Critical Borehole Orientations – Rock Mechanics Aspects

Total Page:16

File Type:pdf, Size:1020Kb

Critical Borehole Orientations – Rock Mechanics Aspects DRILLING Critical Borehole Orientations – Rock Mechanics Aspects By R. BRAUN* Abstract again and again during the development of 3 Significant “Rock Mechanics” This article discusses rock mechanics as- the inclination, and these can often only be Factors pects of the relationship between borehole controlled to a limited extent by classical 3.1 In situ stresses stability and borehole orientation. Two countermeasures (variation of mud pressure The magnitudes and orientations of in situ kinds of instability are considered. One is and its composition). It is therefore worth- stresses have a decisive influence on the failures resulting from normal stresses in while in every case to take a more careful borehole loadings. In order to make a rea- planes perpendicular to the borehole, or look at the rock which is to be penetrated and sonable assessment of these in situ loadings along its axis. These may be tension or shear at the possible interactions of this with the it is essential to distinguish between the vari- failures in the direction of the minimum borehole. These interactions may be geolog- ous different components. and/or the maximum normal stress compo- ical/mineralogical or geochemical, but the First the external loading (also called the to- nent related to the borehole, or peeling/loos- ones discussed here concern rock mechan- tal loading) is to be considered. The vertical ening around the complete borehole perime- ics. The significant rock mechanics factors component of this is the total overburden ter. These can be avoided, or at least mini- and the way in which they can influence pressure and it can therefore be determined mized, by the selection of an appropriate borehole stability are discussed in the directly (for example from the average den- borehole pressure. following sections. sity of the overburden). The minimum total In a borehole in an anisotropic in situ stress stress component corresponds to the closure field, which deviates from a principal in situ pressure of a hydraulic frac. Against these effective stress direction, there occur in ad- 2 Presentation of 3D Parameters loadings acts the pore pressure as an inner dition shear stresses parallel to the borehole Rock mechanics analyses considering three loading. This is however often (above all in axis. These can result in shear failures which dimensions are facilitated by having a suit- low porosity and low permeability rock) cannot be influenced directly by the bore- able method for visualizing the 3D parame- only partially effective and directional in its hole inner pressure. They can therefore only ters (see, top right in Fig. 1, an example of a effect [1]. This behaviour is described by the be avoided by the selection of an appropri- stress state). For this the Schmidt plot is gen- pore pressure effectiveness (3D Biot coeffi- ate borehole alignment. erally used (see the centre of Fig. 1). The pa- cient). The magnitude of this depends on the It is shown that the intensity of borehole in- rameters are plotted unambiguously on a 2D rock structure and the stress situation and stability increases significantly with in- disc using their direction (azimuth) in rela- may have a value between 0 (no pore pres- creasing anisotropy of the effective in situ tion to geographical stresses. The borehole orientations most at north and their dip in risk are approximately the same in compact relation to horizon- and in disturbed rock masses, however the tal. Around the out- presence of weak surfaces results in an ex- side of the disc is tension of the instability. shown the azimuth, beginning at the up- per edge with 0° 1 Introduction (north) and then in- The planning of a borehole’spath usually de- creasing clockwise pends on economic factors. These are ini- (as in a compass). tially defined by the drilling position and the The values of dip are target zone. Then, especially in cases of the shown as circles of development of resources in low permeabil- different radii, with a ity strata and in disturbed rock masses, co- vertical orientation mes a further consideration, that the part of (dip angle 90°) cor- the borehole relevant to production (often a responding to the horizontal end zone) should have an opti- mid-point of the mum orientation in relation to the preferred disc. Parameters flow direction and the propagation direction with a horizontal ori- of hydraulic fracs. Thus not only the end entation (dip angle point but also the way to it comes into the 0°) are plotted planning. However, on understandable cost around the outer reasons, a path which is as short as possible edge of the disc. In will always be sought. addition, the param- With deviated boreholes instabilities occur eter magnitude in * Dr. Roland Braun, Consultancy in Rock Mechanics, Ca- each orientation is puth/Germany (E-mail: [email protected]). indicated by the 0179-3187/10/II colour (see the lower © 2010 URBAN-VERLAG Hamburg/Wien GmbH part of Fig. 1). Fig. 1 An example of a Schmidt plot showing a 3D stress state OIL GAS European Magazine 2/2010 OG 75 DRILLING faulting, distinct strength anisotropies can principal stresses and on the deviation of the occur (see the example in Fig. 2). These are borehole path from the principal stress di- not necessarily identical with the stress rections. As deviated boreholes always have anisotropies. (at least in part) an orientation differing from In zones of looser material (bedding planes, a principle effective in situ stress direction, faults, fracs etc.) the strength may be lower there are (in an anisotropic in situ stress than in compact rock. Such features gener- field) always sections with shear stresses ally have a planar form and can be consid- parallel to the borehole axis. In contrast to ered as weak surfaces or areas. Depending stresses normal and tangential to the bore- on the in situ stress condition and the path of hole wall, these shear stresses are not the borehole, they may also present a risk for modified by the pressure of the drilling mud stability. (for the analytical relationships see [2]). 4 Loading Conditions around 5 Typical Cases Boreholes 5.1 Input parameters and methods of The stability of a borehole is determined by calculation the in situ loading in its immediate vicinity In the following sections some typical cases Fig. 2 3D magnitudes and orientation of principal and by the pressure in the borehole. This are presented in which there may be signifi- uniaxial compressive strength (UCS) pressure, however, only has a supporting ef- cant rock mechanics influences on the sta- fect when the borehole wall is impermeable bility of boreholes. The rock behaviour is as- (filter cake or impermeable rock) or in a low sumed to be brittle (as is often encountered sure effect) and ~1. The sums of the oppos- porosity rock with a correspondingly low in oil and gas fields, deep geothermal sys- ing external and internal loadings (total pore pressure effectiveness. It must also be tems, CO2 storage and in underground stresses and effective pore pressure) are the considered that with loosening at the initia- mines). effective stresses. These are the relevant tion of instability, or following hydraulic As the in situ stresses have a considerable in- stresses for deformations and failures of the fracs, the pore pressure effectiveness in- fluence on the borehole loadings, the case rock, and their use is therefore essential in creases. When this was previously relatively studies cover three typical situations (Fig. stability analyses. low the influence of fluid pressure then in- 3). The effective stresses used for the analy- As well as the stress magnitudes, and the dif- creases. With an unchanged borehole inner ses, as well as the pore pressure effective- ferences in these between the principal com- (e. g. mud) pressure the result is a reduction nesses, are derived from determinations ponents, the orientation of these compo- of the stabilizing effect on the borehole wall. with RACOS® [3] on cores from boreholes nents also has a significant influence on in For the assessment of the conditions in the in different geological structures. For rea- situ stability. Often encountered are trans- zone around the borehole the secondary sons of comparability they have been ad- verse anisotropic in situ loadings with (at stresses there must be considered. These de- justed to refer to a common depth, and to least approximately) identical horizontal pend on the in situ stresses in the unaffected have a vertical–horizontal orientation of the stresses which are generally smaller than the rock mass and on the orientation of the bore- principal stresses with the maximum hori- vertical stress. However stresses produced hole. For a borehole aligned parallel to an in zontal stress acting NW–SE. by tectonic influences can result in horizon- situ principal effective stress the normal Figure 3 shows different stress anisotropies. tal loadings which differ from each other. stresses perpendicular and parallel to the Stress state 1 has a large vertical–horizontal This can (for example, close to geologically borehole alignment are identical with the ef- anisotropy, but only a small horizontal one. young chains of mountains, like the Alps) fective principal stresses in the rock mass, It is often encountered in largely undis- result in conditions in which the maximum and there are no shear stresses in that direc- turbed reservoirs covering a large area. State stress component is approximately horizon- tion. A borehole alignment deviated from 2, in contrast, is typical for areas with fault tal. It should also be noted that the principal the orientations of the in situ principal effec- zones resulting from tectonic action. It has a components of in situ stress are not neces- tive stresses results in different magnitudes large maximum horizontal stress (but still sarily horizontal and vertical.
Recommended publications
  • Mapping Thixo-Visco-Elasto-Plastic Behavior
    Manuscript to appear in Rheologica Acta, Special Issue: Eugene C. Bingham paper centennial anniversary Version: February 7, 2017 Mapping Thixo-Visco-Elasto-Plastic Behavior Randy H. Ewoldt Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Gareth H. McKinley Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Abstract A century ago, and more than a decade before the term rheology was formally coined, Bingham introduced the concept of plastic flow above a critical stress to describe steady flow curves observed in English china clay dispersion. However, in many complex fluids and soft solids the manifestation of a yield stress is also accompanied by other complex rheological phenomena such as thixotropy and viscoelastic transient responses, both above and below the critical stress. In this perspective article we discuss efforts to map out the different limiting forms of the general rheological response of such materials by considering higher dimensional extensions of the familiar Pipkin map. Based on transient and nonlinear concepts, the maps first help organize the conditions of canonical flow protocols. These conditions can then be normalized with relevant material properties to form dimensionless groups that define a three-dimensional state space to represent the spectrum of Thixotropic Elastoviscoplastic (TEVP) material responses. *Corresponding authors: [email protected], [email protected] 1 Introduction One hundred years ago, Eugene Bingham published his first paper investigating “the laws of plastic flow”, and noted that “the demarcation of viscous flow from plastic flow has not been sharply made” (Bingham 1916). Many still struggle with unambiguously separating such concepts today, and indeed in many real materials the distinction is not black and white but more grey or gradual in its characteristics.
    [Show full text]
  • Using Effective Stress Theory to Characterize the Behaviour of Backfill
    Paper 27 Minefill Using effective stress theory to characterize the behaviour of backfill A.B. Fourie, Australian Centre for Geomechanics, University of Western Australia, Perth, Western Australia, M. Fahey and M. Helinski, University of Western Australia, Perth, Western Australia ABSTRACT The importance of understanding the behaviour of cemented paste backfill (CPB) within the framework of the effective stress concept is highlighted in this paper. Only through understand- ing built on this concept can problems such as barricade loads, the rate of consolidation, and arch- ing be fully understood. The critical importance of the development of stiffness during the hydration process and its impact on factors such as barricade loads is used to illustrate why conven- tional approaches that implicitly ignore the effective stress principle are incapable of capturing the essential components of CPB behaviour. KEYWORDS Cemented backfill, Effective stress, Barricade loads, Consolidation INTRODUCTION closure (i.e. the stiffness or modulus of compressibil- ity) that is of primary interest. As the filled stopes The primary reason for backfilling will vary from compress under essentially confined, one-dimen- site to site, with the main advantages being one or a sional (also known as K0) conditions, the stiffness combination of the following: occupying the mining increases with displacement. Well-graded hydaulic void, limiting the amount of wall convergence, use as fills have been shown to generate the highest settled a replacement roof, minimizing areas of high stress density and this, combined with the exponential con- concentration or providing a self-supporting wall to fined compression behaviour of soil (Fourie, Gür- the void created by extraction of adjacent stopes.
    [Show full text]
  • Landslide Triggering Mechanisms
    kChapter 4 GERALD F. WIECZOREK LANDSLIDE TRIGGERING MECHANISMS 1. INTRODUCTION 2.INTENSE RAINFALL andslides can have several causes, including Storms that produce intense rainfall for periods as L geological, morphological, physical, and hu- short as several hours or have a more moderate in- man (Alexander 1992; Cruden and Vames, Chap. tensity lasting several days have triggered abun- 3 in this report, p. 70), but only one trigger (Varnes dant landslides in many regions, for example, 1978, 26). By definition a trigger is an external California (Figures 4-1, 4-2, and 4-3). Well- stimulus such as intense rainfall, earthquake shak- documented studies that have revealed a close ing, volcanic eruption, storm waves, or rapid stream relationship between rainfall intensity and acti- erosion that causes a near-immediate response in vation of landslides include those from California the form of a landslide by rapidly increasing the (Campbell 1975; Ellen et al. 1988), North stresses or by reducing the strength of slope mate- Carolina (Gryta and Bartholomew 1983; Neary rials. In some cases landslides may occur without an and Swift 1987), Virginia (Kochel 1987; Gryta apparent attributable trigger because of a variety or and Bartholomew 1989; Jacobson et al. 1989), combination of causes, such as chemical or physi- Puerto Rico (Jibson 1989; Simon et al. 1990; cal weathering of materials, that gradually bring the Larsen and Torres Sanchez 1992)., and Hawaii slope to failure. The requisite short time frame of (Wilson et al. 1992; Ellen et al. 1993). cause and effect is the critical element in the iden- These studies show that shallow landslides in tification of a landslide trigger.
    [Show full text]
  • Geomechanical Modeling of In-Situ Stresses Around a Borehole
    Geomechanical Modeling of In-Situ Stresses Around a Borehole Samantha Grandi, Rama Rao, and M. Nafi Toks¨oz Earth Resources Laboratory Dept. of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology Cambridge, MA 02139 Abstract In this paper, we present a modelling of the in-situ stress state associated with the severe hole enlargement of a wellbore. Geomechanical information is relevant to assure wellbore stability, i.e., to prevent damages in the formation and later on, the casing. Many of the drilling parameters, as mud weight or the optimal orientation of the borehole, require some knowledge of the mechanical behaviour of the rock. The lack of these kind of data in exploratory areas, where there are usually insufficient constraints for the geological model, increases even more the risk, hence the costs. The present model uses the concepts of poroelasticity theory to compute the stationary 2D, brittle response of the formation around a borehole that is submitted to effective compressive horizontal stresses. The numerical solution is obtained using a finite element approximation. The initial stress state at the far field was estimated combining a frictional-failure theory with the observations of dipmeter caliper in a particular borehole that presents elongations in a preferential di- rection. The direction and relative extension of the observed breakouts at a particular depth are modelled successfully using formation realistic parameters and dimensions, although the exact shape of the borehole (at all angles) was unknown. For the particular case study, the orientation of the breakout is NE-SW, at about 82 degrees azimuth. Therefore, the maximum horizontal stress lies at approximately 350 degrees azimuth.
    [Show full text]
  • Slope Stability
    Slope stability Causes of instability Mechanics of slopes Analysis of translational slip Analysis of rotational slip Site investigation Remedial measures Soil or rock masses with sloping surfaces, either natural or constructed, are subject to forces associated with gravity and seepage which cause instability. Resistance to failure is derived mainly from a combination of slope geometry and the shear strength of the soil or rock itself. The different types of instability can be characterised by spatial considerations, particle size and speed of movement. One of the simplest methods of classification is that proposed by Varnes in 1978: I. Falls II. Topples III. Slides rotational and translational IV. Lateral spreads V. Flows in Bedrock and in Soils VI. Complex Falls In which the mass in motion travels most of the distance through the air. Falls include: free fall, movement by leaps and bounds, and rolling of fragments of bedrock or soil. Topples Toppling occurs as movement due to forces that cause an over-turning moment about a pivot point below the centre of gravity of the unit. If unchecked it will result in a fall or slide. The potential for toppling can be identified using the graphical construction on a stereonet. The stereonet allows the spatial distribution of discontinuities to be presented alongside the slope surface. On a stereoplot toppling is indicated by a concentration of poles "in front" of the slope's great circle and within ± 30º of the direction of true dip. Lateral Spreads Lateral spreads are disturbed lateral extension movements in a fractured mass. Two subgroups are identified: A.
    [Show full text]
  • Soil Mechanics Lectures Third Year Students
    2016 -2017 Soil Mechanics Lectures Third Year Students Includes: Stresses within the soil, consolidation theory, settlement and degree of consolidation, shear strength of soil, earth pressure on retaining structure.: Soil Mechanics Lectures /Coarse 2-----------------------------2016-2017-------------------------------------------Third year Student 2 Soil Mechanics Lectures /Coarse 2-----------------------------2016-2017-------------------------------------------Third year Student 3 Soil Mechanics Lectures /Coarse 2-----------------------------2016-2017-------------------------------------------Third year Student Stresses within the soil Stresses within the soil: Types of stresses: 1- Geostatic stress: Sub Surface Stresses cause by mass of soil a- Vertical stress = b- Horizontal Stress 1 ∑ ℎ = ͤͅ 1 Note : Geostatic stresses increased lineraly with depth. 2- Stresses due to surface loading : a- Infintly loaded area (filling) b- Point load(concentrated load) c- Circular loaded area. d- Rectangular loaded area. Introduction: At a point within a soil mass, stresses will be developed as a result of the soil lying above the point (Geostatic stress) and by any structure or other loading imposed into that soil mass. 1- stresses due Geostatic soil mass (Geostatic stress) 1 = ℎ , where : is the coefficient of earth pressure at # = ͤ͟ 1 ͤ͟ rest. 4 Soil Mechanics Lectures /Coarse 2-----------------------------2016-2017-------------------------------------------Third year Student EFFECTIVESTRESS CONCEPT: In saturated soils, the normal stress ( σ) at any point within the soil mass is shared by the soil grains and the water held within the pores. The component of the normal stress acting on the soil grains, is called effective stressor intergranular stress, and is generally denoted by σ'. The remainder, the normal stress acting on the pore water, is knows as pore water pressure or neutral stress, and is denoted by u.
    [Show full text]
  • 3. Stresses in the Ground
    3-1 3. STRESSES IN THE GROUND 3.1 STRESSES IN DRY SOIL Let A in Fig. 3.1 (a) represent a small cubical shaped element of soil at a depth z in an extensive uniform soil deposit in which the ground surface is horizontal and which has been formed by the gradual accretion of material on the ground surface. Because the soil deposit is extensive (by comparison with distance z) in the horizontal direction the stresses on element A will be identical with the stresses on an adjacent element at the same depth below the ground surface. This means that there cannot be any shear stresses existing on the vertical or horizontal planes which bound element A. In other words the vertical stress ( σv) and horizontal stress ( σH) are principal stresses. The vertical stress on element A can be determined simply from the mass of the overlying material. If ρd represents the density of the soil, the vertical stress is σv = ρd gz (3.1) The horizontal stress is customarily expressed as a proportion of the vertical stress σH = K' o σv = K' o ρd gz (3.2) where K' o = coefficient of earth pressure at rest in terms of effective stresses (see equation (3.7)). This coefficient contains the words “at rest” since the soil was deposited under conditions of zero horizontal strain. In other words, because of the large lateral extent of the soil deposit, the vertical planes on any soil element A do not experience any lateral movement as the stresses increase as a consequence of the accretion of material on the ground surface.
    [Show full text]
  • Consideration on Landslide Mechanism Based on Pore Water Pressure Loading Test Examan Du Mécanisme De Glissement De Terrains Par Essai De Suppression Hydrostatique
    INTERNATIONAL SOCIETY FOR SOIL MECHANICS AND GEOTECHNICAL ENGINEERING This paper was downloaded from the Online Library of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE). The library is available here: https://www.issmge.org/publications/online-library This is an open-access database that archives thousands of papers published under the Auspices of the ISSMGE and maintained by the Innovation and Development Committee of ISSMGE. Consideration on landslide mechanism based on pore water pressure loading test Examan du mécanisme de glissement de terrains par essai de suppression hydrostatique S-Ohtsuka & YMiyata — Nagaoka University of Technology, Nagaoka, Niigata, Japan ABSTRACT: Pore water pressure loading test of clay was conducted under the constant deviator stress. From the test results, the yield and failure stresses were newly defined and the yield stress was found located on the critical state line. With the increase in pore water pressure over the yield stress, the shear deformation developed with long time. The progressive failure with water migration was pointed out as the reason for the slow movement of landslide. Numerical simulation on shear strength of clay against repetitive pore water pressure loading clarified the process of deterioration in shear strength of clay caused by repeats of landslide movement. RESUME: L’essai du chargement de la pression de l’eau interstitielle de argile a été procédé sous la contrainte constante de cisaillement. Selon les résultats, la contrainte d’écoulement et celle de rupture ont été définies et la première a été trouvée aux environs de la ligne de l’état critique. En augmentant la pression de l’eau interstitielle jusqu’au-dessus de la contrainte d’écoulement, la déformation de cisaillement s’est formée et s’est développée en longues heures.
    [Show full text]
  • Lecture 1 : Macroscopic Characterisation of Soils
    Lecture 1 : Macroscopic Characterisation of Soils Kenichi Soga, University of Cambridge 1.1 Introduction All aspects of soil stability—bearing capacity, slope stability, the supporting capacity of deep foundations, and penetration resistance, to name a few—depend on soil strength. The stress-deformation and stress-deformation-time behaviour of soils are important in any problem where ground movements are of interest. Most relationships for the characterization of the stress-deformation and strength properties of soils are empirical and based on phenomenological descriptions of soil behaviour. The Mohr–Coulomb equation is by far the most widely used for strength. It states that τ ff = c + σ ff tanφ (1.1) τ ff = c′ + σ ′ff tanφ′ (1.2) where τff is shear stress at failure on the failure plane, c is a cohesion intercept, σff is the normal stress on the failure plane, and φ is a friction angle. Equation (1.1) applies for σff defined as a total stress, and c and φ are referred to as total stress parameters. Equation (1.2) applies for σ′ff defined as an effective stress, and c′ and φ′ are effective stress parameters. As the shear resistance of soil originates mainly from actions at interparticle contacts, the second equation is the more fundamental. In reality, the shearing resistance of a soil depends on many factors, and a complete equation might be of the form Shearing resistance = F(e,c',φ',σ ',C, H,T,ε,ε, S) (1.3) in which e is the void ratio, C is the composition, H is the stress history, T is the temperature, ε is the strain, ε is the strain rate, and S is the structure.
    [Show full text]
  • Cyclic Response of a Sand with Thixotropic Pore Fluid
    Cyclic Response of a Sand with Thixotropic Pore Fluid C.S. El Mohtar1, J. Clarke1, A. Bobet1, M. Santagata1, V. Drnevich1 and C. Johnston2 1School of Civil Engineering, Purdue University, West Lafayette, IN 2Department of Agronomy, Purdue University, West Lafayette, IN ABSTRACT Saturated specimens of Ottawa sand prepared with 0%, 3% and 5% bentonite by dry mass of sand are tested under cyclic loading to investigate the effects of bentonite on the cyclic response. For the same skeleton relative density and cyclic stress ratio (CSR), the cyclic tests on the sand-bentonite mixtures show a significant increase of the number of cycles required for liquefaction compared to the clean sand. This is caused , as observed in resonant column tests, by an increase of the elastic threshold due to the presence of bentonite, which delays the generation of excess pore pressure. Such behavior can be explained by the rheological properties of the pore fluid. Oscillatory tests conducted with a rheometer on bentonite slurries show that for shear strains as large as 1% these materials exhibit elastic behavior with a constant shear modulus. Moreover, due to the thixotropic nature of the bentonite slurries, their storage modulus shows a marked increase with time. This observation is consistent with the increase in the liquefaction resistance of the sand-bentonite mixtures with time also observed in cyclic triaxial experiments. INTRODUCTION Liquefaction is an important cause of damage to civil infrastructures during earthquakes. Notable examples are: the collapse
    [Show full text]
  • Tensile Strength, Shear Strength, and Effective Stress for Unsaturated Sand
    TENSILE STRENGTH, SHEAR STRENGTH, AND EFFECTIVE STRESS FOR UNSATURATED SAND A Dissertation Presented to the Faculty of the Graduate School University of Missouri – Columbia In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy By RAFAEL BALTODANO GOULDING Dr. William J. Likos, Dissertation Supervisor MAY 2006 Abstract It is generally accepted in geotechnical engineering that non-cohesive materials such as sands exhibit no or negligible tensile strength. However, there is significant evidence that interparticle forces arising from capillary and other pore-scale force mechanisms increase both the shear and tensile strength of soils. The general behavior of these pore-scale forces, their role in macroscopic stress, strength, and deformation behavior, and the changes that occur in the field under natural or imposed changes in water content remain largely uncertain. The primary objective of this research was to experimentally examine the manifestation of capillary-induced interparticle forces in partially saturated sands to macroscopic shear strength, tensile strength, and deformation behavior. This was accomplished by conducting a large suite of direct shear and direct tension tests using three gradations of Ottawa sand prepared to relatively “loose” and relatively “dense” conditions over a range of degrees saturation. Results were compared with previous experimental results from similar tests, existing theoretical formulations to define effective stress in unsaturated soil, and a hypothesis proposed to define a direct relationship between tensile strength and effective stress. The major conclusions obtained from this research include: Theoretical models tended to underpredict measured tensile strength. Analysis of results indicates that shear strength may be reasonably predicted using the sum of tensile strength and total normal stress as an equivalent effective stress (σ’ = σt + σn).
    [Show full text]
  • 11. the Stability of Slopes
    11-1 11. THE STABILITY OF SLOPES 11.1 INTRODUCTION The quantitative determination of the stability of slopes is necessary in a number of engineering activities, such as: (a) the design of earth dams and embankments, (b) the analysis of stability of natural slopes, (c) analysis of the stability of excavated slopes, (d) analysis of deepseated failure of foundations and retaining walls. Quite a number of techniques are available for these analyses and in this chapter the more widely used techniques are discussed. Extensive reviews of stability analyses have been provided by Chowdhury (1978) and by Schuster and Krizek (1978). In order to provide some basic understanding of the nature of the calculations involved in slope stability analyses the case of stability of an infinitely long slope is initially introduced. 11.2 FACTORS OF SAFETY The factor of safety is commonly thought of as the ratio of the maximum load or stress that a soil can sustain to the actual load or stress that is applied. Referring to Fig. 11.1 the factor of safety F, with respect to strength, may be expressed as follows: τ F = ff (11.1) τ where τ ff is the maximum shear stress that the soil can sustain at the value of normal stress of σn, τ is the actual shear stress applied to the soil. Equation 11.1 may be expressed in a slightly different form as follows: c σ tan φ = n τ F + F (11.2) Two other factors of safety which are occasionally used are the factor of safety with respect to cohesion, F c, and the factor of safety with respect to friction, F φ.
    [Show full text]