EXPERIENCE WITH EMPIRICAL ROCK SLOPE DESIGN Alex Duran1, Kurt Douglas2
ABSTRACT There are numerous methods of empirical rock slope design presented in published literature. The methods rely on initial characterisation of the rock mass, typically Bieniawski’s RMR or a close derivative, with factoring to allow for structure, blasting and weathering. Fundamentally an empirical method should be calibrated on the basis of slopes for which failure has occurred, i.e. limiting stability. Published data of case examples to confirm the applicability of each method is limited to low slope heights and/or stable slopes with little or no data for where rock mass failure has occurred. The authors have utilised case studies at several mining operations, where stability has been predominantly influenced by rock mass failure, to enable a review of several empirical rock slope design methods. The review highlights the merits of each methodology and summarises some of their limiting aspects. INTRODUCTION There are several empirical rock mass rating techniques that can be utilised for the design of slopes. Several rating methods discussed in this paper are listed below. SRMR - Slope rock mass rating (Robertson, 1988) RMR - Rock mass rating (Bieniawski, 1976) MRMR - Mining rock mass rating (Laubscher, 1990) RMS - Rock mass strength (Selby, 1980) M-RMR - Modified rock mass classification (Ünal, 1996) SMR - Slope mass rating (Romana, 1985) BQ - Index of rock mass basic quality (Lin, 1998) CSMR - Chinese system for SMR (Chen, 1995) GSI - Geological strength index (Hoek et al. 1995) Correlations between some of these methods and GSI are provided. Finally, presentation of data on slope height versus slope angle plots has been utilised to check on rock mass strength/design estimates provided by several of the methods. EXISTING EMPIRICAL SLOPE DESIGN METHODS Table 1 shows a summary of the various parameters requiring assessment for each of the empirical methods. Generally, each method consists of a basic rock mass rating and a series of adjustments. Table 1 provides the maximum and minimum weightings for each parameter and the factors (denoted by an asterix) included in the assessment. Rock Mass Rating The rock mass ratings discussed in this paper, with the exception of the BQ, have been based upon or are similar to Bieniawski’s RMR. The RMR method has been updated a number of times. The two presented in Table 1 are from Bieniawski (1976), RMR76, and Bieniawski (1989), RMR89. The rock mass rating requires a summation of ratings assessed for each of the following parameters representing intact rock block strength, rock mass block size, defect condition and ground water. RMS, Selby (1980), includes defect orientation and weathering in the basic rock mass rating. The rating values for each method vary slightly depending on their intended usage and calibration. As a number of these methods were developed for the design of support in underground excavations, the parameters and/or weightings may not be applicable to the stability of large slopes. It would be expected that, for rock mass failure in slopes, the intact strength rating would be a relatively minor contributor other than in weak rock. 1 2
Alex Duran, Pells Sullivan Meynink, 10 East Parade, Eastwood, NSW, Australia, 2122,
[email protected] Kurt Douglas, Civil & Environmental Engineering, The University of NSW, Australia, 2052,
[email protected]
ADJUSTMENTS
BASIC ROCK MASS RATING
TABLE 1 : COMPARISON OF WEIGHTINGS FOR VARIOUS ROCK MASS RATING METHODS Reference Intact strength Block size - Spacing
- RQD Defect condition -
Persistence Aperture Roughness Infilling Weathering
Ground water Defect orientation
- Strike - Dip - Slope dip – defect dip Excavation method Weathering Induced stresses Major plane of weakness TOTAL RANGE
RMR76 RMR89 MRMR 0-15 0-15 0-20 8-50 8-40 0-40 * * * * * * 0-25 0-30 0-40 * * * * *
0-10 (60)-0 * * -
* * * * *
* * * *
0-15 * (60)-0 63-100% * * * * -
(52)-100 (52)-100
RMS 5-20 8-30 * 3-14
SMR 0-15 8-40 * * 0-30
* *
* * * * *
1-6 5-20
0-15 (60)-0 * * * (8)-15 -
*
80-100% 30-100% 60-120% -
3-10 -
0-120
25-100
CSMR M-RMR SRMR 0-15 0-15 0-30 8-40 0-40 8-40 * * * * * * 0-30 0-30 0-30 * * * * * * * * * * * * * * * 0-15 0-15 (60)-0 (12)-(5) * * * (8)-15 80-100% 60-115% 70-100%
(60)-115 (63)-141
(7)-105
8-100
GSI 0-15 8-50 * * 0-25 * * * * *
10
18-100
The block size is assessed using defect spacing and RQD. Selby (1980) did not use RQD as he was assessing existing natural slopes where spacing was readily available. RQD was primarily used for the design of support in underground excavations. It is not a good parameter to use for large rock slopes. It is suggested that it would be better, where possible, to use only defect spacing as an indicator of block size. SRMR does not include a groundwater factor whilst, GSI assumes a dry rock mass and MRMR combines the groundwater parameter with defect condition. The authors agree with Robertson (1988) in that a groundwater parameter should not be included in any rock mass rating, as it should be included in the analysis of the slope. The effect of moisture should be accounted for in the intact rock strength parameter and the defect condition parameter if it is considered that a moisture change may reduce the strength of the rock or cause softening of any infill. Robertson (1988) developed SRMR, based on RMR, for weak rock masses. Robertson increased the rating for intact strength by 15. This allowed for a broader range of weightings for rocks with uniaxial compressive strength, UCS, less than 1MPa. The RQD and defect spacing was measured from ‘handled’ core. Defined as core that had been “firmly twisted and bent but without substantial force or use of any tools or instruments”. Core with a UCS greater than 1MPa and without planes of weakness was meant to be unaffected by such handling. The core was handled to prevent problems with core that is soft and soil like being assigned a high RQD. It would be difficult to calibrate users of this method. An alternative to handling core would be to stipulate that weak soil like core should be assigned an RQD of zero. The BQ has been chosen as the Chinese national standard (GB 50218 - 94). Lin (1998) presents the background to BQ. The method uses two parameters to describe the rock mass, the completeness coefficient, Kv, (defined as the insitu sonic velocity over the intact sonic velocity) to account for rock structure and UCS. The two parameters were chosen from a total of nine potential rock mass parameters that were investigated statistically from 103 sites in China. It is not clear as to what BQ was compared against in the statistics. It is interesting to note that no joint condition parameters were included in those investigated. Adjustment Factors Most of the empirical rating methods apply adjustment factors to their basic rock mass rating. These adjustment factors account for such factors as defect orientation, excavation method, weathering, induced stresses and major planes of weakness. Bieniawski (1976 and 1989) applies the adjustments by subtracting them from the rock mass rating. Table 1 shows that the defect orientation adjustment can dominate the RMR. If the defect orientations are deemed “very unfavourable” an adjustment of -60 is required to the
basic rock mass rating. Even for defect orientations denoted as “fair” this adjustment is -25. There is no guideline as to what “very unfavourable” means. Bieniawski (1989) recommends the use of the Romana (1985) SMR corrections for slopes. Romana used the same basic rock mass rating as RMR89 but developed new adjustment factors for joint orientation and blasting to account for the lack of guidelines in the RMR methods. The equation for SMR is shown below. The joint orientation weighting includes a factor for the difference between joint dip and slope angle, F3. This requires an iterative approach for design.
SMR = RMR89 − F1 F2 F3 + F4
(1)
Romana (1985) developed his factors not only for rock mass failures but also for wedge and planar failure. A rock mass rating method should not be used for these two cases as they are defect controlled and can be assessed using such measures as stereographic projection. The CSMR method is based on the SMR method. The CSMR applies a discontinuity condition factor, λ, that describes the conditions of the controlling discontinuity on which the ratings F1, F2 and F 3 are based. This factor ranges from 0.7 to 1.0. The CSMR method also assumes that the SMR method is applicable for a slope height of 80m but must be adjusted for other slope heights, H, using the slope height factor, ξ . The relationship for ξ , based on “an extensive survey” (Chen, 1995), is shown in Figure 1. With the addition of the two new factors, the equation for CSMR is defined as:
CSMR = ξ × RMR76 − λ × F1 F2 F3 + F4
(2)
The CSMR has been based on the SMR and thus has similar problems. CSMR acknowledges the affect of slope height. However, it is the authors view that it is included incorrectly, as height should not be grouped with the rock mass rating but should be addressed during the stability analysis. The MRMR method applies adjustment multipliers to the basic rock mass rating. The multipliers were developed primarily for underground excavations but are also used for slopes. Ünal (1996) developed the M-RMR based on the RMR method with additional features for better characterisation of weak, stratified, anisotropic and clay bearing rock masses. The rating is given below. IUCS, IRQD, IJC, IJS, IGW and IJO are the ratings for UCS, RQD, joint condition, joint spacing, ground water and joint orientation respectively. Fc is the weathering coefficient and Ab and A w are the adjustment factors for blasting and major planes of weakness respectively.
( (
)
M - RMR = Ab Aw Fc I UCS + I RQD + I JC + I JS + I GW + I JO
)
(3)
It is interesting to note that IJO is calculated from the intact borehole core recovery from. Bieniawski’s (1989) adjustments should be used where field surveys are available. It is also not understood why the RQD rating is adjusted for weathering whilst the joint spacing rating is not. The authors consider Aw should not be used. If major planes of weakness exist they should be treated during the analysis phase. MRMR, RMS and M-RMR contain an adjustment for weathering. Weathering should not be used as an adjustment factor in the estimation of rock mass strength. The effect of weathering is to alter the intact strength and defect condition parameters over geological time. ‘Present day’ weathering should already have been accounted for using these parameters. Where further weathering may be expected within the design life of a slope, the parameters for intact strength and defect condition could be adjusted. However, the extent of these effects needs to take into account the scale of influences versus the scale of the slope. The excavation method adjustment (MRMR, SMR, CSMR and M-RMR) was originally designed for support of underground excavations where it has obvious implications. The method of excavation may affect low height slopes, however large slopes are unlikely to be affected by blasting (with regard to rock mass failure). The rock mass involved in the failure is usually remote to the region affected by blasting. Where blasting is believed to have affected the rock mass to a large degree then this affect should be accounted for in the assigning of weightings for block size (smaller) and joint condition (persistence and aperture) and not as an adjustment factor.
Hoek et al. (1995) developed the GSI from RMR for estimating the strength of a rock mass. The strength of the rock mass was then used in a stress analysis of the engineering problem. To prevent ‘double counting’ the in-situ stress adjustment factor, ground water parameter and defect orientation adjustment were not included in the estimation of the GSI. 100
M RMR SRMR RM S
80
GSI = 0.78MRMR + 25.22 2 R = 0.94 60
GSI
Correlations with GSI Table 1 and the above comments show most rating methods are essentially derived from Bieniawski’s RMR. Utilising authors’ case studies and those of Selby (1980), correlations between three rating methods (MRMR, SRMR and RMS) and GSI have been performed by the authors, Figure 2. Some assumptions were made in assessing SRMR for the authors’ case studies, based on the intact strength and character of borehole core, to assess handled RQD and spacing. GSI was chosen since it provides a measure of the basic rock mass quality. Correlation with the other rating systems was not considered appropriate in view of the rating adjustments required. The correlations exhibit a very good fit, even though there is limited data for the correlations with MRMR and SRMR.
40
GSI = 0.67SRMR + 15.10 R2 = 0.84
GSI = 1.07RMS - 22.39 2
R = 0.82
20
0 0
20
40
60
80
100
Rating
Slope Design Figure 2 : Correlations of GSI with MRMR, SRMR, RMS. There have been a number of methods proposed to estimate slope angles from empirical rating systems including shear strength estimates, direct correlations or the use of slope height versus slope angle curves. Bieniawski (1976) and Robertson (1988) provided estimates of cohesion and friction angle values for different RMR and SRMR ranges respectively. Robertson’s shear strength correlations were based on the back analysis of failed slopes in weak rock masses. Laubscher (1990) presents a table of slope angles versus MRMR independent of slope height. Haines and Terbrugge (1991) developed this further, presenting slope curves based on MRMR. Duran and Douglas (1999) questioned the validity of these in the light of additional data and proposed alternative slope curves. Abrahams and Parsons (1987) performed a thorough statistical analysis of Selby’s RMS data and developed the following relationship:
Slope Angle = 2.681RMS − 141.072
(4)
The line of best fit to Selby’s data indicates a slope angle of -74° for a “very weak” rock mass (RMS=25). This is unrealistic and is likely due to the lack of “weak” and “very weak” rock masses (RMS
