ISRM-EUROCK-1993-111_Stability Assessment of Slopes in Closely Jointed Rock Masses

8/12/2019 ISRM-EUROCK-1993-111_Stability Assessment of Slopes in Closely Jointed Rock Masses

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Eurock '93,Ribeiro eSousa & G ro s s m a n n ( e ds ) 1993 Ba l kema, Ro t te rdam 90 54103396

Stability assessment of slopes in closely jointed rock masses

Evaluation de la stabilite de talus de masses rocheuses densement fracturees

Standsicherheitsabschatzung von Abhangen in eng geklufteten Gebirgen

M.IPender

Civil Engineering Department, University of Auckland, New Zealand

M.W.Freeformer Graduate student, University of Auckland, New Zealand

ABSTRACT: A method for the assessment of the stability of slopes in closely jointed rock masses

is presented. A lower bound on the possible rock mass shear strength is obtained. As an example

of the method data on slope height-angle relations for the greywacke slopes at various locations

in the North Island of New Zealand are back analysed. The mobilised strength curves obtainedfor the greywacke rock masses are compared with the shear strength envelopes derived from the

modified (1992) Hoek-Brown failure criterion.

RESUME: Une methode d'evaluation de la stabilite de talus de masses rocheuses fracturees

serrees fait I'objet de cette presentation. Une limite inferieure de resistance possible au

cisaiUement de la masse roche use est obtenue. A titre d'exemple de la methode presentee, des

donnees sur les rapports hauteur/angle du talus sont identifiees par back analysis pour des talus

de grauwacke situes dans differents endroits de I'ile Nord de la Nouvelle-Zelande, Les courbes

de resistance mobilisee obtenues pour les masses rocheuses de grauwacke sont ensuite comparees

avec les enveloppes de resistance au cisaiUement derivees du critere modifie de rupture Hoek-

Brown (1992).

ABSTRACT: Eine Methode zur Bewertung del' Stabilitat von Abhangen eng verfugter Felsmassen

wird vorgestellt. Eine untere Grenze del' moglichen Scherkraft in del' Felsmasse wird erhalten. AIs

Beispiel fur diese Methode werden Daten zuriickgerechnet, die die Beziehung zwischen

Abhangsh6he und Winkel von Grauwacke Abhangen an mehreren Orten auf del' Nordinsel

Neuseelands angeben. Die mobilisierten Krafkurven, die fur die Grauwacke Felsmassen erhhalten

Wurden, werden mit den Scherkraft Mantelkurven verglichen, die sich aus dem modifizierten

(1992) Hoek-Brown Versagenskriterium ergeben.

1 INTRODUCTION

Much of the international rock mechanics

literature is concerned with two types of rock

mass. Firstly there is the so-called intact roc~,

Which is material that, to the naked eye, IS

without defect. Secondly there is the situatio.n

Where the behaviour of the rock mass IS

Controlled by a few well defined and wid.ely

spaced joints. Until recently scant attentl~n

has been given to a third class of rock mass In

W?ich the joint spacing is very cl?se .butWIthout any particular joint, or JOInt direction,

having a dominant effect. This seems to be thecharacteristic of many rock engineering

situations in New Zealand. Rock masses of

this type occur in other parts of the world,

notably the west coast of the United States, so

it is not a problem that is u nique to New

Zealand. It is more likely that the difficulties

are just so great that no line of attack hasbeen readily apparent.

In this paper three separate threads are

developed, and then drawn together in an

example application. Firstly the difficultiesassociated with closely jointed rock masses are


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discussed in more detail. Secondly a method

for the assessment of existing stable slopes is

presented which gives a lower bound on the

possible rock mass shear strength. As an

example of the method existing data about

slope height-angle relations in the greywacke

slopes at various locations in the North Islandare back analysed. Thirdly there is some

discussion of the significance of a curved

failure envelope and the effect of earthquake

loading on a closely jointed rock mass.

The intention of the paper is to set out a

procedure for a rational approach to a diffic-

ult design problem. The basic philosophy of

the method recognises that, as it is unlikely

that an accurate assessment of the true

strength parameters for a given rock mass will

ever be available, an initial approach todesigning any alteration to the slope profile

should aim to ensure that the final state of the

slope is no worse than the initial state.

Although conservative, the method presented

has the advantage of providing a logical

approach which highlights areas of uncertainty.

The precedent method, that is paying due

attention to what has been successful in the

past and incorporating modest improvements,

has been one of the traditional approaches to

design in rock mechanics. The procedureproposed in this paper aims at formalising the

underlying principles of the precedent method

for one type of application. The precedent

established by nature is also considered in the

paper along with the precedent established by

man-made slopes.The major limitation of the method is the

unknown conservatism incorporated. If one

attempts to do no better than replicate the

status quo, an unknown factor of safety is

carried forward. In some cases this unknownfactor of safety could be excessive and so an

economic penalty is unwittingly carried by the

project. On the other hand the method is

simple and inexpensive, thus it is a useful step

in the design process.

2 CLOSELY JOINTED ROCK MASSES

In this section some features of closely jointed

rock masses are discussed briefly to support

the above assertion that the material presents

the geotechnical engineer with great

difficulties.

2.1 The term closely jointed

A rock mass is described as closely jointed

when the joint spacing is small in relation to

the scale of the project in question. The cuts

in the greywacke slopes in and around the city

of Wellington in New Zealand provide a goodexample. In these rock masses, and at many

other locations throughout NZ, the joint

spacing is a fraction of a metre. It is,

therefore, very much smaller than the scale of

the cut slopes which are many tens of metres

high. Furthermore at many locations there is

no clearly defined characteristic joint direction

(notwithstanding that plotting a large number

of joint directions may indicate other than

random joint orientations). As the individual

joints do not seem to have great continuity, aparticular joint cannot exert a dominant effect

on the rock mass behaviour. The behaviour of

the mass is thus a consequence of the

combined action of a large number of

individual joints.At stress levels of interest in slope stability

assessment, the strength of the intact rock

between the joints is usually so high that

failure of the mass is controlled, in a

complicated way, by the joint system.

2.2 Strength measurement

The standard method for assessing the

strength of a geotechnical material is to

recover a sample and test it in laboratory. In

the case of a jointed rock mass it is clearly not

possible to recover a sample that is large

enough to represent the joint system.The next possibility is to measure the

strength of the intact material between thejoints. This is often done as a standard item

of a classification procedure for a rock mass.

Although the strength of intact rock

contributes some information to the overall

picture, and has an important place in the

modified Hoek-Brown failure criterion (Hoek

et al (1992)), it still falls well short of giving

the strength of the rock mass.Another possibility is to test individual joint

specimens and, assuming that the details of the

joint geometry are known, employ some

process for estimating the rock ma~s

properties from given joint properties. ThIS

approach is suspect because scale effects are

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known to occur on measured joint strengths -

the larger the area sheared the smaller the

measured strength, Bandis et al (1981).

Yet another approach is in-situ testing.

Apart from expense, this is also subject to the

additional complication of scale effects. Pratt

et al (1974) have demonstrated this for jointsin diorite, and Bieniawski and Van Heerden

(1975) have shown a similar effect in the

underground testing of coal pillars, which are

closely jointed rock masses by virtue of the

cleat in the coal. As the size of the pillars

increased the observed strength decreased.

Only in pillars with side lengths greater than

1.5m was a size independent strength

observed.

3 METHOD

The approach presented herein is to perform

a back analyses of stable slopes to estimate the

mobilised strength required to explain the

apparent stability of the slope. In principle

there is nothing new about the method of back

~nalysis of existing slopes. The main emphasis

Inthis paper is the application of the methodwhere no procedure of direct strength

measurement is possible. The back analysisprocess gives the shear resistance that must be

mobilised in the slope to maintain stability.

This in turn gives a lower bound on the actual

shear strength for the rock mass.

3.1 Assumptions

If the mobilised strength curve is assumed to

be linear and the rock mass homogeneous the

many slope stability charts available can beUsed. To use stability charts in this manner

one, in effect, makes an additional assumption

that the factor of safety is unity. The strength

parameters which give a marginal state of

stability of the slope provide some information

about the mobilised strength curve. The real

~actor of safety of an apparently stable slopeIS, of course, in excess of 1.0 by an unknown

amount.

Assumptions about the type of failure

mechanism are also required. In closely jointed

media it seems appropriate to assume that ~he

material is approximately homogeneous, I.e.

there are no clearly defined joint planes or

joint sets which control the form of the failure

mode. With this assumption of homogeneity

it is necessary to search for the critical case of

each type of failure mechanism. If, f or

example, a circular failure mode is under

investigation then a search has to be madeuntil the critical circle is found.

A further starting assumption involves the

water pressures in the slope. It may be that

for a given rock slope the position of the water

table in the slope is known. Input about water

pressures is then available. However, in most

cases the water pressures are not known and

some assumption has to be made. This

assumption clearly has an important effect on

the analysis. Since one of the objects of the

back analysis is to arrive at the lower boundset of strength parameters it is apparent that

a lower bound on the actual rock mass

strength is obtained if the slope is assumed to

be dry.

The back analysis procedure starts with the

plotting of slope height and angle data from a

given region for a given rock type. In cases

with a large amount of data it is likely that the

points will plot on a slope-height slope-angle

diagram with scatter. Since it has been

assumed that the closely jointed rock mass isapproximately homogeneous this scatter

represents slopes with various factors of safety.

The lowest factor of safety will exist in the

slopes represented by the upper bound on the

data. The next step is to investigate what

mobilised strength is required to explain the

state of stability of the slope.

3.2 The Casagrande resistance envelope

approach

As more than one parameter is required to

specify a given mobilised strength curve, a

method of obtaining more than one data point

is needed. If attention is concentrated on one

slope geometry this additional information is

obtained by using the Casagrande resistance

envelope concept, Casagrande (1950), Janbu

(1977). In this procedure one analyses a

number of slip surfaces and calculates for each

the average shear stress and effective normalstress (these values are obtained from

equilibrium considerations alone, no

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H rock mass nnit

jweight: y

0.6

0.5

0.4

~ 0.3. . .

0.2

0.1

0.1 0.2

a'/yH

//AV'/~/. /.

Fig. 1 The resistance envelope for a dry

slope with a tension crack behind the crest

(after Baikie (1988)).

assumption of strength parameters is needed).

These average values are plotted, usually in

terms of dimensionless stress quantities, for a

number of trial failure surfaces. The envelope

of all these points gives a boundary on stre.ssesmobilised in the slope analysed. The techruque

is elegant and has much appeal. Salt (1986)

gives an example of the application of t~emethod to slopes in schist in Central Otago In

the South Island of NZ. A possible

disadvantage of the method is the need to

evaluate the average stresses around the

failure surface. To obtain this would require

some post processing of. the output from .a

conventional method of slices stability analysis

programme. Baikie (1988) helps in this regardby converting the Hoek and ~ray (198~)

stability charts for a dry slope Into a resistance

120

upper bound slope angle

100 slope height relation

!

80 . . . , ~ ' Q ) 60.J::

~ ~40 0 ,-00

20

. - . . :

00 75 9015 30 45 60

Slope angle (0 )

Fig. 2 Slope height slope angle data for the

Kawakawa Bay slopes .

envelopes, Fig. 1. The Hoek and Bray ch~rts

are based on the assumption of a tenSIOn

crack exists behind the crest of the slope. It

could be argued that it would be more

consistent with the philosophy spelt out above

if tension cracks were ignored, as ~he

mobilised strength required without te~SlOncracks is less than with them. Compansons

given by Baikie show that tension cracks have

little effect on the results for low angle slopes

but there is a significant difference in the tWO

resistance envelopes for steep slopes.

3.3 The mobilised strength curve

As an example of the application of Baikie's

resistance envelopes the observed height-angle

data for slopes in greywacke at Kawakawa

Bay near Auckland, have been analysed. The, .. . ple

height-angle data, obtained USIn~ sirn d

surveying techniques by Free (1987), ISploUe

in Fig. 2. The resistance envelopes for four

slope angles, 300

, 450

, 600

and 750

, have .b.e:~replotted from Fig. 1 and the mobilis

outerstrength curve has been drawn as an

envelope to the four resistance envelopes. (FO~

the calculations the unit weight of the roc

mass was assumed to be 25kN/m3).At this stage a small point of terminology

866


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0 . 4

75

60'

45'

30'

o1.0 0 Un (MPa) 0 . 4

mobilised strength

0.5 1.0 1.5

o, (MPa)

Fig. 3 Mobilised strength curve for the

Kawakawa Bay slopes.

deserves clarification. As originally formulated

by Casagrande the resistance envelope refers

to one particular slope geometry and gives usthe stress combinations in the slope that are

required to satisfy equilibrium. The advantage

of working with different slope geometries is

apparent in Fig. 3 as the steep slopes give

greater mobilised shear stresses at low normal

stresses whilst the resistance envelopes from

the flatter slopes extend the mobilised strength

data over a wider range of normal stresses. As

each resistance envelope lies beneath the

failure envelope, the envelope of the separate

r~sistance envelopes, such as that drawn in

FIg. 3, gives a better bound on the failure

envelope for the material in the rock slopes.

Herein the term resistance envelope is

cOnfined to information derived from a single

Slope geometry and the term mobilised

strength curve is used when information is

g~ined from the back analysis of slopes with

dIfferent geometries. Extrapolating from the

separate resistance envelopes to the mobilised

strength curve involves the assumption that the

rack mass conditions for each slope are similar

and that no special geological condition is the

explanation for a particular slope geometry.

The resistance envelopes plotted by Baikie

are particularly convenient. It is also possible

to work directly from the Hoek and Bray, or

any other stability charts, to achieve an

equivalent back analysis.

4 EXAMPLES

The process outlined above has been applied

to slopes in jointed greywacke at several

locations in the North Island of NZ. The

extremes of the resulting mobilised strength

curves are plotted in Fig. 4. More details are

given by Pender (1990).

Greywacke is the basement rock for much of

the North Island of New Zealand. In the

unweathered state the intact rock would beclassified, following Hoek et al (1992), as

strong. The close jointing is a consequence of

a complex history of faulting as part of the

boundary between the Pacific and Australia-

India plates passes through the country.

From Figs. 3 and 4 it is apparent that the

mobilised strength curves are not linear c,

relations. This could in part be a consequence

of the back analysis process but it also thought

that the existence of a curved failure envelope

is characteristic of a closely jointed rock mass.

5 CURVED FAILURE ENVELOPE FOR A

CLOSELY JOINTED ROCK MASS

A consensus has gradually emerged among the

rock mechanics community that the failure

envelope for a closely jointed rock mass is

curved rather than linear.

At low normal stresses the apparent friction

angle is large and the apparent cohesion issmall. At high normal stresses the apparent

friction angle is smaller and the apparent

cohesion larger. The above back analyses of

greywacke slopes lend support to this idea

although the mobilised strength curves do not

necessarily have the same form as the failure

envelope for the material. The idea of a

nonlinear failure envelope is further justified

after reviewing strength tests on rough joint

surfaces, Barton (1973); on materials such as

granulated marble, Rosengren and Jaeger(1969) and Gerogiannopoulos and Brown

(1978), that are thought to model closely

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1 . 0

0.5 1.0

an (MPa)

Fig. 4 Range of the mobilised strength curves

for the greywacke slopes analysed.

jointed media; and on assemblages of carefully

fitted blocks, Brown (1970).

Hoek et al (1992) propose a modification to

the Hoek-Brown failure criterion that gives a

curved failure envelope and caters for closely

jointed rock masses by requiring a zero

cohesion intercept. This new criterion has the

form:

where: ac

is the unconfined compressive

strength of the intact rock, a and mb a re

parameters describing the intensity of the

jointing and the condition of the rock mass.

Following the classification given by Hoek et al

(1992) the surface condition of the. of the

joints in the greywacke mass would typically be

in good category, and the structure would be

blocky/seamy. Taking an unconfined

compressive strength of 50 MPa, a = 0.5 a~d

mb = 1.2 gives the failur.e envelope plott~? in

Fig. 5. To match approximately the mobilised

strength envelope values of the three

parameters which are quite unrealistic have to

be used. Thus we conclude that the closely

jointed rock masses, for which the mobilised

strength curves are given in Fig. 4, have a

reasonable factor of safety, assuming, of

course, the applicability of the modified Hoek-

Brown failure criterion to the closely jointedgreywacke rock masses in New Zealand.

1 . 5

1.0" 2

p . . .

;gl-'

0.51.5

modified Hoek

and Brown:

0', = 50 MPa,

a = 0.5, m, = 1.2

mobilised strength curve

for Wellington greywacke

oo 0.5 1.0

an (MPa)

1 . 5

Fig. 5 Comparison between the mobilised

strength curve for the closely jointed

greywacke rock masses in Wellington and ~he

failure envelope derived with the modified

Hoek-Brown criterion.

6 EARTHQUAKE EFFECTS

An additional effect that could have beenconsidered in the above analysis of the

Wellington slopes is the affect of earthquake.s.

All the slopes for which data are plotted rn

Fig. 4 will have been subjected to nu~erousearthquakes. The inclusion of a honzontal

acceleration to represent an earthquake would

improve the apparent strength 'para~eter~

derived, in the same way as the mclu~JOn 0d

water improves the strength. The analysis use

above is easily adapted to handle this case.

Instead of finding the strength parameters t~atgive the required slope height-angle relatlo~

under static conditions, i.e. zero honzonta

acceleration, the strength parameters ar~estimated for some non zero value of th,

horizontal acceleration. The omission of thIS

consideration is further confirmation that the

mobilised strength curves in Fig. 4 are lower

bounds on the actual failure envelopes.

The requirement for satisfactory earthquake

behaviour is another reason for prefe~r~ng ~

curved failure envelope for a closely Jomterock mass. This is a consequence of the stress

. anchanges that occur in a slope during

earthquake. The application of a honzonwl

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t

curved failure envelope for a

closely jointed rock mass

c, c l > extrapolation of the ~

c u ~ ,u r e e n v e , : /

~---'l./' stress path during an earthquake

initial average stress on a

failure surface

Fig. 6 Earthquake loading and the effect of

a curved failure envelope.

acceleration to a slope reduces the normal

stress on potential failure surfaces. A c,

envelope, which models the curved failure

envelope at high normal stresses, will tend to

overestimate the strength available during an

earthquake. This is illustrated in Fig. 6. In a

different context, Hoek (1983) makes a similarpoint about the need to be aware of the

Consequences of failure envelope curvature.

A further aspect of earthquake behaviour

relates to allowable deformations in such an

event. Newmark (1965) and Sarma (1975 &

1979) have treated the earthquake response of

earth dams and slopes on the basis that failure

for a short period, during which limiteddeformation occurs, is acceptable. In the case

of a closely jointed rock mass this is not so

clear. Any deformation during a failureexcursion will lead to loosening of the rock

mass with a consequent loss in the available

~trength, much of which is derived from the

Interlocking of the closely jointed blocks of

rock. This concept is illustrated in Fig. 7.

7 CONCLUSIONS

The difficulty of estimating the shear strength

of a closely jointed rock mass has be~nexplained. A procedure for the back analysis

of existing slopes is put forward as a means of

estimating the mobilised strength required to

failure envelope for a

closely jointed tightly

t interlocked rock mass

failure envelope for a

loosened rock mass . -an

Fig. 7 Change in the failure envelope for a

closely jointed rock mass during loosening.

explain existing states of stability. If the slopes

are assumed to be dry and prior earthquake

performance is not considered, then the back

analysis will yield a lower bound to the actual

failure envelope.

A nonlinear mobilised strength curve was

found to give better modelling of the observed

relation between the slope height and angle

than a linear c, envelope. However the

modified Hoek-Brown failure criterion, when

used with what seem appropriate parametersfrom the classification in Hoek et al (1992),

gives strengths greater than those from the

mobilised strength curves.

The mobilised shear strength envelope

derived for closely jointed greywacke confirms

that the material has a high apparent friction

angle at low normal stresses. If used for design

of different slope configurations this envelope

provides a means of arriving at man-made

slopes which have factors of safety as good, or

as poor, as those of the natural slopes. Themajor limitation of the method is the unknown

conservatism incorporated as the back analysis

process provides no information about the

actual failure envelope for the rock massunder consideration.

8 ACKNOWLEDGEMENT

The assistance, with field work costs, of the

Structures Committee of the of the RoadResearch Unit of the former New Zealand

National Roads Board is gratefully

acknowledged.

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9 REFERENCES

Baikie, L. D. (1988) Casagrande resistaneenvelopes for rock and rockfiII slopes havinjcircular slip surfaces. Canadian GeotechnicaJournal, Vol. 25, pp. 42-49.

Barton, N (1973) Review of a new shea:strength criterion for rock jointsEngineering Geology Vol. 7, pp. 287-332.

Bandis, S., Lumsden, x.c. & Barton, N. (1981:Experimental studies of scale effects on theshear behaviour of rock joints. Int. Jill. RockMech. &Min. Sci., Vol. 18, pp. 1-21.

Bieniawski, Z.T. and Van Heerden, W.L.(1975) The significance of in-situ tests onlarge rock specimens. Int. Jill. Rock Mech.&Min. ScL, Vol. 12, pp. 101-113.

Brown, E.T. (1970) Strength of models of rockwith intermittent joints. Proc. ASCE, Jill. SoilMech. & Found. Div., Vol. 96, pp.1935-1949.

Casagrande, A (1950) Notes on the design ofearth dams. Jour. Boston Society of CivilEngineers. Vol. 37, pp. 405-429.

Free, M. W. (1987) Back analysis of closelyfractured greywacke sandstone and argilliterock slopes, MSc thesis, Geology

Department University of Auckland.Gerogiannopoulos, N.G. and Brown, E.T.(1978) The critical state concept applied torock. Int. Jill. Rock Mech. and Min. Sci.,Vol. 15, pp. 1-10.

Hoek, E and Bray, J.W. (1981) Rock slopeengineering, 3rd. edition, Inst. Min. andMetallurgy, London.

Hoek, E., Wood, D. and Shah, S. (1992) Amodified Hoek-Brown criterion for jointedrock masses, Proc. Eurock'92, Thomas

Telford, pp. 209-213.Hoek, E (1983) Strength of jointed rockmasses. Geotechnique, Vol. 33, pp. 187-223.

Janbu, N. (1977) Slopes and excavations innormally and lightly overconsolidated clays.State-of-the-Art Report, Proc. 9th. ICSMFE,Tokyo, Vol. 2, pp. 549-566.

Newmark, N.M. (1965) Effects of earthquakeson dams and embankments. Geotechnique,Vol. 15, pp. 139-160.

Pender, M. J. (1990) Stability of slopes in

closely jointed rock masses. NZ RoadResearch Unit Bridge Design and ResearchSeminar, RRU Bulletin 84.

Pratt, H.R., Black, AD. & Brace, W.F. (1974)Friction and deformation of jointed quartzdiorite. Proc. 3rd. Congress ISRM, Denver,Vol. IIA, pp. 306-310.

Rosengren, KJ. and Jaeger, J.e. (1968) Themechanical properties of an interlocked low

porosity aggregate. Geotechnique, Vol. 18,pp. 317-326.

Salt, G. (1986) Application of the resistanceenvelope procedure to the determination offield mobilised shear strength. Proc-Australian Geomechanics Society SpecialtyGeomechanics Symposium, Adelaide, pp.134-138.

Sarma, S.K (1975) Seismic stability of earthdams and embankments. Geotechnique, Vol.25, pp. 743-761.

Sarma, S.K (1979) Stability analysis ofembankments and slopes. Proc. ASCE Jill.Geotech. Eng. Div., Vol. 105, pp. 1511-1524.

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ISRM-EUROCK-1993-111_Stability Assessment of Slopes in Closely Jointed Rock Masses