Engineering problems and rock mechanics: some examples

Engineering Geology, 7(1973) 333--358 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

ENGINEERING PROBLEMS AND ROCIf MECHANICS: SOME EXAMPLES

CHARLES JAEGER

Pully (Switzerland) (Accepted for publication December 12~ 1973)

ABSTRACT Jaeger, C., 1973. Engineering problems and rock mechanics: some examples. Eng. Geol., 7: 333--358. The purpose of this paper is to show how rock mechanics interprets geologic information and helps to adapt engineering design to rock conditions. The paper analyses eight case histories of large engineering projects. In five cases the designers took careful account of the conditions prevailing in the rock masses, the rock characteristics, the strength of the rock and the modified stress---strain pattern created by the new structure. The intrinsic curve of the rock mass, the Coulomb condition, the residual stresses and the E-modulus in the families of joints are among the more important characteristics of the rock mass. In two case histories, it is shown how an erroneous estimate of the cleft-water pressures caused disaster. Rock mechanics is a necessary link between engineering and geology.

APPROACH

The criteria on which a rock mass is analysed by an engineer designing a darn, a gallery or a large underground cavity, or estimatihg the stability of a rock slope, are basically different from the criteria guiding a geologist describing the same mass of rock. The starting point for any investigation in rock mechanics in connection with an engineering problem is given by the geological and geomechanical reports produced by the geologists. The engineer is supposed to carefully analyse the detailed description of rock masses, joints, fissures and faults a s given in these reports. The approach of the designing engineer is nevertheless basically different: he has to translate all the information received in terms of strains, stresses, deformations, forces, and stability of structures. His first aim is to decide which rock characteristics and which physical and mechanical properties of rock masses are important for the particular problem he has to solve. At this stage of the investigations, there may be some confusion on what is important and what is not. ~Postal address: Chemin des Vignes, CH-1009 Pully, Switzerland.

334

An example may illustrate the problem: classical tests on rock and rock masses are used for determining the rock crushing strength, its modulus of elasticity E or the modulus of in-situ rock masses. The analysis of these characteristics and the parallel analysis of the families of joints and faults in the mass guide the engineers' decision on the suitability of the rock mass to withstand the thrust of a dam, arch dam or gravity dam. But rock masses acceptable as dam foundations may cause severe difficulties during the outdoor excavations of the rock abutments or the underground excavations of a nearby underground machine hall. The basic problem for the designer is to decide which rock characteristics he wants to know and, if necessary, what additional information he wants from the geologists. REMARKS ON THE STRENGTH OF ROCK AND ROCK MASSES AND ON THE RESIDUAL STRESSES IN ROCK MASSES

The remarks will be limited to simple basic problems; a more general analysis would by far exceed the limits of this paper. (1) A series of laboratory tests determine the strength of rock material; the result of these tests is a so-called "intrinsic curve C" traced on a diagram (o, r) where o and r are the local stresses acting on an element of rock (Jaeger, 1972). This intrinsic curve is, by definition, tangential to all Mohr circles corresponding to the rupture of the rock material under different loading conditions (Fig.l). When the rock is fissured or when there are weakness planes, the intrinsic curve may be replaced by the Coulomb condition represented in the same diagram (0, r) by a straight line: r=c+

otan~

where c is the rock cohesion and ~ the angle of friction along the plane of weakness or the fissure. In-situ tests are used for determining the "intrinsic curve C1" of the rock mass (Fig.2) and, when fissures occur in a dangerous direction, for determining the Coulomb straight line: r =cl

+ o tan~

along the fissure or fault. In some cases the intrinsic curves C or C~ can be replaced locally by a straight line tangential to the curve. The intrinsic curve C and the Coulomb line for rock material, obtained from tests in the laboratory, are usually different from the "intrinsic curve C~" or the Coulomb line obtained from in~itu tests. On the diagram in Fig.2, any point (0, r) located on the intrinsic curve Or on the Coulomb line corresponds to the rupture of the mass. It is essential for the designer to check that rock stresses obtained during the different construction stages and after construction are located well below the curve or line, depending on the type of rock mass; otherwise, rock reinforcement

335

C

a

b

Fig. I. R u p t u r e of rock material, a. Intrinsic curve C in h o m o g e n e o u s b. C o u l o m b condition along a fissure. M I , M 2 . . . = M o h r circles.

rock material.

is required. A t y p e of rock support has to be chosen which suits the rock's state of stress and strain. (2) Tests can be carried out in virgin -- or nearly virgin -- rock masses, the purpose of which is to measure the residual stress components o v and oh in the vertical and horizontal directions (Jaeger, 1972), stresses which exist in the rock mass before starting any excavation. Usually the vertical c o m p o n e n t of the residual stress is approximately equal to a v = p = HTr, where H is the overburden height above the point where the stress has been measured and 7r is the specific weight of the rock mass. The ratio k = a h / a v is a very important coefficient to be considered for all underground excavations, as the stress-strain pattern around an excavation depends on it. Similarly, it is often i m p o r t a n t to know the value of the modulus of elasticity E of the rock. But the modulus of the rock material differs from the modulus of the rock mass and this value E also depends on the m e t h o d of measurement, static or dynamic (Jaeger, 1972). (3) Instead of following the progressive stages and a detailed analysis of one particular engineering job, as has been done in a great number o f technical papers, we shall describe eight modern engineering projects where interesting situations had to be coped with. In each case, the engineer had to

4I 0

Fig.2. Stable c o n d i t i o n s for rock masses, a. Intrinsic curve in h o m o g e n e o u s r o c k mass. b. Coulomb condition along a joint or fissure. The Mohr circles M1, M2 should remain below the curve C1 or the line of Coulomb.

336

decide on suitable design according to the particular problems caused by the rock masses. CASE HISTORIES

The following case histories illustrate the stress--strain conditions which have been described in the previous section. They show h o w engineers had to adapt designs and construction methods of tunnels, underground works, dams, and dam foundations to the actual characteristics of the rock masses. Some unforeseen disasters, due to errors of design, will be described.

Structures in highly deformable material The Heitersberg Tunnel (Andraskay et al., 1972) The first case to be analysed is a marginal one. It concerns a tunnel, some sections of which were excavated in highly deformable material, which should be described as soil rather than as rock. The behaviour of the tunnel lining clearly shows h o w it adapts itself to the deformations of the excavated material, a situation of some interest for a better understanding of the system of "rock mass and lining". The Heitersberg tunnel is a double-track railway tunnel, near Zurich, Switzerland. Along a length of 1.4 km at its western end, the tunnel crosses rough material, which can be better described as soil than as rock. At the eastern end there is real rock, mudstone or sandstone. In the western section, the overburden H is 20 -- 65 m thick. The characteristics of the "soil" material are: 77 = 2.1 t/m2; ~ = 30°; c = 0 t/m2; E = 1,000--2,000 kg/cm 2 Such characteristics correspond to loose material, with very low E-values. The techniques used for the construction of this tunnel have also been used elsewhere, in real rock masses. The reason w h y this example has been chosen is that it has some similarity with problems concerning the Kariba underground power house case. The circular tunnel excavation has a radius R = 5.65 m and it is reinforced with reinforced concrete rings 0.25 m thick, consisting of five segments with five hinges. The vertical load Pv was calculated with Terzaghi's formula: R~ Pv = k tan

[ 1 - - ek t~n ~ / R ]

but, on the basis of deformations measured in other Swiss tunnels, slightly higher values were used for the final calculations. Voellmy's equation was used, which corresponds to the case of Fig.3. This figure shows diagrammatically the passive and active loads on the concrete ring. The deformations were calculated on a computer, assuming the concrete circular ring to be replaced by a polygonal structure with concentrated forces at each angle of the polygon. Fig.4 shows radial active and passive soil pressures on the ring, as resulting from computer calculations.

337

L1[I1111t111111t111[1i[[11111 Loadpv

i::x3ssJve pressure

pp

Fig.3. Heitersberg Tunnel (from Andraskay et al., 1972). Deformation of the circular lining; rotation round the hinges causes passive pressure. Pv ffi vertical load; pp = passive pressure.

The b o t t o m segments are reinforced, their thickness varying from 0.25 m to 0.47 m. The width of any segment is 1 m and the weight is from 4.3 tons to 6.6 tons for the b o t t o m segment. The segments forming t h e concrete rings were precast inside a 20 X 50 m building located outside the tunnel. Vacuum concrete (cured under vacuum) was used, the hardening treatment lasting 15 min. Some difficulties occurred during construction, because the soil under the b o t t o m elements could n o t be properly c o m p a c t e d to the prescribed degree. The eastern section o f the tunnel was excavated in sandstone, which showed visco-plastic characteristics and a k-value varying from 0.6 to a b o u t 2.0, when measured in situ, the average being a b o u t k = 1.0. The main interest of this example is to show -- in addition to the construction techniques used -- that t h e cylindrical structure of the concrete reinforcement, with 5 hinges, is stable when radially compressed by plastic rock or soil, in spite of the number of hinges being superior to 3. This explains h o w a concrete lining, applied to the rock surface, adheres to it following its deformations, and can stand even when fissured. It is wrong, as is o f t e n suggested, to calculate the lining as an arch, supporting odd rock loads. The analysis of large underground excavations with the final-element m e t h o d (Zienkiewicz and Cheung, 1967) always implicitly assumes that t h e "concrete vault" supporting the rock mass is a lining adhering to the rock.

338

~

.-

2" II ¸

o 0

if)

uuu,, \:

~,,-

.~t)

•

339

Foundation rock consolidated by residual compression stresses The Dez Dam (Reza Pahlavi Dam) (Dodds, 1966; Jaeger, 1972) The Dez Dam is a typical example where confining residual loads in the undisturbed rock mass were of major importance to the stability of a doublecurvature thin-arch dam, 204 m high. According to the American designers of the dam, the y o u n g age (Middle to Late Pliocene), variable composition and cementation of the rock and the exacting foundation demand made precise understanding of the physical properties of the rock a necessity. The programme of exploratory work and laboratory research was very extensive. Unconfined and confined crushing tests were carried o u t on 6-inch diameter, 12-inch high, dry and wet cores. It was f o u n d that t h e confining pressure p improves the crushing strength according to the following relationship: oc = 2621 + 2.68 p (in psi values) Measured confining pressures (or residual stresses), corrected for the true direction of the dam thrust, were 339 and 450 psi, which give a rockcrushing strength varying from 3,530 to 3,810 psi, well in excess of the expected local stresses under the dam abutments. This stress and strength analysis was carried o u t under the supervision of the well-known French expert J. Talobre. It corresponds to the case of Fig.2a. The relation binding the crushing strength oc to the confining pressure " p " can be used for tracing t h e intrinsic curve for the Dez Dam foundation rock, as shown on Fig.5. The publications on Dez Dam do n o t give the actual stress pattern under the dam abutments, but, from similar well-known cases, it can be inferred that there is no danger of the Mohr circles coming t o o near to the intrinsic curve of the rock. The dam is stable.

The Pertusillo Dam, Italy (Fumagalli, 1966; Jaeger, 1972) Arch dams are designed and tested with the final-element m e t h o d usually assuming a given constant modulus of elasticity E (rock) for all the rock T

psi

5.000

1,000 0

!

!

1.000

I

5,000

Fig.5. I n t r i n s i c c u r v e f o r Dez D a m .

"

- -

10.000 pSi

340

mass. The ratio E (rock)/E (concrete) is important for the stress pattern developing in the concrete shell. Research work done after the failure of the Malpasset Dam (France) has shown that stresses in very thin arch dams are less dependent on the E (rock)-value than in thicker dams. Malpasset was found to be stable for E (rock)-values as l o w a s 10,000 kg/cm 2. On the contrary, model tests carried o u t in Portugal have shown the danger of locally overstressing the concrete in the dam shell and in the rock itself when E (rock) varies considerably along the foundation line of the dam. Some homogeneity of the rock is desirable along the foundation, and sometimes is more important t h a n the absolute value of E (rock). The foundations of the Pertusillo Dam (Italy), shown in Fig.6, are an excellent but little-known example of a non-homogeneous foundation which had to be analysed with special care. At depth under the project dam, 100 m high, the rock is a weaker marl-clay sandstone "grds" (letter " E " in Fig.6). This underlying sandstone was tested in deep exploratory galleries: rock cores 60--70 cm in diameter were isolated and tested in the laboratory. The measured E-values on these cores were extremely low: E = 10,000--12,000 kg/cm 2, with c -- 1 kg/cm 2 and = 25 ° (about the values found in the left a b u t m e n t of the Malpasset dam). The problem of designing the dam foundation on inclined strata with such a weak rock formation at greater depth would have been most difficult. Seismic measurements of the in-situ rock elasticity, however, gave E (seism)values as high as E -- 500,000 kg/cm 2, pointing to the fact that the in-situ rock had been highly precompressed and compacted during very long geological periods and that this precompression was still there as a residual stress. Triaxial tests in the laboratory confirmed that the material could be compacted after several loading cycles, giving acceptable test results.

~ / ~f I

1 j J

i f

jf

~ D fl J

1 1 1 j 1 1 1 1

f

1 1

f E

J

Fig.6. G e o l o g y of the Pertusillo D a m (after FumagaIli, 1 9 6 6 and Jaeger, 1972). A = concrete, E = 250,000 k g / c m 2, ~'r = 2.5;B = soft sandstone with clay, E $ ffi25,000 kg/crn 2, ffi40,000 k g / c m 2, "rr= 2.4, ~ = 3.0° ;C = stony sandstone, E ~ = 35,000 k g / c m 2, E = 50,000 kg/cm=, ~'r = 2.4, ~ = 30°; D = conglomerates, E = 50,000 k g / c m 2 m e a n m o d u l u s of the whole mass, mr = 2.4, ~ = 30 ° ; E ffimarl--clay sandstone mass, E = 10,000 k g / c m 2 compressibility modulus, 7r = 2.5, ~ = 25 ° , c = 1 k g / c m 2.

341

The dam was tested on a model by Fumagalli and construction proceeded normally, (Fumagalli, 1966; Jaeger, 1972).

Additional remarks on stress--strain conditions in highly stressed, nearly homogeneous rock. Dam foundations and galleries The conditions at Dez Dam and Pertusillo Dam are somewhat similar. In both cases high residual stresses are consolidating the foundations. For Dez Dam, the designer worked on rock strength and stresses. He checked t h a t residual stresses -- due to pressure from rock overburden loading lower-lying rock banks before the river cut the Dez Gorge -- were acting positively on the rock mass. When estimating the total stresses, this residualstress c o m p o n e n t maintains the circles of Mohr well under the intrinsic curve. Implicitly, Fumagalli, who was in charge of the theoretical research work for Pertusillo dam, made a similar reasoning, but his line of approach was on rock elasticity, rather than rock strength. In-situ seismic measurements checked the E (rock)-value in undisturbed rock masses. There is n o t enough information available on the correlation between the E modulus of some rock masses (mudstones, sandstones, etc.) and the stress-strain conditions in the rock. Some Japanese scientists have shown t h a t the Poisson ratio v of a rock mass depends on the state of stress and fissuration of the rock, which, they say, may vary with time. A drop of the E-modulus has been observed at Vajont when fissuration of the rock progressed. However, little is known about rock consolidation by compression, other than a few laboratory results. These remarks concern rock conditions under dam foundations, which have to stand high compressive loads. Conditions around a tunnel or cavity excavated in rock are basically different, as in a direction perpendicular to the rock surface around the cavity, the radial stress on this surface is n o u g h t (o r = 0). Talobre has developed a theory on rock overstressing around a cavity (Talobre, 1957). The diagram on Fig.7 is self-explanatory. When rock stresses around a cavity reach the elastic limit, plastic deformation of the rock or even crushing of the rock

/ ~

~[

I ~ .

T2 fP

~

elastic rock mass

overstrained rock

Fig.7. Overstrained rock around a tunnel. (After Talobre, 1957; Jaeger, 1972.)

342

occurs, causing a drop of the circumferential stress ut . In some cases, the rock deforming plastically will reach a new equilibrium. In other cases, some type of rock support will be required. This is when the skill of the designer is important in making the best choice for an efficient type of support. There are many examples of such situations to be found in the technical literature, and there is no need for further comments here. Lombardi (1970) has recently published some diagrams showing how deep the plastic area may extend into the rock mass, when overstressing occurs. The main variable is obviously the external load: overburden, residual stresses, k-value, etc. Assuming these conditions to be known, it becomes possible to correlate the depth R, of rock plasticity to the pressure p from the rock support acting on the surface of the cavity. Lombardi obtains interesting examples using the finite-element method (f.e.m.). When the gallery is circular, it is possible to obtain similar results using the classical theory of elasticity. (When the gallery or cavity is not circular, it is often possible to trace a circle locally tangent to the cavity surface to be examined.) The formula linking R, to p* (Fig.8) is:

(1

+

5-l

=2u+

RL +l({

‘B

1)

+qsp* s c

!1

*-l =

2+

zp

ra

(y-1)

(1)

c

wherep=a, =a”, for k = 1 (case of Fig.lb for any direction of stresses); p* = pressure caused by rock support; ra = tunnel radius; 5 = (1 + sin cp)/(l - sin cp); for cp = 30”, 5 = 3; uC = crushing strength of rock mass. Two special cases are of interest: When there is no rock support, p* = 0 and: 2p(5-1) (C + 1) UC

(2)

mass

Fig.& Rock support causing a radial load p*. (After Lombardi, 1970.)

343

a formula already developed by Kastner (1962). On the contrary, the whole rock mass behaves elastically when R L = ra; p * then becomes a maximum: 9--

Pm~ -

Oc

~+ 1

(3)

It is also possible to develop a formula giving p * ~ when k ~ 1. These equa-, tions should replace the well-known and often-mentioned equations of Fenner-Talobre (Talobre, 1957), which, in some cases give unsatisfactory results. (Eq.1 will be demonstrated later in another, more technical paper.) Stratified rock masses

Veytaux and Waldeck II underground power stations Very often, rock masses cannot be classified as nearly homogeneous; rock stratifications, fissures a n d faults give to the rock mass the character of a stratified mass and the Coulomb condition has to be introduced along

I

I I

\

?

\

/

\

/

\

/

/

\ \

/ \

// /

/

/

/

/I

f

1

t I

375.95

15.25

_

15.25

I Fig.9. Veytaux underground power house. (From Rescher, 1968.)

344 Ob~Voecken 539.20 Stauziel 0 Absenkziel ~ ~ 492.082

5 o o I ~

I

i z,,,o°g,-u°o

.

2

~

~

i

uu I

l

~

n

176.30S;

k

.

.

.

.

a ~

~-

'

.

•

Unterbecken

~.. . . . . . . . . . . .

Zufahrt.sstoilen

J 100 m NN i 500

',

- ~l~Uf~'~Wasscr~"t°lltm I$7.Sin ~ n k z l e , vccne

i

I ;t i 700m 600

"

A 400

i 300

I 200

] 100

i 0

J 100

i 200

i 300

i 400

i 500

i 600m

Fig.10. Waldeck II: u n d e r g r o u n d p o w e r h o u s e ( f r o m B a r t h , 1 9 7 2 ) . L e g e n d : o b e r b e c k e n u p p e r reservoir; Stauziel = m a x . w a t e r level; 8chr~igschacht = i n c l i n e d s h a f t ; M a s c h i n e n k a v e r n e = m a c h i n e hall; W a ~ e r s c h l o s s = surge t a n k ; Zugangs- u n d Liiftungsstollen = adit a n d a e r a t i o n ; U n t e r w a s s e r s t o l l e n = tailrace gallery; Z u f a h r t s t o l l e n = m a i n access gallery; Auslaufbauwerk = outlet structure.

161.00

J_

IS-

ler~

Fig.lla.

345

\

/

/

/

zonker [ = 4 . 0 0 rn

F i g . l l . Waldeck II: cross-sections o f p o w e r h o u s e , a. S e c o n d s t r e a m l i n e d a l t e r n a t i v e design ( f r o m B a r t h , 1 9 7 2 ) . b. E x c a v a t i o n p h a s e s a n d a n c h o r e d cables. L e g e n d : K u g e l s c h i e b e r = s p h e r i c a l valve; S t o p f b i i c h s e = j o i n t ; T u r b i n e = t u r b i n e ; elektr. S y n c h r o n m a s c h i n e ffi s y n c h r o n o u s g e n e r a t o r ; P u m p e = p u m p ; K u r z a n k e r ffi s h o r t a n c h o r s ; T i e f a n k e r = d e e p a n c h o r , b. E x c a v a t i o n p h a s e s a n d a n c h o r e d cables.

TABLE I C h a r a c t e r i s t i c s o f V e y t a u x a n d Waldeck II u n d e r g r o u n d p o w e r s t a t i o n s

Overburden k ffi O h / a v

E (elastic) E (total) % c (cohesion) Length L Width B Height H Turbines Pumps

Veytaux

Waldeck II

65--150 m 0.40

250 m 0.40 30,000--80,000 kg/cm 2 17,500--70,000 kg/cm 2 > 200 kg/cm 2 1.5--15 kg/cm 2 20 °--37 ° 106 m 27 m 46.60 m 2 horizontal Francis 2 pumps

100,000 ? 3 31.5 ° 136.50 30.50 26.70 4 vertical 4 jets P e l t o n 4 pumps

346

joints in the analysis of the stability of rock masses. Many large caverns, tunnels and galleries have been built in such jointed rock masses in recent years. Most probably, they are in the majority. Two of the more recent large underground power stations built under such conditions are analysed here: the Veytaux underground power station (Fig.9) on the shores of the Lake of Geneva, Switzerland, (Rescher, 1968; Buro, 1970) and the Waldeck II power station (Fig.10, 11) in Germany (Barth, 1972; Abraham and Porzig, 1973). Details about the geology of the sites are given in the relevant publications: Veytaux was excavated in a fissured marl--limestone formation. The station lies in a direction perpendicular to the shore of the Lake of Geneva, a direction favourable to the stress pattern around the excavation. Fissures were found in three main directions, some being filled with clay or mylonite. Waldeck II is located deep inside arock mass formed of stratified mudstones with inclusions of graywacke (Lower Carboniferous). The more important characteristics of the stations are summarised in Table I. The Waldeck II underground power station (Fig.10, 11) has been analysed in detail in a remarkable paper by S. Barth, explaining his philosophy of the design of large structures in rock (Barth, 1972). The design of Waldeck II was developed assuming the rock characteristics to be "average". A detailed programme of measurements was worked out and during the construction rock conditions were checked with the greatest care. In case they were not as expected, alternative designs had been worked out in detail and possible reinforcements foreseen (Abraham and Porzig, 1973). The stability of the large rock vault of Waldeck II is assured by cables and it would have been easy to increase their number, reducing their spacing. The finite-element method and photoelastic model tests were used to follow the progress of the successive stages of the construction. This finite-element method analysis was carried out by Zienkiewicz and Cheung (1967) and their team. Miiller and his team (Baudendistel et al., 1970) have recently published some information on the finite-element method analysis of Waldeck II. Their publication shows how, assuming progressively weaker rock conditions, the calculated stress pattern and the deformation prove the increasing danger to the structure. Cable reinforcements were required there also. The approach to the Veytaux excavation, designed a few years before Waldeck II, and where the rock jointing is very different from that encountered at Waldeck II, was backed by extensive tests on photoelastic models, on the basis of a simplified finite~lement method approach. Local conditions along rock fissures were analysed with a method suggested by L. von Rabcewicz (Rescher, 1968; Von Rabcewicz, 1964). Both designers adopted the "New Austrian Tunnelling Method" (known as the N.A.T.M.) (Von Rabcewicz, 1964), where rock support is by cables. The method requires extensive checking of rock deformations during and after construction, and this was done. A total of 205 cables designed for 125 and 170 tons were used in the Veytaux excavation, the spacing being 2.90 × 4.30 m. For Waldeck II Barth (1972; Abraham and Porzig, 1973) used

347

'

I

~

I

I

I

Z o o

,.o

W

8

m

w~"

i

o

'

o

\ \ \

\ \

II

I I /2

I

IIIII1 o

Z

_o I,-

o °~

0 0

bJ ffl

i

6

^1 8 /

/

/

348

short cables, 4--6 m long, spacing 1.30 m, and designed for 12 tonnes. Long anchors, 23.50 m long, for 170 tons were spaced at 4 m. Barth used optical methods to check that there was no movement of the rock where the long anchors were cemented in the rock. Veytaux power station is equipped with horizontal-axis Pelton wheels, and it was n o t possible to streamline the cross-section of the cavity. With Francis turbines and pumps on the same vertical axis, streamlining of the Waldeck II power house was possible. The designs were made most carefully, combining finite-element method analysis and photoelastic model testing. The different stages of the excavations were equally analysed on photoelastic models. The importance of such research on intermediary construction stages is often overlooked. For Waldeck, some intermediary excavation stages showed concentrations of compression stresses as high as 900 kg/cm 2, far in excess of the rock-crushing strength, which could have caused irreversible damage to the rock. The shapes of the excavations were accordingly modified. Barth, discussing the general stability problems of large excavations, supports the views of Talobre (1957) and Von Rabcewicz (1965) on the plastic deformations of the rock masses and the necessity of providing immediate support to the deforming masses ( F i g . l i b ) . The N.A.T.M. has equally been used in Italy (Mantovani, 1970) and in many other countries (Fig.12).

Excavation o f a large cavity in a migmatic rock mass The Kariba North Bank underground power station (Fig.13, 14) Lecturing in Ziirich on the design and construction of the Innertkirchen underground power station, Dr. Keach, the designer, mentioned large deformations of the rock mass inside the cavity, of up to 20 cm. The excavation was in gneiss of good quality. At the time, (in the middle 1940s) this remark was n o t well understood. Engineers were mainly concerned with the poorer quality of sedimentary rock masses. Today many designers are more suspicious of migmatic rock masses, gneisses or gneiss complexes than of stratified, jointed sedimentary rock masses, where dangerous rock situations are more obvious. It had been known since the beginning of 1972 that major rock falls were occurring from the vault of Kariba North Bank underground machine hall during excavations. These falls were so severe that excavation work came to a standstill in the spring of that year and the circumstances finally caused the financial collapse of the contractor, the Mitchell Kinnear Moodie Group Holdings. Details a b o u t this collapse were amply discussed in several authoritative notes b y Lenssen (1973) in the New Civil Engineer, published in London (issues of 8, 15 and 22 February 1973). These notes several times mention an arbitration report unanimously signed by the three experts John Edney, chairman, John Knfll and Charles Jaeger, on 26 August, 1972. It is possible, based mainly on the facts disclosed by New Civil Engineer, to discuss

349

some technical aspects of this case, which is of great importance to the understanding of strained rock masses. The Consultant had been responsible for the design and construction of the impressive Kariba arch dam, the difficult consolidation work of the right or South Bank rock behind the dam a b u t m e n t and the no-less difficult excavation work of the South Bank underground power house. Compared to the conditions on the South Bank, the rock on the North Bank was qualified as excellent from the point of view of the design of the dam abutment. Fig.13, 14, taken from the New Civil Engineer, tell the story of the Kariba North Bank underground power house. In the contract documents the rock had been described as very good or excellent. Lenssen (1973), writing in New Civil Engineer, describes the case as follows: "Difficulties in the machine hall started mid-1971 with major rock falls from one to 25 tons occurring up to August last year. Two men have been killed and several injured. Most falls stem from the middle portion of the hall -- between chainage 32 m and 90 m -- just to one side of the crown in bolted and unbolted areas."

,,'',~ ~ . . ~. - ~ z " - -'. < . _ , t- ? ~ i

I~

. />(-' , , / , ,..47 .~

~ , " Z';,'T '~1/

r~ ,K... ,'

t

iI

I

I

k

~. Z-" /

¢~,,~,,",-'" / ";'"

/"

/"

~'~J~/,.

,'-'~" ~ /

r--~"

k I I

//

11

/ ~ ' / / /

/

/

//

//

/

/

/

/

-:_'_ . .._/ ...... Le..~h in which ¢ontroctor ~!ai~_k~k_ conditio°~

,~;~-.",~I ~

~'/

4f

3 0 - 4 0 m in - rock sound ond progress going well.

Fig.13. Kariba North Bank machine hall (from Lenssen, 1973). Diagrammatic view of the machine hall showing progress of work and rock-fall area.

35O

[ ] tnterbancleclse®ence s ""

chist bands

Fig.14. Rock profile of the dangerous half of the Machine Hall, as drawn by Dr. G. D. Matheson from the Zambian Geological Survey. This shows how the black bands of biotite schists fold round other rocks, leaving dangerous "noses". (From Lenssen, 1973.)

" T w o geological factors are blamed: the subhorizontal foliation providing a potential structural defect and continuous layers of biotite schist parallel to the foliation, providing a weak plane. According to Prof. R. N. Shackleton, on the site last July at Mitcheli's (the Contractor) request, the falls are due to biotite schist, thickened in the hinges of folds tending to fall out, fractures associated with faulting, and some weathering along joints." "According to Messrs J. D. Keppie, G. D. Matheson and S. Vrana of the Zambian Geological Survey, the biotite schist bands are potentially the weakest rocks in the area, and split very readily parallel to the schistosity." In his short summary of the detailed August 26 Report, Lenssen deals mainly with some problems of geology. The concentration of huge rock falls along a line very near to the crown of the rock vault, slightly on its south side -- and even from bolted areas -- is also a problem for the specialist in rock mechanics. The excavation is sub-parallel to the Zambesi Gorge and very near to it, at some places only 70 m measured in a direction perpendicular to the rock surface. Geologists describe the igneous rock as a "gneiss c o m p l e x " or "migmatite", where many different Wpes of gneiss rocks form a complex, distorted pattern. In addition, there is a very obvious main vertical jointing system, sub-parallel to the Gorge, cutting through the gneiss folds. This system of joints does n o t compare with the jointing observed in sedimentary rock masses and it can be assumed that the joints are of tectonic origin. This seems confirmed by some open cracks, a b o u t 0.30 m wide, which could be

351 observed at different levels, from the t o p of the rock surface, above the cavity, down to the lower levels of the pressure shafts, on the "mountain side" of the excavated cavity (on its north face). Dr. Matheson declares that he has observed similar cracks or "tension gashes" at different locations along the Zambesi River Valley. They can be explained b y the structural geology of the river: the river valley was formed b y subsidence, n o t b y erosion, and the area next to it was under tension. He concludes that the whole rock mass where the large cavity has been excavated is not under compression in a horizontal direction perpendicular t o the gorge. F r o m the point of view of rock mechanics, this decompression of the rock mass causes very unfavourable stress--strain patterns around the cavity. The stress pattern varies during the different stages of the excavation. Tensile stresses can develop at the soffit of the rock vault and become a cause for rock falls, even in bolted areas. Depending on the extension of the tensile areas, short rock bolts will not hold in areas damaged b y tensile stresses. The 3-m deep rock bolts used at Kariba were obviously t o o short. Tensile stresses which would n o t be dangerous in solid rock may be very much so in biotite schists. Commenting further on the August 26 Report, Lenssen writes: "It suggests that the 1 to 2 m thick concrete arch is a facing for the 50 to 100 m deep mass of rock deforming by creep around the excavation. Fissures on the concrete surface passing through the concrete mass are, according to the panel, the projected image of strains inside the rock mass. Further fissures found to be developing in August showed that the rock mass had n o t stabilized, although rock vaults of this size usually stabilize after one or t w o months. The appearance is that the Kariba rock is still deforming b y creep." (in August, 1972). It is worth while to turn back to the case history of the Heitersberg Tunnel and its thin concrete lining, with five hinged segments, deforming heavily under the pressure of plastic rock (or soil) masses. This example of Heitersberg was purposely chosen because the behaviour of this hinged lining explains some aspects of the behaviour of the fissured concrete at Kariba North Bank vault. In spite of fissures, the concrete vault is stable and the explanation given of it in the August R e p o r t is in line with what has been observed at Heitersberg. A concrete support, whatever its thickness, is n o t an arch -- free to deform radially -- b u t a lining which adheres, even if only partially, to the rock mass, transmitting shear forces, and following the general deformation of the rock mass. At the heart of the problems described in the t w o previous sections, there is an opposition of t w o techniques, t w o philosophies. In one case, based on experience of smaller excavations {railway tunnels, hydro-power tunnels, mines, etc.) it is assumed that a rigid concrete support -- concreted when the rock has already started deforming b y internal plasticity or ruptures -- will stand rock pressures and stop deformations. The other philosophy {backed b y Taiobre {1957), Von Rabcewicz (1965), Miiller (1964), Barth (1972) and Italian and Japanese designers, Mantovani {1970), Baudendistel et al. {1970))

352

assumes that an elastic support, shotcrete or cables or both, put in as soon as possible after blasting, will follow elastically the elastic or plastic deformations of the rock masses or of a large vault. The method, which has proved to be very efficient, requires checking of the deformations during the successive stages of the excavation.

Cleft-water pressure in rock pores, fissures and faults. Statics and dynamics The static pressure of cleft water in rock masses has to be considered for the overall stability of some engineering structures. Water circulation in fissures, as opposed to the pressure effect, is equally important (see for example the investigations for Kurobe IV dam, Japan) (Jaeger, 1972). Two major disasters occurring in recent years, the collapse of the Malpasset Dam and the rockslide of Vajont, were due to water-pressure effects. In both cases the way the water pressures were transmitted to rock, causing rupture and final disaster, were quite unsuspected at the time when the structures were designed. It took many years of research to discover the real mechanism of the rock collapse.

The Malpasset Dam collapse (France) (Jaeger, 1964a, b; Bernaix, 1967; Jaeger, 1972). The Malpasset Dam was a very thin arch dam. Its characteristics are given in Table II. TABLE II Characteristics of the Malpasset Dam, France Dam height Thickness at the top Thickness at the base Dam radius (upstream crest)

60.50 1.50 6.76 105.00

m m m m

The dam had been built on a gneiss rock foundation. It collapsed in the night of December 2 1959, before the reservoir had been filled to the top, causing the death of about 450 people in the little town of Fr~jus. An enquiry committee explained that the left abutment of the dam slid along an upwards.inclined slanting rock fault, located only a few metres below the dam's concrete foundation. The whole shell of the dam rotated around the right-hand abutment, the left end of the dam crest~aving moved tangentially by 2.11 m before final collapse. The dam had been correctly calculated, as the calculations were checked and rechecked after the collapse (Fig.15, 16). It took many years of research until an explanation for the collapse was found. Laboratory research carried out in France by Bernaix (1967), proved that the microfissured gneiss of Malpesset reacted very unfavourably to pore pressure. This was explained by the very fiat shape of the microfissures in the gneiss, whereas pore pressure in the rounded rock pores of an ordinary

353

darn section washed away

Fig.15. Plan of Malpasset Dam showing displacements. (From Jaeger,1972.)

o:~

ground level before darn ~ , i , u ~

' ,"',\

• ~

'" r~

"" ~ / - - - T 4 14 rn

T

"~.ground level after darn failu,~.~ r

'

Fig.16. Typical cross-section of Malpasset Dam near left-hand abutment after failure. (From Jaeger, 1972.) limestone, submitted to the Same series of tests, proved n o t to be dangerous. It was further explained that a deep rock fissure opened at the heel of the dam, transmitting the total hydrostatic pressure from the reservoir t o p d o w n to the level of the slanting fault. Detailed stability analyses were carried out, showing h o w the dam structure and foundations became unstable when full pressure was applied along the fault (Fig.17). It was further more discovered that before rotating round its right-hand abutment, the dam had a slight rotation around its crest (Fig.18), opening a thin crack along its heel, on the whole length of the foundation. This crack was the primary cause o f the collapse of the dam.

The Vajont rock slide It was cleft-water pressure in natural rock fissures which caused the gigantic rock slide along the slopes of m o u n t Toc, above the Vajont Gorge in the

354

(b) o

o

.o

.

i:;-:t

,,o

27 m

............

Fig.17. A typical cross-section through the left abutment of the Malpasset Dam. Stability of dam and foundations. (After Mary, 1968 and Jaeger, 1972.)

m t (b) 1001~

50

100 cm ~ (,',)

Fig.18. Displacement of fix points of Malpasset Dam. (a) displacements, (b) levels above the sea. Broken line: average displacements; solid line: central joint. (After Mary, 1968 and Jaeger, 1972.) Italian Alps. The r ock masses which came dow n the m o u n t a i n slope at tr emen d o u s velocity in the night of 9 October, 1963, filled the Vajont Reservoir, causing a giganfi c wave, 150- - 250 m high, t o spill over t h e arch dam o f Vajont and causing the de a t h o f over 2,400 people in t he little t ow n

355 of Longarone, a few miles downstream of the dam. The mechanism causing the unbalance of the gigantic rock masses (about 250.106 m 3 ) was a very complex rupture. The Vajont dam was n o t damaged and still stands as the highest arch darn in the world. Geologists investigating the possibility of a rock slide in the years 1960-1963 n o t e d the chair-like shape of the geological strata. At t h a t time the contact surface between Dogger and Maim was suspected as a possible slip surface. Detailed investigations by Broili (1967) indicated t h a t the slip surface was located slightly higher, cutting inside the Maim formation and not at the c o n t a c t with the Dogger. The slide, mainly rocky formations which, though strongly fractured, have maintained m a n y of their original morphological features, extended from the close vicinity o f the dam to as far as 1,800 m upstream. Evidence on the slopes of Mount Toc reached an elevation of 1400 m and extended as far as 1,600 m away from the shores of the lake. The rock slide swept 300--400 m across the deep gorge and rose more than 100--150 m on the opposite bank. The collapsed material consists of Lower Cretaceous and Maim limestone formations which slid over other underlying Malta and perhaps Dogger (according to a private report by Electroconsult, Milan, 1963) (Fig. 19, 20). The chair-like shape of the sliding surface has already been mentioned. The lower part of the rock mass, on the horizontal section of the sliding surface, was alone in plunging into the water and uplift forces were acting on it (Fig. 21). On the upper part of the slide, rock masses were resting on a steeply inclined surface, well above the water level. There is evidence that rupture started along this inclined section, well in advance of the final rupture and the higher-located rock masses were pressing with all their weight on the lowerlying masses, still anchored to the rock. Geologists described the slow move-

1300 1200 1100 1000

~3

gO0

"'~

8OO 700 6OO 5O0 40C

;SW

C

cl

-

NNE

Fig.19. Idealised geological section through the left bank of the Vajont gorge, a = Vajont gorge; b = north face of Mount Toc; c = Pozza; d = antithetic fractures; e ffifracturing due to external rotation; D ffi Dogger--Maim formation (Oolitic limestone); 1 ffiMaim; 2 = Upper Maim; 3--8 ffiLower Cretaceous; 6--8 ffiUpper Cretaceous. (After Broili, 1967 and Jaeger, 1972.)

356

m e n t o f the slide which lasted several years as visco plastic, until final rupt ure occurred by brittle fracture. The mo s t i m p o r t a n t d o c u m e n t we possess on this period is a diagram showing the correlation o f the water levels in the reservoir and the displacements o f the r o c k masses (Fig.22). Rising water levels caused an acceleration of the r o c k slide. Falling water levels brought the slide to a standstill, until final r u p tu r e occurred. Fig.21 shows a diagram o f forces which explains these movements o f the r o c k masses (Jaeger, 1969). Seismic-wave measurements were carried o u t in the slowly creeping rock masses at different periods. T h e y revealed a sharp drop in the wave velocities shortly before the final sudden r o c k rupture. It is believed t hat this d r o p in the wave velocity can be explained b y an increasing fracture o f t he rock masses which preceded th e final sudden brittle fracture along t he lower part o f the slide. On the night r u p t u r e occurred, earthquake waves were measured at a recording station, located a b o u t 50 km f r o m Vajont. The sudden brittle

1100

goc ~

~

'

~

"\~''%

( 37 mE)

• :

70C

\%'% %

•

5OC SSW

B- B

" / %" -0 ~r ~i I

\.~

o l

. , ' - , ' . ~ . ~-='"J

i I o l l o l 4 J J l ~ l ~ O l j v ~ J

NNE

Fig.20. Geological section through the slip surface; reconstruction on the basis of borehole results, a = topographical surface before the slide; b = topographical surface after the slide; c = reconstructed failure surface and slip surface; d = assumed faults; e = Pozza depression; 7 = borehole. (After Broili, 1967 and Jaeger, 1972.)

tan @1 Fig.21. Equilibrium con~litions of partly immersed rock mass sliding on a chair-shaped slip surface. (After Jaeger, 1969, 1972.)

357 710

700

I

s ~///

1961

1962

V'"

i 1963

Fig.22. Correlation between water levels (solid line) and rock displacements (broken line). (After Miiller, 1964 and Jaeger, 1972.)

fracture lasted 60 to 70 sec (rupture by shear). The duration of the slide was only 20 secs. This duration allows an estimate of the final velocity of the accelerating masses. The height of the wave of water spilling over the crest of the Vajont arch dam, which was 150 m on one side of the dam and 250 m on the other side, allows another estimate of this same velocity. The whole problem is one of fluid mechanics ruled by the theorem of m o m e n t u m . In these two examples, the stress conditions at any point of the rock mass could be represented on the general diagram (o, T) given at the beginning of this paper, provided the stresses are replaced by the "effective stresses" (as in soil mechanics). But in the two cases, the analysis of the forces acting on the whole structure is more i m p o r t a n t than the stress--strain pattern. FINAL REMARKS

The examples described in this paper correspond to different situations of rock masses, either compressed under their own weight or by residual stresses or stratified and jointed. One example illustrates the dangers of some migmatic rock masses which were classified as sound rock but which were not sound. Two examples analyse the effect of cleft-water pressure and uplift forces which changed the stability conditions of the structures and caused disaster. Other examples could have been given, describing different situations. In rock mechanics, there are no simple valid rules to follow. Any situation has to be analysed on first principles. Between engineering and geology, rock mechanics forms a necessary link. REFERENCES Abraham, K. H. and Porzig, R., 1973. Die Felsanker des Pumpspeicherwerkes Waldeck II, Baumachine Bautech., 20 (6,7): 209--220,273--285. Andraskay, E., and Schneebeli, R., 1972. Anwendung yon Stahlbetontiibbingen beim Heitersbergtunnel West. Betonwerk Fertigteiltech., Wiesbaden, 1(9). Andraskay, E., Hofmann, E. and Jemelka, P., 1972. Berechnung der Stahlbetontiibbingen fdr den Heitersbergtunnel, West. Schweiz. Bauzeit., ZUrich, 90(36). See also: Andraskay, E. and Schneebeli, R., 1972.

358 Barth, S., 1972. ~Felsmechanische Probleme beim Entwurf der Kaveme des Pumpspeicherwerkes Waldeck If. Bautechnik, 49(3). Baudendistel, M., Malina, I-L and MiiUer, L., 1970. The effect of the geologic structure on the stabilityof an underground powerhouse. Congr. Rock Mech., 2nd, Belgrade, 1970. Pap., 4/56. Bernaix, J., 1967. Etude G~otechnique de la Roche de Malpasset. Dunod, Paris. Broili, L., 1967. N e w knowledge on the geomorphology of the Vajont slide slip surface. Rock Mech. Eng. Geol., 5.1. Buro, M., 1970. Prestressed rock anchors and shotcrete for large underground powerhouses. Civil Eng., ASCE, M a y 1970. Dodds, R. K., 1966. Measurements and analysis of rock physical properties of the Dez project. A S T M Publ., 31. Dubertret, L., 1971. Report on Kariba North Bank exoavation for the underground powerhouse as seen in November 1971 (manuscr.). Fumagalli, E., 1966. Equilibrio geomecanico del banco di sottofondazione alladigha del Pertusillo.Tunnels Tunneling, 2(1,2). Gibb, Coyne and Sogei, 1961. The Kariba d a m abutment investigations.Rhod. Eng., January 1962. Jaeger, C., 1955. Present trends in the design of pressure tunnels and shafts for underground hydro-electric power stations, I. Proc. Inst. Civil Eng., March 1955. Correspondence on a paper. Proc. Inst. Civil Eng., July 1955. Jaeger, C., 1964a. Rock mechanics for d a m foundations. Civil Eng., 59. Jaeger, C., 1964b. Rock mechanics and d a m design. Water Power, 16:210--217. Jaeger, C., 1969. The stabilityof partly-immersed fissured rock masses, and the Vajont rock slide.Civil Eng., 64: 1204--1207. Jaeger, C., 1972. Rock mechanics and Engineering. Cambridge University Press, London, 417 pp. Kastner, H., 1962. Statik des Tunnel- und StoUenbaues. Springer, Berlin. Keppie, J. D., Matheson, G. D. and Vrana, S., 1972. Interim Report on the Geology of the Kariba North Bank Project. Geol. Surv. Zambia, M a y 1972. Knill, J. L. and Jones, K. S., 1965. The recording and interpretation of geological conditions in the foundation of the Roseires, Kariba, and Latiyan dams. G~otechnique, 15(1). Lane, R. G. T. and Roff, J. W., 1961. Kariba underground works, design and construction methods. Congr. Large Dams, 7th, Rome, 1961, Pap. R.16. Lenssen, S., 1973. Kariba rock sinks Mitchell. The story of Borehole 4, Kariba North. N e w Civil Eng, February 1973. Lombardi, G., 1970. The influence of rock characteristicson the stabilityof rock cavities. Tunnels Tunneling, 2(1,2). Mantovani, E., 1970. Method for supporting very high rock walls in underground power stations. Congr. Rock Mech., 2nd, Belgrade, 1970, Pap. 6/5. Mary, M., 1968. Barrafues--vofltes.Historique, Accidents et Incidents. Dunod, Paris, 159 pp. Matheson, G. D., 1971. Report on a Visit to the Kariba North Bank Project. Geol. Surv. Zambia, June 1971 (manuscr.). Miiller, L., 1964. The rockslide in the Vajont valley.Rock Mech. Eng. Geol., 2: 148--212. Olivier, H., 1961. S o m e aspects relatingto the civilengineering construction of the Kariba hydro-electric scheme. Siviele Ing., S. Afr., April 1961. Peck, R. B., 1962. Advantages and limitations of the observational method. Applied soil mechanics. G~otechnique, 19(2). Rescher, O. J., 1968. Am~nagement Hongrin-L~man. Sout~nement de la centrale en caverne de Veytaux par tirantsen rocher et b~ton projet& Bull. Tech. Suisse Romande, 94:249--280. Talobre, J., 1957. La Mdcanique des Roches. Dunod, Paris. Von Rabcewicz, L., 1964--65. The new Australian tunneling method. Water Power, 16 (1964), 17 (1965). Zienkiewicz, O. C. and Cheung, Y. K., 1967. The Finite Element Method in Structural and Continuum Mechanics. McGraw Hill, London, 288 pp.