EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 9, 189-193 (1984)

REFINEMENT OF A TECHNIQUE FOR DETERMINING ROCK MASS STRENGTH FOR GEOMORPHOLOGICAL PURPOSES

B. P. MOON Department of Geography and Environmental Studies, University of the Witwatersrand, Johannesburg, South Africa

Received 23 May 1983 Revised 19 September 1983

ABSTRACT Use of a field technique recently devised by Selby for the measurement of rock mass strength has resulted in the understanding of the relationship between rock mass strengthand slope form. It is suggested that the accuracy of rock mass strength assessments may be enhanced by further subdividing the rating scales for intact rock strength and the spacing of partings. The relationship between rock mass strength and gradient is reformulated using southern African data, and statistically based confidence limits for identifying strength equilibrium slopes are proposed.

KEY WORDS Rock mass strength Strength equilibrium slopes

INTRODUCTION

Selby’s (1980) rock mass strength classification was developed for the objective assessment of the resistance of rock to denudational processes. Applications of the technique (Selby, l980,1982a, 1982b; Moon and Selby, 1983) have resulted in the understanding of the relationship between the gradients of rock slopes and the mass strengths of the rocks on which they are formed. It has proved possible to distinguish strength equilibrium forms in the landscape, that is, forms which have developed to gradients determined by the mass strength of the rock rather than being controlled by denudational processes or geological structure.

The data and experience gained from applications of the technique in southern Africa have made possible some refinements to the technique. These are presented below.

THE DETERMINATION OF ROCK MASS STRENGTH

The method of rock mass strength determination is detailed elsewhere (Selby, 1980). It is sufficient to note here that in order to rate rock mass strength on a scale from 25 to 100 it is necessary to assign each strength parameter (intact rock strength, weathering, the spacing, orientation, width and continuity of partings, and the movement of groundwater out of the rock mass) to one of five strength classes. Each strength class for each variable is characterized by a numerical rating and the sum of these ratings provides the measure of rock mass strength. The use of five strength classes is in conformity with the engineering rock mass strength classifications on which the technique is based. In establishing a numerical rating for rock mass strength it is unnecessary to adhere to the five-class rating system, particularly for the variables (intact rock strength and joint spacing) which are directly measured and provide continuous data. As the necessity of using intermediate ratings for these parameters has been alluded to (Selby, 1980) a finer division of the scales for these two parameters is

0197-9337/84/020189-O5$01 .OO 0 1984 by John Wiley & Sons, Ltd.

Tabl

e I.

The

geo

mor

phol

ogic

al ro

ck m

ass

stre

ngth

mea

sure

men

t sys

tem

with

con

tinuo

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cale

ratin

gs f

or in

tact

stre

ngth

and

join

t sp

acin

g

Ver

y st

rong

St

rong

M

oder

ate

Wea

k V

ery

wea

k

Inta

ct s

treng

th

Rat

ing

100-

70

69-5

7 56

-53

52-5

0 49

48

47

46

45

-44

43

42

4

14

0

39-3

8 37

-36

35-3

3 32

-29

28-2

5 24

-17

<17

20

19

18

17

16

15

14

13

12

11

10

9 8

7 6

5 W

eath

erin

g U

nwea

ther

ed

Slig

htly

wea

ther

ed

Mod

erat

ely

wea

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ed

Hig

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wea

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ed

Com

plet

ely

wea

ther

ed

!z %

85

4

Rat

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10

9 7

5 3

Join

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acin

g (m)

>3

3- 2.

2-

1.9-

1

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1.4-

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0.6-

0.5- 0.4-

0.3-

0.

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1.9

1.6

1.4

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1.0

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0.7

0.6

0.5

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0.25

0.

2 0.

15

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0.07

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5 .0

3 .0

25

432

<.02

R

atin

g 30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

Join

t or

ient

atio

n >

30"

int

o sl

ope

Rat

ing

20

Join

t wid

th

Rat

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< 0.

1 m

m

7

2 8

18

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9 5

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oriz

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l <

30"

out

of

slop

e >

30"

out

of

slop

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30"

into

slo

pe

0.1-

1 m

m

6 1-

5 m

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5 5-

20 m

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4

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111

> 2

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m

2

Con

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fill

Con

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l R

atin

g 7

6 5

4 1

Gro

undw

ater

R

atin

g N

one

6 Tr

ace

5 Sl

ight

4

Mod

erat

e 3

Gre

at

1

SHORT COMMUNICATIONS 191

suggested (Table 1). The use of such finer divisions does not increase the complexity of the application of the technique, and initial testing has indicated an improvement in the accuracy of strength determinations (Moon, 1983).

THE RELATIONSHIP BETWEEN ROCK MASS STRENGTH AND SLOPE FORM

Regression analysis of rock slope data from Antarctica and New Zealand produced the relationship between rock mass strength and slope form depicted in Figure 1 (Selby, 1980). It is more usual in regression analysis to regress the dependent variable (gradient) on the independent variable (rock mass strength), and following that, to express gradient in terms of rock mass strength and not vice versa. Although the result of the initial analysis correctly indicates the relationship between the two variables, the standard error of estimating gradient from a knowledge of rock mass strength (5.1’; Selby, 1980) is incorrectly determined. This is because in deriving the regression equation it is the errors in the dependent, rather than the independent, variable that should be minimized.

Data from 82 southern African rock slopes have been combined with Selby’s published data to re-formulate the gradient-rock mass strength relationship (Figure 2). Although the correlation coefficient is lower than that found for New Zealand and Antarctic slopes, calculation of the standard normal variate shows the difference to be statistically insignificant. The standard error of estimating gradient from mass strength data is 13.9”. In work published since 1980 the gradient-rock mass strength relationship has been used as a basis for

identifying strength equilibrium slopes. This has been done using a ‘strength equilibrium envelope’ (Figure 1) constructed about the regression line. The assumption that all of the New Zealand and Antarctic slopes measured are strength equilibrium forms is not necessarily valid, and this being so it is suggested that statistically based limits for strength equilibrium slopes would be more appropriate. In recent work (Moon, 1983) 90 per cent confidence limits derived from the standard error of the regression have been used for identifying strength equilibrium slopes (Figure 2). Oversteepened and low-angled denudational slopes as well as structurally controlled slopes will be represented by points which fall outside the limits for strength equilibrium. In studies where the focus has been on strength equilibrium slopes or in which the relationship

100 I I 1 I I I I I

t 40t di 10

0 Antarctic data

New Zealand data

1’ , Envelope for strength L J equilibrium slopes

1 0 I I I I I I I

10 20 30 40 50 60 m 80 90 ibo Angle of slope (S’)

Figure 1 . The relationship between rock mass strength and gradient (after Selby, 1980, 1982a)

192

100-

90

e x -

M -

A 60-

5 L -

o V

P

.- 50-

8 - w

40-

30

20

10

SHORT COMMUNICATIONS

-

-

-

-

Undercut slopes Recently formed fault scarps

Structurally controlled slopes ? Solutional slopes Richter slopes Regolith covered slopes Low-angle rock benches

Regression line relating gradient to rock mass strength

1 90% confidence limits for strength equilibrium slopes K Rock mass strength (RMS) 90 100

Figure 2. The revised relationship between gradient and rock mass strength, and classification of slope types in relation to the strength-gradient relationship

between gradient and rock mass strength has been sought the arbitrary limits have sufficed. When determination of the controls of slope form is important, statistically based limits are a necessity.

CONCLUSION

Studies incorporating rock mass strength measurements contribute to an understanding of the geomorpholo- gical control exerted by rock properties. The suggested refinements to the technique enhance its usefulness since the precision of rock mass strength measurements is improved and its use in determiningcontrols of slope form has been placed on a sound statistical footing. Further applications and possible further refinement should establish the technique as a valuable tool in all avenues of geomorphological research where rock resistance is an important consideration.

ACKNOWLEDGEMENTS

This paper stems from research undertaken for a Ph.D. degree at the University of the Witwatersrand. I acknowledge with gratitude the financial assistance from the University of the Witwatersrand and the C.S.I.R.,

SHORT COMMUNICATIONS 193

and the advice offered by Professor M. J. Selby who also granted permission for the use of slope data.

REFERENCES

Moon, B. P. 1983. ‘Rock mass strength and the morphology of rock slopes in the Cape mountains’, unpublished Ph.D. thesis, University of

Moon, B. P. and Selby, M. J. 1983. ‘Rock mass strength and scarp forms in southern Africa’, Geogrqfiska Annaler, 65A (1-2). 135-146. Selby, M. J. 1980. ‘A rock mass strength classification for geomorphic purposes: with tests from Antarctica and New Zealand’, ZeitschriJ

Selby, M. J. 1982a. ‘Rock mass strength and the form of some inselbergs in the central Namib Desert’, Earth Surface Processes and

Selby, M. J. 1982b. ‘Form and origin of some borhardts of the Namib Desert’, Zeitschrifrfur Geomorphologie, 26(1), 1-15.

the Witwatersrand, Johannesburg.

fur Geornorphologie, 24(1), 31-51.

Lcmdforms, 7, 489-497.