principles of rock mechanics explains the fundamental concepts of continuum mechanics and rheology as applied in studies of rock deformation. The wellbore instability, a classical rock mechanics problem, is one of the most complex problems that encountered during drilling and completion, which cost the drilling industry certainly more. What is the response of rocks under dynamic earthquake type loading. Further, because solid mechanics poses challenging mathematical and computational problems, it as well as fluid mechanics has long been an important topic for applied mathematicians concerned, for example, with partial differential equations and with. Is there an equivalent set of closed form equations to the kirsch equations but for an elliptical hole rather than a circular hole. Compulsory introduction engineering rock mechanics is the study of rock mechanics and rock engineering. Knowledge of the magnitudes and directions of these induced stresses is essential.
What is the bearing capacity of rock on surface an at depths. Applied rock mechanics training course petroskills arm. Determination of minimum and maximum stress profiles using. The kirsch equation is commonly used to calculate the stresses around the borehole. Aadnoy, reza looyeh, in petroleum rock mechanics second edition, 2019. The elastic stress field around a circular opening is given by the socalled kirschsolu. Like others have said, the kirsch equations are really only for isotropic media and a circular opening.
Excavation design in massive elastic rock snu open courseware. The equations of motion, or equilibrium, can be considered to be satis. Natural phenomena involving solid mechanics are studied in geology, seismology and tectonophysics, in materials science and the physics of condensed matter, and in parts of biology and physiology. The stress level defines the loading on the borehole wall, and the rock strength the resistance to withstand this load. Ground control no excavation no problem all rock in the ground subjected to compressive stresses and if excavation is made the rock left standing has to take more load because the original support provided by the rock within the excavation has been removed. Typical steps that could be followed in the analysis of this problem are. We will start all the way back in 1898 with kirsch s solution for stresses around a hole, which is of course not a crack, and work our way up to ellipses and finally cracks. A computer model for estimation of horizontal stress and.
Harrison book covers the basic rock mechanics principles, how to study the interactions between these principles and a discussion on the fundamentals of excavation and support and the application of these in the design of surface and underground structures. Hoek and brown 1, 2 introduced their failure criterion in an attempt to provide input data for the analyses required for the design of underground excavations in hard rock. Rock mechanics problemsrock mechanics problems how will rock react when put to mens use. Continuous, homogenous, isotropic and linear elastic material chile. Lecture notes mechanical properties of rocks earth. When an opening is excavated in this rock, the stress field is locally disrupted and a new set of stresses are induced in the rock surrounding the opening. According to basic equations of transverse isotropy, the compatibility equation in polar coordinates is firstly formulated. These rocks undergo metamorphism under high temperature and pressure to form metamorphic rocks. Lecture 9 introduction to rock strength david hart. The structure could includebut not limited to a drill hole, a mining shaft, a tunnel, a reservoir dam, a repository component, or a building.
Kirsch equations for stress analysis around circle excavations. During preliminary design, the information presented in equations 10. Fairhurst was amongst the first to advocate the use of hydraulic fracturing for in situ strain determination. May 06, 2011 kirsch equation 1898 analytical or closed form solution for circular opening in 2d. The stress level defines the loading on the borehole wall, and the rock. They allow the determination of stresses and displacements around a circular excavation. Engineering design based on simplified analytic solutions e. Since the kirsch equations are based on insitu stress values, therefore investigation of factors. In rock mechanics, the kirsch equations are the most widely used suite of equations from the theory of elasticity. Fracture mechanics interpretation of leakoff tests. This paper was prepared for presentation at the 45th us rock mechanics geomechanics symposium held in san francisco, ca, june 2629, 2011. What is the modulus of elasticity of rock and how to get it. Lectures on rock mechanicslectures on rock mechanics sarvesh chandrasarvesh chandra professor dt tfciilei idepartment of civil engineering indian institute of technology kanpur kanpur, 208016 india email.
National exams may 2016 04gcolas, rock mechanics 3 hours duration notes. Equation 4 can only be used if the rock is isotropic. This text is intended to address the fundamental concepts of rock mechanics and their applications. Are kirsch equations for fractured rocks applicable for a. If the rock is anisotropic, equation 4 is replaced by equation 28 in lecture notes 5.
Production and laboratory data can be evaluated simultaneously by utilizing dars to study the potential of induced faulting and reservoir compaction. Study on damage mechanics model of mechanical and electrical couple of threedimensional coal and rock jingpeng 1hu,2 1 hu iz hoe conom s and p lytechn cll eg, hou na 2 china u nversit yof m ngand technol g be j, na email. However, in nearsurface excavations, where the rock stresses are lower, the fractures more frequent, and the rock mass more disturbed and weathered, there is more concern about the validity of the chile model 5 of 37 erik eberhardt ubc geological engineering isrm edition. Displacement analytical solution of a circular hole in. Elective halfmodule must be taken with engineering geology ce309 lecturer. It is a linear elastic model which assumes that the borehole is penetrating, that is, fluid is pumped into the formation, or. Theoretical and applied rock mechanics literatures are very large to list all publications or even to discuss all possible concepts.
Numerical techniques in rock engineering appendix a. A thorough understanding of rock behavior is essential for strategic planning in the petroleum and mining industry, in construction operation, and in locating subsurface repositories. Transformation of displacement, strain and stress tensors in 3d appendix b. 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. The kirsch equations 2,3,10 and their derivatives are the most important equations related to applied rock mechanics. The kirsch equations are a set of closedform solutions, derived from the theory of elasticity, used to calculate the stresses and displacements around a circular excavation. Rock mechanics is concerned with the application of the principles of engineering mechanics to the design of structures built in or of rock. The kirsch equations describe the elastic stresses around the hole in an infinite plate in one directional tension.
Loading an infinite plate with circular hole of radius a with stress. The origins of this equation are in the calculation of near wellbore stresses and apply to fracture initiation at the wellbore wall kirsch, 1898. Rock mechanics problems how will rock react when put to mens use. It may fail catastrophically if the load frame is soft. The kirsch equation is valid up to the conventional leakoff point, but beyond leakoff the hole is fractured, and an elastoplastic bridge model applies to ultimate failure. Geoscience and rock mechanics 1 module c 1 stresses around a borehole i argentina spe 2005 course on earth stresses and drilling rock mechanics maurice b. 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. This text can help ensure that ground models and designs are correct, realistic, and produced costeffectively. The simplest design problem in mining rock mechanics. The depth of the tunnel is such that it is probable that in situ and induced stresses will be an important consideration in the design of the excavation. As illustrated in figure 1 the four columns represent the four main modelling methods. Kirschs equations and the corresponding deformation strain and displacement fields were derived for a tunnel with and without a circular support. This equation assumes a consistent body of rock above point.