Proceedings of the International Symposium on Weak Rock / Tokyo /21-24 September 1981

Stability analysis of a rock slope

against toppling failureR.EVANSCountry Roads Board, Victoria, Australia

S.VALLIAPPAN & D.McGUCKINUniversity of New South Wales, Sydney, Australia

H.L.RAJA SEKARMetropolitan Water Sewerage & Drainage Board, Sydney, Australia

1. INTRODUCTION

TOPPling failure is one of the modes offailures specifically related to rockslopes. Since toppling involves over-turning of blocks or rotation of a system0: parallel steeply tipping columns aboutPlvotal points, this mode of failure isquite common in rock masses with regularbedding planes or joints. There are sev-~ral classes of toppling which may occurln rock slopes and a detailed discussiono(nthis topic can be found elsewhere

Goodman and Bray,1976).

Among the various kinds of toppling:escribed by Goodman and Bray (1976), the

lexural toppling, the block toppling andthe block-flexure toppling belong to onec~ass. Another important class of topp-ll~g is known as secondary toppling inwhlch the failures are initiated by someundercutting agent. The primary failuremechanism involves sliding or physicalbreak-down. The various mechanisms under(~conda:y toppling are :

) Sllde toe toppling due to the loadingof the potentially toppling rocks byanother instability.

(2) Slide base toppling due to the bedsbeing dragged along by overlyingmaterial.

(3) Slide head toppling where movementscause blocks to topple higher up aslope.Toppling and slumping by weatheringof underlying rock.Tension crack toppling 'due to theformation of new cracks above steepslopes.

(4 )

(5 )

f The problem investigated in this paperaIls int th .toe maln category of 'secondary

a~~p~;)g' and into the sub-classes of (4)

Among the various stability analysesused to investigate toppling failures inrock slopes, the limit equilibrium methodhas been adopted by Attewell and Farmer(1976) as well as Goodman and Bray (1976).In the limit equilibrium method, the modeof failure is assumed prior to the cal-culation of factor of safety whereas inmany cases, the mode of failure is theunknown factor. Furthermore, the limitequilibrium method considers only theequilibrium of forces and does not takeinto account the properties of the jointas well as the continuum. Also, it cannotrealistically model the progressive fail-ure of the slope. The discrete elementmethod has been adopted by G. Hocking(1978) for the analysis of toppling-sliding mechanisms. This method is betterthan the equilibrium method because thefailure surface is not assumed a prioriand the movements of blocks are determinedto evaluate the stability of the slope dueto toppling mechanism. However, thismethod, at present, lacks in predictingthe cracking of the rock mass.

The finite element method has been usedfor investigating the toppling failure byKalkani and Piteau (1976) and Brown et al(1980). Kalkani and Piteau adopted a twodimensional elastic analysis which includ-ed the effects of raising the water tableto investigate the toppling failure atHell's Gate Bluffs in Canada. The zonesof tensile stresses for low and highgroundwater were determined.

Brown et al (1980) used the finiteelement technique to study the Nevis Bluffrock slo~~ failure in New Zealand. Theirinvestigation is, in fact, a back analysisof the slope which failed in 1975. Theresults of the analysis indicated that the

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failure was due to initial flexural topp-ling which propagated cracking and thensliding.

In this paper, the results of an inves-tigation into the mechanism of secondarytoppling failure of rock slopes are dis-cussed with specific reference to a rockslope failure in the Grose Valley of NewSouth Wales. The geologi al influencessuch as weathering and creep are takeninto account in the finite element anal-ysis. The geological featlJres of the in-vestigated area, the finite element mod-elling and the results of the analysis aredescribed in the following sections.

2. CASE STUDY

2.1 Geological Features

The Grose Valley of New South Wales islocated approximately 90 km west of Sydneyand has been the site of a number of largerock failures. The Grose Valley, whichis up to 600 m deep has been formed byriver erosion through a sequence of alter-nating sandstones and claystones, withmassive sandstone beds (the Banks WallSandstone and Burra-Moko Head Sandstone)forming a 110 m high vertical cliff face.

The stratigraphy of the Grose Valleyhas been described in detail by Crook(1951), and, briefly, consists of thePermian Shoalhaven Group and IllawarraCoal Measures overlain by the TriassicNarrabeen Group. The Narrabeen Group ismade up of the Caley Formation and theGrose Formation, the former unit beingclaystones while the latter are predomin-antly sandstones. The Grose Formationmakes up the prominent cliffs of theGrose Gorge. All these units are essen-tially horizontally bedded.

Several large rock failures have occurr-ed at Burra-Moko Head, in the Grose Valley,the most recent having taken place inearly 1975. Burra-Moko Head is the sub-ject of repeated rock failures. A view ofthe rock failure is shown in l'ig. 1 anda plan is presented in Fig. 2. Fig. 1shows the top of the exposed face withstrong limonite staining being evident.Fir. 1 and Fig. 2 also show the triangul-ar rock pillar remaini~g after the failure.

At the base of the cliff, evidenceexists of the basal claystone (Caley For-mation) being highly weathered and thesandstone cliff being undercut. 'I'he rockfailure itself is bounde by joints and

the basal claystones are substantiallyin situ. This indicates that the mech-anism of failure is more likely to be atoppling type rather than a bearing cap-acity type.

2.2 Finite Element Model

A two dimensional plane strain nonlinearanalysis has been adop ed for this inves-tigation. Quadratic quadrilateral iso-parametric elements have heen u~ed forthe discretization of the continuum and'Goodman' type joint elements have beenused for modelling the joints. The non-linear effects include 'no-tension' cut-off and creep. Hence, two separate anal-yse-s were carried out, one for each ofthe nonlinear effects. In the 'no-tensiorlanalysis the cracking was assumed to de-velop when the principal stresses at apoint were tensile and the 'initial stres~method was used as an iteration techniqueto take into account this nonlinearity.For the creep analysis, a power law in theform of

where is the incremental effectivecreep strain,is the effective stressae

K and n are material constantshas been used and the 'initial-strain'method was adopted as the iterative tech-nique.

Fig. 3 shows the finite eLerneuC meshalong with the geological classificationof the various layers in the slope. Theproperties of these various materials arelisted in Table 1. These material proper-ties represent a collection of data basedon laboratory tests but reduced to thein-situ behaviour of rock mass by fieldseismic work, (Evans, 1978). To modelthe weathering at t~e base of the column,various elements have been assigned mat-erial properties with a gradation inweathering from hiGhly weathered to freshfrom the free face. The bench t.hat, isshown in the mesh indicates a lithologychange and h nce the outer elements areassigned as being lightly weathered sand-stone. Only two colwnns of joints areinclu ed in the mesh for the main reasonthat the field evidence indicates thatthe vast majority of movement occurs with-in this distance. No horizontal discon-tinuities are included since the fieldobservations do not indicate any movementalong these interfaces. Moreover, the

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computing time required for the analysiswas also taken into consideration in mod-elling the actual geological formation ofthe slope.

3. DISCUSSION OF RESUUPS

The results of the elastic analysis ofthe slope with joints due to gravity load-ing have been plott d in Pig. 4. Fig. 4~~hows the deformed mesh near the free faceand it can be seen that the column tiltsbackwards. From the contours of theprincipal stress, 01 plotted in Fig. 4b.it can be observed that there are sometensile zones at the crest and the toe ofthe slope. Lookin at the horizontaldisplacements of the two joints it wasfound that only very small areas of thejoints are open.

The displacem nts an the stresses forthe 'no-tension' analysis have beenobtained only for half the total gravityloading since convergence could not beobtained for the full loading. Thel' sults for this case are given in Fig. 5·

The deformed mesh plotted in Fig. S~ in-dicates a strong tendency towards a topp-ling failure. 'I'hetwo columns of elementsin the immediate vicinity of the ver·ticalface are significantly dilated. Lookingat the deformed face of the slope, thereis a definite tendency towards backtilt-ing at the base of the column whereas atendency of the upper section to toppleforward is indicated by the bulgIng outof that part. It is interesting to notethat this phenomenon has been actually ob-served in the field (Evans, 1978). Thebasal element which repr sent the weath-ered Caley Formation are highly deformedindicating a tendency towards minor under-cutting. The contours of the principalstress, 01 plotted in "'ig.c; b supportthe natu)'e of the deformations shown inPig. "a. Tensile or crack d zones in thevicinity of the toe and crest r-r-gi oos canbe noted.

Due to the pre ence of joints, thestresses in the top outermost plement havebeen relieved. I'romthe horizontal dis-plac'ernentsof't.hetwo joints it was ob-Served that the bottom sect.ion of t.hejoints are closed whereas the uppersect.ionis t.otally open. Under these conditions,the stahility of the slope can be arhievedonly i['rock anchors m-e seat.ed far'br-hi ndthe inner ,jointand proter-ably locatedncar L1,P to of the r lif'f'['\lce.

'I'hodC'f'ormntionbohav Lour 81,0W11 by theso

models ('(lnfirris the n"t,IlI'Poft.opp.l i n., L •. L1m' " , p r i nc ipal.L,' uas.i lweathering to induce differential settle-ment. The extent and magnitude of basalbacktilting is mostly dependent on theexact nature of the basal weatheringpattern and the variation of stiffnesscharacteristics of the rock mass. A rapidweathering gradation where the horizontaldept.bto fresh rock is only a few metersmay preclude basal backti1tin .

In the present investigation, only theweathered rorks were considered to beundergoing creep and the fresh rocks wereassumed not to creep. The dei"ormed mesh['orcreep analysis is shown in Fig. 6a.lt can be seen that the free face isalmost vertical but the basal elements inthe weathered Caley Formation are highlydeformed showing a strong tendency tound rcutting. Of course, t e actual mag-nitudes of displacements will dependlargely on the adopted creep equation andthe actual material properties providedfor the analysis. Fig. 6b shows the con-tours of 01 and it can be noted that theextent and magnitude of tensile stresseshave been increased considerably comparedto the elastic analysis. The tendency ofthe sinusoidal movements of he jointswith alternate open and closed regions canbe seen from Fi[;.6n.

4. CONCLUSIONS

The investigation of toppling j~ilureusing only the gravity loading has indic-ated that the no-t nsion analysis withjoint elements appears to model the topp-ling mechanism in a realistic way. Thisanalysis where the basal claystone is con-sidered to show progressive ~ecrease inweathering inwards from the free face,reveals lower backtilting of the failingrock colwnn and upper forward tilting.The elem nts in the rock column have under-gone considerable dilation vhi Lc the toeregion of th· slope cracked indicatinglocal failure of weathered rocks.

The creep analysis indicates a largert nsile zone and the tendency for under-cuttin to occur. Undercutting occursbecause th weathered creepin rock cannotsustain the overburden load and tends to'contract' inwards. The overall nature ofthe toppling failure is critically depen-dent on the basal weathering pattern andthe rate of weathering in relation 0ero ion of'the outer weathered materials.

The finite element analysis indicates

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- -_._. _. --_ .. ------

vlat.e r i a l Rock Type Degree of' E(GPa) v DensiLy K nroperty Hea.thering K (GPa/m) Kn (GPa/rn kN/m3

umber s

1 Sandstone & Frer;h 1~.0 0.26 26.0cla.ysLone

2 " " 7.0 0.26 25.0-- -----

3 Sands Lone " 9·6 0.22 2h.O

~ Claystone " 6.8 O,~() 25·0-

5 " 81i.ghtly 3.0 0.311 ?~,O 8.?x!O-l 1,07WeaLhered

22.0 T11XI0-7_._----

6 " Moc1eraLely 1.7 0.h2 O.~7Weathered

7 " CompleLely 0.1 0.h5 20.0 1 .8xl0-6 0.2'3Weathered

8 Sandstone Slightly 2 .I~ 0.26 23.0 -9 1.001.OxlOWeathered

9 Joint in " 1.0 2.6Sands Lone

10 Joint in " 0.8 1.5Claystone

the progressive naLure of toppling andgeneral degradation processes whereby Len-sile or cracked regions develop and fail-ure ensues. The principal meLhod of elim-inating cracked regions is the use ofstructural restrainLs in the form of sLeeldowel bars, rock bolts or rock anchors.For the case study presented in Lhis paper,Lhe analysis indicates Lhat rock bolts oranchors must be seaLed rar back into theslope and they should be locat d prefer-ably near the top of the slope.

5. REFERENCESALtewell, P.B. and Farmer, I.W. 1976,

Principles of EngineerinG Geolocy,Chapman and Hall, Great Britain.

Brown, 1., Hittinger, M. and Goodman, R.1980, PiniLe Element Study of the NevisBlufr (new Zealand) Rock Slope Failure,Rock Mechanics, 12: 235-2115.

Crook, K.A.W., 1957, The Stratigraphy a.ndPetrology of the Narrabeen Group in theGrose River District, J. Proe. Roy. Soc.N.S.W., 90: 61-79.

TARLE 1: Material Prop0rLy Da.LH

Evans, R.S., 1978, Time Dependen L FacLorsInfluencing the Rock Slope Stability 01'Lhe lllawarra EscarpmenL, N.S.W., I'h.D'I'he si s , Tlw Uui ve r s i t.v o f N.S.vl.

Goodman, R.E. and Bray, J.\~., 19'(6,Toppling of'Hock Slopes, Proc. Spccial-iLy Conf. on Rock ~IKg. for PoundaLion~and Slopes, ASCE Publication, 2: 20l-23~.

Hocking, G., 1978, AnaLysis of Toppling -Sliding Mechanisms for Rock Slopes,Proc. 19Lh U.S. Symposium on RockMechanics.

Kalkani, E.C. and Piteau, D.R., 1976,FiniLe ElemenL Analysis of TopplingFailure at lIell"s Gate Bluffs, BritishColumbia, Bull. Assoc. Eng. GeologisLs,13: ~: 315-327.

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N

1

FIG.2. PLAN OF ROCK FAILURE AT BURRA-MOKOHEAD

FIG.l. FAILURE AT BURRA-MOKO HEAD

8.lo int s-, j

3.Sandstone _4.Claystone3.Sandstone

r: 5,6,7 ___ 4. Cl ays tone

\ 3.Sandstone~ 2.Sandstone & Claysto

<.1.Sandst

~'..

ne

one &one

FIG.3. FINITE ELEMENT MESH FOR SECTION A-A IN FIGURE 2

669

50100

a) ORIGINAL AND DEFORMED MESHScale:- u :u = 1:10x y

FIG.4. ELASTIC ANALYSIS

100 50b) CONTOURS OF PRINCIPAL STRESS,Ol

50

100

PartiallyCracked

a) ORIGINAL AND DEFORMED MESHScale:- u :u = 1:10

x y

FIG.5. NO-TENSION ANALYSIS

b) CONTOURS OF_PRINCIPAL STRESS,Ol 100 50

a) ORIGINAL AND DEFORMED MESHScale:- u :u = 1:6x y

FIG.6. CREEP ANALYSIS

b) CONTOURS OF PRINCIPAL STRESS,Ol

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