luther extensions to theBishop 8c Morgensteznslope stability chartsRJChandler* and TA Peizinj

s (118 I+~ ~ Is I I I ~ ~ i le imae ~ Qeameaeme eal

1'ean in ('u ir ~ I 1 ~ V ~ iul ( Sgiiil ieai.l 0 sM ~ 6 a

~asia Iaiai (igni aal tat 8 il IIae o leam> act 6 is m ~ ~

Yil i (in S I lan aTiTeaiiI eggs as ~ mgm we Bma 0 ia s.

The design charts for the effective stressstabiTity analysis of slopes given by Bishop8 Morgenstezn (1960)'nd O'onnor &Mitchell (1977) are extended to slopes ofinclnation 0.5:1(horisontaLvertical) andvalues of the dimensionless stability factorc'/yH up to 0.15.The present results areshown to agree with those of the earlierworkers, whose results, included here,enable slopes to be designed in the rangeof inclination O.S:1to 5:1,for values ofc'/yH

=Oto0.16,andri'20 to40.

IatroductionOver the years the stabiTity chartspresented by Bishop &Morgenstern(1960)have proved very valuable for thepreliminary design ofslopes in terms ofeffective stresses. The range of strengthand slope inchnations that theyconsidered was, however, limited tovalues of the stability coefficient c'/yH nogreater than 0.0Sand slope inclinations in

the range 2:1to 8:1(horisontaLvertical).The range of strengths was later extendedby (YConnor 86 Mitchell (1977),whoconsidered values ofc'/yH up to 0.10.

We have extended fuzther both the rangeofvalues ofc'/yH (to 0.1S)and the slopeincination(up to 0.5:1);followingO'onnor &Mitchell we consider valuesof If('etween 20'nd 40 .The results arepresented here in tabular fozm. This

'Depaztzrieztt of Civil Eztgineexiztg, hnpezialC(3Hegfg, London

"'g llPE/ 63.ce

sga

2:I-Bishop 6Morgenstem

u3'1 (1960)

ei =10 to ag

0cu Sil-o

800 0.025 0.05Values of c'/ YH

d ConnorMitchell(1977)6' 20'o

23. 60

16.3a

Ia

Ffg.l.8lapelncllnatlans and values ofc'/ylf caznddaredby the variousauthors.

Unit weight of soil YUrit weight ol water YPmaometric height hr ~ (tre

ZY

Efy'.2. D ttm<<ansofsyznbals usecL

further extension of the method not onlyallows steeper slopes to be considered,but the higher values ofc'/yH enable thedesign ofslopes composed of relativelyhomogeneous soft rocks such as chalkand Keuper MarL The range ofdata whichwe provide is compared with those of theearlier publications in Efy; 1.We haveincluded the results ofBishop &Morgenstern and O'onnor &Mitchellwith our ownresults, so that the completesuite of stability coefficients is available tothe potential user.

MethodsThe analyses were canied out with amicrocomputer, using the BishopSimplified method for a circular arc failuresuzface (Bishop 1988)s,programmed tolocate the most critical failure surface. Asdescribed by Bishop &Morgerstern(1960),the Bishop Simplified equation forthe factor of safety, F, maybe written in

dimensionless terms. Thus F is dependanton the geometry of the particular problem.and on the parameters c'/yH, P'nd rwhere c'nd P're the effective stressstrength parameters, y is the unit weight ofthe soil, H the vertical height of the slopeand r„the average value of r„within theslope. The pore pressure parameter r„isde5ned

incog.

2, as are the slopeinclinat'on,(ti, and the depth factor, D.

There is a linear relationship between Fand r„for given values of c'/yH, P', P andD, which may be given (Bishop &Morgenstern 1960)as:F=m —nr„ . (1)The mndts of the stabQity analyses maythus be expressed m terms of m and n.

Our computations followed similarprocedures to both Bishop 86Morgensteznand O'onnor &MitchelL The former used20 trial circular arcs to establish thecritical arc, the latter 100.We used 24 (6 x4 grid), guided by Spencer's observations(1967)gthat the contours of safety factorare approximately elliptical with theirmajor axis normal to the surface of theslope, and that the centre of the critical arcis normally on or just upslope of thepezpendicular bisector of the slope. Acheck was made that a minimum value of Flay within the grid; where necessary, thecalculations were repeated with anewgrid location so that a minimum value of Fwas obtained.

The values m and n in Eq.(1)werecomputed using a regression analysisapplied to the Fversus r„data.

Bishop &Morgenstern and O'onnor &Mitchell canied out their computationsusing values ofr„=0, 0.3and 0.7;we used0, 0.3and 0.6.

We also investigated the inQuence of thechoice of 20 or 40 as the number of slicesused in the analysis on the resulting valueofF.For the case ofc'/yH = 0.100,D = 1.5,P = 4:1,with values ofP'n the range 20'to

2:1m n

Oloifg ifadmafsfm

311 411

m n m 05:1

m 0

20' +0.1 +0.12 +OA +2.0

+1.0 +1.8 —02 -1.1

30'+0.9 +2.8 —0.8 -1.0

+0.3 +1.1+0.3 +0.9

+0.1 +0.0 +0.3 +0.1 +0.4 +03 +0.4 +O.S+1.1 +2A +0.6 +1A +0.4 +2.0

1 +02 -02 0 +0.1 -0.2 -1.0+1.2 +1.8 +0.6 +OA +0.2 —0.7 +0.4 +0.8

Table 1.Differences(+ 96)ln values ofzn and n abtalned by (1)CYCennar*MtchaU(1972) and g) thfs paper, cenZpared with lmshop 00 Marffenstazn (1900),lo(r c'lylf = 0.09, D = 1.0.

GROUND ENGINEERING MAY 1989

33

100-

80-H

(m) Usingeo- stability

coefficients

40-

(19/ 8),kPa,0.15m~

Table 2.c'/yH = 0; am vnlnea ofD.

Qopo 0.5:1 I:I 2:1m n m n m n

20'.182 0.910 0.364 0.728 0.728 0.91025'A3 1.166 OA66 0.933 0.933 1.16630'A9 1.443 0577 I.ISS 1.1$S 1.4433P OAO 1.7Sl 0.7N 1ASS IAN 1.75141P 0.420 2.NS O.N9 1.670 1.678 2.098

3:1m n

4:1m n

5:1m n

1.092 1.213 1.45d 1.547 1.820 1.8921.399 1554 1.865 1.982 2.332 2.4241.732 1.924 2.309 2.454 2.N7 3.Nl2.101 2.334 2.Nl 2.977 3.501 3.6392317 2.797 3.3S6 3.S66 4.196 4.362

20-cot (1

3:1 2.1 1:1 0.5:1 0.25:1I I I I I I I I

O 2O 40 eO 8O.Slope inclination, P

Hg.3. Cosuyns&on ofaloye beft7btveranafnclfnatfonrelatfonabl$ sdcalcnlatedby different tnethoda; carveJrnm Chandler(1 ON).

34

TaMe3. c'/yH= 0.2$;D = J.OO

Slope 0$nl 1:1m n m n

20'5230.733 0.707 0.76425'306 0.740 OAL39 0.97430'.667 OAI7S 0.9N 1.20235'.755 1.010 1.142 1.454OAIS7 1.1N 131S 1.731

2:Im n

3:1m n

4:1m n

5:1m n

1.124 1.022 1342 1.347 1.962 I.d98 2.380 2 NO1.356 IA2 1$75 1.69d 2AN Z 141 2.921 Zdftd1.606 1.567 2AS 2.078 2A73 2622 3300 Z 1911.NO 1.NS 2.Q5 2.505 3.396 3.160 4.1Sd 3,0492.190 2.247 3.090 2.993 3.904 3.778 4.NS 4.$92

TaMe4 c'lyH = O.2OJD = J.2O

Qopo ILS:1 1:1m n m h

20'.996 0.943 I AI76 1.N625' Ad 'I.'198 IAS IAI

1A72 IAN IA02 IA3135'.737 1.773 1.9051.974N'345 2.118 L$12 L362

2:Im n

3:I 4:Im n

5:1m n

1%9 1216 1.610 1.478 1,961 1.775 2.334 2.0901A19 1547 2.007 1.091 2A37 2269 X$97 2.6691.9S6 1.915 2A31 2.342 2.9Q LN6 3811 3~LNI 2AI 2.901 2.841 3824 3AN 1.191 3.9902.7Q 2.77$ 3A31 3.399 1.164 4A64 4.950 4704

TaMe$.c'lyH O.OOOJD = J.OO.

Qopo OA:I 1:Ih' h

20'ASS 0.7N 0.9'12 LSI02S'L797 'IAOI

IAIDO

1.04230'L9N 1117 1A2 1&735' A02 IA17 1&9 IA69417 1.140 IA17 1859 1.7SS

2:1m h

3illn h

4:Im n

5:Im n

1AO 1AI71 IA40 1.307 2A3 1.776 2.7N ZOP I1A24 IAS 2.193 1.7$7 L770 Z211 3A6 Z651IAS IA30 L574 Z 1$7 3&1 Zd93 3.934 3A'$92.1701.9$0 2.990 Z$92 3A03 MQ 4897 3.9272505 L332 3A51 3.071 4A25 Z Sl 5344 444$

TaMeO.c'/yH= O.OOOlD= J.2O.

Qopo OA:I I:1m n m h

20'.172 0.9N ILQ I.N425' A05 1&2 1809 1A330'IA$ 6 18101.7N 1.66930'.935 IA30 2AN7 2A074; X245 2.174 2A29 L390

2:Im n

3:Im n

4:Im n

Silm n

TaMe1.c'/yH= O.OOOJD= J.OO

Qopo 05:I lilm n m n

20'A91 IA9 1861 1%325'426 1A37 1.910 1.7N2.187 LOIS $207 2.10135'507 2A36 2.704 X$41N'A40 2.915 3.17$ 3AS6

2:1m n

3:Im n

41m n

5:Im n

1.752 IAOI L011 1.705 L337 1.993 2AOS L2N2.143 1.903 2A67 2.179 X$67 LQ4 3302 2.902ZSN L342 2.964 2A96 3A43 3.120 3.967 3A773ANI 2832 351S 3'AI2 3.771 4.707 4AS3874 3A9 4136 3.91S 4803 4807 5543 5.171

GROUND ENGINEERING MAY 1989

1509 I~ IAd 1.193 2.230 1.799 2A43 2.107%22 1895 $222 I897 2.705 2.2S7 3211 Zd902.1dl 1.9SO 2A45 2.342 3AI 2419 3A9 3,3242535 L344 3.114 LN9 3.79S 3.413 4811 4,0252.9Q 2.791 3A42 3AOS 4A42 4.090 5&3 4406

40'andr„to values of 0, 0.3and 0.6, thevariationin factor of safety lay between 0and 1.63%(average 0.4%).In everyinstance the value of Fobtained with 30shces was the lower. We subsequentlyused 30 slices for aU our analyses, so thatin that respect our results wiU yieldmarginally conservative values ofF.

ComI$ arlsoawith yrevious resultsO'onnor 4MitcheU compared theirresults with Bhahop 8 Morgenstern's forc'/yH = 0.06andD = 1.00,andwehavedone the same. The results ot thiscomparison are ahownin TaMe J,expressed as percentage differencesfrom the original

Bishop'sMorgensternm

and n values. O'onnor 8c Mitchell's resultsshow slightly ckeer agreement withBishop 8c Morgenstern's than do ours, withtheir values ofm andnbeing on average0.38%higher, while our results average0.78%higher. The use ot such values inEq.(1)wiU result in a correspondingpercentage increase inF compared withthe other worker's results. Theseditferences are sufficiently small to be ofno practical importance.

It is also possible to compare, indirectly,our results with those ofTaylor (I846)s.Chandler (1884) used Taylor'0 work toconstruct aslope height versus inclinationrelationship tor aslope having the soilproperties c'0kPa, (ti' 34', f„0.16and y = 33kw/ms, obtaining therelationship ahowninRfg.2. Ourextension ot the Bishop 4 Morgenaternresults enable this relationship, whichinvolves slope incinathna in the range 1:1to 0.6:1,tobe checked. It is seen that thecaicuINed points agree extremely weUwiththe relationship obtained from

Taylor'ada'reseatioa

ofresultsIn the tables that foUow (Tablee2te JO),we present reauha ofour computations, towhich we have added for the user'a

convenience the results obtained byBishop &Morgenstern and O'onnor &Mitchell We are thus able to give thestabiTity coefficient for slopes in the range0.5:1(P= 64') to 1:5(P= 11.3'),for valuesofc'/yH = 0to0.15,and/' 20'to40'.

As Bishop &Morgenstern pointed out

(p 136),for the special case where c' 0the failure surface is a plane parallel to theslope surface (the Minite slope'ase) and

F = tang'(1 —r„sec'P)/tang ...(2)

Thus m and n (TaMe 3)may be easilyevaluated as m = tan 46'/tanP, andn = m sec'Itl.

The previous authors presented theirresults in both tabulations and in chartform. We believe that the tabulations areused far more frequently than the charts,and therefore only include the tabulations.A particular benefit of the charts is that it ispossible to show (for given values of/, 46',c'/yH and D) contours ofvalues ofr„(r+which yield the same value ofF for valuesofD = 1.00and 1.25;and also for D = 1.25and 1.50.The value of r„used for designcan then be compared with thecorresponding value ofr, to provide animmediate indication whether or not thereis a more critical deeper slip surface. Thisis not so conveniently achieved withtables, but a partial solution, followedhere, is outlined in the following section.

Use of tablesThe tables give values of m and n to beinserted in the equationF=m —nr„ (1)to obtain the factor of safety, F, of the slopefor given values of c'/yH, P', r„and slopeinclination/, all ofwhich are defmed inFldf.2. A method for obtaining a value ofr„within the slope for use in Eq.1 is given byBishop &Morgenstern(1960).

For values ofn appearing in the tables initalics there is the possibility of a deeper,more critical failure surface if the designvalue ofr„isequal to or less than 0.5.Theuser should then check this possibility,using the table giving the next highestvalue of D for the same value of c'/yH. It isalso possible that a deeper critical surfacemay exist where the design r„is greaterthan 0.5.No indication of this is given in thetables, so the user should also check thispossibility at higher values of D. Thisproblem does not occur when c' 0(TaMe 2);nor, as is often the case, when astronger stratum lies at or close to the baseof the slope.

TaMe$.c'/yH= O.OZ$;D= 1.OO.

03:1m n

1:1m n

2:1m n

3:1m n

4:1m n

5:1m n

20'5o

30'5'0'3145

O.NO 1.088 0.837 1.610 1.1N 2.141 1.443 2.664 1.801 3.173 Z 1300.950 1.013 1245 1.053 1.872 1.386 2.502 1.8153.12d Z2$9 3.742 2.71$1.064 1238 1.416 1296 2.142 1.N6 2.884 2201 3.623 2.7$S 4.357 3.3311.190 1.485 1.605 1564 2.443 2.030 3.306 24$9 4.177 3.331 5.024 4.N11.332 1.762 1.798 1.824 2.772 2.386 3.775 3.14$ 4.785 3.94$ 5.77d 4.7$9

TaMe O. c'lyH = O.OZ$;D = 1.2$

05:Im n

1:1m n

2:1m n

3:1m n

4:1m n

5:1m n

20'5o

30'5'IP

TaMe lO. c'/yH = O.O?$;D = J.$0.

05:Im n

1:1m n

2:1 3:1m n

4:1m n

5:1m n

20'50

30'5'0'.637

1.305 1.706 1.349 1.918 1.514 2.199 1.728 2.548 1.985 2.931 2.2721.977 1.663 2.052 1.708 2.308 1.914 2.660 2.2N 3.083 2.530 3.552 2.9152.340 2.041 2.426 2.1N 2.735 2.3SS 3.158 2.714 3.d59 3.128 4.218 3.5852.741 2.459 2.841 2.537 3211 2.854 3.708 3.285 4.302 3.786 4.961 4.3433.193 2.931 3.310 3.031 3.742 3.397 4.332 3.926 5.026 4327 5.788 5.185

TaMe II.c'lyH= O.IOOID = l.OO.

Slope 0.5:1 1:1 2:1m n m n m n

3:1m n

4:1m n

5:1m n

20'50

30'5'0'.993

0.797 1.263 0.871 1.841 1.M3 2.421 L472 2.982 1.8153.549 2.1$71.106 1.025 1.422 1.078 2.102 L430 2.785 LS4$ 3.358 Z303 4.131 2.7431222 '1.259 1.592 1.306 2.378 1.714 3.183 Z2$8 3.973 ZS30 4.751 3.3721.347 1.508 1.781 1.57d 2.692 2.086 3.612 2.71$ 4.516 3.3$9 5.426 4.8$91.4N 1.7N 1.995 1.879 3.025 2.445 4.103 3.230 5.144 4.N1 6.187 4.831

TaMe 12.c'/yH = O.MO; D = 1.2$.Slope 0.5:1 1:1

m n m n

2:1m n

3:1m n

4:1m n

5:1m n

20'50

30'5'0'.489

1.036 1.529 1.095 13174 1.301 2.283 1.558 2.751 ES43 3.2531.735 1.313 1.799 1.394 2.197 1.642 2.681 1.972 3.233 2.330 3.8331.997 1.602 2.091 1.718 2540 2.0N 3.112 2.415 3.753 2.8$8 4.4512280 1.908 2.414 2.076 2.922 2.415 3.5N 2.914 4.333 3.458 5.1412597 2.253 2.763 2.453 3.345 2.855 4.119 3.457 4.987 4.142 5.921

2 1$82.7SS3.3724.0724.872

TaMe13. c'lyH = O.lOOID = 1.$0.

Slope 0.5:1m n

1:1m n

2:1m n

3:1m n

4:1m n m

5:1

20'5o

30'5'0'.778

1.314 1.863 1.371 2.079 1.528 2.387 1.742 2.768 2.014 3.1582.119 l.d74 2211 1.732 2.477 1.942 2.852 2.215 3.297 2.542 3.7962.489 2.063 2.586 2.122 2.908 2.385 3.349 2.728 3.881 3.143 4.4682.N2 2A84 3.0N 2.553 3.385 2.884 3.900 3.3N 4.520 3.NO 5.2113.347 2.957 3.469 3.04d 3.924 3.441 4.524 3.941 5.247 4.542 6.040

2.2852.9273.6144.3725.2N 37

GROUND ENGINEERING . MAY 1989

1.336 1.023 1.387 I.N7 1.688 1.285 2.071 1.543 2.492 1.S1$ 2.954 2.1731.575 1.284 1.656 1.386 2.N4 1.641 2.4d9 1.957 2.972 Z31$ 3.523 2.7301.NO 1.560 1.943 1.701 2.352 2.015 2.NO 2.385 3.499 2.857 4.149 X3$72.109 1.865 2.245 2.025 2.728 2.385 3.357 2.870 4.079 3.4S7 4.831 4.0432.424 2.210 2.5N 2.403 3.154 2.841 3.889 3.428 4.729 4.128 S.N3 4.830

TaMe14. c'/yH= 0.12S;D = 1.00.

Slope

20'5030'5'0'.5:1

1:1m n m n

2:1m n

3:1m n

4:1m n

5:1m n

1.121 O.N8 1.425 0.881 2.042 1.148 2.689 1.$41 3.263 1.784 3.868 2.1241.254 1.051 1.596 1.112 2.323 1.447 3.062 L9N 3.737 2.271 4.446 27211.37d 1.267 1.769 1.337 2.618 1.777 3.457 2.298 4253 2.S10 5.073 3.3681.505 1.530 1.956 1.586 2.929 2.115 3.880 2.7054.823 3.407 5.767 4.0481.612 1.743 2.171 1.891 3.272 2.483 4.356 3.1S3 5.457 4.NB 6.551 4.893

Table 1$.c'/yH = 0.12$;D = 1.2$.Slope

2(P25o

30'5'0'$

:I 1:1m n m n

2ilm n

3:1m n

4:1m n

5:1m n

1.642 1.057 1.671 1.102 2.054 1.324 2.492 1.$79 2.983 1.8d1 3.496 2.1671.8N 1.326 1.941 1.402 2.377 1.671 2.894 1.993 3.481 2.379 4.078 2.7$32.156 1.626 2.234 1.727 2.727 2.042 3.324 2.431 4.009 2.91d 4.712 3.40$2.447 1.948 2.557 2.085 3.110 2.452 3.801 2.928 4.586 3.$N 5.414 4.12S2.767 2.295 2.922 2.490 3.542 2.913 4.338 3.494 5.237 4.161 6.207 4.94$

TaMe16. c'/yH = 0.12$;D = 1.$0.

Slope

20'$0

30'5'0'$

:1 1:1ni n m n

2:1m n

3ilnl h

4ilm n

5:1m n

1.920 1.322 2.015 1.385 2.234 1.545 2.565 1.749 2.963 2.N4 3.400 2.287

2.261 1.683 2.3N 1.754 2.638 1.972 3.028 2.229 3.5N 2.550 4.019 2.9132.631 2.073 2.745 2.145 3.072 2.425 3.529 2.749 4.083 3.149 4.692 3.5983.039 2.504 3.160 2.577 3.549 2.923 4.084 3.324 4.727 3.813 5.436 4.3623.497 2.982 3.628 3.065 4.N9 3.485 4.712 3.980 5.456 4.566 6.278 5.226

TaMe 17.c'/yH= 0.1$0;D= 1.00.

Slope 0.5rl 1:1m h nl h

2:1m n

3:1m n

4:1m n

5:1nl h

20'5o

30'5'0'.248

0.813 'I.585 0.886 2.261 1.170 2.895 1.448 3.579 LNd 4230 2.159

1.386 1.034 1.761 1.126 2.536 L4d2 3.259 1.S14 4.052 22N 4.817 Zld51525 1.260 1.944 1.370 2.836 1.791 3.657 2.2454567 2.S11 5.451 3.4161.660 1.539 2.134 1.619 3.1dl 2.1$3 4.098 2.721 5.137 3.4N 6.143 4.1171.NS 1.832 2.346 1.901 3.512 2.535 4.597 3.2$8 5.782 4.NB 6.913 4.8N

TaMe 16.c'/yH = 0.1SO;D = 1.2$.Slope 0.5:1

m n

1:1m n

2:1nl h

3:1nl h

4:1m n

5:1m n

20'50

30'5'0'aMe10.

c'/yH= 0.1$0; D = 1.$0.

0.5:1m n

1:1 2:1m n m n

3:1m n

4:1m n

5:1m n

1.796 1.079 1.813 1.107 2.229 1.334 2.701 LBN 3.225 1.873 3.780 2.182

2.042 1.344 2.083 1.409 2.560 1.692 3.107 2.0153.724 2.384 4.363 2.7692.309 1.639 2.377 1.734 2.909 2.065 3.542 2.464 4.262 2.941 5.995 X406

2.NS 1.971 2.700 2.094 3295 2.475 4.018 2.946 4.846 3.$34 5.697 4.129

2.934 2.335 3.066 2.449 3.728 2.938 4.556 3.509 5.498 4.1956.490 4.947

Linear interpolation may be used, withoutsignincant loss of accuracy, forcalculations involving intermediate valuesofc'/yH, IJ) 'nd cotti.

Worked exampleThe example chosen is that used byBishop &Morgenstern (1960),an earthslope for which the relevant designparameters are P' 30', c'/yH = 0.035,r„=0.5,and which has a slope inclinationcottJ = 4:l.

Referring to TaMe 3(c'/yH = 0.025;D = 1.00),it is seen that the value ofn,2.622, is shown in italics. Since the designvalue of r„(0.5)lies just within the range 0.5to 0, there will be a deeper more criticalfailure surface. Thus it is necessary to turnto TaMe 4(c'/yH = 0.025, D = 1.25).Thisgives m = 2.953,n = 2.806, which whensubstituted into Eq. 1, along with r„=0.5,yields F = 1.550.

Similarly, from TaMe S(c'/yH = 0.050,D = 1.00)a deeper more critical failuresurface is again indicated. Thus Table 6(c'/yH = 0.050,D = 1.25)givesm = 3.221,n = 2.819,and Eq. 1 yields F = 1.812.

Interpolating linearly for c'/yH = 0.035givesF = 1.550+ 0.4 x 0.262

= 1.65.

AcknowledgementsWe are grateful to the Institution of CivilEngineers and the Canadian GeotechnicalJournal for aQowing us to reprint theresults previously obtained by Bishop &Morgenstern and O'onnor &Mitchell.

References1.Bishop, AW and Morgenstern, NR (1960).Stabilitycoefficients for earth slopes. Gdotechnigue 10, 129-150.2. O'onnor, MJ and Mtchell, RJ (1977).An extensionof the Bishop &Morgenstern slope stabiTity charts.Canadian Georechnical Journal 14, 144-151.3.Bishop, AW (1955).The use of the slip circle in thestability analysis of slopes. Gdotechnigue 5, 7-17.4.Spencer, E (1967).A method ofanalysis ofthestabiTity ofa~cuts assuming parallel intersliceforces. Gdotschnique 17, 11-26.S.Taylor, DW (1948).Fundamentals of soil mechanics.New York, Wiley. (pp4S6-462).6.Chandler, RJ (1984).Recent European experience oflandslides in overconsoiidated days and soft rocks.Proc 4th lnt Symposium on Landslides, 1,61-6l.

38

20'5o

30'5'0'.061

1.335 2.1642.402 1.691 2.5202.772 2.N2 2.9023.181 2.514 3.3193.643 3.0N 3.788

1.391 2.394 1.550 2.748 1.756 3.174 2.020 3.641 2.3081.768 2.798 1.978 3.212 2.237 3.711 2.561 4.259 2.9242.168 3.236 2.441 3.718 2.758 4.293 3.156 4.931 3.6042.6N 3.715 2.940 4.269 3.333 4.938 3.819 5.675 4.3643.0N 4.255 3.503 4.896 3.983 5.667 4.569 6.517 5.228

GROUND ENGINEERING MAY 1989