390 Appendix II J Persistence • Persistence implies the areal extent or size of a discontinuity within a plane. It can be crudely quantified by observing the discontinuity trace lengths on the surface of exposures. It is one of the most important rock mass parameters, but one of the most difficult to quantify. • The discontinuities of one particular set will often be more continuous than those of the other sets. The minor sets will therefore tend to terminate against the primary features, or they may terminate in solid rock. • In the case of rock slopes, it is of the greatest importance to attempt to assess the degree of persistence of those discontinuities that are unfavorably orientated for stability. The degree to which discontinuities persist beneath adjacent rock blocks without terminating in solid rock or terminating against other discon- tinuities determines the degree to which failure of intact rock would be involved in eventual failure. Perhaps more likely, it determines the degree to which “down-stepping” would have to occur between adjacent discontinuities for a slip surface to develop. Persistence is also of the greatest importance to tension crack development behind the crest of a slope. • Frequently, rock exposures are small com- pared to the area or length of persistent dis- continuities, and the real persistence can only be guessed. Less frequently, it may be possible to record the dip length and the strike length of exposed discontinuities and thereby estimate their persistence along a given plane through the rock mass using probability theory. How- ever, the difficulties and uncertainties involved in the field measurements will be considerable for most rock exposures. Persistence can be described by the terms listed in Table II.8. K Number of sets • The mechanical behavior of a rock mass and its appearance will be influenced by the num- ber of sets of discontinuities that intersect one Table II.8 Persistence dimensions Very low persistence <1m Low persistence 1–3 m Medium persistence 3–10 m High persistence 10–20 m Very high persistence >20 m another. The mechanical behavior is especially affected since the number of sets determines the extent to which the rock mass can deform without involving failure of the intact rock. The number of sets also affects the appearance of the rock mass due to the loosening and displacement of blocks in both natural and excavated faces (Figure II.4). • The number of sets of discontinuities may be an important feature of rock slope stability, in addition to the orientation of discon- tinuities relative to the face. A rock mass containing a number of closely spaced joint sets may change the potential mode of slope failure from translational or toppling to rotational/circular. • In the case of tunnel stability, three or more sets will generally constitute a three- dimensional block structure having a con- siderably more “degrees of freedom” for deformation than a rock mass with less than three sets. For example, a strongly foliated phyllite with just one closely spaced joint set may give equally good tunneling conditions as a massive granite with three widely spaced joint sets. The amount of overbreak in a tun- nel will usually be strongly dependent on the number of sets. The number of joint sets occurring locally (e.g. along the length of a tunnel) can be described according to the following scheme: I massive, occasional random joints; II one joint set; III one joint set plus random; IV two joint sets; V two joint sets plus random; VI three joint sets; Discontinuities in rock masses 391 1 One joint set Three joint sets plus random (R) 2 3 R 1 Figure II.4 Examples illustrating the effect of the number of joint sets on the mechanical behavior and appearance of rock masses (ISRM, 1981a). VII three joint sets plus random; VIII four or more joint sets; and IX crushed rock, earth-like. Major individual discontinuities should be recorded on an individual basis. L Block size and shape • Block size is an important indicator of rock mass behavior. Block dimensions are determ- ined by discontinuity spacing, by the number of sets, and by the persistence of the discon- tinuities delineating potential blocks. • The number of sets and the orientation determine the shape of the resulting blocks, which can take the approximate form of cubes, rhombohedra, tetrahedrons, sheets, etc. However, regular geometric shapes are the exception rather than the rule since the joints in any one set are seldom consistently parallel. Jointing in sedimentary rocks usually produces the most regular block shapes. • The combined properties of block size and interblock shear strength determine the mech- anical behavior of the rock mass under given stress conditions. Rock masses composed of large blocks tend to be less deformable, and in the case of underground construction, develop favorable arching and interlocking. In the case of slopes, a small block size may cause the potential mode of failure to resemble that of soil, (i.e. circular/rotational) instead of the translational or toppling modes of failure usually associated with discon- tinuous rock masses. In exceptional cases, “block” size may be so small that flow occurs, as with a “sugar-cube” shear zones in quartzite. • Rock quarrying and blasting efficiency are related to the in situ block size. It may be helpful to think in terms of a block size dis- tribution for the rock mass, in much the same way that soils are categorized by a distribution of particle sizes. • Block size can be described either by means of the average dimension of typical blocks (block size index I b ), or by the total number of joints intersecting a unit volume of the rock mass (volumetric joint count J v ). Table II.9 lists descriptive terms give an impression of the corresponding block size. Values of J v > 60 would represent crushed rock, typical of a clay-free crushed zone. Rock masses. Rock masses can be described by the following adjectives to give an impression of block size and shape (Figure II.5). 392 Appendix II (i) massive—few joints or very wide spacing (ii) blocky—approximately equidimensional (iii) tabular—one dimension considerably smaller than the other two Table II.9 Block dimensions Description J v (joints/m 3 ) Very large blocks <1.0 Large blocks 1–3 Medium-sized blocks 3–10 Small blocks 10–30 Very small blocks >30 (iv) columnar—one dimension considerably larger than the other two (v) irregular—wide variations of block size and shape (vi) crushed—heavily jointed to “sugar cube” II.2.5 Ground water M Seepage • Water seepage through rock masses results mainly from flow through water conduct- ing discontinuities (“secondary” hydraulic conductivity). In the case of certain sedimentary (a) (b) (c) (d) Figure II.5 Sketches of rock masses illustrating block shape: (a) blocky; (b) irregular; (c) tabular; and (d) columnar (ISRM, 1981a). Discontinuities in rock masses 393 rocks, such as poorly indurated sandstone, the “primary” hydraulic conductivity of the rock material may be significant such that a proportion of the total seepage occurs through the pores. The rate of seepage is proportional to the local hydraulic gradient and to the relevant directional conductiv- ity, proportionality being dependent on lam- inar flow. High velocity flow through open discontinuities may result in increased head losses due to turbulence. • The prediction of ground water levels, likely seepage paths, and approximate water pres- sures may often give advance warning of stability or construction difficulties. The field description of rock masses must inev- itably precede any recommendation for field conductivity tests, so these factors should be carefully assessed at early stages of the investigation. • Irregular ground water levels and perched water tables may be encountered in rock masses that are partitioned by persistent impermeable features such as dykes, clay-filled discontinuities or low conductivity beds. The prediction of these potential flow barriers and associated irregular water tables is of con- siderable importance, especially for projects where such barriers might be penetrated at depth by tunneling, resulting in high pressure inflows. • Water seepage caused by drainage into an excavation may have far-reaching con- sequences in cases where a sinking ground water level would cause settlement of nearby structures founded on overlying clay deposits. • The approximate description of the local hydrogeology should be supplemented with detailed observations of seepage from indi- vidual discontinuities or particular sets, according to their relative importance to sta- bility. A short comment concerning recent pre- cipitation in the area, if known, will be helpful in the interpretation of these observations. Additional data concerning ground water trends, and rainfall and temperature records will be useful supplementary information. • In the case of rock slopes, the preliminary design estimates will be based on assumed values of effective normal stress. If, as a result of field observations, one has to conclude that pessimistic assumptions of water pressure are justified, such as a tension crack full of water and a rock mass that does not drain readily, then this will clearly influence the slope design. So also will the field observation of rock slopes where high water pressures can develop due to seasonal freezing of the face that blocks drainage paths. Seepage from individual unfilled and filled dis- continuities or from specific sets exposed in a tunnel or in a surface exposure, can be assessed according to the descriptive terms in Tables II.10 and II.11. In the case of an excavation that acts as a drain for the rock mass, such as a tunnel, it is helpful if the flow into individual sections of the structure are described. This should ideally be performed immediately after excavation since ground water levels, or the rock mass storage, may be depleted Table II.10 Seepage quantities in unfilled discontinuities Seepage rating Description I The discontinuity is very tight and dry, water flow along it does not appear possible. II The discontinuity is dry with no evidence of water flow. III The discontinuity flow is dry but shows evidence of water flow, that is, rust staining. IV The discontinuity is damp but no free water is present. V The discontinuity shows seepage, occasional drops of water, but no continuous flow. VI The discontinuity shows a continuous flow of water—estimate l/ min and describe pressure, that is, low, medium, high. 394 Appendix II Table II.11 Seepage quantities in filled discontinuities Seepage rating Description I The filling materials are heavily consolidated and dry, significant flow appears unlikely due to very low permeability. II The filling materials are damp, but no free water is present. III The filling materials are wet, occasional drops of water. IV The filling materials show signs of outwash, continuous flow of water—estimate l/ min. V The filling materials are washed out locally, considerable water flow along out-wash channels—estimate l/ min and describe pressure that is low, medium, high. VI The filling materials are washed out completely, very high water pressures experienced, especially on first exposure—estimate l/ min and describe pressure. Table II.12 Seepage quantities in tunnels Rock mass (e.g. tunnel wall) Seepage rating Description I Dry walls and roof, no detectable seepage. II Minor seepage, specify dripping discontinuities. III Medium inflow, specify discontinuities with continuous flow (estimate l/ min /10 m length of excavation). IV Major inflow, specify discontinuities with strong flows (estimate l/ min /10 m length of excavation). V Exceptionally high inflow, specify source of exceptional flows (estimate l/ min /10 m length of excavation). rapidly. Descriptions of seepage quantities are given in Table II.12. • A field assessment of the likely effectiveness of surface drains, inclined drill holes, or drainage galleries should be made in the case of major rock slopes. This assessment will depend on the orientation, spacing and apertures of the relevant discontinuities. • The potential influence of frost and ice on the seepage paths through the rock mass should be assessed. Observations of seepage from the surface trace of discontinuities may be misleading in freezing temperatures. The pos- sibility of ice-blocked drainage paths should be assessed from the points of view of sur- face deterioration of a rock excavation, and of overall stability. II.3 Field mapping sheets The two mapping sheets included with this appendix provide a means of recording the qualitative geological data described in this appendix. Sheet 1—Rock mass description sheet describes the rock material in terms of its color, grain size and strength, the rock mass in terms of the block shape, size, weathering and the number of discontinuity sets and their spacing. 396 Appendix II Sheet 2—Discontinuity survey data sheet describes the characteristics of each discontinuity in terms of its type, orientation, persistence, aperture/width, filling, surface roughness and water flow. This sheet can be used for recording both outcrop (or tunnel) mapping data, and oriented core data (excluding persistence and surface shape). Appendix III Comprehensive solution wedge stability III.1 Introduction This appendix presents the equations and proce- dure to calculate the factor of safety for a wedge failure as discussed in Chapter 7. This compre- hensive solution includes the wedge geometry defined by five surfaces, including a sloped upper surface and a tension crack, water pressures, dif- ferent shear strengths on each slide plane, and up to two external forces (Figure III.1). External forces that may act on a wedge include tensioned anchor support, foundation loads and earthquake motion. The forces are vectors defined by their magnitude, and their plunge and trend. If neces- sary, several force vectors can be combined to meet the two force limit. It is assumed that all forces act through the center of gravity of the wedge so no moments are generated, and there is no rotational slip or toppling. III.2 Analysis methods The equations presented in this appendix are identical to those in appendix 2 of Rock Slope Engineering, third edition (Hoek and Bray, 1981). These equations have been found to be versatile and capable of calculating the stabi- lity of a wide range of geometric and geotech- nical conditions. The equations form the basis of the wedge stability analysis programs SWEDGE (Rocscience, 2001) and ROCKPACK III (Watts, 2001). However, two limitations to the analysis are discussed in Section III.3. As an alternative to the comprehensive ana- lysis presented in this appendix, there are two 1 5 2 3 4 L H1 Line of intersection Figure III.1 Dimensions and surfaces defining size and shape of wedge. shorter analyses that can be used for a more lim- ited set of input parameters. In Section 7.3, a calculation procedure is presented for a wedge formed by planes 1, 2, 3 and 4 shown in Fig- ure III.1, but with no tension crack. The shear strength is defined by different cohesions and fric- tion angles on planes 1 and 2, and the water pressure condition assumed is that the slope is saturated. However, no external forces can be incorporated in the analysis. A second rapid calculation method is presen- ted in the first part of appendix 2 in Rock Slope Engineering, third edition. This analysis also does not incorporate a tension crack or external forces, but does include two sets of shear strength parameters and water pressure. Comprehensive solution wedge stability 399 III.3 Analysis limitations For the comprehensive stability analysis presen- ted in this appendix there is one geometric limitation related to the relative inclinations of plane 3 and the line of intersection, and a specific procedure for modifying water pressures. The following is a discussion of these two limitations. Wedge geometry. For wedges with steep upper slopes (plane 3), and a line of intersec- tion that has a shallower dip than the upper slope (i.e. ψ 3 >ψ i ), there is no intersection between the plane and the line; the program will ter- minate with the error message “Tension crack invalid” (see equations (III.50) to (III.53)). The reason for this error message is that the calcula- tion procedure is to first calculate the dimensions of the overall wedge from the slope face to the apex (intersection of the line of intersection with plane 3). Then the dimensions of a wedge between the tension crack and the apex are calculated. Finally, the dimensions of the wedge between the face and the tension crack are found by subtract- ing the overall wedge from the upper wedge (see equations (III.54) to (III.57). However, for the wedge geometry where (ψ 3 > ψ i ), a wedge can still be formed if a tension crack (plane 5) is present, and it is possible to cal- culate a factor of safety using a different set of equations. Programs that can investigate the sta- bility wedges with this geometry include YAWC (Kielhorn, 1998) and (PanTechnica, 2002). Water pressure. The analysis incorporates the average values of the water pressure on the slid- ing planes (u 1 and u 2 ), and on the tension crack (u 5 ). These values are calculated assuming that the wedge is fully saturated. That is, the water table is coincident with the upper surface of the slope (plane 3), and that the pressure drops to zero where planes 1 and 2 intersect the slope face (plane 4). These pressure distributions are simu- lated as follows. Where no tension crack exists, the water pressures on planes 1 and 2 are given by u 1 = u 2 = γ w H w /6, where H w is the ver- tical height of the wedge defined by the two ends of the line of intersection. The second method allows for the presence of a tension crack and gives u 1 = u 2 = u 5 = γ w H 5w /3, where H 5w is the depth of the bottom vertex of the ten- sion crack below the upper ground surface. The water forces are then calculated as the product of these pressures and the areas of the respective planes. To calculate stability of a partially saturated wedge, the reduced pressures are simulated by reducing the unit weight of the water, γ w . That is, if it is estimated that the tension crack is one- third filled with water, then a unit weight of γ w /3 is used as the input parameter. It is considered that this approach is adequate for most purposes because water levels in slopes are variable and difficult to determine precisely. III.4 Scope of solution This solution is for computation of the factor of safety for translational slip of a tetrahedral wedge formed in a rock slope by two intersecting dis- continuities (planes 1 and 2), the upper ground surface (plane 3), the slope face (plane 4), and a tension crack (plane 5 (Figure III.1)). The solu- tion allows for water pressures on the two slide planes and in the tension crack, and for differ- ent strength parameters on the two slide planes. Plane 3 may have a different dip direction to that of plane 4. The influence of an external load E and a cable tension T are included in the ana- lysis, and supplementary sections are provided for the examination of the minimum factor of safety for a given external load, and for minimizing the anchoring force required for a given factor of safety. The solution allows for the following conditions: (a) interchange of planes 1 and 2; (b) the possibility of one of the planes overlying the other; (c) the situation where the crest overhangs the toe of the slope (in which case η =−1); and (d) the possibility of contact being lost on either plane. [...]... failure criterion Int J Rock Mech Mining Sci & Geomech Abstr 12(3), 227–29 Hoek, E (1994) Strength of rock and rock masses, ISRM News Journal, 2(2), 4–16 Hoek, E and Bray, J (1977) Rock Slope Engineering, 1st edn, IMM, London Hoek, E and Bray, J (1981) Rock Slope Engineering, 3rd edn, Inst Mining and Metallurgy, London, UK Hoek, E and Brown, E T (1980a) Empirical strength criterion for rock masses J Geotech... in Surface Mining, Soc Mining, Metallurgy and Exploration, Littleton, CO, 97 105 Golder, H Q (1972) The stability of natural and man-made slopes in soil and rock Geotechnical Practice for Stability in Open Pit Mining (eds C O Brawner and V Milligan), AIME, New York, 79–85 Goodman, R E (1964) The resolution of stresses in rock using stereographic projection Int J Rock Mech Mining Sci., 1, 93 103 Goodman,... Wyllie, D C (1980) Toppling rock slope failures, examples of analysis and stabilization Rock Mech., 13, 89–98 Wyllie, D C (1987) Rock slope inventory system Proc Federal Highway Administration Rock Fall Mitigation Seminar, FHWA, Region 10, Portland, Oregon Wyllie, D C (1991) Rock slope stabilization and protection measures Assoc Eng Geologists, National Symp on Highway and Railway Slope Stability, Chicago... Rock mechanics, Luleå University of Technology Sjöberg, J (2000) Failure mechanism for high slopes in hard rock Slope Stability in Surface Mining, Society of Mining, Metallurgy and Exploration, Littleton, CO, pp 71–80 Sjöberg, J., Sharp, J C and Malorey, D J (2001) Slope stability at Aznalcóllar In: Slope Stability in Surface Mining (eds W A Hustralid, M J McCarter and D J A Van Zyl), Society for Mining, ... ASCE 106 (GT9), 101 3–35 Hoek, E and Brown, E T (1980b) Underground Excavations in Rock, London, Inst Mining Metallurgy, London, UK Hoek, E and Brown, E T (1988) The Hoek–Brown failure criterion—a 1988 update Proc 15th Canadian Rock Mech Symp (ed J.C Curran), pp 31–8 Toronto, Dept Civil Engineering, University of Toronto Hoek, E and Brown, E T (1997) Practical estimates or rock mass strength Int J Rock. .. Deformation of Rock Am Soc Testing and Materials, Spec Tech Publication, No 477, 174–96 Goodman, R E (1976) Methods of Geological Engineering in Discontinuous Rocks West Publishing Co., St Paul, MN, 472 pp Goodman, R E (1980) Introduction to Rock Mechanics John Wiley and Sons, New York Goodman, R E and Bray, J (1976) Toppling of rock slopes ASCE, Proc Specialty Conf on Rock Eng for Foundations and Slopes,... Test Mat., 52, 1260–71 412 References Bandis, S C (1993) Engineering properties and characterization of rock discontinuities In: Comprehensive Rock Engineering: Principles, Practice and Projects (ed J A Hudson) Vol 1, Pergamon Press, Oxford, pp 155–83 Barrett, R K and White, J L (1991) Rock fall prediction and control Proc National Symp on Highway and Railway Slope Maintenance, Assoc of Eng Geol.,... pp 445–62 Yu, X and Vayassde, B (1991) Joint profiles and their roughness parameters Technical note, Int J Rock Mech Min Sci & Geomech Abstr., 16(4), 333–6 Zanbak, C (1983) Design charts for rock slope susceptible to toppling ASCE, J Geotech Engng, 109 (8), 103 9–62 Zavodni, Z M (2000) Time-dependent movements of open pit slopes Slope Stability in Surface Mining Soc Mining, Metallurgy and Exploration,... Morgenstern, N R and Price, V E (1965) The analysis of the stability of general slide surfaces Geotechnique 15, 79–93 Morris, A J and Wood, D F (1999) Rock slope engineering and management process on the Canadian pacific Railway Proc 50th Highway Geology Symposium, Roanoke, VA Morriss, P (1984) Notes on the Probabilistic Design of Rock Slopes Australian Mineral Foundation, notes for course on Rock Slope Engineering, ... P and Guo, H (2000) An orthotropic Cosserat elasto-plastic model for layered rocks J Rock Mech Rock Engng., 35(3), 161–170 Adhikary, D P., Dyskin, A V., Jewell, R J and Stewart, D P (1997) A study of the mechanism of flexural toppling failures of rock slopes J Rock Mech Rock Engng, 30(2), 75–93 Adhikary, D P., Mühlhaus, H.-B and Dyskin, A V (2001) A numerical study of flexural buckling of foliated rock . 2.8272 × 10 7 lb u 1 = u 2 = u 5 = 108 4.3 lb/ft 2 ; V = 2.0023 10 6 lb N 1 = 1.5171 × 10 7 lb N 2 = 5.7892 × 10 6 lb ⎫ ⎬ ⎭ Both positive therefore contact on planes 1 and 2. S = 1.5886 × 10 7 lb Q. tension crack full of water and a rock mass that does not drain readily, then this will clearly influence the slope design. So also will the field observation of rock slopes where high water pressures. this appendix. Sheet 1 Rock mass description sheet describes the rock material in terms of its color, grain size and strength, the rock mass in terms of the block shape, size, weathering and the number