209

References DOW R.B./1956/: Some rheological properties under high pressure Rheology, 1, Acad. Press, New York. FUSSG~tNGER E.-GROMA B. /1975/: Zist'ovanie rezidu:ilnej nap~itosti ,v zosuvn~'ch dzemiaeh /in Slovak/. Zbornik konferencie: Sti/:asn~ stay mechaniky zemin v (~SSR, SSM-SAV Bratislava 5,369 - 376. FUSSGANGER E. -JADROIN D. /1976/: Prieskum zosuvn3;ch fizemi pri vyu:~iti niektor~'ch gpeci~ilnych met6d a skdgok /in Slovak/. Mineralia Slovaca, 8, 1, Spigsk~i Nov~i Ves, 23 - 35.

IB U L L E T I N

MENCL V. /1962/: M,~feni napiatosti v mSkk~,ch hornin',ich /i~ Czech/. V~stnik IJ'I~'G,27,209 - 212. MENCL V. /1966/: Mechanika zemin a skalnich hornin /in Czech/. Academia~ 189,245 - 248~ Praha. NEMCOK A. - PASEK J. - RYBAR J./1972/: Classification of landslides and other mass movements. Rock Mechanics, 4, 2, 71 -78. SKEMPTON A.W. /1964/: Long-term stability of clay slopes. Geotechnique, 14, 2, 77 - I01. ZfitRUBA Q.- MENCL V. /1969/: Landslides and their control. Academia-Elsevier, Praha, 205 p.

of the InternationalAssociationof ENGINEERING GEOLOGY

de I'Association Internationale de GEOLOGIE DE L'INGENIEUR

N~

209--212 ,KREFELD1977

I

EFFECT OF COHESION ON STABILITY OF FISSURED ROCK SLOPES ETUDES DE LA STABILITE DES VERSANTS ROCHEUX FRACTURES EN PRESENCE DES FORCES DE COHESION GAZIEV E.G., Princ. Spec. Rock Foundation Div., Institute Hydroproject, Moscow, USSR RECHITSKI V.I., Eng. Rock Foundation Div., Institute Hydroproject, Moscow, USSR

Summary : The pattern of failure of fissured rock slopes depends substantially on their interior structure. Sometimes separation and downfall of individual blocks from the slope surface occur, and sometimes this downfall takes the form o f an avalanche, depending on the interaction of beds forming the slope. The nature of failure changes sharply with increased cohesion between the rock blocks (when the cohesion reaches its critical value C . ) and does not depend on the joint pattern. The sliding rock mass moves as a whole in this case, on a subvertical rupture surface.

R~sum6: Le caract~re de destruction des versants rocheux fractures d~pend consid~rablement de la structure interne de ceux-ci Parfois, la d~sagr6gation et l'~boulement de blocs s~par6s se produisent, dans d'autres cas l'6boulement prend la f o r m e d ' u n e avalanche, due h l'interaction des couches constituant le versant rocheux. Cependant avec l'augmentation des forces de cohesion entre les blocs d'un massif rocheux, le caract~re de destruction change brusquement (lorsque la coh6sion atteint sa valeur critique C . ) et ne d~pend plus de la structure fractur~e du versantl Le massif total en glissement se ddplace alors comme un bloc entier, avec formation d'une surface de rupture subverticale.

1. lnl~xluction The mechanism and the nature of slope failure in jointed rocks depend to a great extent on the internal structure of the rock mass. As model studies have shown /Hofmann, 1970; Rengers, 1970; Gaziev and Rechitski, 1974a, 1974b: Gaziev, 1977/, a correct assessment of a rock slope stability can be done only on the basis of knowledge of the true mechanism of sliding rock mass rupture. This problem is of a great importance in slopes formed of bedded rocks, where the bedding orientation and degree of blocs interaction are governing the nature and the mechanism of failure caused by sliding. For instance, when beds dip gently towards the slope surface, the individual blocks separate from the slope surface /Fig. 1/. Slopes with beds steeply dipping towards the slope surface and undercut by a gently dipping joint, feature a very interesting failure pattern. As theoretical and experimental studies have shown /Gaziev and Rechitski, 1974a, 1974b; Gaziev, 1977/, the bed which possesses the lowest degree of stability and causes the failure occurs at a certain depth from the slope surface and is kept in the state of equilibrium by overlying strata. The disturbance of the state of equilibrium results in a precipitate

process of sliding of one layer after another and to an avalanchelike failure of the entire slope/Fig. 2a/. However, as the studies of the writers have shown, the presence and magnitude of cohesion forces on the bedding planes are a substantial factor influencing the mechanism of the slope failure alongside with the slope structure. For instance~ ff the slope presented in Fig. 2a is failing layer by layer with no cohesion at all or with low cohesion forces, in case of high cohesive forces the separation of a certain part of the rock mass takes place, which behaves as an integral whole/Fig. 2b/. With cohesion forces lying between their extreme values the rock ma~ failure is featuring an intermediate pattern: the sliding rock mass falls into parts, which represent groups of connected rock blocks. 2. The concept of cohesion and determination of cohesion in stability analysis Let us examine possible displacements along a joint in the rock mass. The shear strength of the joint is described by a curve similar to that shown in Fig. 3.

210

Fig. 1 : Failure of slope with beds gently dipping towards the slope surface and absence of cohesion.

If the rock block situated on this joint is loaded with a tension force acting at the angle O between the force vector and the joint plane, forces resisting to rupture or to dis[~lacement of a block will arise in the block base. When O = 0 , these forces are controlled by the value of C in Fig. 3, when O = 90 ~ . the resistin~ forces are .equal to the joint tension strength C and when 0 <: O < 90 , the resistance forces wdl be governOed by ,,cohesion" C o depending on the angle O/Fig. 3/. TO

O

9

9

'

3. Failure of rock slopes with cohesion forces present on bedding planes The pattern of failure of rock slopes with beds gently and steeply dipping towards the slope surface and absence of cohesion in bedding planes is illustrated by Figs. 1 and 2a. Failure of slopes with beds steeply dipping towards the slope surface and with low values of cohesion forces proceeds practically in the same way as with no cohesion. In this case the stability factor can be determined from the expression:

l.ig. 2 : Failure of slope with beds steeply dipping towards the slope surface: a) without cohesion forces, b) with high cohesion forces.

'1:

4 ~

J

where: i(j) is the serial number of the layer in the slope; ki is the partial stability factor of individual layer in the rock mass; Kj is the integral stability factor of the sum of layers, from the first one to the j-th. Fig. 4a shows the curves of variation of stability factors of individual layers 4k.) and of the integral stability factor K. for a rock slope with Beds steeply dipping towards the slope ~Jurface and undercut by a gently dipping fracture. These stability factors were calculated by the method advanced by the writers Gaziev and Reehitski, 1974b; Gaziev, 1977 . 9

|

'

,

o Fig. 3:

:)

6

Diagram of the shear strength of joint in the region at' tensile normal stresses.

211

The comparison of calculations made for the same slope using equations i l 7 and 12/. ~ ith various values of cohesion in ~tecply dipping joints, enabled us to plot the diagram shown in Fig. 5 and consisting of two lines - AB and MN, which represent different modes of rock mass failure.

7,/. 7%,/,/7:.' ' 7;.//yIl,Tiig,'// U/f///.;." ;,'i'i5 ' ,' ///I/,

///lii/,'!,

',

///',"

,/////'/ ,/,,~//,."/I.'/;.-,,..'iflz

//;//

K

,

9L

i

1.4

!

'

/

i

B

i

1.3

i

ic< I

1.2 K 1.0

Kj

0.9

1t

', ;

|

C.

08

i

10

15

20

25

30

35

4O

2.3 2.1

-'i

2.0

O

c!c

2.2

84

1.9

5

15

10

20

25

30

35

C
C.

C>C.

-C

Fig. 5 : Diagram of the slope stability t'actor vs. the value cohesion.

of

The curve AB represents the ,,layer by layer" failure of slope with low values of cohesion (C ~ C,), while the curve MN describes the displacement of the rock mass as of an integral block, with high cohesion values (C ~>C,).

1.8 K 16

/

A

1 5

MJJ

The point of intersection of the two lines determines the critical value of cohesion - C,.

40

Fig. 4 : I-.xample of the slope stability analysis: a) withlow value ot cohesion, b) with high value of cohesion. In spite of the fact that individual beds in the rock mass have stability factors lower than unity /beds 9 to 17/, the rock mass as a whole is stable (K > 1).

If the beds dip gently towards the slope surface, even insignificant cohesion qualitatively changes the failure pattern. In this case no dmvnfall of individual rock blocks from the slope surface occurs /Fig. l/, but rock masses consisting of groups of blocks are displaced forming a step-like failure surface /Fig. 6/.

With increase of cohesion forces on steeply dipping bedding planes the pattern of rock mass failure changes sharply. No downfall of separate layers occurs and the beds are moving as a whole part of the rock mass. The separation of the rock block from the entire rock mass occurs over a step-like surface as a rule close to vertical/Fig.2b/. In order to determine the stability factor for this case, possible alternatives of separation of the blocks with the weight G M and length L along the gently dipping sliding surface should be examined. The required stability factor will be equal to the minimum stability factor for the entire number of blocks examined: /-Il K = rain t ~ L

tan ~ I

CIL + C20 h sin~ 2 +

)

/2/

G M sin c: 1

where /21 and C / are the friction factor and cohesion in the gently dipping slide surface correspondingly;C~o is the cohesion in steeply dipping joints at angle e = ~ 9 - c~l to the bedding plane: G M is the weight of the rock block under consideration /per unity of the slope width/; L is the length of the rock mass under consideration along the gently dipping slide surface: h is the height of the potential plane of rupture of the rock block under consideration; ccI and cc9 are angles of dip of the gently dipping slide surface and steeply'dipping joints. Fig. 4b shows the diagram of variation of stability factors with increasing distance from the slope foot and with high values of cohesion between rock beds. The minimum value of K assumed to be the design stability factor was found at the distance corresponding to location of layer No. 36.

Fig. 6 : Failure o f slope with beds gently dipping toward the slope surface, in the presence of cohesion forces.

212 The stability analysis of slopes showing such structure also can be performed using equation /2/. where, instead of the angle co, the corresponding angle of dip of the conjugate set of joints is to be substituted. Such uniformity of stability analysis for rock masses of different structure is caused by the fact that with adequate cohesion in the rock mass the pattern of the rock mass failure does not depend on its structure/Figs. 2b and 6/. References

GAZIEV E.G.-RECHITSKI V.I. /1974a/: Study of jointed slopes failure patterns on models. 2rid International Congress of the IAEG, V - 22, S~o Paulo.

I BULLETIN

GAZIEV E.G.- RECHITSKI V.I. /1974b/: Stability of stratified rock slopes. Advances in Rock Mechanics, 3rd Congress of the ISRM, vo[. I1 - B, Denver. GAZIEV E.G. /1977/: Ustoychivost skalnikh massivov i metody ikh zakreplenia/in Russian/. Stroiizdat, Moscow. HOFMANN H. /1970/: Das Verformungsverhalten eines regelm~issig gekli~fteten Diskontinuums beim Abbau einer steilen Felsb6schung, 2nd International Congress of the ISRM, 7 - 1, Beograd. RENGERS N.- MULLER -SALZBURG L. /1970/: Kincmatische Versuche auf geomechanischen Modellen. Rock Mechardes, Suppl. l, Wien - New York.

of the International Association of ENGINEERINGGEOLOGY del'Association Internationale de GEOLOGIEDE L'INGENIEUR N ~

21Z--214

, K R E F E L D 19"77 i

DEVELOPMENT OF A LANDSLIDE SLOPE PROFILE FORMATION DU PROFILE DE TALUS DE GLISS.EMENT (MODELAGE CENTRIFUGE)

GOLDSTEIN M.N., TUROVSKAYA A.Y., Dnepropetrovsk Institute of Railway Transport Engineers, Chair of Foundation Engineering, Dnepropetrovsk, USSR* Summary: T h e b e g i n n i n g o f a landslide m o v e m e n t is a c c o m p a n i e d by decrease in t h e c o e f f i c i e n t o f stability K s to a c e r t a i n m i n i m u m . A d r o p in K s is c o n d i t i o n e d by the decrease in soil s t r e n g t h in the shearing z o n e , w h i c h occurs u n d e r so small d e f o r m a t i o n that t h e slope profile and, h e n c e , even the acting forces r e m a i n practically u n c h a n g e d . S u b s e q u e n t d i s p l a c e m e n t results in the slope mass s u b s i d e n c e and Ks increase. When, in c o n s e q u e n c e o f t h e successively repeated sliding cycles, the residual value o f soil resistance in t h e shearing zone is achieved, t h e slope p a ~ e s into a state o f limit subsidence.

Rdsu md: Le d6but d'activit6 de glissement est suivi de la r e d u c t i o n du c o e f f i c i e n t de stabilit~ Ks j u s q u ' h une c e r t a i n e valeur m i n i m u m . La r 6 d u c t i o n K s est c o n d i t i o n n 6 e par la d i m i n u t i o n de la stabilit6 du sol dans la z o n e de d 6 p l a c e m e n t qui a lieu avec la d 6 f o r m a t i o n si petite que la c o n f i g u r a t i o n du talus et par c o n s 6 q u e n t des e f f o r t s de c i s a i l l e m e n t ne c h a n g e n t pas p r a t i q u e ment. Q u a n d en d6finitive les cycles de glissement repet6s s u c c e s s i v e m e n t la stabilit6 du sol dans la z o n e de d 6 p l a c e m e n t s'616ve a u n e valeur r~siduelle, la talus passe h l'6tat de la d~clivit~ limite. Generally, a slide cycle occurs in two basic substantially different stages. At the first stage the distortion develops under conditions of the prelimiting state of a slope with the coefficient of stability K s > 1, and at fl~e second stage under the translimiting state conditions with K < 1. The moment characterized by K s = I separates the two sta~es. The first stage is an undamping process of local weakening in the massif at a constant shear stress, the slope profile being preserved. The slope develops with a drop in the stability coefficient, provided that the influence of the external factors is excluded. The second stage is a period of an apparent displacement accompanied by the slipping surface development, i.e. a period of the disjunction of a landslide body and of its downward movement/subsidence/ until equilibrium is attained. Changes in the slope state show a different course at this sta~: the initial serious loss of stability /the decrease of K s from one to a certain minimum value complying with the culmination point of the landslide cycle development/ changes with time by the zradual increase of K_to a value even slightly more than one/after K s reaching one, the displacement

of the landslide body continues under inertia/. This testifies to the completion of a landslide cycle. The decrease in the coefficient of stability at the beginning of the second stage/the transition of the slope into the translimiting state/ can be attributed to a conspicuous reduction of the clay soil resistance in the shearing zone, which occurs at such a small shift that tangential stress remains practically unchanged. The intensive slope mass subsidence at the nearly unchangeable close to residual shear resistance determines the subsequent increase of K s. By the residual resistance the authors mean a minimum steady shear strength of clayey soik conforming to the conditions of the optimum moistening of the displacement surface. Generalized equation of the residual resistance resulting from various laboratory tests of clays, takes the form Sres = 0.09 + 0.14 o /S and o'values are given in kg.cm'2/. The coefficient of stability decrease at the beginning of the second stage /noted by the authors, contrarily to the customary notion

* Dnepropetrovsk Institute of Railway Transport Engineers, Chair of Foundation Engineering, 320629 Dnepropetrovsk - I0, Universitetskaya St. 2