Rock mass strength parameters mobilised in tunnels

Rock mass strength parameters mobilised in tunnels

RESEARCH PII:S0886-7798(96)00060-0 Rock Mass Strength Parameters Mobilisecl in Tunnels B. Singh, M. N. Villadkar, N. K. Samadhiya, and V. K. Mehrotra...

773KB Sizes 10 Downloads 287 Views

RESEARCH PII:S0886-7798(96)00060-0

Rock Mass Strength Parameters Mobilisecl in Tunnels B. Singh, M. N. Villadkar, N. K. Samadhiya, and V. K. Mehrotra

Abstract--Experience suggests that there is an enhancement in the strength of rock mass around the tunnels due to constraints in fracture propagation. In this paper, mobilised strength parameters and modulus of deformatton have been deduced from back analysis of the field experience for the purpose of realistic non-linear stress analysis of arched underground openings in nearly dry rock masses, and modified correlation,: have been suggested. It is also inferred from field observations that sympathetic failure of rock mass may take place at all points almost simultaneously within the failure zone if deviatoric strain exceeds a critical value at any point. Block shear tests support Hoek and Brown's (1980) criterion, which is recommended for analysis of rock slopes and open cut mines.

Introduction n s t r u m e n t a t i o n of u n d e r g r o u n d openings in a complex geological e n v i r o n m e n t is the key to t h e i r success. Back a n a l y s i s of the d a t a observed in t h e initial stages of excavation provides 'valuable knowledge of the constants of the selected constitutive model, which m a y t h e n be used in the forward analysi,~ to predict performance of t h e support system. The experience of back analysis of d a t a from m a n y project sites is presented in this p a p e r to prove t h a t there is a significant e n h a n c e m e n t of strength of rock masses around tunnels. The rock mass surrounding the tunnels performs much b e t t e r t h a n the theoretical expectations except n e a r thick and plastic s h e a r zones, faults, thrusts, intrat h r u s t zones, and in water-charged rock masses. Hoek (1994) h a s reviewed t h e r e s e a r c h on constitutive models extensively a n d h a s suggested the use of the Geological S t r e n g t h I n d e x (GSI), which is equal to RMR~6 (Bieniawski 1976), i.e.: GSI = RMR76 for RMR76 > 18 (la) = 9 log~ Q' + 44 (lb) Q' = ( R Q D / J ) • ( J / J ) = Modified Tunnelling Quality Index (lc) S o m e t i m e s it is difficult to assess RMR in very poor rock masses. It m a y be e v a l u a t e d r e l i a b l y for n e a r l y d r y rocks from Q' using t h e correlation p r e s e n t e d by Goel et al. (1995), which shows a high coefficient of correlation of 0.92, as follows: RMR79 = 8 I n Q'+ 30 + Ratings of% and Joint orientation (ld)

I

Present address: Prof. Bhawani Singh; Prof. M. N. Viladkar; and N. K. Samadhiya, Lecturer, Dept. of Civil Engineering, University of Roorkee, Roorkee 24,7667, India; and V. K. Mehrotra, Superintending Engineer, U.P.I.D.O., Roorkee, India. Tunnelling and Underground 5pace Technology,Vol. 12, No. 1, pp. 47-54, 1997 Copyright © 1997 Elsevier Science Ltzi Printed in Great Britain. All rights re~erved 0886-7798/97 $17.00 + 0.00

Effect of Intermediate Principal Stress on Tangential Stress at Failure in Tunnels The i n t e r m e d i a t e principal stress (02 ) along the t u n n e l axis m a y be of t h e o r d e r of about h a l f the t a n g e n t i a l stress (01) in deep tunnels. According to W a n g and K e m e n y (1995), 02 has a strong effect on c 1 a t failure, even if 03 equals 0. T h e i r polyaxial l a b o r a t o r y t e s t s on hollow cylinders suggest the following s t r e n g t h criterion: (2) = 1 + A [ e °3/~2 ] [G2\ l - F e(~3/G2 /q¢) where F = m a t e r i a l c o n s t a n t (0.10-0,20) A = m a t e r i a l c o n s t a n t (0.75-2.00) % = u n i a x i a l compressive s t r e n g t h (02 = o 3 = 0) In the case of u n s u p p o r t e d tunnels, 03 = 0 on its periphery. Therefore, Eq. 2 simplifies to ~ l - 1 + A { ~ 2 } 1-r q-~-qc

(3)

It m a y be inferred t h a t o 2 will tend to enhance the strength, ~1 by 75-200 percent w h e n 02 = % I n fact, the s t r e n g t h m a y be e n h a n c e d much more, since p r o p a g a t i o n of fractures will occur only on t h e excavated face (Bazant et al. 1993). Murrell's (1963) criterion also suggests a 100 percent increase in 01 at failure w h e n 02 = 0.5 - 0, and o 3 = 0.

Modified Hoek and Brown Strength Criterion Hoek (1994) has suggested t h e following modified criterion for s t r e n g t h of j o i n t e d rock masses: ~'1 = (~3 + q¢ [m (~3/cI¢+ s]" (4a) n = 0.50 a n d (4b) n = 0.65 - GSI/200 _<0.60 for GSI < 25 (4c) q¢ = u n i a x i a l compressive s t r e n g t h of rock m a t e r i a l

Pergamon

It is i n t e r e s t i n g to note t h a t t h e r a t i o qt ..... /q~ from Eq. 4a w o r k s out to be 0.5 [- m + ( m 2 + 4 - s)~/2], which is a p p r o x i m a t e l y s/m. As such, t h e tensile s t r e n g t h of rock m a s s (qt . . . . ) m a y be given as: qt.... = s • q¢/m for n = 0.50 (4d)

t h e middle H i m a l a y a s suggest t h a t the tensile s t r e n g t h is significant, a n d not 0. Hoek and Brown (1980) observed from l a b o r a t o r y t r i a x i a l t e s t s t h a t q¢ decreases w i t h t h e size of the specimen (d) as follows:

In addition, t h e stable half-tunnels excavated in h a r d jointed rock m a s s e s in n e a r l y vertical slopes for hill roads in

Notations A B

= rock m a t e r i a l constant (0.75-2.0) in Eq. 2 = w i d t h of t h e u n d e r g r o u n d opening in rock m a s s (m) Bs = w i d t h of the self-supporting opening (m) Ed = modulus of deformation of rock m a s s E = modulus of deformation of rock m a t e r i a l F = rock m a t e r i a l constant (0.1 - 0.2) in Eq. 2 GSI = Geological S t r e n g t h Index (Eq. l a , Eq. lb) H = h e i g h t of overburden above t u n n e l (m) Q = rock m a s s quality = RQD/J - Jr/Ja . Jw / SRF Q' = t u n n e l l i n g quality index = R Q D / J • J / J Q~H = rock m a s s quality for wall of t u n n e l s RMRT~ = Rock M a s s Rating (Bieniawski 1979) SRF = s t r e n g t h reduction factor a

--

Ua

r a d i u s of t u n n e l p e a k cohesion of rock m a s s (Eq. 13) r e s i d u a l cohesion of rock m a s s (Eq. 19a) -= correction factor for o v e r b u r d e n (Fig. 6) normalized ground response (reaction) curve for wall of the tunnel in squeezing rock condition c o n s t a n t of rock m a s s in Hoek and Brown's s t r e n g t h criterion (Eq. 4a) c o n s t a n t of rock m a t e r i a l in Hoek a n d Brown's s t r e n g t h criterion, as obtained from t r i a x i a l tests on rock cores ~- exponent in the modified Hoek and Brown's equation, (0.50-0.60) in Eq. 4a ---- a t m o s p h e r i c p r e s s u r e (0.1 MPa) u n i a x i a l compressive s t r e n g t h of rock = material uniaxial compressive strength of rock m a s s = u n i a x i a l tensile s t r e n g t h of rock m a s s = c o n s t a n t of rock m a s s in modified Hoek a n d Brown's s t r e n g t h criterion (Eq. 4) r a d i a l d i s p l a c e m e n t of t u n n e l

tX

=

),

=

5

=

cp cr

f

m

m

n

Pa qc

qcmass qtmass S

~ (~

=

=

= =

c o n s t a n t of rock m a s s for p r e s s u r e dependency of modulus of deformation c o n s t a n t of rock m a t e r i a l for effect of size on UCS unit weight of rock m a s s (g/cc or t/m 3) m a j o r a n d m i n o r principal s t r a i n s , respectively p e a k angle of i n t e r n a l friction of rock m a s s (Eq.12) r e s i d u a l angle of i n t e r n a l friction of rock m a s s (Eq. 19b) effective major principal stress effective i n t e r m e d i a t e principal stress effective minor principal stress.

48 TUNNELLINGAND UNDERGROUNDSPACE TECHNOLOGY

q~o¢o=

(4e)

= 0.18 (Hoek a n d Brown 1980) = 0.22 (South African mine failure data, Barton 1993) 0.20 (recommended by B a r t o n 1993) d o -~ d i a m e t e r of l a b o r a t o r y core specimen q¢o = UCS of rock s p e c i m e n of d i a m e t e r d o Hoek (1994) h a s s u g g e s t e d t h e following correlations b e t w e e n m, s a n d GSI for GS1 > 25 a n d u n d i s t u r b e d rock masses: m - e x p [ G S I - 100 ]=0.135(Q,)~3 m~ -

2s

(5)

s=exp[GSI91001=O.O02Q' (6)

m r = constant for rock m a t e r i a l obtained from triaxial tests.

A s s e s s m e n t of Constants m and s E q u a t i o n s 5 a n d 6 m a y be simplified for all types of rock m a s s e s as m mr

=

S9/28

=

SU3

(7)

F u r t h e r , Eq. 4a defines t h a t u n i a x i a l c o m p r e s s i v e s t r e n g t h of rock m a s s as q¢.... = qc s" (8) I t h a s been observed from the a n a l y s i s of about 150 case histories from all over t h e world (Barton et al. 1974 and Singh et al. 1992) a n d some a d d i t i o n a l case histories of V e r m a n (1993) and Goel (1994), shown by u n s u b s c r i p t e d dots and crosses in F i g u r e 1, t h a t rock m a s s will fail in d r y t u n n e l s (Jw = 1) if t h e o v e r b u r d e n H (m) is given by: H _>350 QI~ (9a) >_483 QI/3/(B - Bs) °-1 V e r m a n (1993) H _>275 Q"/3/B°.I Goel (1994) where B = w i d t h of the u n d e r g r o u n d opening (m) B = w i d t h of t h e self-supporting opening (m) Q = rock m a s s q u a l i t y

(9b) (9c)

The a n a l y s i s of d a t a p r e s e n t e d b y Goel (1994) shows t h a t the above correlations (Eq. 9a, 9b, 9c) a r e i n d e p e n d e n t of the u n i a x i a l compressive s t r e n g t h of rock m a t e r i a l s r a n g i n g from 2 to 150 M P a (Fig. 2.). M u l t i p l y i n g Eqs. 9a a n d 9c by 27 on both sides a n d r e p l a c i n g 2.7" H by q ..... yields t h e a p p r o x i m a t e mobilized u n i a x i a l compressive s t r e n g t h of rock m a s s in t h e t u n n e l s (for Q < 10, Jw = 1, q¢ > 2 MPa), as follows: qcm~ = 700 7 Q~/3 t/m 2 (10a) = 7 7 Q '~ MPa = 5.57(Q')l/3/B °j M P a (Goel1994), (10b) where 7 = u n i t weight of rock m a s s (t/m 3) F u r t h e r , A y d a n et al. (1993) h a v e o b t a i n e d a correlation b e t w e e n @ (degrees) a n d q¢ (MPa) by a n a l y s i n g t h e laborat o r y t e s t d~ata (35 d a t a points) as follows: @p= 20 q¢0.2~ (11) According to Barton et al. (1974), an a p p r o x i m a t e correlation for p e a k angle of i n t e r n a l friction of the rock m a s s is

Volume 12, N u m b e r 1, 1997

2000

1000

a

--

b

-"

d

-

f g

-

h

-

-

MANERI BHALI PROJECT S A L A L PROJECT TEHRI DAM PROJECT SAN JAY VIDYUT PARIYOJNA KOLAR GOLD MINES CHHIBRO KHODRI TUNNEL GIRl HYDEL TUNNEL LOKTAK HYDEL TUNNEL KHARA HYDEL PROJECT

0 NON-SQUEEZING



"+l

CONDITION

SQUEEZING CONDITION

(g) ROCK

BURST

4,

1-159 - BARTON'S CASE HISTORIES

E .w,

Z LIJ r'~ ¢r :3 rn n"

•f

SQUEEZING 00

500 -

ILl

e9

Og

•9 ®•

oe

o

142 • g

II

Q.

"I-

Od 90148

141

NON- SQUEEZING

•h

159

•f

•f

"h/6;

200 --

co ,.~

Og

o104

o105

oo oc

oi o101

oi

08

b 100 0"001

521 a 0.01

45 o

0,1 ROCK M A S S

I 0 . 67 v 1

I 10

74 O,

?o5

I 100

QUALITY, Q

Figure 1. Condition for squeezing ground failure. as follows: tan Cp = J / J < 1.5 and therefore, peak cohesion, cp = q . . . . (1 sin ¢p) / 2 cos Cp

(12) (13)

It is a s s u m e d t h a t hydrostatic stress conditions exist at great depth, where failure of rock mass and squeezing m a y occur. Thus, tangential stress will be about 27H where mild squeezing m a y be initiated. A better empirical relation m a y be obtained ifin-situ stress data are available for a large n u m b e r of sites. Anisotropy caused by the joint orientation does not appear to be significant, according to Eq. 10a, for the tunnels. The geomechanics classification of Bieniawski (1979) also suggests a lesser role of joint orientation in the case of tunnels. However, in the rock slopes joint orientation plays a dominant role. Therefore, Eq. 10a is not valid for rock slopes. Table 1 compares Lhe uniaxial compressive strength of the rock mass, i.e., q ...... , with the range of values of q+, the uniaxial compressive strength of rock material for different projects in India. It was expected t h a t mobilised q ..... should be close to the range ofuniaxial compressive strength of rock material (qc) in the case of weak rock (low UCS), but of good rock mass quality (Q) because q~.... will be approximately equal to q¢ tbr a massive rock mass. Table 1 (Mehrotra 1992) shows t h a t this is surprisingly true for augen gneiss, slates, limestone, schist, and phyllite. It is heartening to know t h a t q . . . . does not cross the upper limit ofq¢ for Q < 10. Obviously, for highly jointed rock mass, mobilized qcm~swill be much lower than q . Further, extensive field data collected by Goel (1994) shows t h a t generally predicted q ..... (Eq. 10a) is less than q~, as shown

Volume 12, N u m b e r 1, 1997

in Figure 3 (qc > 2 MPa). The agreement between q .... and qc will be improved after size correction is applied, in the case of a massive rock mass (Q > 10). Recently, Grimstad and Bhasin (1996) modified Eq. 10a by incorporating the unconfined compressive strength of rock material (q~ in MPa) for hard rocks, as follows: (qc) .7.Q~3 q ..... = 100 " 7

MPa

(14) However, the data presented in Table 1 do not support Eq. 14, as the correction for q¢ leads to underestimation of q ..... for weak massive rock masses (qc < 100 MPa). The correction m a y be true for good or massive hard rocks (qc > 100 MPa and Q > 10), where q ..... will depend directly on

1500 o •

i

l

I NON- SQUEEZING SQUEEZING

100(

I| 35¢

"•

v/ll=/.C~//=//////'f, "////////////// o o

o(

i//////////////////////////

@

100 q¢ , M Pa

150

Figure 2. Effect of uniaxial compressive strength on squeezing criterion.

TUNNELLINGAND UNDERGROUNDSPACETECHNOLOGY4 9

20()

Table 1. Comparison of estimated uniaxial compressive strength of rock mass and m a x i m u m uniaxial compressive strength of rock cores.

Project

Rock type

Rock Mass Quality

RMR79,

Unit qcmass Range of UCS,(qc) Weight MPa of rock material g/cc from MPa ~' Eq. 8 2.64 43.45 7.90-37.30

(Q)

lSanjay Vidyut Augen gneiss Pariyojna,H.P. with large crystals of quartz Lakhwar Dam Slates Project, U.P. Lakhwar Dam Trap Project, U.P. Kotlibelh Dam Lime stone Project, U.P. Srinagar Dam Metabasic Project, U.P. Uttassu Dam Quartzite Project, U.P. Tehri Dam Phyllite Project, O.P. Nathpa Jhakri iSchist Project, H.P. Notes:

44

13

18-45

0.3:3.1 (1.1) 1.7-11.7 (4.5) 0.1-0.4 (0.7) 3.3:4.7 (3.9) 0.3-19.0 (2.4) 0.3-4.1 (1.1) 0.7-32.0

30-61 11-53 37-60 27-71 18-50

(2.7)

2.64-2.79 (2.71) 2.63-2.84 (2.74) 2.08-2.43 (2.26) 2.72-2.88 (2.8) 2.51-2.87 (2.69) 2.61-2.82 (2.71) 2.64-2.76

(2.7)

19.58 31.67 14.05 30.85 22.49 19.58 26.30

1.0-38.0 (0-20.5 Sat) 98.0-196.5 (71.5-163.0 Sa0 21.0-49.0 (16.0-40.0 Sat) 70.9-104.0 (63.0-88.5 Sat) 67.0-128.0 (54.5-112.5 Sat) 38.0-133.0 (25.5-95.5 Sat) 20.0-50.0 (10.25 Sat)

1. Value in bracket show average values. 2. Sat means ucs in saturated condition.

+ Rock Mass Rating (Bieniawski 1979). Unconfined Compressive Strength.

qc and is likely to be less than q. Further, the strength reduction factor (~]s) from Eq. 6 (Hoek 1994) is nearly same as that from Eq. 14 (for SRF = 5 and Q > 10). However, for jointed rocks (Q < 10), Mehrotra (1992) inferred from 21 block shear tests on saturated and weathered rock mass that shear strength is practically independent of q~ (Table 2). Eq. 10a shows the same trend. Thus, Eqs. 12 and 13 are suggested to estimate peak strength parameters, i.e., cohesion (c) and angle of internal friction (¢_) for stress analysis of und[erground openings in place of ~alues given by Bieniawski (1976, 1979). The strength parameters given by Bieniawski (1979) and Hoek

(1984), as given in Eqs. 5 and 6, may be used for saturated and weathered rock slopes where freedom of fracture propagation is greater or wedge failure is dominant. Further, there is a greater likelihood of failure taking place along critical joints in slopes. Indeed, a block shear test gives cohesion parameters close to Bieniawski's (1979) values for saturated and weathered rock masses (Mehrotra 1992). If these values are used in tunnels, it is found that squeezing could occur frequently, even in jointed hard rock masses under low overburden, which is far from the truth. Equations 10a and 10b indicate that there is a significant strength enhancement because of constraints of fracture propagation, which is limited to the tunnel periphery. The strength enhancement may also be due to intermediate principal stress (Eq. 3). Moreover, the overall behaviour of the rock mass in the tunnel is observed to be of the continuum type. Thus, because of restricted dilatancy and in-situ stress along the tunnel axis, failure in the tunnel may not be governed by critical joints. This is unlike the block shear test, in which fracture propagation occurs on all sides and along the critical joint as well. Thus, Hoek's Eq. 6 appears to underestimate the values of parameters in tunnels. Therefore, a more realistic correlation is suggested to predict the mobilized value ofs by combining Eq. 8 and Eq. 10a.

100(3

o

100

oo ° oo o~ oo,,,~ooo

~

o

o

o

o

2

10

oo

.r ~

=7.1(.QA

0'33

¢ - ~

o -

4

~

N.A

%!6oi

o o

03o o

o

o.oi

0'1 ROCK

1 MASS

QUAUTY,Q

I

10

NON-SQUEEZING - SQUEEZING

--

--

--

sn 100

_

5 0 TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY

(15a)

1000 -

Figure 3. Plot between uniaxial compressive strength of rock material, qc and Q.

7 ~,qc QV3 for Q < 10, Jw = 1, cL < 100 MPa

m/mr

=

5"Sy(Q')V3 q~ B°-3

(Goel 1994)

s 1/3

(15b) (16)

Volume 12, Number 1,

1997

It may be noted that q ..... and s according to Eq. 10b and 15b are greater than those from derived from Eq. 10a and 15a, because Q considers the stress reduction factor SRF, whereas Q' ignores SRF. It appears logical that strength enhancement of roct," mass may decline with increasing SRF. Eqs. 10a and 15a are therefore considered safer, as well as more realistic. More experience with back analysis in future would help us improve these correlations. In the case of rocks with water-sensitive minerals (shale, slate, phyllite, etc.), saturation (or absorption of water) has an adverse effect on the strength ofrock material (Mehrotra 1992). The values ol~ strength given by Eq. 10a and 10b should be reduced accordingly. Experience further suggests that the streng~h of a saturated poor rock mass will decrease significantly with time after excavation as a result of saturation softening. However, more data are needed on the mobilized uniaxial compressive strength of saturated rock masses in order to infer any practical conclusion. For flat roof openings within coal mines, Kim and Gao (1995) have recommended Russian empirical equations. Laubscher (1984) found the following correlation for q¢.... of pillars in hard rock mines: q . . . . . = q~ (RMR - rating for % ) / 1 0 6 (17) It is heartening to find that Eqs. 17 and 10a predict nearly the same q ..... for qc = 50 MPa, except for very good rock masses (RMR > 60 and Q > 10). Equations 14 and 17 tally closely for good rocks (Q > 10 and q~ > 100 MPa). Research should there fore be done to study the applicability of Eqs. 10a and 14 (Q > 10) for the design of mine pillars, after using a reduction factor of, say, 1/3, to account for blasting damage, weathering, the adverse effect of joint orientation, scale effect, and reduction in the intermediate principal stress (Laubscher 1984).

MPa), with varying joint frequencies and inclination of joints, etc. Their test data suggest the following approximate correlation, irrespective of rock mass classification: q. . . . . =[Edl °7 qc

S

[ErJo3=0

(18a)

= l E d } ~4

L rJ

(18b)

= e {1/40(0.o564RMR-5.64)}

(18C)

s

for inclined joints. Eq. 18c is plotted in Figure 4. The proposed correlation (Eq. 15a) for n = 0.5 is also shown in Figure 4 for % = 100 MPa. It is heartening to note that the proposed correlation is also verified by the laboratory trend. It may also be noted that both of the equations proposed by Hock and Brown (1980) and Hock (1994) grossly underestimate the strength of the rock mass around tunnels. Experience of back analysis of rock slopes with unfavourable joints indicates that the strength of the saturated rock mass is very low. Thus, the latter criterion may be applicable to saturated rock slopes and open cast mines (Fig. 4). The block shear test data of Mehrotra (1992, 1996) for saturated and weathered rock mass (Table 2) are plotted in Figure 4. The q. . . . . was obtained by drawing Mohr's circle touching failure envelope. The values ofs are plotted against the geometric mean of Q values. The data are in agreement with the correlation of Hoek and Brown (1981) and results of back analysis of critical rock slopes. The q~.... is thus inferred to be about 0.38~Q 1~ MPa for slopes in saturated and weathered rock mass (see Table 2 and Fig. 5). The cohesion along a discontinuous joint plane may be estimated from Eqs. 12 and 13, assuming q ..... as above. In the case of weak and saturated rock mass, time-dependent effects should be studied by performance monitoring of underground structures in a water-charged rock mass.

Comparison of Variious Correlations Between s and RMR or Q Ramamurthy (1985) and his colleagues (Roy 1993) have conducted extensive t]:iaxial tests on dry models of jointed rock mass using plaster of paris as model material (q~ = 9.46

NORWEGIAN GEOTECHNICAL INSTITUTE TUNNELLING QUALITY ]NDEX,Q jGo¢o/GOOD IGOOOj IEXCRI POOR ],OOR IFAIR ]OOOO |¥ERYIEXTREM,

XCEPTIONALLY!I EXTREMELY

r POo R 0.001

i! 0.01

VERY

POOR

.1

1.0

4

F

10 ~)

I

1.0 E •

CSIR/RMR



NGI /(2

40

100

400

1000

I

RAMAMURTHY AND ROY (1993) FOR MODELS OF DRY JOINTED ROCK MASS (EQ. 1 8 c )

L- O MEHROTRA(1992)/O f

0.1

®

J

® ®

0'01

PROPOSED EQ 15a DRY TUNNELS

FOR

HOEK (1994) FOR SATURATED, UNWEATHERED ROCK MASS HOEK AND BROWN(19B0) FOR SATURATED WEATHERED ROCK MASS SLOPES

0 .O01

® O. 0001

0

'

10

20

ERr' POOR J .

30

'

POOR

40

I'

50

60

70

FAIR

I

GOOD

'

80

910

100

I VERY GOOD I RMR/GSI

SOUTH AFRICAN COUNCIL FOR SCIENTIFIC AND INDUSTRIAL RIESEARCH G E O M E C H A N I C S C L A S S I F I C A T I O N

Figure 4. Plot of strength reduction parameter S, rock mass classifications, and different rock structures.

Volume 12, Number 1, 1997

TUNNELLINGANDUNDERGROUNDSPACETECHNOLOGY51

Modulus of Deformation of Rock Mass Verman (1993) analysed the observed data of 60 tunnel sections and found the following correlation between the modulus of deformation (Eo) and Rock Mass Rating RMR79 (Bieniawski 1979). E d = 0.3 H ~ 10/RMa:~-20)/3s GPa (19a) H = height of overburden above tunnel (m) > 50 m Also, the modulus of deformation of poor rock mass is pressure-dependent and is given by o



3





Q

Eo = modulus of deformation of rock mass at c 3 = p~ p~ = atmospheric pressure (0.1 Mpa) a = 0.16 for hard rocks = 0.35 for weak rocks.

i

I

0-4

I

I

0.~ 1.2 1.6 UCS OF ROCK MASS

I

I

2.0

2./~

Figure 5. Uniaxial compressive strength of rock mass from block shear tests on saturated and weathered rock mass (Mehrotra 1992).

The stress concentration around arched openings may be reduced significantly, depending upon the value of Thus, the likelihood of squeezing is further reduced to some extent where E d is highly pressure-dependent. If non-linear stress analysis is done by accounting for the effect of confining pressure o n Ed, then qem s in Eqs. 10a and 10b should be reduced by a factor that is t~e ratio of actual maximum stress concentration in a circular tunnel and an assumed stress concentration of 2.0.

Table 2. Block shear tests on saturated and weathered rock mass (Mehrotra 1992).

S. ,Rock type

Q

RMR

qc saturated

N.

MPa 1.

2.

Results of block shear tests shear strength

g/cc

envelope

rock mass

kg/cm 2

MPa

J o i n t e d Trap and 8.0-14.5161-72 60-120 2.74-2.80 ~ -- u^" 4 ^-0` +0.002 ~0-698j Metabasic (10.8) -do-

UCS of !

s

Predicted from qcmass = 0.38rQ 1/3

2.30

0.00065

2.30

=2.45(o- + 0.95) 0-691

1.54

0.00030

1.41

41-58 35-70 2.39-2.66

=2.25(0- + 1.05) 0.688

1.32

0.00060

1.41

2.0-3.5 (2.6)

43-56 20-60

=2.15(~ + 1.10) 0.675

1.32

i0.00100

1.44

0.3-2.5 (0.9)

24-40 60-120 2.74-2.80 T =2.25(0` + 0.60) 0.676

1.15

10.00016

1.00

0.1-2.5 22-36 35-70 2.39-2.66 ;x = 2 . 0 0 ( ¢ + 0.65) 0.672 (0.5)

0.92

0.00030

0.76

0.3-1.0 23-37 20-60 (0.5)

T =1.75(o- + 0.70) 0.655

0.75

0.00035

0.84

0.4-1.5 29-37 20-40 2.08-2.43 T =1.50(o- + 0.75) 0.646 (0.75)

0.59

0.00040

0.76

1.5-4.0 42-59 6 0 - 1 2 0 2.74-2.80 (2.5)

3. Jointed sandstone

1.9-5.1

and Quartzite

(3.1)

. Jointed Slate, Xenolith and

2.72

Phyllite 5. Jointed Trap and

Metabasic 6. Jointed Sandstone

and Quartzite . Jointed Slate, Xenolith and

2.72

Phyllite 8. Jointed Limestone

52 TUNNELLINGANDUNDERGROUNDSPACETECHNOLOGY

Volume 12, Number 1, 1997

It may be mentioned again that saturation reduces E d significantly in both rock material and rock masses with water-sensitive minerals (Mehrotra 1992,1996). In the case of river valley projects, post-construction saturation takes place around underground openings after the project is commissioned. It is therefore important to take the postconstruction saturation into account in the analysis.

....

HYPOTHETICAL GRC

~

REALISTIC GRC

\

.

Rapid Sympathetic Failure of the Rock Mass within the Entire Failure Zone in Tunnels In ductile materials, failure is dependent only on the state of stress or strain at a particular point; its failure behaviour does not depend upon the state of stresses at nearby points. In the case of brittle materials like rocks, there may be unstable and widespread fracture propagation in the entire shear failure zone, starting from the point of maximum shear strain. In continuum analysis, complex and unstable fracture,, propagation cannot be simulated easily. In work softening analysis as well, this simulation is unsatisfactory at ve:ry large strains because local loss of strength does not aul:omatically lead to sudden loss of cohesive strength throughout the shear failure zone. The continuum chaxacterization of a zone of unstable fracture propagation may be possible by analysis of the sympathetic failure process. Therefore, complete loss of residual cohesion of rock mass may be assumed to occur at a very fast rate throughout the shear failure zone when deviatoric strain (E~-e3) exceeds a critical limit at any point within this failure zone. It appears that fracture propagation will be governed by a strain limit rather than stress limit. The sympathetic failure is like the weakest link failure, in which the failure of a link results in complete loss of strength in the entire chain. This sympathetic failure process is observed in tunnelling through highly squeezing ground conditions (H (m) >> 350 QZ/~)with an inadequate support system. Figure 6 shows normalized ground response (reaction) curves for roof and wall, respectively, for obsd f. Pw obsd Pw Pw

= MEASURED WALL SUPPORT PRESSURE : PREDICTED WALL SUPPORTPRESSURE : jO'~-r2(SQWALL)-1/3 MPa

-3

OA

fw

= FUNCTION REPRESENTING GROUND RESPONSE CURVE FOR TUNNEL WALL

~3

t

: CORRECTION FACTOR FOR OVERBURDEN

6o

o.

,=,2 uJ u~

=

=0

so/

N

\\ / - ROOF

/


~"--

~-//

LONSET OF SYMPATHETIC FA,LURE PROCESS

\ - . - - ~ ~ ~o ~- - ~

~- . . . . . . . . . Cr~=O ONSET OF SYMPATHETIC FAILURE I 6 *1, TUNNEL

CLOSURE

Figure 7. Effect of sympathetic failure of rock mass on theoretical ground response curve of squeezing ground. such tunnelling conditions (Singh et al. 1992). It may be noted that there is a sudden large jump in the support pressures after about 6% of tunnel wall closure. The corresponding critical deviatoric strain will be 12%, neglecting small volumetric changes. The sudden increase in support pressure may be 3 to 4 times the lowest values at the optimum closure. Of course, the critical sympathetic strain failure limit will be different for hard rocks and for medium hard rocks, etc. In the non-linear analysis, this large jump could not be simulated satisfactorily, even after considering the work softening constitutive equations of the rock mass. This would be possible if the critical strain of sudden sympathetic failure is assumed to be, say, 10% for weak rock masses to be on the safer side (Fig. 7). If the deviatoric strain (~,-e 3) or (~0-~r) is less than 10%, analysis may be done assuming appropriate residual cohesion of the rock mass. At the event of over straining at any point beyond 10%, a rapid loss of residual cohesion to 0 may be assumed at all points within the failure zone simultaneously whenever deviatoric strain is less than the critical limit. Therefore, the theoretical ground response curve will be as shown by the solid line in Figure 7, whose shape matches the observed curve in Figure 6. Thus, the proposed sympathetic failure criterion may enable the designers to advise caution on the permissible limit of closures/displacements to field engineers when thick plastic shear zones are or highly squeezing ground conditions are encountered in tunnels and caverns. The experience of back analysis of data of squeezing ground in Figure 6 (Daemen 1975) further suggests the following approximate values ofmobilised residual strength parameters of the rock mass: Cr= 0.1 MPa (20a) Or = 0p--10° E 14 ° (205) It may be recalled that cohesion of a very poor rock mass (RMR = 25) is about 0.1 MPa, according to Bieniawski (1979). The same may be taken as the value of residual cohesion because the rock mass within the broken zone may be fractured because of overstressing, and thereby turns into a very poor rock mass.

02

Conclusions

NOTE : 1-T-OBSERVED SUPPORT PRESSURES IN INDIAN PROJECTS (SINGH et al,1997

(ua/o)

Cr:O

v1

I I 5 10 OBSERVED TUNNEL WALL CLOSURE ('h)

Figure 6. Normalized observed ground response (reaction) curve for tunnel wall in squeezing rock mass.

Volume 12, Number 1, :[997

15

The back analysis and forward analysis of instrumented underground openings are the key to success in the design of support system. The following constitutive equations of rock mass are suggested on the basis of experience of back analysis of data of 60 instrumented tunnels. (Q < 10, qc > 2 MPa, Jw = 1, J/Ja < 1.5).

TUNNELLINGANDUNDERGROUNDSPACETECHNOLOGY53

1. The s t r e n g t h of the rock m a s s in arched u n d e r g r o u n d openings is significantly e n h a n c e d because of r e s t r a i n e d d i l a t a n c y and p r e s t r e s s i n g of rock wedges by in-situ stress along t h e axis of t u n n e l s and caverns. The analysis of field d a t a of t u n n e l s suggests t h a t the mobilized u n i a x i a l comp r e s s i v e s t r e n g t h is about 7 y Q,3 Mpa. The p e a k angle of i n t e r n a l friction, Opm a y be t a k e n as the m i n i m u m v al u e of t a n 1 (J/Ja) for the critically oriented joints, b u t is less t h a n 57 ° . The mobilised residual cohesion is a p p r o x i m a t e l y equal to 0.1 MPa and is not negligible. The mobilised residual angle of i n t e r n a l friction is about 10 ° less t h a n the peak angle of i n t e r n a l friction, Cp. 2. The a p p r o x i m a t e values of the constants m and s in the modified Hoek and Brown's (1980) equation for t u n n e l s are deduced to be m/ m r = s 1/3 s° = 7 • 7" Q~3/qc n = 0.50 n = 0.65 - RMR79/200 < 0.60 for RMR79 < 25 3. Modulus of deformation is p r e s s u r e - d e p e n d e n t for j ointe d rock m a s s e s and is given a p p r o x i m a t e l y as Ed = 0.3 H" 10 (RMR:-20)/38 G P a (~ = 0.16 to 0.35 4. S y m p a t h e t i c failure of the rock mass m a y occur at all points almost s i m u l t a n e o u s l y within a failure zone, whene v e r the deviatoric s t r a i n exceeds the critical value; this occurs about 10 p e r c e n t of the t i m e in t h e case of w e a k and jointed rock masses. 5. For good or m a s s i v e rock masses (Q > 10 and q¢ > 100 MPa), a modified correlation of G r i m s t a d and B h a s i n (1996) a ppe ar s to be applicable: q¢ .7yQ~3 qcmass = 100

MPa

6. On the other hand, th e Hoek and Brown (1980) criterion is applicable to the rock slopes and open-cast mines c ha ra ct er i s ed by w e a t h e r e d and s a t u r a t e d rock mass. Extensive block s h e a r tests suggest q ..... to be 0.38 y Q1/3 MPa, as joint o ri en t at i o n becomes a v e r y i m p o r t a n t factor because of u n r e s t r a i n e d dilatancy. The above p a r a m e t e r s m a y be used only for 2D analysis of u n d e r g r o u n d openings. Research is in progress on the s t r e n g t h criterion of the rock mass for 3D analysis t a k i n g into account the effect of th e in-situ i n t e r m e d i a t e principal stress. []

References Aydan, O.; Akagi, T.; and Kawamto, T. 1993. The squeezing potential of rocks around tunnels: theory and prediction, Rock Mechanics and Rock Engineering 26(2), 137-163. Barton, N. 1993. Predicting the behaviour of underground openings inrock. Proc. Workshop on the Norwegian Method of Tunnelling, New Delhi, 85-105.

54 TUNNELLINGAND UNDERGROUNDSPACE TECHNOLOGY

Barton, N.; Lien, R.; and Lunde, J. 1974. Engineering classification of rock masses for the design of tunnel support. Rock Mechanics 6, 189-236. Bazant, Z. P.; Lin, F. B.; and Lippmann, H. 1993. Fracture energy release and size effect in bore hole breakout. Int. Jnl. Num. and Analytical Methods in Geomech. 17, 1-14. Bieniawski, Z. T. 1976. Rock Mass Classification in rock engineering. Proc. of the Syrup. in Cape Town ( Z. T. Bieniawski, ed.), 97-106. Bieniawski, Z. T. 1979. The geomechanics classification in rock engineering applications. Proc. IVth Congress Int. Society Rock Mechanics, Montreux, Vol. 2, 41-48. Daemen, J. J. K. 1975. Rational design of tunnel support: tunnel support loading caused by rock failure. Ph.D. Thesis, University of Minnesota, U.S.A. Goel, R. K. 1994. Correlations for predicting support pressures and closures in tunnels. Ph.D. thesis, Visvesvarya Regional College of Engineering, Nagpur, India. Goel, R. K.; Jethwa, J. L.; and Paithankar, A. G. 1995. Indian experiences with Q and RMR Systems. Tunnelling and Underground Space Technology 10(1), 97-109. Grimstad, E. and Bhasin, R. 1996. Stress strength relationships and stability in hard rock. Proc. Conf. Recent Advances in Tunnelling Technology, New Delhi, India, Vol. 1, 3-8. Hoek, E. and Brown, E. T. 1980. Underground Excavations in Rock. London: Institute of Mining and Metallurgy. Hoek, E. 1994. Strength of rock and masses. News Journal of the ISRM, 2(2), 4-16. Kim, K. and Gao, H. 1995. Probabilistic approaches to estimating variation in the mechanical properties of rock masses. Int. Jnl. Rock Mech. and Mining Sci. and Geomech. Abstracts 32(2), 111120. Laubscher, D. H. 1984. Design aspects and effectiveness of support system in different mining conditions. Trans. Inst. Mining and Metallurgy 93, A-70-81. Mehrotra, V.K. 1992. Estimation of engineering parameters of rock mass. Ph.D. Thesis, 267. University ofRoorkee, Roorkee, India. Mehrotra, V. K. 1996. Failure envelopes for jointed rocks in lesser Himalaya. Jrnl. of Rock Mechanics and Tunnelling Technology (Indian Society ofRock Mechanics and Tunnelling Technology), 2(1), 59-74. Murrell, S. A. F. 1963. A criterion for brittle fracture of rocks and concrete under triaxial stress and the effect of pore press ure on the criterion. Proc. Vth Syrup. on Rock Mech., University of Minnesota, Minneapolis, Minn., U.S.A. (C. Fairhurst, ed.), 563577. Oxford, England: Pergamon Press. Ramamurthy, T, 1985. Stability of rock mass. Presented at 8th IGS Annual Lecture, Roorkee, India. Published in Indian Geotechnical Journal, 1-74. Roy, Nagendra. 1993. Engineering behaviour of rock masses through study of jointed models. Ph.D. Thesis, Civil Engineering Dept., I.I.T., New Delhi. Singh, Bhawani; Jethwa, J. L.; Dube, A. K.; and Singh, B. 1992. Correlation between observed support pressure and rock mass quality. Tunnelling and Underground Space Technology 7(4), 59-74. Verman, Manoj. 1993. Rock Mass-Tunnel Support Interaction Analysis. Ph.D. Thesis, University of Roorkee, Roorkee, India. Wang, R. and Kemeny, J. M. 1995. A new empirical failure criterion for rocks under polyaxial compressive stresses. XXXVth U.S. Syrup. on Rock Mechanics, Reno, Nevada (J. J. K. Daemen and R. A. Schultz, eds.), 453-459.

Volume 12, N u m b e r 1, 1997