Relax Your Mind

Shear displacement

Figure 10.13 An illustration of the size-dependence of shear stress-deformation behaviour for nonplanar joints. (After Bandis, Lumsden and Barton (1981) 'Experimental studies of scale effects on the shear behaviour of rock joints'. Int. J. Rock Mech. Min. Sci., 18)

The analysis of a rock structure should not start without first preparing a complete statement of the factors involved. These usually include the geometry and intended purpose of the structure together with the main elements of the rock engineering matrix described previously. That is, the structure of the rock, mechanical properties of intact rock materials and the discontinuities, the nature of water and stress conditions in the mass and the proposed construction/excavation method. It is not usually possible to take each factor into full account, so that analysis is often based on simplified mathematical or physical 'models'. The choice of simplifying assumptions and the errors that these assumptions are likely to introduce are matters for engineering judgement, and it is often advisable to check a design by carrying out more than one type of analysis wherever possible. 'Failure' of the structure needs to be defined (e.g. excessive displacements) and potential failure mechanisms need to be identified so that design calculations are addressed to these specifically. The adequacy of the initial design can be checked by instrumentation and monitoring and modified if necessary.

Design methods for the stability of the rock structure consider either the resulting stresses in the surrounding rock or the displacements which are induced or which become kinematically feasible, e.g. wedge failure on joint planes. In applying methods of stress analysis, judgement is required in deciding whether or not the rock should be regarded as a continuum, and then whether as an infinite space or half space. Various conditions of anisotropy and of inelastic behaviour can be simulated with some models. In discontinuous media, methods are available to analyse the displacements, provided parameters describing rock joint behaviour can be determined.

Figure 10.14 Tilt tests for obtaining joint roughness and basic friction parameters. (After Barton (1986) 'Deformation phenomena in jointed rock'. G6otechnique, 36, 2)

A useful first approach is design by 'rule of thumb' using design principles that experience has shown to give satisfactory results. Where no precedent exists simple rules can be established by undertaking a programme of field observations to determine relationships between 'cause' and 'effect'. This is more likely to succeed if it is preceded by an attempt to establish, using theory and simple methods, those parameters that might prove fundamental to the design, and the trends to be expected.9 80 Empirical design rules are usually only safe to apply in the context for which they were originally formulated, and extrapolation can be unreliable, particularly if the method has no theoretical basis.

An example of empirical methods based on precedent practice is the classification of rock in relation to support requirements for underground openings, namely the Q system, RSR and others (see section 10.3.1).

Physical, as opposed to mathematical, models can be used in a laboratory analysis of stresses or displacements in a rock structure, and can sometimes also be applied to the study of fracture and failure.81

Elastic models may be used to analyse stresses mainly but are applicable where the rock may reasonably be assumed to behave elastically. The most common type, a photoelastic model, is machined from a stress-birefringent material such as glass or plastic. When loaded and viewed in polarized light the model exhibits coloured fringes (isochromatics) that follow contours of maximum shear stress in the model. Black fringes (isoclinics) visible in plane polarized light indicate the principal stress directions. Stress-freezing and other methods are available for analysis of problems in three dimensions. Other types of elastic model have also been used, e.g. metal sheet with resistance strain gauges or moire fringe grids mounted on the surface. Elastic modelling has been largely superseded in most applications by

Usual range

Figure 10.15 Correlation chart for the Schmidt hammer, relating rock density, compressive strength and rebound number. (After Miller (1965) 'Engineering classification and index properties for intact rock'. PhD thesis, University of Illinois)

Schmidt hardness (/?)

Figure 10.15 Correlation chart for the Schmidt hammer, relating rock density, compressive strength and rebound number. (After Miller (1965) 'Engineering classification and index properties for intact rock'. PhD thesis, University of Illinois)

computer analyses that afford greater flexibility, require fewer simplifying assumptions and less preparation time, and can also solve inelastic problems. Photoelastic models, however, can still be useful in presenting a visual and easily understood representation of stress distributions, and can cope easily with complex geometrical configurations.

Inelastic physical models and block models to study displacements are built from materials chosen, according to principles of dimensional similarity, to scale-down prototype properties such as density, strength and deformability.82 Physical models have been used, for example, to investigate the behaviour of rock slopes, underground excavations at various stages of construction, and subsidence above mine workings.85 Gravity can be simulated by building the model lying on a flat surface with a movable backing sheet which can be drawn in the downward direction: the friction forces on the blocks simulate gravity forces. Such models are known as 'base-friction models'.84 Simple and approximate physical models can be valuable at the early stages of analysis in helping to visualize possible kinematic mechanisms and in formulating the problem, but care is needed to select appropriate scaling factors.

The equations governing electric potential differences and currents are analogous to the equations governing stress distributions or water flow in the rock mass. Thus, stress or water problems can be simulated and solved by electric analogue methods.85-86 The conducting paper method, of limited accuracy and flexibility but simple, uses an impregnated paper with probes to monitor surface potential differences. The resistance network method uses a grid of interchangeable or variable resistors, can solve anisotropic and heterogeneous problems and is more accurate, but has the disadvantage of restricting measurements to a limited number of nodal points. Analogues other than electric ones are possible, e.g. the Hele-Shaw method uses the flow of viscous fluids between closely spaced parallel plates.87

Analysis of stresses, strains and displacements based on principles of classical stress analysis and continuum mechanics88 assume that the material is continuous throughout and that conditions of equilibrium and compatibility of displacements are satisfied for given boundary conditions. The constitutive equation, i.e. the relationship between stress, strain and time for the rock mass, must be known or assumed in order to formulate the problem. This relationship can in theory be established by testing, although in practice, tests serve only to measure the parameters in an idealized constitutive equation such as one of linear elasticity. A satisfactory constitutive equation should account for rock behaviour both before, during and after failure in intact material. In most rock structures, zones of fractured rock can develop owing to the induced stresses exceeding the rock strength (zones of 'overstress') which, because they are confined by unfractured material, do not lead to collapse. It is important to recognize when it is or is not reasonable to assume that a problem may be analysed as a continuum. The presence of fractures or discontinuities does not invalidate the premises of continuum mechanics provided that a constitutive equation can be formulated for an 'element' or test specimen that incorporates a large number of such discontinuities. Soil materials, for example, contain discrete grains bounded by discontinuities but can be tested in this way, thus allowing continuum mechanics to be applied to soil problems.

Having formulated an appropriate equation for the material the problem is solved taking into account the geometry and boundary conditions for the rock structure, and ensuring that conditions of equilibrium and compatibility of displacements are satisfied. Particular solutions which are most useful in considering tunnels or underground openings are those for circular holes in stressed elastic media. Equations for analysing thick-walled cylinders or circular holes in an infinite elastic solid (Kirsch equations) will determine the radial and tangential stresses around the surface and within the rock and the displacements surrounding the opening.8' A wide range of exact or 'closedform ' solutions are available for solving two-dimensional problems of various geometries, particularly for linear elastic behaviour, but few solutions have been formulated for three-dimensional problems. Boussinesq and Cerruti give solutions for normal and shear point-loading on a three-dimensional elastic half-space that can be used to build up, by a process of simple superposition, the distribution of stresses and displacements for any system of applied loads.90-" Savin'2 gives closed-form solutions for stress concentrations around holes in an elastic plate; these and other solutions are reviewed by Obert and Duvall." In practice, it is unnecessary to derive solutions to particular problems because published collections exist of most analytically tractable problems. Such a collection by Poulos and Davis94 is most thorough. It is important, however, to ensure that an appropriate solution is being applied to each design problem.

For many design problems in rock mechanics it is necessary to seek a more detailed understanding of stress distribution than can be obtained by superposition of standard analytical solutions. Conditions of complex geometry, rock mass anisotropy, nonlinear constitutive behaviour and nonhomogeneity require more versatile methods of solution. To solve the many stress analysis problems for which no solution in closed form is available one must resort to numerical approximation methods for solving the continuum mechanics equations. These methods are now widely used since computers have become generally available. There are two categories of computational methods of analysis, namely differential methods and integral methods (see later). For the first of these the problem is divided up into a set of discrete elements and the solution based on numerical approximations of the governing equations, i.e. the differential equations of equilibrium and the stress-strain-displacement relations.

The finite difference (relaxation) method90 has had a long-established use in civil engineering. Partial differential equations that define material behaviour and boundary conditions are replaced by finite-difference approximations at a number of discrete points throughout the rock mass. The resulting set of simultaneous equations is then solved. A finite difference computer program is available specifically designed for modelling soil and rock behaviour and is based on the Lagrangian method (FLAC).95 It is capable of modelling elastic, anisotropic-elastic and elasto-plastic material properties and can simulate joint slip planes. Its main advantage is in solving for large displacements and collapse due to plastic flow, and is generally applicable to slope and foundations analyses as well as underground excavations.

The finite element method'*'''' is similar in many respects, except that the rock mass is subdivided into a number of structural components or interacting elements that may be of irregular and variable shape (Figure 10.16). A judicious selection of element is critical to the efficiency of computation. The elements are assumed to be interconnected at a discrete number of points on their boundaries, and a function is chosen to define uniquely the state of displacement within each element in terms of nodal displacements at element boundaries.

Strain may then be defined and, hence, stress using the constitutive equation for the material. Nonlinear and heterogeneous material properties may readily be accommodated, but the outer boundaries of the model (or 'problem domain') must be defined arbitrarily. The boundary conditions, in terms of relative fixity and degrees of freedom, may influence the area of interest to the analysis depending upon how distant these boundaries can be set in the model. There are practical limitations on the number of elements used in relation to computer storage, and the elements themselves need to be well-conditioned shapes (triangles or rectangles). Nodal forces are determined in such a way as to equilibriate boundary stresses, and the stiffness of the whole model may then be formulated as the sum of contributions from individual elements. The response of the structure to loading may then be computed by the solution of a set of simultaneous equations. Finite element computer programs have been written for a variety of rock mechanics problems, to tackle both two- and three-dimensional situations, elastic, plastic, and viscous materials, and to incorporate 'no-tension zones', joints, faults and anisotropic behaviour. The method is also used to solve water-flow problems, heat-flow problems, and an even wider scope of situations unrelated to rock engineering.

Analytical techniques, which are based on continuum idealization, are not always suitable for jointed rock problems. Numerical methods such as the finite element method or finite difference method in which rock masses are simply considered as elastic or elasto-plastic continua, are not suitable to model the geometric irregularity in natural jointing.

Several methods have been proposed to simulate such discontinuous media. They are divided into two groups: (1) 'equivalent' continuous analyses in which the jointed rock mass is represented by a homogeneous, anisotropic and continuous medium;98 99 and (2) the methods which can deal with discontinuities directly and can express positively the behaviour of discontinuous rock masses.

Finite element techniques using joint elements100 have been used in the analysis of certain problems, particularly in configurations involving a relatively small number of major faults or joints. However, for models with dense jointing, a large number of degrees of freedom are required.

The distinct element method or dynamic relaxation method101 allows a problem to be formulated assuming rock blocks to be rigid, with deformation and movement occurring only at the joints and fissures so that for this type of analysis in its simplest form no information is needed on the deformability and strength of intact rock. The method is a discontinuum modelling approach which is suitable in cases where the behaviour of the rock mass is dominated by the properties of joints or other discontinuities. In such cases the discontinuity stiffness (i.e. force/displacement characteristics) is much lower than that of intact rock. Calculations are based on laws relating forces and

Figure 10.16 Finite-element method. An example showing finite-element mesh for the analysis of stresses acting on a pressure tunnel lining. Elements of varying stiffness have been used to simulate rock zones of varying competence. (Grob, et al. (1970) Proceedings, 2nd international conference on rock mechanics, Belgrade. Paper 4-69)

Figure 10.16 Finite-element method. An example showing finite-element mesh for the analysis of stresses acting on a pressure tunnel lining. Elements of varying stiffness have been used to simulate rock zones of varying competence. (Grob, et al. (1970) Proceedings, 2nd international conference on rock mechanics, Belgrade. Paper 4-69)

displacements between blocks (e.g. laws of elasticity or friction) and on the laws of motion (e.g. creep, viscosity or Newton's laws). Behaviour of the model is constricted to be compatible with boundary force or displacement conditions. Large movements can be modelled - not normally possible with any accuracy using a finite-element method. The method of computation is ideally suited for considering the development of rock movements incrementally with time (Figure 10.17). The distinct element method first described by Cundall10' treats the rock as an assemblage of blocks interacting across deformable joints of definable stiffness. It is a development of the relaxation method and the dynamic relaxation method described by Otter, Cassell and Hobbs.102 A force-displacement relationship governs interaction between the blocks and laws of motion determine block displacements caused by out-of-balance forces. Several forms of distinct element codes have been developed to cover a variety of in situ conditions. The Universal Distinct Element Code (UDEC), has been developed recently which provides, in one code, all the capabilities that existed separately in previous programs. Features exist for modelling variable rock deforma-bility, nonlinear inelastic behaviour of joints, plastic behaviour and fracture of intact rock, and fluid flow and fluid pressure generation in joints and voids. An automatic joint generator produces joint patterns based upon statistically derived joint parameters. The program can simulate the influence of the far-field rock mass for both static and dynamic conditions as it is coupled to a boundary element program which represents the effects of a static, elastic far-afield response, and nonreflecting boundary conditions are available for dynamic simulations.105 The technique has three distinguishing features which make it well suited for discontinuum modelling:

(1) The rock mass is simulated as an assemblage of blocks which interact through corner and edge contacts.

(2) Discontinuities are regarded as boundary interactions between blocks; joint behaviour is prescribed for these interactions.

(3) The method utilizes an explicit time-stepping algorithm which allows large displacements and rotations and general nonlinear constitutive behaviour for both the rock matrix and the joints.

The boundary element method104 and the displacement discontinuity methodm are integral methods of stress analysis, in which the problem is specified and solved in terms of forces (or tractions) and displacements on the surface or boundary of the model. The boundary (such as a tunnel perimeter) is divided into discrete elements whilst the far-field boundary may be infinite (or semi-infinite). Thus 'discretization' errors are restricted to the problem boundary, and variations in stresses and displacements are fully continuous. The field equations at a point within the continuum are satisfied exactly, and errors are associated with the approximations occurring at the boundary only. The boundary forces or tractions determine the stresses in the surrounding medium which are evaluated using expressions for stress components at any point in an infinite medium.106 Elastic displacements around the excavation are calculated by making use of standard solutions for displacements in an infinite medium due to point or line loads. The methods are not particularly well suited to heterogeneous, anisotropic or nonlinear material behaviour. A reasonably clear and concise

Figure 10.17 The dynamic relaxation method. The figure shows progressive collapse of a stack of cylinders, with displacements computed as a function of time using the dynamic relaxation method. Similar calculations can be used to show the collapse of rectangular blocks such as comprise a rock mass. (After Cundall (1971) 'A computer model for simulating progressive large-scale movements in blocky rock systems'. Proceedings, international symposium on rock mechanics rock fracture, Nancy. Paper 2-8)

Figure 10.17 The dynamic relaxation method. The figure shows progressive collapse of a stack of cylinders, with displacements computed as a function of time using the dynamic relaxation method. Similar calculations can be used to show the collapse of rectangular blocks such as comprise a rock mass. (After Cundall (1971) 'A computer model for simulating progressive large-scale movements in blocky rock systems'. Proceedings, international symposium on rock mechanics rock fracture, Nancy. Paper 2-8)

description of the method is presented in the appendices of a practical manual on underground excavations.62 This further provides a collection of stress distributions calculated using the boundary element method around single openings of various shapes within different stress fields. Reference to these is useful as a first assessment of stress concentration around proposed excavations.

More recently'07 a boundary element formulation has been presented for modelling structural discontinuities, joints, faults and heterogeneous rock. The model is divided into regions, each one homogeneous, separated by interfaces which can represent discontinuities. The solution, however, is an iterative approximation to account for nonlinear joint equations.

The displacement discontinuity method is particularly suited to the analysis of tabular openings (such as coalmines). It is able to work in three dimensions, data input is relatively easy, and will model multiple seam-mining layouts or folded or faulted single-seam deposits.

Various coupled computational analyses (or 'hybrid' methods) have been devised to make advantageous use of the boundary element integral method for modelling the far-field region of a problem, and to couple this with an appropriate differential method (relaxation, finite element or distinct element) to model the immediate surroundings of the excavation. A domain of complex behaviour is thus embedded in an infinite elastic continuum. Lorig and Brady'0'109 have described the coupling of the discrete element method with boundary elements, and Ushijima and Einstein"0 a three-dimensional finite element code with boundary elements.

In the limiting equilibrium method'" a rock mass is considered under conditions where the mass is on the point of becoming unstable. The method gives no information on magnitudes of displacement or on rock behaviour prior to failure, so that the design calculations cannot readily be checked by instrumentation and monitoring of rock movements.

Equilibrium is examined by relating the shear and normal forces on the sliding surface to the sliding resistance of that surface. Shear tests are necessary to evaluate sliding resistance, but otherwise a constitutive equation for the rock mass is not required. The geometry and position of the sliding surface must be predicted in advance, and for this reason the method has been most commonly applied to slope stability problems where the sliding surface is more readily predicted than in underground situations. The development of computers has made it possible to use conveniently some very powerful limit equilibrium methods.69

Slope design9 usually employs limiting equilibrium analysis. A first step is to assess whether any kinematic mechanisms of potential slope failure are likely to be more closely approximated by a plane failure, a sliding wedge, rotational slip or a toppling failure model, and to identify the beds, joints or faults that could conceivably control such a failure, as illustrated in Figure 10.18. Throughgoing discontinuities such as faults, beds or older pre-existing failure surfaces are likely to be of considerably greater significance than impersistent or rough features. The presentation and analysis of geological structure data using the method of stereographic projections (stereonets)10 is invaluable for such an assessment. Clearly, the collection in the field of the geological data relevant to the problem is of paramount importance, as described in Chapter 8.

Quick and approximate calculations at this stage help to assess whether there is indeed a problem, and whether a more detailed analysis is justified. These can employ hand calculations or design charts9 using data for rock strength and water pressures estimated after examining the rock in situ. Worst and

Poles of N individual

Poles of N individual

Figure 10.18 Representation of structural data concerning four possible slope failure modes, plotted on equatorial equal-area nets as poles and great circles, (a) Circular failure in heavily jointed rock; (b) plane failure in highly ordered structure such as slate; (c) wedge failure on two intersecting sets of joints; (d) toppling failure caused by steeply dipping joints. (After Brown (1981) Rock characterization, testing and monitoring. Committee Testing Methods International Society Rock Mechanics. Pergamon, Oxford)

Figure 10.18 Representation of structural data concerning four possible slope failure modes, plotted on equatorial equal-area nets as poles and great circles, (a) Circular failure in heavily jointed rock; (b) plane failure in highly ordered structure such as slate; (c) wedge failure on two intersecting sets of joints; (d) toppling failure caused by steeply dipping joints. (After Brown (1981) Rock characterization, testing and monitoring. Committee Testing Methods International Society Rock Mechanics. Pergamon, Oxford)

best estimates can be used to give upper and lower bounds in the stability calculations. More rigorous calculations then require in situ measurement of shear strength or the back analysis of existing slides, water pressure monitoring and permeability testing. A flowchart showing the main steps in assessing the stability of a rock slope is presented in Figure 10.19. A most comprehensive practical manual' presents full details of the methods mentioned above, to which reference should be made.

The two-dimensional methods of analysis most often used in soil mechanics should not normally be applied to rock problems although Hoek'4 describes the use of the nonvertical slice method of Sarma.112 This limit equilibrium method is ideally suited to many rock slope problems because it can account for specific structural features such as faults. Vector methods' are particularly suited to the limiting equilibrium analysis of three-dimensional wedges. The kinematics of stability are also of greater relevance in rock than in soil, and techniques are available for selecting probable from improbable slides on the basis of kinematic considerations."3

Natural or excavated rock slopes might be shown to be stable overall whilst the possibility remains of minor rockfalls occur-

ring due to loosened blocks. These may be controlled by full stabilization methods, or by protection methods such as catch fences and ditches to arrest or retard the tumbling blocks. Experimental work, notably by Ritchie"4 and others,"5 has examined the trajectory of falling blocks and enabled guidelines to be developed for slope-toe rock traps. A design chart for ditch and fence rock traps is shown in Figure 10.20. Protection measures are generally not expensive but require continual maintenance, whereas stabilization measures such as rockbolt-ing, buttressing, trimming, mesh and shotcrete which may need little maintenance can be very expensive to install, especially for high slopes.

Owing to the inherent variability of the orientation of discontinuities, even though they occur in 'sets', the design of rock slopes may in some circumstances lend itself to a probabilistic analysis."6-"8 For example, the resisting forces are due to the shear resistance of the joint planes and the disturbing forces are due to the weight of the rock block or wedge, both of which are functions of joint orientation. Whereas normal 'deterministic' analysis is based on a factor of safety for the ratio of resisting to disturbing forces, probability density functions or distributions can be derived to describe each of these. The probability of failure is then a function of these two distributions.

10.4.6 Foundation design

Rocks generally, have a high allowable bearing pressure which may be reduced by the presence of weak layers, discontinuities and weathering. The allowable bearing pressure depends on the compressibility and strength of the rock mass and the permissible settlement of the structure.

Detailed design calculations for foundation rock are generally required only if the rock is weak and/or broken or the loading is unusually high, and in these cases the problems are usually associated with settlement prediction rather than foundation bearing failure. The compressibility of the rock mass is related to the strength and modulus of intact rock, the lithology, and the frequency, nature and orientation of the discontinuities. Guidance on allowable bearing pressures and a method of calculation may be obtained from the British Standard Code of Practice."9 These values are not necessarily suitable for very large heavy foundations nor for structures sensitive to settlement which should be considered having regard for the size of foundation, the variation in strength and nature of fracturing both with depth and laterally, and the variation in modulus with intensity of stress.120

Typical problems that require a more detailed study include the design of end-bearing piles or caissons carried to rock, particularly when the depth of overlying less competent materials is such as to require a minimum diameter of excavation with correspondingly high bearing pressures. The design of rock-socketed piers has been reviewed by Rowe and Armitage12' and they have produced a number of design charts for their proposed method. Piling in chalk has been reviewed comprehensively by Hobbs and Healy.122 Certain types of structure are particularly vulnerable to differential settlements, and others are particularly massive so as to impose high foundation loads (e.g. arch dams and the heavier types of nuclear reactor)120 125 and in these instances rock foundations require careful design.

Site exploration is primarily aimed at locating suitable foundation levels, and the relative, rather than the absolute, competence of strata. Rock-quality maps can be useful in making this choice. The depth of rock weathering (Chapter 8) is often of particular significance. Approximate allowable bearing pressures can be estimated empirically"9 and often at this stage the foundation design can be modified or improved by grouting.

More detailed analyses of foundation behaviour may employ closed-form elastic or plastic solutions or the various computational methods of analysis described in section 10.4.4. These require information of rock deformability that is usually obtained by in situ plate-loading tests or from borehole dilat-ometer tests. Seismic refraction and other geophysical methods may be useful to assess the character of the rock mass on a large scale. Foundations on argillaceous rocks can be subject to plastic deformation under high contact stresses and may require a study of long-term (time-dependent) behaviour. Stability analyses - taking into account particularly any uplift forces due to water pressure - in addition to settlement calculations are necessary when designing dam foundations and abutments, and when a foundation is situated above a rock slope. Limiting equilibrium methods are appropriate for these analyses, although rock foundation-structure interaction analyses using computational methods of analysis are appropriate for any major structures.

Underground openings for civil engineering purposes require perhaps the most rigorous use of rock mechanics practice in their design and construction. They are so demanding because of the severe consequences of being unsuitable or unsafe for their intended purpose. Tunnels and caverns for, say, railway systems or hydro-electric power complexes are not only occupied by the public in some cases, but even minor instability or surface ravelling of small blocks is wholly intolerable to the function of the works. The responsibility on the designer given the natural variability of the materials is very great and it is also necessary to recognize the essential requirements of the various uses to which caverns may be put. In the above examples stability in every sense is essential but the effects on the groundwater regime may be of lesser importance. There are some caverns used for storage of water, oil or gas, and mining openings in which limited minor instability might be permissible, but to maintain, for example, an unlined gastight cavity, it is essential that drainage of the surrounding rock pore water and fissure water does not occur.

The most demanding of purposes for caverns for the designer is the storage of radioactive waste, and this requirement is one explanation for the recent most rapid advance in rock mechanics field experimentation and development of understanding. Stability is essential and must be considered both for the very long term and in relation to extreme thermal effects and radionuclide absorption on rock mass properties, as well as to the dynamic disturbing forces of possible future seismic events. The prediction of groundwater flow around and away from nuclear repositories must consider the stress and thermal effects on hydraulic conductivity of joints and fissures, and the hydrothermal migration or convection effects on groundwater. Such details can be examined theoretically using the computational methods described above, but the determination of realistic input parameters remains a major problem.

The shapes and sizes of underground excavations are often dictated by economic and functional considerations, but their precise location and orientation should be adjusted to suit ground conditions wherever possible. Optimum orientation requires a knowledge of the geological structure, rock mass structure and also of the directions and relative magnitudes of principal stresses in the ground prior to excavation, and so detailed layouts of proposed works should be held in abeyance until after the investigation stage if possible.

A guide to the most important steps in the stability design of underground openings is given in Chapter 1 of a comprehensive manual by Hoek and Brown62 and full details of the various methods are given. In the design process it is necessary to characterize and zone the rock mass 'geo-mechanically', to determine constitutive relations and strength criteria for each zone, and then bearing these and the proposed geometry of the opening in mind to select the appropriate method of analysis which will render where potential zones of instability lie. The criteria for support design must then be decided upon, e.g. it is common to provide rockbolts of sufficient length and number to support the deadweight of tension zones or 'overstressed' rock determined by stress analysis by anchoring back into 'sound' rock as illustrated in Figure 10.21. The definition of relevant 'failure' criteria which may be influenced by water pressure or seepage considerations, dynamic seismic forces or limiting displacements is a significant design input. Each failure state must then be tested for various stages of the excavation progress because areas of stress concentration will vary. When the excavation sequence and support element dimensioning are decided, verification of performance monitoring is necessary.

A useful design method which is valuable in developing an understanding of the mechanics of rock support is known as rock-support interaction analysis.''2 Although the method makes numerous simplifying assumptions (e.g. a circular excavation in a uniform in situ stress field is assumed) the principles may potentially be extended to more general cases. The method analyses stress and displacement in the surrounding rock and in the support elements, taking into account rock mass properties, the in situ stress, the development of a 'zone of plastic failure'

Tension zone from finite element study

63-mm X 3-m long drainholes at 1.5 X 2.5m O.C. in walls and 1.2 X 1.8 m O.C. in roof 3__

25-mm X 6 or 7.6 long rockbolts

Tension zone from finite element study

Note: Shotcrete on roof and walls

Figure 10.21 Example of rockbolt support for a major cavern. (After Cikanek and Goyal (1986) 'Experiences from large cavern excavation for TARP'. Proceedings, symposium for large rock caverns, Helsinki. Pergamon, Oxford)

Note: Shotcrete on roof and walls

Figure 10.21 Example of rockbolt support for a major cavern. (After Cikanek and Goyal (1986) 'Experiences from large cavern excavation for TARP'. Proceedings, symposium for large rock caverns, Helsinki. Pergamon, Oxford)

around the opening, the stiffness of the support and the timing of its installation after excavation. Whenever an excavation is made there will be inward radial movements (convergence) of the surrounding rock which, in practice, are not instantaneous. In the meantime, supports such as rockbolts or arches are installed and, as convergence continues, so the supports will provide reaction forces. The characteristics of the rock are represented by a 'ground response curve' and the support pressure by a 'support reaction line'. Methods of response curve calculation which make use of nonlinear peak strength and residual strength criteria, and the method for pressure tunnel design have been described.124125

Certain types of civil engineering excavation may give rise to subsidence problems, e.g. unsupported chambers for storing water and gas. Furthermore, the civil engineer is often affected in his surface construction operations by mining excavations beneath the site. Subsidence can be predicted to some extent although, since the phenomenon is essentially time-dependent, the analysis is complex and often based on empirical observations.126

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