ROCK SLOPE STABILITY ANALYSES

Transcription

1 Chapter 5 ROCK SLOPE STABILITY ANALYSES 5.1 ROCK MASS CLASSIFICATION In a mountainous region, construction of road corridor requires original and modified slopes to be stable (Sharma et al. 2013). The improper extension of activities on natural slope conditions for construction of roads and modification of cut slopes for the purpose of widening of the road through blasting and breakage, exposes inherent discontinuities and develops new cracks, which further affects the stability of the rock slope (Singh et al. 2013). Hence, it is necessary to understand the geological and geotechnical parameters before construction of any roads and even after construction to prevent slope failure. The stability of a slope can assess quickly and reliably through rock mass classification systems (Taheri and Tani 2010). Rock mass classification is an essential tool for the assessment of the behavior of rock cut slopes, on the basis of most significant inherent and structural parameters (Pantelidis 2010). The main purpose of rock mass classification is used to present quantitative data and guidelines (Liu and Chen 2007). The proposed classification systems incorporated various parameters, which are favorably affects the stability condition. The parameters include number of joint sets, spacing of discontinuities, condition of discontinuities (discontinuity length, separation, roughness, infilling, and weathering), orientation of discontinuities, groundwater conditions and strength of the intact rock material. The rock mass classification is an indirect method, which quantitatively estimates the stability of a rock mass. The estimated stability conditions of any classification system represented in the form of subjective terms viz. very bad, bad, acceptable, good and very good. The resultant value obtained through classification systems can be used to estimate the strength of rock mass and necessary rock support. 100

2 5.2 METHODS Rock Mass Rating (RMR) System Bieniawski (1973) was first proposed a geomechanical classification or the Rock Mass Rating (RMR) system at the South African Council of Scientific and Industrial Research (CSIR), for the application of designing tunnels, mines, dam, and underground excavations. The application of RMR system in the assessment of slope stability of cut slopes was introduced by Bieniawski (1976 & 1979). The Bieniawski s (1973) classification has undergone several modifications, from the time when the classification first proposed (Bieniawski 2011). Changes in the classification system includes, reduction of classification parameters from 8 to 6 in 1974, adjustment of ratings and reduction of recommended support requirements in 1976, modification of class boundaries to even multiples of 20 in 1979, adoption of ISRM (1978) rock mass description, and so forth. (Singh and Goel 2011). Hence, it is always necessary to mention which version is used when adopting the system. In the present study, the 1989 version of classification system was adopted. To apply the geomechanics of classification system, a given site should be divided into a number of geological structural units in such a way that each type of rock mass is represented by a separate geological structural unit (Singh and Goel 1999). The RMR system (Bieniawski 1989) classifies discontinuous of rock masses into five parameters as; Uniaxial Compressive Strength (UCS) of intact rock material Rock Quality Designation (RQD) Spacing of discontinuities Condition of discontinuities Groundwater conditions The ratings of five parameters of the RMR system are given in Table 5.1. Ratings for the individual parameters are summed to get the total RMR value. The maximum value of RMR is 100. Based on RMR total value, the rocks are classified into very poor rock (0-20), poor rock (21-40), fair rock (41-60), good rock (61-80), and very good rock (81-100) as listed in Table

3 Table 5.1 Rock Mass Rating (RMR) system Parameters Strength of Intact Rock Material Point-load Strength index Uniaxial compressive strength Range of Values >10 Mpa 4 10 MPa 2 4 Mpa 1 2 Mpa >250 Mpa MPa MPa MPa For this low range Uniaxial compressive test is preferred Rating Drill core Quality RQD 90% - 100% 75% - 90% 50% - 75% 25% - 50% <25% Rating Spacing of discontinuities >2 m m mm mm <60 mm Rating Discontinuity length <1 m 1 3 m 3 10 m m >20 m (persistence) Rating Separation (aperture) None <0.1 mm mm 1 5 mm >5 mm Condition of Rating discontinuities Roughness Very rough Rough Slightly rough Smooth Slickensided Ground water Rating Infilling (gouge) None Hard filling <5 mm Hard filling >5 mm Soft filling <5 mm Soft filling >5 mm Rating Weathering Unweathered Slightly weathered Moderately weathered Highly weathered Decomposed Ratings Inflow per 10 m tunnel length None < >125 (l/m) (Joint water press)/ (Major 0 < >0.5 Principal σ) General conditions Completely dry Damp Wet Dripping Flowing Rating (after Bieniawski 1989) 5 25 Mpa 1 5 MPa <1 MPa 102

4 Table 5.2 Rock mass classes and their engineering properties Rock Mass Classes Determined From Total Ratings Rating 100 < < < < <21 Class number I II III IV V Description Class Number Average Stand-up time Cohesion of rock mass (in kpa) Friction angle of rock mass (in degree) Very good rock Good rock Fair rock Poor rock Meaning of Rock Classes Very poor rock I II III IV V 20 years of 15 m span 1 year of 10 m span 1 week for 5 m span 10 hrs for 2.5 m span 30 min for 1 m span > <100 > < Slope Mass Rating (SMR) System (after Bieniawski 1989) For the purpose of assessment of rock slope stability, Romana (1985) derived SMR system from the studies of natural and cut slopes along the roads. The Slope Mass Rating (SMR) system is an extension of RMR system and it includes adjustment factors for orientation of discontinuity with slope and the method of excavation (Jhanwar 2011). The detailed quantitative description of the adjustment factors is one of the main advantages of SMR classification (Irigaray et al. 2003). SMR is calculated using Eq. 5.1 by adding correction factors of the joint-slope relationship (multiplication of F1, F2, and F3) (Table 5.3) and method of excavation (F4) to the basic RMR (Bieniawski 1989). The adjustment factor for the method of excavation (F4) depends on whether one deals with a natural slope or one excavated by preslitting, smooth blasting, mechanical excavation, or poor blasting (Table 5.4). Where, Slope Mass Rating (SMR) = RMR + (F1 x F2 x F3) + F4 (5.1) RMR is Rock Mass Rating F1 - depends on parallelism between joints and slope face strikes. 103

5 F2 - refers to joint dip angle in the planar mode of failure. F3 - indicates the relationship between the slope face and joint dip. Conditions are favorable when slope face and joints are parallel and very unfavorable when the slope dips 10 º more than joints. F4 - The adjustment factor for the method of excavation. CASE P α -α Table 5.3 Adjustment ratings for joints (after Romana 1985) Very Favorable Favorable Fair Unfavorable Very Unfavorable > <5 W α -α T α -α -180 P/T/W F β P/W < >45 β P/W F T F P β -β > (-10 ) <-10 W β -β T β +β < > P/T/W F (P: Planar failure; W: Wedge failure T: Toppling failure; α : Dip direction Joint; α : Plunge direction of line of intersection of two discontinuities; α : Dip direction of slope; β : Inclination of Slope; β : Dip of Joint; β : Plunge of line of intersection of two discontinuities) Table 5.4 Adjustment ratings for methods of excavation of slopes Method Natural Slope Pre-splitting Smooth Blasting Blasting or Mechanical Deficient Blasting F (after Romana 1985) On the basis of the values of slope mass rating the stability of rock slopes classified (Romana 1985), as fully stable (81-100), stable (61-80), partially stable (41-60), unstable (21-40) and very unstable (<20) as given in Table 5.5. Accordingly the very unstable cut slope may require re-excavation, unstable slope may need extensive corrective measures, partially stable slopes may have to be supported with systematic supports such as rock 104

6 bolts, and rock anchors and stable to fully stable slopes may need occasional to no supports. Table 5.5 Various stability classes as per SMR values Class No V IV III II I SMR Description Very Bad Bad Normal Good Very Good Stability Probable Type of Failure Support Completely Unstable Big Planar or Rotational Re-excavation Factor of Safety Unstable Planar or Big Wedge Important corrective measures Partially Stable Planar or many Wedges Systematic supports Stable Blocks Occasional supports Completely Stable None None (after Romana 1985) Since the RMR and SMR assessment did not rate stability in terms of factor of factor of safety (F), detailed stability analysis of critical rock slope sections was carried out for plane, wedge, and topple mode of failures. The determination of factor of safety for critical rock slope sections is based on the Hoek and Bray (1981) method. In this method, the stereoplots of all the critical sections have been used as effective tool to identify the potential slope problem (Markland 1972). The factor of safety is less than 1 is indicating the unstable condition Plane Failure in Rock Slopes Plane failure occurs when a geological discontinuity strikes parallel to the slope face and dips into the excavation at an angle greater than the angle of friction (Hoek and Bray 1981). The different geometry of slope with tension crack in the case of planar failure is shown in Figure 5.1 (a & b). a) A slope having tension crack in its upper surface. b) A slope with a tension crack in its face. 105

7 Figure 5.1 (a) Geometry of slope with tension crack in upper slope surface Planar Analysis (after Hoek and Bray 1981) Figure 5.1 (b) Geometry of slope with tension crack in slope face planar Analysis (after Hoek and Bray 1981) The transition from one case to another occurs when the tension crack coincides with the slope crest (Eq. 5.2), i.e. When the tension crack position and depth are unknown, the only reasonable procedure is to assume that the tension crack is coincident with the slope crest and that is water-filled. In this case the z/h can be estimated using the Eq z/h = (1 Cotψ. Tanψ ) (5.2) The following general conditions must be satisfied, for the sliding phenomenon on a single plane (Figure 5.2): 106

8 a. The plane on which sliding occurs must strike parallel or nearly parallel to the (within approximately ±20 ) to the slope face. b. The dip of the failure plane must daylight in the slope face i.e. the dip must be lesser than the dip of the slope face (ψ > ψ ). c. The dip of the failure plane must be greater than the angle of friction of this plane i.e. ψ > ϕ. d. Release surfaces which provide negligible resistance to sliding must be present in the rock mass to define the lateral boundaries of the slide. e. To simplify the computation, it is usual to consider a slice of unit thickness at right angles to the slope face. Figure 5.2 Geometry shows conditions of plane failure (Source: Hoek and Bray 1981) The assumptions for plane failure analysis are a) The failure surface and tension crack strike parallel to slope face. b) The tension crack is vertical and assumed that it is filled with water to a depth z c) Water enters into the sliding surface along the base of the tension crack and percolates all along the sliding surface d) The forces W (weight of the sliding block), U (uplift force due to water pressure on the sliding surface) and V (force due to water pressure in the tension crack) all act through the centroid of the sliding mass (Figure 5.1), that means the failure is not due any other moments. 107

9 e) The shear strength of the sliding surface is defined by cohesion (c) and a friction angle (ϕ) which are related by the Eq. 5.3 (Mohr Coulomb failure criterion). τ = c + Tan ϕ (5.3) f) It is assumed that release surfaces are present at the lateral boundaries of the failure. The factor of safety of this slope condition is given by the total force resisting sliding to the total force tending to induce sliding as; F =.... (5.4) Where, from Figure 5.1 A = (H z). Cosecψ (5.5) U = γ. z (H z). Cosecψ (5.6) V = γ. z (5.7) W = γh ((1 (z/h) ) Cotψ Cotψ ) (5.8) For the case: tension crack in the upper slope surface (Figure 5.1 a) W = γh ((1 z/h) Cotψ. (Cotψ. Tanψ 1)) (5.9) For the case: tension crack in the upper slope surface (Figure 5.1 b) In order to simplify the calculations, Eq. 5.4 can be rearranged in the following dimensionless form: Where F = ( / ).. ( ).. (5.10) P = (1 z/h). Cosecψ (5.11) When the tension crack is in the upper slope surface Q = ((1 (z/h) Cotψ Cotψ ) Sinψ (5.12) When the tension crack is in the slope face 108

10 Q = ((1 (z/h) Cotψ (Cotψ. Tanψ 1)) (5.13) R =. Z W. (5.14) S =.. Sinψ (5.15) The P, Q, R and S are all dimensionless ratios Wedge Failure in Rock Slopes The wedge failure is concerned with the failure of slopes in which structural features upon which sliding can occur strike across the slope crest and where sliding takes place along the line of intersection of two such planes (Hoek and Bray 1981). The general geometry of wedge failure, which is considered for present analysis, is given in Figure 5.3. The geometry showing the numbering of intersection lines and planes is given in Figure 5.4. The geometry of wedge used for stability analysis including the influence of cohesion and of water pressure on the failure surfaces is shown in Figure 5.5. The water pressure distribution assumed for this analysis is based upon the hypothesis that the wedge itself is impermeable and that water enters the top of the wedge along lines of intersection 3 and 4 and leaks from the slope face along lines of intersection 1 and 2. The resulting pressure distribution is shown in Figure 5.5, the maximum pressure occurring along the line of intersection 5 and the pressure being zero along lines 1, 2, 3 and 4. This water pressure distribution is believed to be representative of the extreme conditions which could occur during very heavy rain. The numbering of the lines of intersection of the various planes involved in this problem is of extreme importance since total confusion carries in the analysis if these numbers are mixed-up. The numbering used throughout the analysis is as follows: 1 Intersection of plane A with the slope face 2 Intersection of plane B with the slope face 3 Intersection of plane A with upper slope surface 4 Intersection of plane B with upper slope surface 5 Intersection of planes A and B 109

11 It is assumed that sliding of the wedge always takes place along the line of intersection numbered 5. Figure 5.3 Wedge failure geometry Figure 5.4 Geometry of wedge showing the numbering of intersection used for stability analyses (Source: Hoek and Bray 1981) 110

12 Figure 5.5 Geometry of wedge used for stability analysis including the influence of cohesion and of water pressure on the failure surfaces (Source: Hoek and Bray 1981) The factor of safety of this slope is derived from the detailed analysis of this problem published by Hoek et al Where, F = (c. X + c. Y) + A. X Tanϕ + B. Y Tanϕ (5.16) c and c are the cohesive strengths of planes A and B ϕ and ϕ are the angles of friction on planes A and B γ is the unit weight of the rock γ is the unit weight of water H is the total height of the wedge X =. (5.17) Y =. (5.18) A =.... (5.19) 111

13 B =.... (5.20) X (Eq. 5.17), Y (Eq. 5.18), A (Eq. 5.19), and B (Eq. 5.20) are dimensionless factors which depend upon the geometry of the wedge. Where, ψ and ψ are the dips of planes A and B respectively and ψ is the dip of the line of intersection 5. The angles required for the solution of these equations can conveniently be measured on a stereoplot of the data which defines the geometry of the wedge and the slope (Figure 5.6). Figure 5.6 Stereoplot of data required for wedge stability analysis 112

14 5.3 SLOPE STABILITY ANALYSES OF ROCK SLOPES The detailed slope stability analyses were carried out over moderate and high hazard zones (facets) identified through LHEF rating scheme (BIS 1998). For this detailed study, three facets were selected respectively fall in moderate hazard (facet 2) and high hazard zone (facet 3 & 4) along Ghat road of Kolli hills. In these three sections, six potential rock slope sections (Table 5.6 & Figure 5.7) were identified for Rock Mass Rating (RMR), Slope Mass Rating (SMR) and factor of safety analyses. Table 5.6 Location details of rock slope sections Facet Section ID Longitude Latitude Land Mark Facet 2 RS E N at 14/70 HPB Facet 3 RS E N at 25/70 HPB Facet 3 RS E N at 26/70 HPB Facet 3 RS E N at 29/70 HPB Facet 4 RS E N at 35/70 HPB Facet 4 RS E N at 37/70 HPB (HPB-Hairpin Bend) Compressive Strength - Point Load Lump Strength Index The strength of rock specimens can be characterized by widely used tests viz., unconfined and confined compression tests, shear tests, and direct and indirect tension tests (Goodman 1989). The minimum load at which the rock fails is an important measure in all geotechnical investigations. In the present work, the rock samples were collected in the field for the purpose of determination of strength of intact rock material. The sizes of the lumps were chosen based on the criteria given in (BIS 8764: 1998). The standard thicknesses of the lumps were taken as 5 cm. The point load test was carried out using AIM testing machine (Plate 5.1). 0.3 W < D < W (5.21) Where, W = Minimum width of the specimen in cm. If the size is not even, then W is obtained from W1, W2 and W3 as follows: W = (W 1 +W 2 +W 3 )/3 (5.22) 113

15 Figure 5.7 Locations selected for RMR, SMR, and Factor of Safety analyses 114

16 D = Minimum cross sectional thickness of specimen in cm. The initial load of about 2 KN was applied and the dial reading was set to zero. The load was applied continuously by pumping the handles of the machine till failure. Point load strength index was calculated using the Eq The results of compressive strength index of rock samples are shown in Table 5.7. (5.23) Where, I L (50) =Point load lump strength index; P=Load at failure in kgf; D=Mean cross sectional thickness of specimen in cm; W=Mean width of specimen in cm; D=Standard size of lump = 5 cm. Plate 5.1 Showing point load test instrument with sample placed 115

17 Rock Section ID RS 1 RS 2 RS 3 RS 4 RS 5 RS 6 Sample No Table 5.7 Results of compressive strength index of rock samples Peak Load Failure (in kgf) Point Load Strength Index (in Mpa) Mean Diameter (D) (cm) Mean Width (W) (cm) Point Load Index (in kgf/cm2) Point Load Index (in Mpa) Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Sample Overall Compressive Strength of Rock Section (in Mpa)

18 5.3.2 Collection of Field Data The RMR and SMR parameters were determined for each structural unit in the field for all the rock slope sections and recorded in data sheet (Table 5.8 to 5.13) Rock Quality Designation (RQD) index The Rock Quality Designation (RQD) index was proposed by Deere et al. (1967), which provides a quantitative estimate of rock mass quality from drill core logs. Palmstrom (1982) were given the method of estimation of RQD through visible discontinuity traces on surface. In this method, the RQD may be estimated by volumetric joint count method i.e. sum of the number of joints per metre cube (unit volume) for all joint sets. The method recommended a relationship for clay-free rock masses as given in Eq RQD = Jv (5.24) Where, Jv is the sum of the number of joints per metre cube for all joint (discontinuity) sets Spacing of discontinuities Discontinuities are common features in rock masses. The term discontinuity covers joints, beddings or foliations, shear zones, minor faults, or other surfaces of weakness (Devkota et al. 2009). Discontinuity spacing is an important parameter used in classification schemes, which measures the distance between two adjacent discontinuities should be measured for all sets of discontinuities (Wines and Lilly 2002). In the Ghat road section, mostly 3 set of joints were identified. The average discontinuity spacing of each joint set were measured and listed in the Tables Condition of discontinuities Discontinuity condition measures the discontinuity length, separation, roughness, infilling, and weathering condition of the wall rock or plane of weakness for all set of joint sets were measured in the field. 117

19 Groundwater condition If actual water pressure data are available, these should be stated and expressed in terms of the ratio of the seepage water pressure to the major principal stress (Singh and Goel 2011). A general groundwater conditions can be described for a particular slope are completely dry, damp, wet, dripping and flowing. It is very much desirable to take field data soon after the monsoon season to estimate the field condition on the basis of the nature of surface indications (Anbalagan 1992) Orientation of discontinuities It refers to the direction and dip of discontinuities. The direction should be measured with reference to magnetic north. The dip angle is the angle between the horizontal and discontinuity plane taken in a direction in which the plane dips. The influence of the direction and dip of discontinuities is considered with respect to the slope face orientation (Singh and Goel 2011). The slope orientation (slope direction and slope dip amount) and discontinuity orientation (direction and dip amount) for all the rock section were measured in the field (Plate 5.2) using Brunton compass (Table 5.14). In rock slope sections, the huge boulders are temporarily protected by bushes and trees along slope (Plate 5.3) Estimation of Rock Mass Rating (RMR) Based on the parameters observed in the field and point load test, the ratings of individual RMR parameter for each structural unit were assigned according to the Rock Mass Rating (Bieniawski 1989). The total RMR value for a rock section is calculated by means of algebraic sum of all the RMR parameter ratings. The area depicts class II (RS-1, 2 & 6) and class III (RS-3, 4, & 5) of RMR classes. The cohesion (c) and angle of internal friction (Φ) for every rock mass have been determined from the rock mass rating values. The RMR values, ratings of observed parameters and their class description, cohesion of rock mass, and angle of internal friction of rock mass of selected rock sections are given in Table

20 Plate 5.2 Geometrical measurement of structural parameters at Rock Section - 3 near 26/70 hairpin bend, Kolli hills Ghat road Plate 5.3 Huge rock boulder along slope in a critical stage of slide, being temporarily protected by bushes at rock section 6 (35/70 Hairpin Bend) 119

21 Table 5.8 RMR and SMR parameters for Rock Section (RS-1) Orientation of Slope ROCK SECTION (RS-1) Section ID RS 1 Landmark Exact Point at 14/70 HPB Latitude/Longitude N E Rock Type Slope Height (in m) Slope Direction Slope Inclination Cut Slope Dip Amount Description Excavation Method PARAMETERS Charnockite 8.0 m N Root Penetration, Highly fractured zone, well grown trees can be seen over the rock mass, dry scrub can be visible Blasting ROCK MASS RATING (RMR) PARAMETERS MEASUREMENTS 1 STRENGTH OF INTACT ROCK (MPa) ROCK QUALITY DESIGNATION 88.6 (RQD in %) 3 SPACING OFDISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set m 0.6 m 0.9 m 4 CONDITION OF DISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set - 3 (i) Discontinuity Length 3-10 m 3-10 m 3-10 m (ii) Separation <0.1 mm to None 1-5 mm to >5 mm None (iii) Roughness Slightly Rough Slightly Rough Slightly Rough (iv) (v) Infilling Weathering Hard Filling <5 mm to None Slightly to Unweathered Soft Filling >5 mm to <5mm Moderately to Slightly Weathered 5 GROUNDWATER CONDITIONS WET SLOPE MASS RATING (SMR) PARAMETERS None Slightly Weathered to Unweathered 6 ADJUSTMENT FACTOR ORIENTATION OF DISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Strike N 75 N 155 N 290 Dip Direction N 165 N245 N 20 Dip Amount

22 Table 5.9 RMR and SMR parameters for Rock Section (RS-2) Orientation of Slope ROCK SECTION (RS-2) Section ID RS 2 Landmark Exact Point at 25/70 HPB Latitude/Longitude N E Rock Type Slope Height (in m) Slope Direction Slope Inclination Cut Slope Dip Amount Description Excavation Method PARAMETERS Charnockite 8.60 m N Highly fractured zone with root penetration, layer of 2m soil cover can be seen at top layer, high & well grown trees can be seen, scrub present Blasting ROCK MASS RATING (RMR) PARAMETERS MEASUREMENTS 1 STRENGTH OF INTACT ROCK (MPa) ROCK QUALITY DESIGNATION (RQD in %) 3 SPACING OF DISCONTINUITIES 95.2 Joint Set - 1 Joint Set 2 Joint Set m 1 m 0.75 m 4 CONDITION OF DISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set - 3 (i) Discontinuity Length 3-10 m m 1-3 m (ii) Separation None >5mm None (iii) Roughness Slightly Rough Slightly Rough Slightly Rough (iv) Infilling None Soft Filling >5mm None (v) Weathering Unweathered Highly Weathered Unweathered 5 GROUNDWATER CONDITIONS Flowing SLOPE MASS RATING (SMR) PARAMETERS 6 ADJUSTMENT FACTOR ORIENTATION OF DISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Strike N 155 N 250 N 290 Dip Direction N 260 N340 N 205 Dip Amount

23 Table 5.10 RMR and SMR parameters for Rock Section (RS-3) ROCK SECTION (RS-3) Section ID RS 3 Landmark Exact Point at 26/70 HPB Latitude/Longitude N E Rock Type Slope Height (in m) Orientation of Slope Direction Slope Slope Inclination Cut Slope Dip Amount Description Excavation Method PARAMETERS Charnockite 14 m N The rock mass intersected by 3 set of joints highly fractured zone, A layer of weathered boulders can be seen, root penetration, top layer covered by short to medium trees, scrub can be seen Blasting ROCK MASS RATING (RMR) PARAMETERS MEASUREMENTS 1 STRENGTH OF INTACT ROCK (MPa) ROCK QUALITY DESIGNATION (RQD in %) 3 SPACING OF DISCONTINUITIES 32.5 Joint Set - 1 Joint Set 2 Joint Set m 0.5 m 0.18 m 4 CONDITION OF DISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set - 3 (i) Discontinuity Length m 3-10 m 1-3 m (ii) Separation None to 1-5 mm None to 1-5 mm None (iii) Roughness Slightly Rough Slightly Rough Slightly Rough (iv) Infilling None None None (v) Weathering Slightly Weathered Slightly Weathered Slightly Weathered 5 GROUNDWATER CONDITIONS Flowing SLOPE MASS RATING (SMR) PARAMETERS 6 ADJUSTMENT FACTOR ORIENTATION OF DISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Strike N 125 N 150 N 210 Dip Direction N 215 N 240 N 300 Dip Amount

24 Table 5.11 RMR and SMR parameters for Rock Section (RS-4) Orientation of Slope ROCK SECTION (RS-4) Section ID RS 4 Landmark Exact Point at 29/70 HPB Latitude/Longitude N E Rock Type Slope Height (in m) Slope Direction Slope Inclination Cut Slope Dip Amount Description Excavation Method Sample No PARAMETERS Charnockite 13 m (8+5 above rock mass) N Root Penetration, Medium height trees, scrubs, a thick layer of soil cover over rock mass, highly weathered boulders can be seen, bamboo trees existed Blasting ROCK MASS RATING (RMR) PARAMETERS MEASUREMENTS 1 STRENGTH OF INTACT ROCK (MPa) ROCK QUALITY DESIGNATION 16 (RQD in %) 3 SPACING OFDISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set m 0.35 m 0.27 m 4 CONDITION OF DISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set - 3 (i) Discontinuity Length 1-3 m 1-3 m 1-3 m (ii) Separation >5 mm None None (iii) Roughness Smooth to slightly Rough Slightly Rough Slightly Rough (iv) Infilling Soft Filling >5 mm None None (v) Weathering Highly Weathered Slightly Weathered Slightly Weathered 5 GROUNDWATER CONDITIONS Flowing SLOPE MASS RATING (SMR) PARAMETERS 6 ADJUSTMENT FACTOR ORIENTATION OF DISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Strike N 245 N 120 N 40 Dip Direction N 335 N 210 N 130 Dip Amount

25 Table 5.12 RMR and SMR parameters for Rock Section (RS-5) Orientation of Slope ROCK SECTION (RS-5) Section ID RS 5 Landmark Exact Point at 35/70 HPB Latitude/Longitude N E Rock Type Slope Height (in m) Slope Direction Slope Inclination Cut Slope Dip Amount Description Excavation Method PARAMETERS Charnockite 16 m N Highly fractured large rock mass with root penetration, scrub present, soil material deposited over rock mass which is transported from other places, scrub exists. Blasting ROCK MASS RATING (RMR) PARAMETERS MEASUREMENTS 1 STRENGTH OF INTACT ROCK (MPa) ROCK QUALITY DESIGNATION 32.5 (RQD in %) 3 SPACING OFDISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Joint Set m 0.27 m 0.31 m 0.45 m 4 CONDITION OF DISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Joint Set - 4 (i) Discontinuity Length 3-10 m 1-3 m 1-3 m m (ii) Separation None None None >5 mm (iii) Roughness Slightly Rough Slightly Rough Slightly Rough Slightly Rough (iv) Infilling None None None None (v) Weathering Slightly Weathered Slightly Weathered 5 GROUNDWATER CONDITIONS Wet SLOPE MASS RATING (SMR) PARAMETERS Slightly Weathered Moderately Weathered 6 ADJUSTMENT FACTOR ORIENTATION OF DISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Joint Set - 4 Strike N 185 N 205 N 125 N 60 Dip Direction N 92 N 120 N 230 N 325 Dip Amount

26 Table 5.13 RMR and SMR parameters for Rock Section (RS-6) Orientation of Slope ROCK SECTION (RS-6) Section ID RS 6 Landmark Exact Point at 37/70 HPB Latitude/Longitude N E Rock Type Slope Height (in m) Slope Direction Slope Inclination Cut Slope Dip Amount Description Excavation Method Sample No PARAMETERS Charnockite 8.5 m N Highly fractured zone with criss-cross joints, scrub exist, medium to low height trees. Blasting ROCK MASS RATING (RMR) PARAMETERS MEASUREMENTS 1 STRENGTH OF INTACT ROCK (MPa) ROCK QUALITY DESIGNATION 82 (RQD in %) 3 SPACING OFDISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set m 0.51 m 0.32 m 4 CONDITION OF DISCONTINUITIES Joint Set - 1 Joint Set 2 Joint Set - 3 (i) Discontinuity Length 3-10 m 3-10 m 1-3 m (ii) Separation None None 1 to 5 mm (iii) Roughness Slightly Rough Slightly Rough Slightly Rough (iv) Infilling None None None (v) Weathering Slightly Weathered Slightly Weathered Slightly Weathered 5 GROUNDWATER CONDITIONS Wet SLOPE MASS RATING (SMR) PARAMETERS 6 ADJUSTMENT FACTOR ORIENTATION OF DISCONTINUITIES Joint Set - 1 Joint Set - 2 Joint Set - 3 Strike N 160 N 80 N 60 Dip Direction N 65 N 185 N 325 Dip Amount

27 5.3.4 Estimation of Slope Mass Rating (SMR) The structural values (Table 5.14) of selected rock slope and their discontinuities were plotted on the stereo-net plot (Figure 5.8 & 5.9), to find out the type of failure and plunge of discontinuity for each rock slope section. The relationship between the slope and discontinuities were made to determine the adjustment ratings for F1, F2, and F3. In the study area, the cut slopes are formed by mechanical excavation of slopes, and is often combined with some preliminary blasting. The method of excavation neither increases nor decreases slope stability, so the adjustment factor for F4 is given as 0. These F1, F2, F3, and F4 values were added with the RMR basic value to find out the Slope Mass Rating (SMR) values (Table 5.16). Slope mass rating were calculated using Eq. 5.1 for six rock sections located in facet 2, 3, & 4. The procedure for calculation is explained in the following pages. Table 5.14 Geometry of structural discontinuities at various rock slopes Orientation Orientation of Discontinuities Rock of Slope (Direction & Dip Amount) Section Direction/ No. Joint Set 1 Joint Set 2 Joint Set 3 Joint Set 4 Inclination RS 1 N 315 / 44 N 165 / 88 N 245 / 16 N 20 / 70 - RS 2 N 330 / 48 N 260 / 80 N 340 / 16 N 205 / 16 - RS 3 N 325 / 31 N 215 / 10 N 240 / 22 N 300 / 21 - RS 4 N 265 / 58 N 335 / 54 N 210 / 29 N 130 / 65 - RS 5 N 285 / 62 N 92 / 41 N 120 / 64 N 230 / 11 N 325 / 83 RS 6 N 270 / 68 N 65 / 30 N 185 / 42 N 325 /

28 Table 5.15 Estimated Rock Mass Rating (RMR) for Rock Sections ROCK MASS RATING (RMR) Rock Section No. Rock Type Strength of Intact Rock RQD Rating Spacing of Discontinuity Condition of Discontinuity Ground water Condition RMR Value Description Class C (in kpa) ϕ (in degree) RS-1 Charnockite Good Rock II RS-2 Charnockite Good Rock II RS-3 Charnockite Fair Rock III RS-4 Charnockite Fair Rock III RS-5 Charnockite Fair Rock III RS-6 Charnockite Good Rock II

29 Figure 5.8 Stereonet plots of rock section 1, 2 and 3 show slope and discontinuity relationship 128

30 Figure 5.9 Stereonet plots of rock section 4, 5 and 6 show slope and discontinuity relationship 129

31 Slope Mass Rating Calculation for Rock Section (RS-1) The analysis made through stereo-net plot shows that, the most unfavorable condition is the result of intersection formed by the discontinuities J2 & J3. Hence, it is a case of probable wedge failure. Direction and Inclination of J2=N 245 /16 Direction and Inclination of J3=N 20 /70 α Direction of line of intersection of two discontinuities=n 294 β Direction of slope inclination=n 315 α Plunge of line of intersection of two discontinuities=10 α Inclination of Slope=44 F1= α -α = 21 F2 = β = 10 F3= β -β = -34 F4= 0 RMR = 68 Calculation of SMR = RMR + (F1 x F2 x F3) + F4 = 68 + (0.40 x 0.15 x (-60)) + 0 SMR = = Slope Mass Rating Calculation for Rock Section (RS-2) The analysis made through stereo-net plot shows that, the most unfavorable condition is the result of intersection formed by the discontinuities J1 & J2. Hence, it is a case of probable wedge failure. Direction and Inclination of J1=N 260 /80 Direction and Inclination of J2=N 340 /16 α Direction of line of intersection of two discontinuities=n 347 β Direction of slope inclination=n 330 α Plunge of line of intersection of two discontinuities=16 α Inclination of Slope=48 F1= α -α = 17 F2 = β = 16 F3= β -β = -32 F4= 0 RMR = Calculation of SMR = RMR + (F1 x F2 x F3) + F4 = 68 + (0.70 x 0.15 x (-60)) + 0 SMR = =

32 Slope Mass Rating Calculation for Rock Section (RS-2) The analysis made through stereo-net plot shows that, the most unfavorable condition is the result of J2 discontinuities. Hence, it is a case of probable planar failure. Direction and Inclination of J2=N 340 /16 α Dip Direction of Joint=N 340 β Dip of Joint=16 α Direction of Slope Inclination= N 330 β Inclination of Slope=48 F1= α -α = 17 F2 = β = 16 F3= β -β = -32 F4= 0 RMR = Calculation of SMR = RMR + (F1 x F2 x F3) + F4 = (0.85 x 0.15 x (-60)) + 0 SMR = = Slope Mass Rating Calculation for Rock Section (RS-3) The analysis made through stereo-net plot shows that, the most unfavorable condition is the result of J3 Discontinuity. Hence, it is a case of probable planar failure. Direction and Inclination of J3=N 300 /21 α Dip Direction of Joint=N 300 β Dip of Joint=21 α Direction of Slope Inclination=N 325 β Inclination of Slope=31 F1= α -α = 25 F2 = β = 21 F3= β -β = -10 F4= 0 RMR = Calculation of SMR = RMR + (F1 x F2 x F3) + F4 = (0.40 x 0.40 x (-50)) + 0 SMR = =

33 Slope Mass Rating Calculation for Rock Section (RS-4) The analysis made through stereo-net plot shows that, the most unfavorable condition is the result of intersection formed by the discontinuities J1 & J2. Hence, it is a case of probable wedge failure. Direction and Inclination of J1=N 335 /54 Direction and Inclination of J2=N 210 /29 α Direction of line of intersection of two discontinuities=n 260 β Direction of slope inclination=n 265 α Plunge of line of intersection of two discontinuities=20 α Inclination of Slope=58 F1= α -α = 5 F2 = β = 20 F3= β -β = -38 F4= 0 RMR = Calculation of SMR = RMR + (F1 x F2 x F3) + F4 = (1.0 x 0.40 x (-60)) + 0 SMR = = Slope Mass Rating Calculation for Rock Section (RS-5) The analysis made through stereo-net plot shows that, the most unfavorable condition is the result of J4 Discontinuity. Hence, it is a case of probable planar failure. Direction and Inclination of J4=N 325 /83 α Dip Direction of Joint=N 325 β Dip of Joint=83 α Direction of Slope Inclination=N 285 β Inclination of Slope=62 F1= α -α = 40 F2 = β = 83 F3= β -β = 21 F4= 0 RMR = Calculation of SMR = RMR + (F1 x F2 x F3) + F4 = (0.15 x 1.0 x (0)) + 0 SMR = 57 0 =

34 Slope Mass Rating Calculation for Rock Section (RS-6) The analysis made through stereo-net plot shows that, the most unfavorable condition is the result of intersection formed by the discontinuities J2 & J3. Hence, it is a case of probable wedge failure. Direction and Inclination of J2=N 185 /42 Direction and Inclination of J3=N 325 /42 α Direction of line of intersection of two discontinuities=n 256 β Direction of slope inclination=n 270 α Plunge of line of intersection of two discontinuities=17 α Inclination of Slope=68 F1= α -α = 14 F2 = β = 17 F3= β -β = -49 F4= 0 RMR = 67 Calculation of SMR = RMR + (F1 x F2 x F3) + F4 = 67 + (0.70 x 0.15 x (-60)) + 0 SMR = =

35 Table 5.16 Results of Slope Mass Rating (SMR) for Rock Sections RS-1 to RS-6 Rock Section ID RS 1 RS 2 RS-2 RS 3 RS 4 RS 5 RS 6 Critical Sections J2 & J3 J1 & J2 J2 J3 J1 & J2 J4 J2 & J3 Class No II II II III I III II SMR Description Good Good Good Normal Very Bad Normal Good Stability Stable Stable Stable Partially Completely Partially Stable Unstable stable Stable Probable Planar Big Planar Planar or Block Block Block Block Type of or or many Failure Failure Failure Failure Failure many Wedges Rotational wedges Support Occasional Occasional Occasional Systematic Systematic Occasional Re-excavation supports supports supports support support supports 134

36 5.3.5 Estimation of Factor of Safety (F) The rock slope sections considered for the RMR and SMR study is taken for the factor of safety analyses. There are six rock sections were considered and studied for the analysis of slope stability along Ghat road section of Kolli hills. Structural readings (slope and joint set), cohesion and friction angle values were plotted in the stereonet and made analysis to find out the possible failure modes i.e. type of failure. The possible critical failure modes from all the sections were identified and given in the Table Table 5.17 Identified critical sections for factor of safety analyses Mode of Failure Section ID Joint Sets Rock Section 2 Joint set 2 Planar Failure Rock Section 3 Joint set 3 Rock Section 1 Joint set 2 & Joint set 3 Rock Section 2 Joint set 1 & Joint set 2 Wedge Failure Rock Section 4 Joint set 1 & Joint set 2 Rock Section 6 Joint set 2 & Joint set 3 135

37 Planar Failure Analysis of Rock Section 2 (Joint set 2) Locality: Hairpin Bend 25/70, Kolli hills Ghat road section, Highly Jointed Charnockite. RMR = (Class II, Good Rock), SMR value = (Class II, Good, Stable). Three sets of joints are observed in this slope section. The slope (N 330 º /48 º ) and joint orientations (J1: N 260 /80 ; J2: N 340 /16 ; J3: N 205 /16 ) were measured in the field and plotted in the streoplot (Figure 5.10). The cut slope amount is 78 and the height of the slope ft (8.60 m). The angle of friction ϕ=32.5 (taken from discontinuity parameters). The analyses of stereoplot indicate that the Joint 2 (N 340 /16 ) is found close (approximately parallel) to the slope direction. Hence, it is considered as planar failure condition and factor of safety was calculated as per Hoek and Bray Eq (Table 5.18). The tension crack position and depth are unknown, hence it is assumed that the tension crack is coincident with the slope crest and that is water-filled (Hoek and Bray 1981). Hence, the z/h is calculated using the Eq The calculated factor of safety for Joint set 2, when, z z = 1 i.e. the tension crack is completely filled with water was Figure 5.10 Stereonet plot for planar stability analysis Rock Section 2 136

38 Section ID Rock Section 2 Joint 2 Table 5.18 Planar Stability Calculation Sheet - Rock Section 2 Input Data Function Value Calculations using Formula Results ψ = 16 ψ = 78 γ = lb/ft 3 γ = 62.5 lb/ft 3 c = lb/ft 2 H = ft ϕ = 32.5 Cosec ψ = Cot ψ = Cot ψ = Sin ψ = Cos ψ = Tan ψ = Tan ψ = Tan ϕ = γ z γ = z = 1 z H = c γh = z/h = (1-Cotψ. Tanψ ) = ( x ) z/h =0.939 P = (1 z/h).cosecψ = ( ) P = Q = ((1 (z/h) 2 ) Cotψ Cotψ ) Sinψ Q = ((1 (0.939) 2 ) ) Q = (0.1999) = When, z W /z = 1; R = γ W /γ. z W /z. z/h = (0.3778)(1)(0.939) When, z W /z = 1; S = z W /z. z/h. SinΨp = (1)(0.939)(0.2756) When, Z /z = 1 (i.e.) The tension crack is completely filled with water (z= Z ), the Factor of Safety (F) = 1.46 F = (2c/ H).P + (Q.cotψ R(P+S)) Tan / Q + R.S cotψ F = (2.4134) ( x ( )) / x x F = ( ) / F = / = / = 1.46 Q = R = S =

39 Planar Analysis Rock Section 3 (Joint set 3) Locality: Hairpin Bend 26/70, Kolli Hills Ghat road section, Highly Jointed Charnockite. RMR = (Class III, Fair Rock), SMR value = (Class III, Normal, Partially stable). Three sets of joints are observed in this slope. The slope (N 325 /31 ) and joint orientations (J1: N 215 /10 ; J2: N 240 /22 ; J3: N 300 /21 ) were measured in the field and plotted in streoplot (Figure 5.11). The cut slope amount is 85 and the height of the slope ft (14 m). The angle of friction ϕ=30.5 (taken from discontinuity parameters). The analyses of stereoplot indicate that the Joint 3 (N 300 /21 ) is found close (approximately parallel) to the slope direction. Hence, it is considered as planar failure condition and factor of safety was calculated as per Hoek and Bray Eq (Table 5.19). The tension crack position and depth are unknown, hence it is assumed that the tension crack is coincident with the slope crest and that is water-filled (Hoek and Bray 1981). Hence, the z/h is calculated using the Eq The calculated factor of safety for Joint set 3, when, z z = 1 i.e. the tension crack is completely filled with water was Figure 5.11 Stereonet plot for planar stability analysis Rock Section 3 138

40 Table 5.19 Planar Stability Calculation Sheet - Rock Section 3 Section ID Input Data Function Value Calculations using Formula Results Rock Section 3 Joint 3 ψ = 21 ψ = 85 γ = lb/ft 3 γ = 62.5 lb/ft 3 c = 5223 lb/ft 2 H = ft ϕ = 30.5 Cosec ψ = Cot ψ = Cot ψ = Sin ψ = Cos ψ = Tan ψ = Tan ψ = Tan = γ z γ = z = 1 z H = c γh = z/h = (1-Cotψ. Tanψ ) = ( x ) P = (1 z/h). Cosecψ P = ( ) = 0 Q = ((1 (z/h) 2 ) Cotψ Cotψ ) Sinψ Q = ((1 (0.966) 2 ) ) Q = (0.0866) = When, z W /z = 1; R=γ W /γ.z W /z.z/h R=(0.3778)(1)(0.966) When, z W /z=1; S=z W /z.z/h.sinψ S=(1)(0.966)(0.3584) When, Z /z = 1 (i.e.) The tension crack is completely filled with water (z=z ), the Factor of Safety (F) = 0.22 F = (2c/ H).P + (Q.cotψ R(P+S)) Tanϕ / Q + R.S cotψ F = (1.3748) ( x ( )) / x x F = ( ) / F = ( ) / = / = 0.22 z/h =0.966 P = Q = R = S =

41 Wedge failure case Rock Section 1 (Joint set 2 & Joint set 3) Locality: Hairpin Bend 14/70, Kolli Hills Ghat road section, Highly Jointed Charnockite. RMR = 68 (Class II, Good Rock), SMR value = (Class II, Good, Stable). Three sets of joints are observed in this slope. The slope (N 315 /44 ) and joint orientations (J1: N 165 /88 ; J2: N 245 /16 ; J3: N 20 /70 ) were measured in the field and plotted in streoplot (Figure 5.12). The cut slope amount is 80. The analyses of stereoplot indicate that the plunge (N 294 /10 ) formed due to intersection of J2 & J3 is found close (approximately parallel) to the slope direction. Hence, it is considered as wedge failure condition and factor of safety was calculated as per Hoek and Bray Eq (Table 5.20). The calculated factor of safety for the intersection of J2 & J3 was Figure 5.12 Stereonet plot for wedge stability analysis Rock Section 1 Input Data from stereonet: Intersections 1=15 ; 2=70 ; 3=16 ; 4=44 ; 5=11 ; Pole of Plane A( N )=74 ; Pole of Plane B( N )=20 ; θ. =82 ; θ =40 ; θ =36 ; θ =13 ; θ =50 ; θ. =28 ; θ. =16 ; ϕ =37 ; ϕ =42 ; γ= lb/ft 3 ; γ 2γ =0.1889; γ =62.5 lb/ft 3 ; c = lb/ft 2 ; c = lb/ft 2 and H = ft (8.00 m). 140

42 Table 5.20 Wedge Stability Calculation Sheet - Rock Section 1 Input Data Function Value Calculations using formula Results ψ = 16 Cos ψ = A = Cosψ Cosψ. Cosθ. Sinψ. Sin θ A = ψ = 70 Cos ψ = ψ = 11 Sin ψ = A = x x θ. = 82 Cos θ. = B = Cosψ Cosψ. Cosθ. Sinψ. Sin θ B = Sin θ. = B = x x θ = 40 θ = 36 θ. = 16 θ = 13 θ = 50 θ. = 28 ϕ = 37 ϕ = 42 γ = lb/ft 3 γ = 62.5 lb/ft 3 c = lb/ft 2 c = lb/ft 2 H = ft Sin θ = Sin θ = Cos θ. = Sin θ = Sin θ = Cos θ. = Tan ϕ = Tan ϕ = γ 2γ = c /γh = c /γh = X = Sinθ Sinθ. Cosθ. X = x Y = Sinθ Sinθ. Cosθ. Y = x F = ((3c γh). X + (3c /γh). Y) + (A (γ /2γ). X). Tanϕ + (B (γ /2γ). Y). Tanϕ F = ( x ) + ( x ) + ( ) x ( ) x F = X = Y = F=

43 Wedge failure case Rock Section 2 (Joint set 1 & Joint set 2) Locality: Hairpin Bend 25/70, Kolli Hills Ghat road section, Highly Jointed Charnockite. RMR value (basic) = (Class II, Good Rock), SMR value = (Class II, Good, Stable). Three sets of joints are observed in this slope. The slope (N 330 /48 ) and joint orientations (J1: N 260 /80 ; J2: N 340 /16 ; J3: N 205 /16 ) were measured in the field and plotted in Stereoplot (Figure 5.13). The cut slope amount is 78. The analyses of stereoplot indicate that the plunge (N 347 /16 ) formed due to intersection of J1 & J2 is found close (approximately parallel) to the slope direction. Hence, it is considered as wedge failure condition and factor of safety was calculated as per Hoek and Bray equation 5.16 (Table 5.21). The calculated factor of safety for the intersection of J1& J2 was Figure 5.13 Stereonet plot for wedge stability analysis Rock Section 2 Input Data from stereonet: Intersections 1=03 ; 2=77 ; 3=4 ; 4=48 ; 5=16 ; Pole of Plane A( N )=75 ; Pole of Plane B( N )=10 ; θ. =78 ; θ =33 ; θ =32 ; θ =3 ; θ =69 ; θ. =22 ; θ. =28 ; ϕ =33 ; ϕ =42 ; γ= lb/ft 3 ; γ 2γ=0.1889; γ =62.5 lb/ft 3 ; c = lb/ft 2 ; c = lb/ft 2 and H = ft (8.60 m). 142

44 Table 5.21 Wedge Stability Calculation Sheet - Rock Section 2 Input Data Function Value Calculations using formula Results ψ = 16 Cos ψ = A = Cosψ Cosψ. Cosθ. Sinψ. Sin θ A = ψ = 80 Cos ψ = ψ = 16 Sin ψ = A = x x θ. = 78 Cos θ. = B = Cosψ Cosψ. Cosθ. Sinψ. Sin θ B = Sin θ. = B = x x θ = 33 θ = 32 θ. = 28 θ = 3 θ = 69 θ. = 22 ϕ = 33 ϕ = 42 γ = lb/ft 3 γ = 62.5 lb/ft 3 c = lb/ft 2 c = lb/ft 2 H = ft Sin θ = Sin θ = Cos θ. = Sin θ = Sin θ = Cos θ. = Tan ϕ = Tan ϕ = γ 2γ = c /γh = c /γh = X = Sinθ Sinθ. Cosθ. X = Y = Sinθ Sinθ. Cosθ. Y = x F = ((3c γh). X + (3c /γh). Y) + (A (γ /2γ). X). Tanϕ + (B (γ /2γ). Y). Tanϕ F = ( x ) + ( x ) + ( ) x ( ) x F = ) + ( ) X = Y = F=

45 Wedge failure case Rock Section 4 (Joint set 1 & Joint set 2) Locality: Hairpin Bend 29/70, Kolli Hills Ghat road section, Highly Jointed Charnockite. RMR value (basic) = (Class III, Fair Rock), SMR value = (Class I, Very Bad, Completely Unstable). Three sets of joints are observed in this slope. The slope (N 265 /58 ) and joint orientations (J1: N 335 /54 ; J2: N 210 /29 ; J3: N 130 /65 ) were measured in the field and plotted in Stereoplot (Figure 5.14). The cut slope amount is 68. The analyses of stereoplot indicate that the plunge (N 260 /20 ) formed due to intersection of J1 & J2 is found close (approximately parallel) to the slope direction. Hence, it is considered as wedge failure condition and factor of safety was calculated as per Hoek and Bray Eq (Table 5.22). The calculated factor of safety for the intersection of J1 & J2 was Figure 5.14 Stereonet plot for wedge stability analysis Rock Section 4 Input Data from stereonet: Intersections 1=27 ; 2=54 ; 3=28 ; 4=50 ; 5=20 ; Pole of Plane A( N )=61 ; Pole of Plane B( N )=36 ; θ. =73 ; θ =12 ; θ =47 ; θ =8 ; θ =60 ; θ. =27 ; θ. =34 ; ϕ =30 ; ϕ =21 ; γ= lb/ft 3 ; γ 2γ=0.1889; γ =62.5 lb/ft 3 ; c = lb/ft 2 ; c = lb/ft 2 and H = ft (13 m) 144

46 Table 5.22 Wedge Stability Calculation Sheet - Rock Section 4 Input Data Function Value Calculations using formula Results ψ = 29 Cos ψ = A = Cosψ Cosψ. Cosθ. Sinψ. Sin θ A = ψ = 54 Cos ψ = ψ = 20 Sin ψ = A = x x θ. = 73 Cos θ. = B = Cosψ Cosψ. Cosθ. Sinψ. Sin θ B = Sin θ. = B = x x θ = 12 θ = 47 θ. = 34 θ = 8 θ = 60 θ. = 27 ϕ = 30 ϕ = 21 γ = lb/ft 3 γ = 62.5 lb/ft 3 c = lb/ft 2 c = lb/ft 2 H = ft Sin θ = Sin θ = Cos θ. = Sin θ = Sin θ = Cos θ. = Tan ϕ = Tan ϕ = γ 2γ = c /γh = c /γh = X = Sinθ Sinθ. Cosθ. X = x Y = Sinθ Sinθ. Cosθ. Y = x F = ((3c γh). X + (3c /γh). Y) + (A (γ /2γ). X). Tanϕ + (B (γ /2γ). Y). Tanϕ F = ( x ) + ( x ) + ( ) x ( ) x F = X = Y = F=

47 Wedge failure case Rock Section 6 (Joint set 2 & Joint set 3) Locality: Hairpin Bend 37/70, Kolli Hills Ghat road section, Highly Jointed Charnockite. RMR value (basic) = 67 (Class II, Good Rock), SMR value = (Class II, Good, Stable). Three sets of joints are observed in this slope. The slope (N 270 /68 ) and joint orientations (J1: N 65 /30 ; J2: N 185 /42 ; J3: N325 /42 ) were measured in the field and plotted in Stereoplot (Figure 5.15). The cut slope amount is 76.The analyses of stereoplot indicate that the plunge (N 256 /17 ) formed due to intersection of J2 & J3 is found close (approximately parallel) to the slope direction. Hence, it is considered as wedge failure condition and factor of safety was calculated as per Hoek and Bray Eq (Table 5.23). The calculated factor of safety for the intersection of J2 & J3 was Figure 5.15 Stereonet plot for wedge stability analysis Rock Section 6 Input Data from stereonet: Intersections 1=42 ; 2=40 ; 3=41 ; 4=41 ; 5=17 ; Pole of Plane A( N )=48 ; Pole of Plane B( N )=48 ; θ. =77 ; θ =7 ; θ =74 ; θ =6 ; θ =52 ; θ. =29 ; θ. =14 ; ϕ =39 ; ϕ =38 ; γ= lb/ft 3 ; γ 2γ=0.1889; γ =62.5 lb/ft 3 ; c = 6964 lb/ft 2 ; c = lb/ft 2 and H = ft (8.5 m) 146