• Int . J . Rdck Mech . Min. Sci. & Geomech, Abstr . Vol. 15, pp. 237-247. Pergamon Press 1978. Printed in Great Britain

Determining Rock Mass Deformability: Experience from Case Histories Z. T. BIENIAWSKI*

This paper discusses the results of extensive in-situ rock deformability tests conducted on three major engineering projects in South Africa: the Orange River Water Project, the Drakensberg Pumped Storage Scheme and the Elandsberg Pumped Storage Scheme. These projects featured testing pro- grammes involving many different methods, thus enabling comparisons and assessments of the reliability of the various in-situ tests. A review is also presented of the in-situ deformability data ,from those important projects throughout the world which are well documented. It is shown that in-situ tests pose a number of uncertainties even for rock mechanics specialists and a new approach to assessing rock mass deformability based on the Geome- chanics Classification of rock masses is suggested.

I N T R O D U C T I O N

Deformability is recognised as one of the most impor- tant parameters governing the behaviour of rock mas- ses [1 4]. In fact, Miiller [5] suggested over ten years ago that deformation rather than stress be used as a basis for a stability assessment of rock masses. The advantage of this approach is obvious since deforma- tion can be measured directly while stress being a ficti- tious physical quantity cannot be observed or measured; it can only be deduced from measurements of its effects, i.e. strain or deformation.

Deformability is characterised by a modulus describ- ing the relationship between the applied load and the resulting deformation. The fact that jointed rock masses do not behave elastically has prompted the usage of the term modulus of deformation rather than modulus of elasticity or Young's modulus. The Commission of Terminology of ISRM? published the following defini- tions [6]:

Modulus of deformation: the ratio of stress to corre- sponding strain during loading of a rock mass in- cluding elastic and inelastic behaviour;

Modulus of elasiicity or Young's modulus: the ratio of stress to corresponding strain below the propor- tionality limit of a material.

Since rock masses are discontinua, tests conducted on small rock specimens in the laboratory generally do not yield the deformability data which would be directly applicable to the whole rock mass from wldich the specimens were taken. A specimen is usually a con- tinuous structure or approaches such a state for practi-

* Professor of Mineral Engineering, Pennsylvania State University, 104 Mineral Sciences Building, University Park, PA 16802, U.S.A.

+ ISRM, International Society for Rock Mechanics.

cal purposes. The smaller the specimen the fewer the discontinuities present and hence a smaller specimen may be expected to have a higher modulus and strength than a large specimen.

As there is no reliable method of predicting the over- all deformation data of a rock mass from the results of laboratory tests on small specimens, in-situ tests on large specimens are necessary. Such tests also have the advantage that the rock specimen is tested under the same environmental conditions as are prevailing in the rock mass.

Consequently, although in-situ tests are expensive and time consuming, they have been employed throughout the world on most major rock engineering projects. Yet, there are a number of controversial ques- tions pertinent to in-situ tests. One can argue, for example, as to whether the interpretation of the measured in-situ data is at best an estimation, open to criticism and thus not justifying the high expendi- ture, or whether the in-situ tests are truly necessary and should not be replaced by less costly approaches. Very few projects to date have featured a sufficient number of different tests to allow a meaningful com- parison of in-situ test data. The available information is listed in Table 1.

There are many types of in-situ tests: compression tests [7], shear tests [8], plate-bearing tests [9, I0], flat jack tes ts- -both small [11] and large [12-14], radial press tests [15], pressure chamber tests [16], borehole jacking [17, 18] or dilatometer tests [19] and 'petite sis- mique' geophysical tests [20,21]. This paper is limited to those static in-situ tests which are specifically rele- vant to the determination of the modulus of deforma- tion. Hence, compression tests and shear tests, which are fully discussed elsewhere [7,8], are not dealt with here. Furthermore, radial press tests and pressure

237

. 238 Z. T. Bieniawski

TABLE 1. COMPARISON OF DEFORMABILITY MODULUS FROM IMPORTANT PROJECIS

Case Name of project, reference, No. rock type and date

In-situ modulus, Laboratory modulus, Type of No. of GPa GPa

in-situ test tests Range Mean Range Mean Remarks

1 Oroville Dam [23] Massive amphibolite 1961

2 Tumut 2 [11] Gneiss/granite 1962

3 Poatina [43] Mudstone 1965

4 Dworshak Dam [17,18] Massive granite gneiss 1966

Tehachapi Tunnel [ 17,18] Fractured diorite gneiss 1967

Crestmore Mine [17,18] Massive marble 1968

7 Turlough Hill [42] Granite 1969

8 Lake Delio [44] Gneiss 1970

Plate bearing 5 8,3-12.4 10.4 74.5- 105.0 Tunnel relaxation 22 4.1 51.7 17.9 Flat jacks 30 9.7-113.5 51.8

Plate bearing 6 1.8-52,0 6.9 41.5-86.1 Tunnel relaxation 3 11.0 Flat jacks 6 34.5-83.0 57.5 Pressure chamber 2 13.8-20.6 17 7 Flat jacks ? 16.6-22.1 20.6 31.0-45.0

Plate bearing 24 3.5~-34.5 23.5 Goodman jack G 14 11.6-18.6 14.5

S 16.5-36.4 23.6 H 42.8-74.5 53.5

Plate bearing 4 3.5-5.5 4.8 - Goodman jack G 4 4.1-7.1 5.8

S 3.5-7.9 5.8 H 15.9- 26.9 22.5

Plate bearing 2 12.0-18.7 15.0 - Flat jacks 12.4-20.5 12.4 Goodman jack G 9.3- 11.7 10.4

S 11.7-17.0 14.0 H 36.5 46.2 40.9

Large fiat jacks 4 9.6 40.2 29 .2 8.0-20.2

Plate bearing 12 7.5--20.4 9.5 15.0--32.4 Pressure chamber 20 9.7-26.2 18,2

9 Gordon Scheme [45] Plate bearing 8 - 19.0 38.0--91.0 Quartzite Dilatometer 2 25.0 1971 Tunnel relaxation 10 25.0

Flat jacks 16 28.0-96.0 58.0

10 Churchill Falls [46] Plate bearing 10 34.5-48.2 41.5 45.0-75.0 Massive gneiss 1972

11 Waldeck II [47] Plate bearing ? 3.0--7.0 5.0 Greywacke Radial press 4.5-10.0 - 1973 Tunnel relaxation --- 15.0

12 Mica Project [48] Plate bearing 12 8.3-48.3 27.6 24.5-32.0 27.0 Quartzite gneiss Flat jacks 19 - 28.8 1974 Goodman jack 132 - - 16.6

13 Channel Tunnel [41] Plate bearing ? 2.03-3.41 2.4 0.4441.91 0.7 Chalk 1975

14 LG-2 Project [49] Plate bearing '? 38.0~ 60.9 50.0 Massive granite 1976

15 Dinorwic [40] Flat jacks 8 Slate RQD index -- 50.0 1977

$9.0 Wide scatter in fiat jack results yet rock uniform

59.1 Large scattex in plate bearing results 30:t

34.5

51.7 G = original results by Goodman [17]

77.9 S = corrected by Heuze and

Salem [18]

47.5 H :: same data recalculated by Hustrulid [24]

15.0

28.5 From 19661 to 1973, at the Witbank-- Breyten coalfields,

67.0 S.A., 44large scale in-situ tests were conducted on coal pillars in compres- sion [7]. These tests

55.0 gave the in-situ modulus E u = 4.0 GPa (2.9-5.0 GPa)

20.0 while the laboratory modulus of the coal was EL = 5.2 GPa (4.6-6A GPa)

8010

75.0-140.0 105.0 Fla! jack tests unsuccessful

chamber tests are also excluded because they are used only in special circumstances [15].

I N T E R P R E T A T I O N OF IN-SIT U DEFORMABILITY DATA

It is clear from Table 1 that selecting a modulus of deformation for design purposes, and a method for determining that modulus, is not an easy decision. Usually, the lowest and hence the most conservative value is chosen, but in such a case one may doubt the necessity of conducting the expensive in-situ tests

in the first place. In addition, there are uncertainties associated with all the in-situ tests listed in Table 1 so that the field is not without problems.

To illustrate the uncertainties one need only consider the plate-bearing test which is by far the most common type of in-situ test used in rock mechanics. Few major projects such as underground powerhouses, large dams or important tunnels have been constructed without their use. The test simply involves applying a load to a rock surface, by means of hydraulic jacks or fiat jacks. and measuring the resultant deformations. The test appears deceptively easy in principle but the interpre-

Determining Rock Mass Deformability 239.

3 2 1.5 50

4O :30 1.5

2 2O

3

~ 5

o ~

2

2 3 4 5 I0 ' 20 30 40 50 Modu lus ER , GPa

5 2 1.5 5O

°o f i EB 1.5 30 2 no zo 3

~_ EB ° .

ud IO

~ 4 3

2

I I I i I 2 3 4 5 IO 20 50 40 50

Modu lus EB, GPo

Grani te ° I Before Grani te : 1 A f t e r Shale Dprou t inc j Shale I I g r°u t ing Quartz i te Quar tz i te

Fig. 1. ln-situ modulus of deformation data from plate bearing tests, after Rocha and da Silva [4].

tation of the results is affected by many factors and it is not uncommon that considerable confusion can arise on the meaning of the results [9].

In this respect one may quote from Rocha and da Silva [4] who state that " . . . the current plate-bearing test method yields results whose significance is often difficult or impossible to assess". They say that this was confirmed in more than 500 such in-situ tests con- ducted by the Laboratorio Nacional de Engenharia Civil (LNEC), in spite of the loading area being 1 m 2 which was larger than the size usually adopted. Figure 1 demonstrates the difficulties met by Roch and da Silva in the interpretion of the results. Two values of the modulus of deformation were obtained from each horizontal and vertical plate-bearing test and the data obtained by loading the opposite faces should, of course, be comparable. Figure 1 shows data from 118 horizontal tests, while Fig. lb shows the data from 130 vertical tests. It will be seen that the scatter of the results is very marked although the tested surfaces were at a distance of not more than 3m. As will be seen from Fig. 1 about 30% of the points correspond to the ratios of more than 2 between the deformation moduli obtained on the opposite faces and for 14~o of the points this ratio exceeds 3. Surely, the properties

of the rock did not differ so much in a small and care- fully chosen region of 3 m width. The data must have been influenced by the test method.

In fact, Dodds and Schroeder [22] have recently listed no less than six factors affecting plate-bearing test resultsithis for a test that is supposed to be 'the best understood'!

Other commonly-used tests also suffer from similar uncertainties. For example, the large flat jack test [4] suffers from considerable theoretical uncertainties as experienced by Deklotz and Boisen [12] and by Vogler et al. [13]. The theoretical solution for the results of the popular small flat jack test [11,50] is limited to flat jacks of square shape and openings of this shape are difficult to produce reliably in the field. This usually leads to high values of the modulus of deformation and a wide scatter in the results even where the rock mass is very uniform [23].

Borehole tests, such as the dilatometer [19] test or the Goodman jack [17] test also have their problems. Rocha [19] does not believe that the dilatometer is re- liable because it tests too small a volume of the rock and induces tensile stresses in the borehole, resulting in the modulus values being 2-3 times lower than the in-situ values determined by the plate-bearing test. The Goodman jack [17] is a much more practical instru- ment but there is controversy today [18,24,25] over whether it is the contact angle between the loading platen and the borehole surface or the stiffness ratio of the platen material (steel) to that of the rock which necessitates a correction to the results. Depending on which correction is chosen, the difference in the results can be significant (see Table 1, cases 4, 5 and 6).

Finally, the 'petite sismique' method [20], although appearing to hold great promise, has seldom been used to date and still requires a thorough assessment [21].

It is obvious that what is called for is a systematic evaluation and comparison of the various techniques with the aim of providing some general guidelines for future use. Accordingly, the following case histories constitute an attempt to provide some answers derived from three major South African projects, each featuring a number of in-situ deformability tests. These case his- tories are the Orange River Project, the Drakensberg Scheme and the Elandsberg Scheme.

CASE HISTORY 1: O R A N G E R I V E R P R O J E C T

The Orange River Project is a large water scheme aimed at harnessing the Orange River in South Africa primarily for irrigation purposes. The main works of this project comprise the 90 m high Hendrik Verwoerd Dam as a main storage dam with a reservoir shoreline of over 500 km irrigating 9000 farms, the P.K. le Roux Dam with the 240MW Van Der Kloof powerhouse, the 82 km long Orange-Fish Tunnel and an extensive canal system. The Hendrik Verwoerd Dam was com- pleted in 1972, the Orange-Fish Tunnel in 1975, the

240 Z.T. Bieniawski

3c • / z~' , f

n ° • Si l ty mudstones ~ ¢ " A (.9 • Muddy siltstones (3

; o Sandstones Ld •

• ~.,0" • , / ' •

A * ' " "

3 ~ °

I ' A • • • 'k .o .

"~' ~ i I ' ' I l I 0 5 IO 15 2 0 25 3 0

Lob•ro tary modulus of deformation EL, GPo

I 3 5 4 0

Fig. 2. Comparison of in-situ and laboratory moduli of deformation determined at the Orange-Fish Tunnel, after Olivier [27].

P.K. le Roux Dam and its powerhouse in 1977, while the rest of the scheme is still under construction.

In view of the importance of the Orange River Pro- ject, extensive site investigations were conducted 1-26] for the two dams (both founded entirely on dolerite) and for the Orange-Fish Tunnel (constructed predomi- nantly in horizontally bedded mudstones)1-27].

For the Verwoerd Dam, the site investigations in- cluded [26] drilling over 10,000 m of core and excavat- ing many trenches, pits and test adits. The rock mass was sound dolerite of a very good quality (RQD > 80%), highly homogeneous and showing little weathering. Horizontal foliation was the predominant feature~spacing 1-1.7 m--with some vertical jointing spaced 8-10 m apart. The joints were of excellent condi- tion and there was a very slight inflow of water. This rock mass was classified in accordance with the Geo- mechanics Classification [28], ranging in quality from upper class II (good rock)--rating 75, to class I (very good rock)---rating 85.

Laboratory tests gave the average uniaxial compres- sive strength of dolerite as 310 MPa with the modulus of elasticity of 72.4 GPa (ranging from 63.4 to 77.2

GPa). ln-situ tests were conducted in 5 test adits and in-

cluded 18 plate-bearing tests (11 horizontal and 7 verti- cal) of which 8 were in dolerite and 10 in shale). In addition, two pressure chamber tests were conducted which included tunnel relaxation measurements. For the first time in South Africa, the 'petite sismique' method [20] was employed with which 40 profiles were made. However, no stress measurements were con-

ducted. For the le Roux Dam [26,29], located 130km down-

stream of the Verwoerd Dam, 250 bar•holes were drilled with a total length of core of 11,750 m. In addi- tion, four test adits were constructed, varying from 60 to 200 m in length, and one shaft. The RQD of the rock was 100% and although the dolerite was even less weathered than that at the Verwoerd Dam, the joints were continuous and filled with gouge. The rock

mass [30] had a Geomechanics Classitication rating o!

71, class II--good rock. ln-situ tests included t5 plate- bearing tests in the dolerite (10 horizontal and 5 verti- cal). No stress measurements were conducted.

The 82 km long Orange-Fish Tunnel, the longest corJ- tinuous tunnel in the world, is located in horizontally- bedded mudstones, siltstones and sandstones with occa- sional dolerite intrusions. The rock masses in the tunnel varied considerably in their quality, having the Geo- mechanics Classification rock mass rating RMR = 41 70. ln-situ deformability tests [26] included three pressure chamber tests and 20 plate-bearing tests the results of which are plotted in Figs. 2 and 3. Extensive stress measurements were conducted at 18 localities along the tunnel involving 38 measurements with the ('SIR triax- ial strain cell. The results showed that the horizontal stresses were greater than the vertical stresses in all sections of the tunnel, the ratio OH~dr varying between 1.0 to 2.6 with an average of i.84. It was ;also found that the measured vertical stress was smaller than the calculated overburden stress by a factor of 2 to 3~

The results of all the tests from the three sites are summarised in Table 2.

CASE HISTORY 2: DRAKENSBERG SCHEME

The Drakensberg Pumped Storage Scheme, a 1000 MW power facility currently being constructed 1,16] for the Electricity Supply Commission (ESCOM) featured a rock mechanics feasibility study 1,31] as well as in-situ rock stress measurements and plate-bearing tests 1-32]. In addition, as a part of the research pro- gramme, other investigations such as 'petite sismique', geomechanics rock mass classification and rock modulus laboratory tests were conducted 1,33].

50

~. ,4o / / 1 : I

- , I / []

- / I O / 0 Ver t i ca l 15 / / ~ f " ~ Hor izonta l

/ " ' i t~ Hor izonta l

/ / / . . . o . . . .

6 ; I / . . i ' " / 1 : 4

V L . . . - . . . o _ _ - - . !

5 I0 15 20 25 30 M o d u l i E e o n d ER, GPo

ET" Modu lus in roof E B = Modu lus in f loor EL= Modulus =n le f t wall ER= Modulus in r i gh t wal l

Fig. 3. Comparison of in-situ deformability data from plate bearing tests at opposite faces of test adits at the Orange--Fish Tunnel [27].

Determining Rock Mass Deformability

TABLE 2. DEFORMABILITY DATA FROM THE ORANGE RIVER PROJECT

241

Name of site Rock type

ln-situ modulus of deformation, G P a Plate Pressure Petite Ratio*

bearing chamber Relaxation sismique EM/EL

Hendrik Dolerite

Verwoerd Dam Shale

P.K. le Roux Dolerite Dam

O r a n g ~ Muds tone Fish Siltstone Tunnel Sandstone

25.5 - 31.7 23.5 26.5 28.1 0.36 (17.1-37.6) 21.5

12.8 I __ 12.1 0.40

26.0 22.0 31.8 26.5 0.30

(18.6-40.6)

Ev~,. = 13.0 _+6.5

EHor. = 17.8 +8.3

10.0 - - 0.70

* EM, in-situ determined modu lus of deformation of the rock mass, in GPa. E L, laboratory determined modulus of the rock material at 50% of the uniaxial strength, in GPa.

The rock strata within the site area consists of hori- zontally-bedded mudstones, siltstones and sandstones. The test sites were located in the underground explora- tory tunnels shown in Fig. 4. There was one test niche in the main adit (for preliminary testing of the equip- ment), three niches in the machine hall test enlargement and six in the plate bearing test adit. All were excavated in unweathered interbedded siltstone with near hori- zontal bedding closely spaced. Some minor jointing was also evident but no groundwater inflow was observed. The R Q D of the core was 80-100%, while the rock mass had an overall Geomechanics Classification [28] rating RMR = 46-55, i.e. class III (fair rock). The rock mass in the machine hall pilot heading (four test sites) contains fine grained sandstone in addition to interbed- ded siltstone. This improved the RMR rating which ranged from 62 to 67, i.e. class II (good rock).

The 30 rock stress measurements [33] using the CSIR triaxial cell showed that the average horizontal stress component was twice the vertical component, but back analysis of the convergence measurements in exploratory excavations [34] showed this ratio to be approximately three (a n = 12 MPa and av = 4 MPa). The measured vertical stress component was slightly greater than the calculated overburden pressure.

The plate-bearing tests involved five vertical tests (in- cluding one preliminary test), six horizontal tests and three in the 45 ° direction. Displacements were measured on one side of the test adit by triple-point extensometers anchored in one borehole typically at positions 0.3m, l m and 6 m from the rock surface. The loaded area was 0.5 m 2 and the maximum loading capacity was 9.0MPa. The adit cross-section was mainly 2.5 x 2.5 m and the modulus values were cor- rected to allow for the confining effect of the adit using the three-dimensional boundary integral equation method [16]. Cores recovered from the extensometer boreholes at the plate-bearing test sites were used for determining the RQD index and for laboratory tests to establish their strength and deformability in uniaxial compression.

In each plate-bearing test, up to four cycles were per- formed in a two-day operation after which, in the fifth

cycle, the load was kept constant at the maximum load for 12 h and then the test was concluded.

The results showed that the average modulus in the vertical direction (normal to the bedding planes) was 18.3 GPa, while the modulus in the horizontal direction (parallel to the bedding planes) was 25.0 GPa. The average laboratory determined values of the modulus from 21 tests were 19.4 G P a and 28.5 GPa, respectively. The in-situ tests at 45 ° yielded the average modulus of 23.4 G P a which was in between the values obtained from the vertical and horizontal tests.

'Petite sismique' geophysical profiles--32 shear wave traverses--gave a shear wave frequency range from 294 to 714 Hz, corresponding to a static in-situ modulus of deformation between 7.0 to 28.3 GPa with an aver- age of 14.1 GPa.

CASE HISTORY 3: ELA N D S BERG SCHEME

The 1000 M~W Eiandsberg Pumped Storage Scheme [35] featured extensive exploratory tunnels in which wide ranging in-situ rock mechanics tests were conducted. The main reason for these investigations was that the 22 m span envisaged for the main under- ground cavern (197 m long and 47 m high) fell outside the limits of accumulated experience in South Africa for the rock mass conditions expected at Elandsberg.

Test enlargement Machine hall

odii ~ ~ ~S

Explorotory adit

$

1@ ~ J~ ; S Test

heading

/ N /

t I o ioo m S-Boreholes for

stress measurements

Fig. 4. Layout of exploratory excavation at the Drakensberg scheme.

242 Z.T. Bieniawski

The powerhouse complex of the scheme is to be situ- ated in greywacke (RQD = 75-859/o) which includes minor amounts of phyltite (RQD = 65-70~/o). Bedding foliation is near vertical striking parallel to the long axis of the cavern and this represents the main jointing feature of the scheme. Two further joint sets can be identified in addition to minor faulting. Water inflows of between 70 to 250 l./min have been recorded in the exploratory adit. In 1969, an earthquake with a recorded magnitude of 6.3 on the Richter scale occurred 15 km from the site, while in 1977 an earth- quake of 5.0 magnitude was recorded in the same area.

Design investigations for this scheme included exten- sive geological investigations, rock mechanics testing in the exploratory tunnels and enlargements [36,37] and finite element analyses for the spacing and shape of the caverns. This program was accompanied by

detailed laboratory tests which aimed at providing, where possible, a correlation between the laboratory and the in-situ data [33].

The in-situ tests had four objects: (i) state of stress in the rock mass before and after excavation; (ii) rock mass deformability characteristics; (iii) rock mass per- meability using a network of piezometers; and (iv) em- pirical data for rock reinforcement using convergence measurements, borehole extensometers, monitoring rockbolts and Gliitzl cells. The layout of the in-situ tests conducted in the exploratory tunnels at Elands- berg is shown in Fig. 5.

In addition to all these tests the Geomechanics Classification [28] was used throughout the works to

assess rock mass conditions. It was found that the greywacke rock mass was predominantly of class II (good rock) having a rock mass rating RMR = 66-80. The phyllite rock mass was of class III (fair rock) with RMR = 43-60.

The 23 in-situ stress measurements (13 triaxial cells, 10 small fiat jacks) showed that the horizontal stresses are between 0.7 and 1.5 times the vertical stress, which in turn is about twice the calculated over-burden pres- sure.

In order to determine the in-situ modulus of defor- mation for the greywacke and phyllite rock masses and to fulfill the primary engineering requirements of the client, two testing methods were used, namely, plate- bearing tests and small fiat jacks. With the agreement of the client, a further five different testing methods were applied, thereby fulfilling a research objective which accompanied this project. This was to assess the reliability, convenience and economics of each method and to check whether a correlation between all the results obtained could be established. Thus, in addition to those methods which were dictated by the practical engineering requirements for the scheme, the Elands- berg project also served as an in-situ laboratory for trying out a variety of techniques.

The methods employed were: (1) plate-bearing tests; (2) small fiat jack tests; (3) large fiat jack tests: (4) Goodman jack tests; (5) tunnel relaxation measure- ments; (6) 'petite sismique' geophysics; and (7) quality

G G

SM !i G G s M G

LFj* T SM |I

ZONES ' " ISM SM

0 50 I00 m Fig. 5. Layout of exploratory excavations at the Elandsberg scheme: PBT, plate-bearing tests; SFJ, small flat jacks; LFJ, large fiat jacks; GJ, Goodman jack tests; PS, 'petite sismique" surveys; SM, stress

measurements; RB, tests on rockbolts; G, geological drilling.

index assessments (geomechanics rock mass classifica- tion) of the modulus reduction ratio (in-situ modulus to laboratory modulus).

The principles of these methods are fully described elsewhere: plate-bearing tests by Dodds [9] and Mis- terek et al. [10]; small flat jack tests by Alexander E11], Wareham [50] and van Heerden et al. [37], large fiat jack tests by Rocha [4] and Vogter et al.[I31; Good- man jack tests by Goodman et al. [17], Heuze and Salem[18] and Hustrulid[24], tunnel relaxation measurements by Kruse[38]; 'petite sismique' by Schneider [20] and Hoek and Londe [21]; rock mass classifications by Bieniawski [28].

A special feature of the plate-bearing tests at Elands- berg was that the test niches were much larger than those at Drakensberg. The dimensions were 6 x 4 m normal to the direction of loading and 2.5m in the

' direction of loading. The large size of the test niches was selected to meet the theoretical requirement [8] that the nearest rock wall normal to the loaded surface should be about five radii of the loaded area away from it.

In the case of the Goodman jack tests at Elandsberg, the modulus so obtained was corrected for the stiffness

,ratio (Erock/Esteei) effect in accordance with a three- dimensional finite element analysis conducted by Heuze and Salem [18].

Since the reader may not be fully familiar with the 'petite sismique' method, more information on this technique is given in the Appendix.

The results from the Elandsberg tests are summarised in Table 3.

AN APPROACH TO ASSESSING I N - S I T U DEFORMABILITY OF ROCK ~ E S

The three case histories confirmed that there are in- deed some uncertainties in all of the in-situ tests employed. Nevertheless, it was also found that provided one does not rely on any one method alone but that two or more methods are used to cross-check the results, in-situ tests can form ~ reliable and essential basis for assessing rock mass deformability. The need

Determining Rock Mass Deformability

TABLE 3. DEFORMABILITY TESTS AT ELANDSBERG

243

No. of Modulus of deformation, GPa Rock type Method tests Range Mean Std. dev. Remarks

Plate bearing 27.1-58.3 39.6 17.2 Vertical tests 12 42.0-57.6 48.9 1 7 . 1 Horizontal E W (fracture zone is (33 results) 29.7-59.4 38.6 10.9 Horizontal N-S lower limit, solid zone upper limit) 34.2-58.2 44.0 13.3 Average

G Small fiat jacks 10 31.7-63.9 45.5 9.4 Semi-circular jacks (37 results)

r Large flat jacks 3 34.0-56.0 42.2 8.9 e Goodman jack 39 17.3-35.3 28.4 11.6 Using Heuze and Salem [18] y correction w Tunnel relaxation 23 38.7-48.4 42.5 18.2 From convergence a measurements c Petite 43 15.5M3.1 26.0 11.6 Dynamic modulus k sismique 30.6-91.2 GPa e (Average: 65.0 GPa)

Quality R Q D 34 11.4-76.9 35.5 24.4 RQD = 75-8506, indices Geomech 45 35.2 68.8 41.3 8.4 RMR: 66-80 All in-situ tests 40.1 14.1 EM/EL = 0.59 Laboratory tests 32 66.9-77.9 73.4 3.8 (0.47-0.79)

Small fiat jacks 9 25.2~,7.9 33.7 6.9 Semi-circular jacks P Goodman jack 6 6.0-20.0 12.0 6.2 h Tunnel relaxation 4 9.7 39.6 20.0 13.4 From convergence y measurements 1 Petite sismique 25 12.3-21.5 15.4 4.6 1 Quality R Q D 5 8.4-19.6 11.2 5.4 RQD = 65-70°~ i indices Geomech 7 15.1-22.4 20.1 2.6 RMR = 43 60 t All in-situ tests 18.7 6.5 E~a/E L = 0.33 e Laboratory tests 3 46.0-69.0 56.0 11.9

for cross-checking the results becomes apparent when one considers the large scatter in the in-situ data obtained (see Table 3). The choice of the design value for the in-situ modulus of deformation then becomes a matter of engineering judgment and this can present some problems unless a cross-check on the in-situ test results is possible.

It is believed that what is needed is a systematic and integrated approach to field investigations instead of conducting in-situ tests for the sake of conformity with other projects.

The recommended guidelines, which have emerged from the three case histories discussed, are as follows:

Firstly, a detailed engineering geological assessment of the rock mass conditions is required which should be expressed in quantitative terms by an engineering classification of the rock masses encountered.

Secondly, at least two different types of in-situ tests should be selected and a sufficient number of the tests conducted to determine in-situ rock mass deformability in the representative structural regions of the rock masses. For this purpose, the plate-bearing test and the Goodman jack test are recommended.

Thirdly, the stress field should be established in the test areas concerned by means of either an overcoring technique or small flat jacks. This last method would also provide an additional check on rock mass defor- mability. Stress measurements are necessary for the in- terpretation of in-situ deformability results because the

* RQD, rock quality designation which is a modified core recovery including only the pieces of sound rock 100 mm or longer.

stress field was found to be one of the most important factors affecting plate-bearing tests [22].

Fourthly, since in-situ tests are performed at a few localities only, seismic velocity geophysical surveys should be conducted to determine the continuity of the rock mass conditions throughout the area of the pro- posed engineering project. The 'petite sismique' tech- nique (see Appendix) would provide a check on the static in-situ modulus of deformation as well as a check on the quality of the rock mass by comparing the field seismic velocity with the sonic velocity of intact rock tested in the laboratory.

Fifthly, diamond drilling of good quality core of NX size (54 mm diameter) must be undertaken at the plate bearing and other test sites so that the RQD* can be established and samples can be selected for laboratory tests to determine the static modulus and the sonic vel- ocity for intact rock specimens.

Before elaborating any further on these five items, it must be pointed out--should the argument be advanced that the above philosophy of approach is too expensive--that the overall costs of the extensive in-situ tests at the Elandsberg Scheme were less than 1~o of the cost of the project.

While items 2-5 above are of about equal importance for the interpretation of in-situ deformability data and do not require further explanation, the very first item is of such crucial importance in the planning and locat- ing of the in-situ tests that it calls for special attention.

The reason for this statement is that a quantitative engineering classification of rock masses is understood to be a classification which can provide a preliminary

244 Z.T. Bieniawski

estimate of the possible in-situ rock mass deformability. Knowing whether a high or a low in-situ modulus of deformation is to be expected, such an assessment by a classification will enable a decision to be taken as to the number of in-situ tests needed, their frequency and the type of tests suitable for cross-checking the results. For example, if a high modulus is expected (25-30 GPa or more) and the rock conditions are fairly uniform, only a few in-situ tests will be needed. On the other hand, for rock masses with a modulus of 10 GPa or less a much more comprehensive in-situ test- ing programme must be designed.

Two immediate questions which may be posed are: why should a rock mass classification be selected for this purpose and how reliable are any estimates by this means? The answer to these questions have emerged from the study of the three case histories presented earlier.

It should first be stated that estimates of rock mass deformability by means of quality indices are not new; Deere et al. [1] suggested ten years ago that the RQD index and/or the seismic velocity index be used for this purpose. However, a detailed study of this aspect by Coon and Merritt [39] in 1970 did not provide enough evidence to support such a concept. The reason, for this is that neither the RQD nor the velocity index are sufficient on their own to describe fully the overall condition of a rock mass. The RQD disregards the in- fluence of joint tightness, orientation, continuity and gouge material.

The seismic velocity index is defined as the square of the ratio of the field seismic wave velocity to the sonic velocity in a laboratory specimen, (V~/VL) 2. The ratio is squared to make the velocity index equivalent to the ratio of the dynamic moduli. This index, how- ever, has too many uncertainties to be reliable on its own. Such uncertainties are the different sensitivities of the seismic and sonic waves as well as the difficulties in generating and identifying elastic waves in rock masses and in rock materials. Coon and Merritt [39] concluded that neither the RQD nor the velocity index are reliable for predicting directly in-situ rock mass deformability. In fact, in some cases the predicted in- situ modulus of deformation was nearly three times greater than the corresponding laboratory modulus of intact rock. However, they suggested that the answer to this problem was to predict the modulus reduction ratio instead, that is, the ratio of the in-situ modulus of the rock mass EM to the laboratory modulus of the rock material Er. This ratio was found to be a better choice than the ratio of the field seismic modulus Es to the in-situ modulus EM because the Es/EM ratio proved to be too scattered and too unreliable in deter- mination.

The EM/Er ratio showed a reasonable correlation with the RQD (correlation coefficient 0.544) but not so much with the velocty ratio (correlation coefficient 0.368). Nevertheless, the RQD data were derived mainly from one project, the Dworshak Dam in the U.S.A., although a few results were also included from

w w

o

Q)

m

o

, o

0 Results from Dworshak Dam [~110 Deere et OL, 1 9 6 7 [ I ] r~ ~/~lllJ

~ : • Orange-Fish Tunnel-vert ical '- u.o! lacking tests Olivier, ,977127] e~ ~ / ~ - I ~

• Orange-Fish Tunnel-horizontal 10 e B I jacking tests o ~ -

m Drakensberg tests • • jl~• i 0.6 • Elandsberg tests I L ~ - e ° . i

E] Orange River project • ~ll/q- ~ • • J Diepsloot _/== O

0.4 •

. o/: 0. P i

| t i J I i i f i t J 0 20 40 60 80 I00

Rock quality designation, %

Fig. 6. Comparison of RQD with modulus reduction ratio: EM, modulus of rock mass to Et., modulus of roCk material.

three other projects. The data used involved RQD >~ 60%. Care was also taken to improve the RQD correlation by obtaining a 'weighted' rock quality with depth, i.e. correcting the RQD values for the fact that the core is more fractured nearer the rock surface.

No further research was done in this respect from 1970 to date, but in the meantime the relationship de- rived from the Dworshak Dam tests was used to deter- mine in-situ deformability for projects in other coun- tries [40]. Yet, in a number of cases the RQD approach proved impossible to apply. For example, in addition to the limitations of the RQD to describe fully the con- dition of the rock masses, it was found that it was not uncommon that the in-situ modulus of deformation was higher than that determined in the laboratory as shown by the tests for the Channel Tunnel [41], the Turlough Hill project in Ireland [42] and the Tumut 2 project in Australia [11].

Since the modulus reduction ratio cannot by defini- tion exceed unity, the results from these projects could not be applied to the RQD vs modulus reduction ratio

1,0

Jl~o.8 .9 4-- O

0.6

0.4

~ o.e o

• O.range- River Dams

- x~ Diel~loot B Drakensberg B ElandSl~g v Scientio • Witbonk 0 Orange Fish

tunnel

J

[B 0 / . / 0

7 1 t 8

= = I , ~ I i I

I0 2O 30 40 50 60

C l a s s

70 8Q 90 ~oo

Geomechanics rock mass rating

Fig. 7. Relationship between rock mass rating and ratio ot detbrma- tion modulus of rock mass Eu to that of rock material E~

Determining Rock Mass Deformability 245

o 80 a. t9

I.IJ

o

,..- 4 0 o

E 2o

E M = 2 R M R - I O 0

/

Q Elandsberg Scheme g = ] S [] vrakensoerg..~cneme

t90ranae~-~sn/unnet • Wifbdnk Coalfield o Le Roux Dam EB Dinorwic Scheme • Gordon Scheme

I I I I 50 60 70 80 9 0

Geomechanics rock moss ra t ing , RMR

Fig. 8. Relationship between in-situ modulus and rock mass rating.

I O O

relationship--whatever the reason for the higher in-s i tu

results (the authors of these tests did not give any explanation). It emerged, however, that one of the prob- lems was that the laboratory tests may not have been

conducted in accordance with the standardized pro- cedures and that the laboratory data compared a tan- gent modulus at 50% strength with the in-s i tu modulus on the recovery cycle.

It is obvious therefore that the RQD index and the modulus reduction ratio are not ideal to estimate in-s i tu

rock mass deformability. Nevertheless, a check was car- ried out during the present study and the results are given on Fig. 6. It will be seen from this figure that there is a large scatter of the results and that for RQD < 70~, it is not clear how the relationship should be applied.

This state of affairs has prompted the present research, applying the rock mass rating (RMR) of the Geomechanics Classification [28] to predict d i r e c t l y the in-s i tu modulus of deformation of rock masses without using the modulus reduction ratio. An attempt to relate the modulus reduction ratio to the geomech- anics rock mass rating also showed too much scatter, as shown in Fig. 7, and a different method of presen- tation was, therefore, selected. In Fig. 8, the in-s i tu

modulus of deformation is plotted vs the Geomechanics rock mass rating. Using the least-squares method, the following numerical relationship was observed:

E M = 1.76 × R M R - 84.3 (1)

where

EM = in-s i tu static modulus of deformation in GPa

R M R = rock mass rating in accordance with the Geomechanics Classification [28].

This empirical equation (1) has a correlation coeffi- cient of 0.9612 which is much higher than that in the case of the RQD index (correlation 0.544) and the vel- ocity index (correlation 0.368). Equation (1) yields the prediction error of 17.8% which is defined as the differ-

ence between the observed value and the predicted value expressed as a percentage of the predicted value.

In view of the high correlation, the coefficients in equation (1) were rounded off since the aim of this research was to e s t i m a t e the in-s i tu modulus for a pre- liminary assessment of rock masses. This resulted in the following equation:

EM = 2 x R M R - 100. (2)

Equation (2) with a prediction error of 18.2% is a simple equation to remember and sufficiently accurate for practical engineering purposes.

It is believed that the Geomechanics Classification and equation (2) may be used for estimating the in-s i tu

modulus of rock masses during the planning stage of a design investigation for a rock engineering project.

C O N C L U S I O N

The case histories involving three major engineering projects in South Africa have shown that the uncertain- ties inherent in the various in-s i tu tests can be overcome by proper planning and interpretation of in-s i tu tests.

For this purpose an approach is recommended in- volving the Geomechanics Classification of rock masses on the basis of which it is possible to estimate, by equa- tion (2), the in-s i tu modulus of deformation with an accuracy better than 20%, which is sufficient for practi- cal purposes.

Acknowledgements--The author wishes to thank the Electricity Sup- ply Commission for permission to publish the in-situ test data for the Elandsberg Scheme. These data, as well as those from the Drak- ensberg in-situ tests, were obtained by the CSIR team under the author's direction. The Orange-Fish Tunnel test results were reported by Olivier 1-27] in his doctoral dissertation, which was supervised by the author.

Received 6 September 1977; in revised form 30 November 1977.

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246 Z.T. Bieniawski

2. Duffaut P. Deformations in rock mechanics. Proc. Int. Syrup. on Rock Mech, pp. 3-12. Editorial Blume, Madrid (1968).

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9. Dodds D. J. Interpretation of plate loading test results. Field Testing and Instrumentation of Rock. A.S.T.M. Special Technical Publication 554, pp. 20-34. A.S.T.M., Philadelphia (1974).

10. Misterek D. L., Slebir E. J. & Montgomery J. S. Bureau of Reclamation procedures for conducting uniaxial jacking tests. Field Testing and Instrumentation of Rock. A.S.T.M. Special Technical Publication 554, pp. 35--51. A.S.T.M., Philadelphia (1974).

11. Alexander' L. G. Field and laboratory tests in rock mechanics. Proc. 3rd Aust.-N.Z. Conf. on Soil Mech & Foundation Engng., pp. 161-168. Sydney (1970).

12. Deklotz E. J. & Boisen R. D. Development of equipment for determining deformation modulus and in-situ stress by means of large flat jacks. A.S.T.M. Special Technical Publication 477, pp. 117-125. A.S.T.M., Philadelphia (1970).

13. Vogler U. W., Deffur R. D. & Bieniawski Z. T. CSIR large fiat jack equipment for determining rock mass deformability. Proc. Syrup. Exploration for Rock Engng. (Edited by Bieniawski Z. T.) Vol. 2, pp. 105-111. A. A. Balkema, Rotterdam (1976).

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15. Misterek D. L. Analysis of data from radial jacking tests. A.S.T.M. Special Technical Publication 477, pp. 27--38. A.S.TM., Philadelphia (1970).

16. Bowcock J. B., Boyd J., Hock E. & Sharp J. Drakensberg Pumped Storage Scheme--rock engineering investigations. Proc. Symp. Exploration for Rock Engng. (Edited by Bieniawski Z. T.) Vol. 2, pp. 121-139. A. A. Balkema, Rotterdam (1976).

17. Goodman R. E., Van T. K. & Heuze F. E. Measurement of rock deformability in boreholes. Proc. lOth Syrup. Rock Mech., pp. 523-545. American Institute of Mining Engineers, New York (1972).

18. Hueze F. E. & Salem A. Rock deformability measured in-situ problems and solutions. Proc. Syrup. Field Measurements in Rock Mech. (Edited by Kovari K.) pp. 375-388. Zurich (1977).

19. Rocha M. Present possibilities of studying foundations of con- crete dams. Proc. 3rd Int. Congr. Rock Mech,, Vol. IA, pp. 879-896. International Society for Rock Mechanics, Denver (1974).

20. Schneider B. Contribution a l'etude des massifs de fondation de barrages. Trans. du labor de geol. de la fac. des sci. de Grenoble Monsoir No. 7, 235 p. Grenoble (1967).

21. Hock E. & Londe P. The design of rock slopes and founda- t ions-general report. Proc. 3rd Int. Congr. Rock Mech., Vol. IA, pp. 613-654. International Society for Rock Mechanics, Denver (1974).

22. Dodds D. J. & Schroeder W. L. Factors bearing on the interpre- tation of in-situ testing results. Proc. 2nd Rapid Excavation and Tunnelling Conference (Edited by Pattison H. C. & D'Appolonia E.) pp. 397-414. American Institute for Mining Engineers, New York (1974).

23. Kruse G. M. Powerplant chamber under Oroville Dam. Proc. Rapid Excavation and Tunnelling Conference (Edited by Pattison H. C. & D'Appolonia E.) pp. 333-380. American Institute of Mining Engineers, New York (1974).

24. Hustrulid W. A. An analysis of the Goodman jack. Proc 17th Syrup. Rock Mech., Snowbird, Utah, pp. 4B10-1~8 (1976).

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26. International Orange River Consultants. Geologitai Imestiyation~ and Rock Mechanics Tests on H. F Verwoerd and ran der Klot~ Dam sites. Johannesburg (1965)

27. Olivier H. J. Orange-Fish Tunnel Some Engineering Geologicai Aspects. Univ. of Orange-Free Stale, Ph.D. tbesis, Bloemfonteir~ (1977).

28. Bieniawski Z. T. Rock mass classifications in rock engineering, Proc. Syrup. Exploration .for Rock Engng. (Edited by Bieniawski Z. T.) Vol, 1, pp. 97-106. A. A. Balkema, Rotterdam (1976).

29. Bowcock J. B. Van der Kloof hydro-electric power station. Pro~. Syrup. Exploration for Rock Engn#. (Edited by Bieniawski Z. T3 Vol. 2, pp. 149-158. A. A. Balkema, Rotterdam (1976).

30. Bieniawski Z. T. & Orr C. M, Rapid site appraisal for dam foun- dations by the Geomechanics Classification. Trans 12th Int. Congr. Large Dams, 483-501. ICOLD, Mexico City (1976). Bieniawski Z. T., Pells P. I. N. & Orr C. M. Drakensberg Pumped Storage Scheme: rock mechanics feasibility study of the underground power station. Rep. Coun. scient, ind Res. S. Afr. Pretoria No. ME 1325 (1974). Van Heerden W. L. & Maschek R. K A. Drakensberg Pumped Storage Scheme: plate bearing tests~ Rep. Coun. scient, ind. Res. S. Aft., Pretoria No. ME 1477 (1976) Bieniawski Z. T. Design investigations for rock caverns in South Africa. Proc. First Int. Syrup. on Storage in Excavated Rock Caverns, Stockholm, Vol. 3, pp~ 107-112 (I977). Sharp J. C., Richards L. R. & Byrne J. Instrumentation consider- ations for large underground trial openings in civil engineering. Proc. Symp. Field Measurements in Rock Mech., Zurich (Edited by Kovari K.) pp. 587-610 (1977): Bieniawski Z. T. Elandsberg Pumped Storage Scheme: rock engineering investigations. Proc. Syrup. Exploration for Rock Engng. (Edited by Bieniawski Z. T.) Vol. l, pp. 273--289. A. A. Balkeman, Rotterdam (1976).

36. De Wit B., Coetzer S. J., Houghton D. A. & Bieniawski Z. T. Elandsberg Pumped Storage Scheme: rock mechanics studies in the tailrace test enlargement. Rep Coun. scient, ind. Res. S. Aft'., Pretoria No. ME 1490 (1977).

37. Van Heerden W. L., Maschek R, K. A., de Wit B. & Botha M. L. Elandsberg Pumped Storage Scheme: in-situ tests to deter- mine rock mass deformability characteristics. Rep. Coun. scient. ind. Res. S. Aft'., Pretoria No. ME 1517 (1977). Kruse G. H. Deformability of rock structures, California State Water Project. A.S.T.M. Special Technical Publication 477, pp. 58-88. A.S.T.M., Philadelphia (1970)i Coon R. F. &Merritt A. H. Predicting in-situ modulus of defor- mation using rock quality indexes. A.S.T.M. Special Technical Publication 477, pp. 154-173. A.S~T.M., Philadelphia (t970), Douglas T. H., Richards L. R. & O'Neill D. Site investigation for main underground complex.---Dinorwic Pumped Storage Scheme. Proc. Syrup. Field Measurements in Rock Mech, Zurich (Edited by Kovari K.) pp. 551-568 (i977).

41. Tyrell A. P. Ground instrumentation for the Channel Tunnel project. Proc. Syrup. Exploration for Rock Engng. (Edited by Bieniawski Z. T.) Vol. 1, pp. 233-241. A. A: Balkema; Rotterdam (1976).

42. O'Donoghue J. D. & O'Flaherty R_ M. The underground works of Turlough Hill. Water Power 26, 5-12 (1974).

43. Endersbee L. A. & Holt0 E. O. Civil engineering design and studies in rock mechanics for Poatina Underground Power Station. J. Aust. Inst. Engrs 35, 187-206 (1963).

44. Dolcetta M. Problems with large underground stations in Italy. Proc. Syrup. Underground Rock Chambers (Edited by Lane K. S.) pp. 243-286. A.S.C.E, New York (t973).

45. Lack L. J., Bowling A. J. & Knoop B. P. Rock mechanics studies and instrumentation for the Gordon Underground Power Station. Proc. 2nd Austr.-N.Z. Confl on Geomechanics, Brisbane, pp. 274-280 (1975).

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31.

32.

33.

34.

35.

38.

39.

' 4 0 .

Determining Rock Mass Deformability 247

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APPENDIX : THE 'PETITE SISMIQUE' TECHNIQUE

While the conventional seismic techniques utilise exclusively seis- mic wave velocities, the 'petite sismique' method involves the measurement of the following seismic parameters of the shear wave: frequency, velocity, at tenuation and half wavelength [20]. These values are used not only to 'identify' a specific rock mass but also to estimate the static modulus of deformation.

In operation, the 'petite sismique' survey is similar to a conven- tional surface seismic refraction survey. The additional features are as follows:

(a) Constant amounts of seismic energy are imparted to the rock mass by allowing the sledgehammer to fall over a vertical distance o f l m.

(b) Time interval and gain readings are recorded at successive geo- phone/hammer intervals of 2-3 m up to a final distance of 25-30 m. The readings are taken by recording the time taken for the first arrivals of various portions of the shear wave and the gain control setting of the seismograph necessary to obtain a waveform of con- sistent amplitude. Pictorial representat ion of this data is given in Fig. 9.

(c) The seismic parameters of half wavelength (½2) and frequency (f) are computed from the following equations:

22 = (t~ - tAWs

f = [2(tB - tA)] I

no 45

=~ 40 LU

o: 35

E ~ 30

• ~- 2 5

' ~ 2 0

u 15

IO

~ 5

0

o Data from Schneider [20] / ~x Drakensberg siltstone/sandstone /

(~ Ell~:dd:b;rr; gpr:;,~ii ;; k e /

EM = O.05 4 f - 9 ~ , t X ~ O : rdo Do m

S o.o/

J f l I I I t L I J I00 200 300 400 500 600 700 800 900 I000

Shear wave frequency f, Hz

Fig. 10. Correlat ion between static modulus of deformation EM and shear wave frequency f from 'petite sismique'.

where

V s = field shear wave velocity, tA = travel t ime of first arrival of positive peak, see Fig. 9, tB = travel t ime of first arrival of negative peak, see Fig. 9.

(d) Field compressional wave velocities, if measured during the survey, may be used to compute the seismic modulus of deformation of the rock mass.

The most important feature of the 'petite sismique' technique is the relationship between the shear wave frequency, f, and the field static modulus of deformation, EM. This empirical correlation is given in Fig. 10 and is of the following form:

EM(GPa) = 0.054 f - 9.2 w h e r e f i s given in Hz.

+ v e ! 1"

v e

T I M E ORIGIN

A

,._--^.,A .h_ ._A A~ ~ ' - " v - v V i ~ , - ~ v - lip V

BACKGROUND NOISE

FREQUENCY (Hz) "

1 f = 2 (t B - 1 A)

C

I I I I I I t IA :e i c

V V V vv

TIME (ms) L w

Fig. 9. Typical shear wave representation on oscilloscope showing measurements conducted during 'petite sismique' surveys.