Engineering Geology 168 (2014) 9–22

Contents lists available at ScienceDirect

Engineering Geology

j ourna l homepage: www.e lsev ie r .com/ locate /enggeo

Estimation of support pressure during tunnelling through squeezing grounds

R.D. Dwivedi a,⁎, M. Singh b, M.N. Viladkar b, R.K. Goel a

a CIMFR Regional Centre, CBRI Campus Roorkee, Uttarakhand 247667, Indiab Department of Civil Engineering, IIT Roorkee, Roorkee, Uttarakhand 247667, India

⁎ Corresponding author. Tel./fax: +91 1332 275998.E-mail address: rddwivedi@hotmail.com (R.D. Dwived

0013-7952/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.enggeo.2013.10.020

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 August 2012Received in revised form 21 October 2013Accepted 23 October 2013Available online 1 November 2013

Keywords:SqueezingDimensionally correctJoint factorSupport pressureEmpirical correlation

High in situ stresses and poor quality of rock mass are primarily responsible for the squeezing behaviour of rockmasses. This phenomenon is prevalent especially in the Himalayan region and hence rock engineers and engi-neering geologists have frequently encountered problems of stability during construction in this region. Highin-situ stresses, poor rockmass quality, large overburden depth and large radius or spanwidth of a tunnel or cav-ern in weak rocks are the factors which are responsible for the occurrence of squeezing ground condition. Thepresent study involves development of a dimensionally correct empirical correlation for assessment of supportpressure in tunnels which are excavated in squeezing ground condition. The correlation uses the concept of‘joint factor’ as a measure of rock mass quality, allowable closure, depth and radius of opening as the governingparameters. Data from 52 different tunnel sections and one set of data from amine gallery have been consideredfor analysis. The predicted results have been compared with the results obtained via existing approaches, basedon rock mass quality (Q) and rock mass number (N). It was observed that the proposed correlation holds betterwith a correlation coefficient of 0.92 and estimated values of support pressure from the approach show betteraccordance with the observed values of support pressure as compared to other existing correlations based onQ and N values. The proposed correlation makes use of parameters which can be easily obtained at projectsites. Therefore, it can become a handy tool for site engineers to predict the support pressure in squeezing groundconditions and take appropriate measures for the stability of underground excavations.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Himalayan region is full of geological surprises with regard to theunderground constructional activities due to frequently changing geol-ogy (Singh and Goel, 2006). The region is highly tectonically active andsqueezing of underground structures has been a major problem facedby geologists and engineers (Panthi and Nilsen, 2007). Due to this rea-son, the region has been a study centre of activity for many researchers.In the present study, the authors have also chosen the case studies fromthe Himalayan region.

Stability is the major concern in underground construction in weakrockmasses due to the presence of discontinuities and high in situ stressconditions. High insitu stress or anisotropic stress condition causes rockbursting, squeezing or other stress induced stability problems (Selmer-Olsen and Broch, 1977). Stress induced stability problems in weak rockmasses are characterized by squeezing. Thus, a combination of weakrock mass with high in situ stress multiplies the squeezing problem.The term ‘squeezing rock’ originates from the pioneering days of tunnel-ling in the Alps during the excavation of railway tunnels between theyears 1860 and 1910 (Kovari et al., 2000). Squeezing in tunnels is atime-dependent ground movement around the opening. This behaviouris primarily related to the progressive yielding and time-dependent

i).

ghts reserved.

deformation and degradation in the strength properties of the ground.Terzaghi (1946) described squeezing in rock as the displacement ofground under no volume change conditions. According to Barla (1995),squeezing around the tunnel openingmay stop throughout the construc-tion process or it may prolong for a considerable amount of time. Accord-ing to Kovári (1998), squeezing is the phenomenon of large deformationsthat develop during tunnelling through weak rocks and if an attempt ismade to arrest these deformationswith the help of a lining, support pres-sure builds up andmay reach values beyond the structurally manageablerange. The only feasible solution in heavily squeezing ground is a flexibletunnel support system in combination with a certain amount of over-excavation in order to accommodate the deformations (Cantieni andAnagnostou, 2009).

Squeezing conditions may vary over short distances due to rockheterogeneity and variations in rock mass properties. Thus, in case ofunreliable predictions of support pressure at the design stage, tunnelconstruction in squeezing ground becomes a herculean task claiminghigh cost and delay in time. However, if the support pressure can be reli-ably predicted using the governing parameters which can be easilyassessed in the field and accordingly appropriate stabilisation measuresare implemented, a good tunnelling rate can be achieved (Barla et al.,2011).

Empirical equation relating the support pressure and rock massquality index (Q) given by Grimstad and Barton (1993) suggests thatthe support pressure is independent of the tunnel size, whereas the

10 R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

support pressure increases significantly with tunnel size for squeezinggrounds (Singh et al., 1992; Bhasin and Grimstad, 1996; Goel et al.,1996; Bhasin et al., 2006). Empirical correlations, which have been pro-posed earlier for prediction of the support pressure in squeezing grounds,lack in dimensional correctness. In view of this, authors have made anattempt to develop a dimensionally correct empirical approach (correla-tion coefficient = 0.92) to predict the support pressure in squeezinggrounds. The correlation uses data from the case histories of tunnels con-structed in squeezing grounds of the Himalayan region. The parametersconsidered in this approach are: joint factor (as a measure of quality ofrock mass), allowed radial deformation, radius and depth of tunnel.

2. Geology and tunnelling problems encountered in tunnels

2.1. Chhibro–Khodri hydroelectric project

The project was constructed on river Tons, a tributary of Yamunariver located about 45 kmNorth of Dehradun in the state of Uttarakhand,India. Tunnel with a finished diameter of 7.5 mwas constructed betweenChhibro and Khodri to utilise discharge of the Chhibro powerhouse togenerate 120 MW of power through a surface powerhouse at Khodri.

The Chhibro–Khodri tunnel passes through three geological Forma-tions namely, Mandhali series (Paleozoic), Subathu–Dagshai (LowerMiocene) and Nahan series (Upper Tertiary). Mandhali series consistsof boulder slates, graphitic & quartzitic slates and Bhadraj quartziteunit with 5–10 m thick crushed quartzite along Krol thrust (Figure 1).Subathu–Dagshai series is comprised of 1–3 m thick plastic black claysalong the series thrust and red&purple crushed, brecciated and shearedshales and siltstones, minor grey and green crushed quartzites, 20–22 m thick black clays with thin bands of quartzites and 5–10 m thicksoft and plastic black clays along the Nahan thrust (Jain et al., 1975).Nahan series is comprised of greenish grey to grey micaceous (UpperTertiary) sandstones, purple siltstones, red, purple, grey and occasionalmottled blue concretionary clays. General strike of these litho units isnearly perpendicular to the tunnel axis with the dip ranging from 20°to 60° in NNW to NNE direction (Shome et al., 1973). There are twomain boundary faults running from the state of Punjab in the North tothe state of Assam in the East along the foothills of the Himalayas. Thefaults are known locally as the Nahan and the Krol thrusts. The dips ofthe Nahan and the Krol thrusts vary from 27° to 30° due N10°E toN10°W and 26° due N26° W respectively. The strike is almost normalto the tunnel alignment. In situ stresses were measured using flat jacktechnique and ratio of horizontal to vertical in situ stresses (k) wasdetermined to be equal to 1.

Major tunnelling problemswere faced within the intra-thrust zonesdue to squeezing ground conditions. In order to minimise the frequentrock falls, multi-drift method was employed for construction at faces.The tunnel was excavated by drill & blast method.

Heavy steel ribs of 300 mm × 140 mm and 150 mm × 150 mmsections, with 20–25 mm thick plates welded on both flanges were

Fig. 1. Geological cross-section alAfter Jain et al. (1975).

erected at 0.25–0.50 mspacing to cope upwith high squeezing pressures.The progress rate was tremendously slowed down to 5–6 m per month.Load cells and closure studs were installed up to 3.5 m behind the face.The observed support pressure varied from 0.65 to 1.3 MPa giving anaverage support pressure of 0.975 MPa in the vertical direction (Jethwaet al., 1980).

2.2. Giri–Bata hydroelectric project

This project with an installed capacity of 120 MW was constructedon Giri river, a tributary of river Yamuna. It is located near Girinagar inSirmour district of the state of Himachal Pradesh in India. A 7.1 kmlong head race tunnel with a finished diameter of 3.60 m was driventhrough a ridge separating the valleys of Giri and Bata rivers (Dube,1979).

The tunnel traverses throughBlaini series rock formations of carbon-iferous age for a length of about 1500 m and through highly jointed claystones, highly crushed phyllites and siltstones for the remaining length.The Blainis are dark grey to black quartzitic slates containing angular toround pebbles and boulders firmly embedded in a clay–silt matrix.The rock formations showed extensive jointing and shearing atplaces and the strike generally remained parallel to the tunnel alignment(Figure 2). Joints were spaced at 45–50 mm dipping with 60°–70°. Theseformations were highly crushed exhibiting an angle of internal frictionbetween 20° and 26°. In situ stresses were measured using flat jacktechnique and ratio of horizontal to vertical in situ stresses (k) wasdetermined to be equal to 2.

Most of the tunnelling problems were faced in zones of phyllites andslates. The tunnelwas excavated bydrill & blastmethod andwas support-ed by steel ribs. Load cells and closure studs were installed up to 3 mbehind the face. Blaini's slates, near the fault at chainage 1350 malso posed serious problems during construction because of hightunnel closures (N7%). Support pressure was observed in the range of0.2–0.5 MPa. Plain cement concrete lining of 300 mmaverage thicknesswas applied as final support.

2.3. Loktak hydroelectric project

This project lies 39 km south of Imphal, the capital city of ManipurState in North-East India. It diverts 58.8 m3/s of water from LoktakLake to supply 16.8 m3/s for irrigation. The remaining 42 m3/s ofwater with a gross head of 312 m is used to generate 105 MW ofpower from three units. Finished diameter of 6.5 km longhead race tun-nel was 3.65 m.

Loktak tunnel traverses through lake deposits, terrace deposits andshales with thin bands of sandstones and siltstones. In the first stretchof about 830 m, the tunnel passes through lacustrine deposits. Terracedepositswere encountered in thenext stretch of 420 mand the remain-ing part of the tunnel traverses trough splintary shales, sandy shaleswith variation of slaty and phyllitic types and some sandstones under

ong Chhibro–Khodri tunnel.

Fig. 2. Geological cross-section along Giri–Bata tunnel.After Dube (1979).

11R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

the rock cover of 300 m. The sandstones were bedded and flaggy in na-ture, whereas the shales were thinly laminated (Figure 3). The generaltrend of the rock masses was in N–S direction i.e. perpendicular to thetunnel axis. In situ stresses were measured using flat jack techniqueand ratio of horizontal to vertical in situ stresses (k) was determinedto be equal to 1.

Fig. 3. Geological section alongAfter Malhotra et al. (1982).

Fig. 4. Geological section alonafter Goel (1994).

The tunnelwas excavated by drill & blastmethod. Serious difficultieswere experienced during excavation due to excessive deformation ledby high squeezing behaviour of laminated shales.

Load cells and closure studswere installed up to 4 mbehind the face.Support pressure of 0.4–0.6 MPa and large tunnel deformations ofabout 7% of tunnel diameter were observed. Conventional tunnelling

Loktak head race tunnel.

g Maneri stage I tunnel.

Fig. 5. Geological section along Maneri stage II tunnel.After Varshney (1988).

Fig. 6. Geological section along Kaligandaki ‘A’ headrace tunneL.After Panthi and Nilsen (2007).

12 R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

was adopted to go ahead in the squeezing section of the tunnel. Thediameter of the excavated tunnel was increased to accommodate theexcess deformation.

2.4. Maneri Bhali Hydroelectric Project Stage-I

This project is constructed on river Bhagirathi, a tributary of riverGanges located in Uttarkashi, in the state of Uttarakhand in India togenerate 84 MWof power. A circular head race tunnel of 4.75 m finisheddiameter and 8.56 km length was constructed in Maneri-Bhali HydelScheme Stage-I.

The rockmasses exposed in the area are quartzites, quartzites inter-bedded with thin bands of slates, chlorite schists, phyllites, metabasicsand basic intrusives belonging to the Garhwal group (Jain et al., 1976).The general strike directions in Maneri, Heena and Tiloth areas are:N 10°–80°, N 250°–280°, and N 290°–350° respectively whereas dips

Fig. 7. Geological section along NaAfter Kumar (2002).

(directions) are 25°–45° (N 100°–170°), 25°–35° (N160°–190°) and35°–45° (N 20°–80°) respectively. These lithological units are intenselyfolded and faulted due to tectonic disturbances. The tectonic activity inthe area has developed closely spaced jointing, brecciation and shearingeven in the quartzites. The tunnel passes through metabasics andbasic chlorite-schists initially and then enters into folded quartzites(Figure 4). Two cross shear zones, 0.40 m wide, intersect above thetunnel crown (Goel et al., 1988). In situ stresses were measuredusing flat jack technique and ratio of horizontal to vertical in situstresses (k) was determined to be equal to 0.33.

Tunnelling activities at depths varying from 700 m to 900 m throughmoist and thinly foliated metabasics were beset with severe squeezingproblems.

The tunnel was supported by Indian Standard medium weight(ISMB) 150 mm × 150 mm steel ribs spaced at 0.60 m. Load cells andclosure studswere installed up to 3 mbehind the face. The data analysis

thpa Jhakri head race tunnel.

Excavated tunnel

(a)

A

Joints

(b)

A

RQ

P

θ

Fig. 8. (a) Loading on a rock mass element ‘A’ near springing level in a circular tunnel.(b) Enlarged element ‘A’.

Table 2Parameter r for different ranges of σci.After Ramamurthy and Arora (1994).

σci (MPa) r values Remarks

2.5 0.30 Finegrained micaceousto coarse-grained5.0 0.45

15.0 0.6025.0 0.7045.0 0.8065.0 0.90100.0 1.00

Table 3Joint strength parameter r for gouge material in joint near residual state.After Ramamurthy and Arora (1994).

Gouge material Friction angle, ϕ (degrees) r = tan(ϕ)

Gravelly sand 45 1.0

13R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

shows that the maximum deformation was observed to be 7.3% at thecontact of metabasics and quartzites (Goel, 1994).

Coarse sand 40 0.84Fine sand 35 0.70Silty sand 32 0.62Clayey sand 30 0.58Clay–siltClay-25% 25 0.47Clay-50% 15 0.27Clay-75% 10 0.18

2.5. Maneri Bhali Hydroelectric Project Stage-II

The project is constructed on river Bhagirathi, a tributary of the riverGanges and located in the lower Himalaya about 150 km north-west ofthe holy town, Rishikesh in India, with an installed capacity of 304 MW.It comprises of 16 km long head race tunnel (HRT) with a finisheddiameter of 6.0 m.

The head race tunnel passes throughquartzites,meta-volcanics (alsocalled metabasics), limestones and epidiorites of the Garhwal group andphyllites, slates and greywackes of Tehri Formations. The Garhwalgroup thrusts over the Tehri formations. Rock masses, in general, aremoderately jointed. Several cross shear zones are also encountered inthe area. The general dip of foliations as well as of bedding planes variesfrom 40° to 80° in N–E direction. The tunnel encountered moderately fo-liated, jointed and sheared metabasics (also called meta-volcanics) andquartzites in a length of more than 3000 m. The sheared and jointedmeta-basics, massive to moderately jointed quartzites, pyriteferrousslates with thin intercalations of quartzites and jointed limestone, mas-sive phyllites and greywackes with calcareous lenses, and thinly beddedgreywacke were encountered during tunnelling (Figure 5). The lithologi-cal contacts and the contacts between the formations were mostlysheared. In situ stresses were measured using flat jack technique andratio of horizontal to vertical in situ stresses (k) was determined to beequal to 0.33.

Tectonically active and young rock masses of the lower Himalayas,as seen so far, are highly shattered andweak causing frequent squeezingground conditions. The Maneri stage-II tunnel was not an exception.The tunnel was excavated by drill & blast method. Severe squeezingground conditions were encountered during tunnelling in the zones ofmeta-basics, sheared meta-basics, greywackes and phyllites.

ISMB 150 mm × 150 mm steel ribs were installed at 0.5 m spacingfrom centre to centre. Load cells and closure studs were installed up to3 m behind the face. Support pressures of 0.17 MPa and 0.29 MPawere observed in metavolcanics and sheared metabasics rock typesrespectively, whereas tunnel deformation were observed between2.5% to 3%.

Table 1Joint orientation parameter n for different joint orientation angles.After Ramamurthy and Arora (1994).

β (degrees) 0 10 20 30 40 50 60 70 80 90

n 0.82 0.46 0.11 0.05 0.09 0.30 0.46 0.64 0.82 0.95

Note: β-angle of joint with loading direction.

2.6. Noonidih–Jitpur Colliery

The Noonidih–Jitpur Colliery (a captive coal mine of M/S Indian Ironand steel Company Limited, Jamshedpur, India) is located in Jharia Coal-fields near Dhanbad in the state of Jharkhand in India.

Underground working of this colliery consisted of partially or fullydeveloped areas in two seams with thickness of 3.5 m and 2.44 m andat a depth of 134 m and 73 m respectively. These seams dipped atabout 8.7°. Two other seams had thicknesses of 2.44 m and 4.57 mand at depths of 233 m and 268 m respectively. These seams wereworked through two shafts. A main roadway of 3.5 m width was exca-vated through weak coal at a depth of 450 m to excavate a 9 m thickcoal seam. In situ stresses were measured using hydraulic fracturingtechnique and ratio of horizontal to vertical in situ stresses (k) wasdetermined to be equal to 0.86.

Drill & blast method of excavation was adopted to drive the mainroad. Problem of excessive deformationwas observed in themain road-way due to high stresses.

Fig. 9. Plot of (10Pobs/σv) versus 10σ7 Jf3 σh0.1 / {σci0.1(d0.2 + Jf / 1434)}.

Table 4Data collected from various case histories.

S. no. Name of tunnel Rock type Reference Q Jr Jn N a, m H, m d = u/a (%) Jnjoint/m

n r Jf

1. Chhibro–Khodri adit Crushed red shales Jethwa (1981), Goel (1994), Choudhari (2007) 0.05 1.5 12 0.375 1.5 280 2.8 14.3 0.09 0.445 3572. Chhibro–Khodri HRT Crushed red shales 0.024 1.2 4 0.5 4.5 680 6 12.9 0.09 0.384 3733. Chhibro–Khodri adit Soft & plastic black clays 0.022 1.2 4 0.11 1.5 280 4.5 12.9 0.09 0.384 3734. Chhibro–Khodri HRT Soft & plastic black clays 0.022 1.2 4 0.11 4.5 580 2 12.9 0.09 0.384 3735. Giri–Bata HRT Blaini's slates Dube (1979), Goel (1994), Choudhari (2007) 0.36 1 6 2.55 2.3 380 7.6 7.69 0.07 0.384 2866. Giri–Bata HRT Crushed phyllites 0.12 1 4 0.6 2.3 240 5.5 8.45 0.07 0.364 3327. Loktak HRT MFSS 0.015 0.5 6 0.1725 2.4 300 7 9.45 0.09 0.268 3928. Maneri Stage-I HRT Sheared metabasics Jethwa (1981) 0.16 1.2 9 3.75 2.9 450 7.3 18.1 0.22 0.268 3079. Maneri Stage-II HRT Metavolcanic Goel, 1994; Choudhari (2007) 0.8 1.2 4 4 1.25 480 2.5 5.75 0.05 0.445 25810. Maneri Stage-II HRT Sheared metabasics 0.18 1.2 9 0.9 3.5 410 3 6.85 0.82 0.445 30811. Noonidih Colliery MG Weak coal Jethwa (1981) 0.59 1 6 5.9 3.5 450 3 71.4 0.82 0.344 25312. Tala Hydro HRT AGO (adverse geological occurrences): completely sheared,

highly weathered biotite schist associated with banded gneiss,amphibolites and quartzites in thin bands

Sripad et al. (2007) 0.007 1 15 0.07 3.4 337 2.1 16.91 0.09 0.445 422

13. Tala HRT, Bhutan 0.011 1 15 0.11 3.4 337 3.8 16 0.09 0.445 39914. Tala HRT, Bhutan 0.006 1 15 0.06 3.4 337 3.1 16.48 0.09 0.445 41115. Tala HRT, Bhutan 0.006 1 15 0.06 3.4 337 2.2 16.48 0.09 0.445 41116. Tala HRT, Bhutan 0.08 1 15 0.8 3.4 337 2.2 13.39 0.09 0.445 33417. Kaligandaki ‘A’ HRT Graphic phyllites NEA (2002), Panthi and Nilsen (2007) 0.029 1 15 0.125 4.35 550 2.3 3.29 0.05 0.18 36518. Kaligandaki ‘A’ HRT Graphic phyllites 0.023 1 15 0.115 4.35 600 1.4 3.33 0.05 0.18 37019. Kaligandaki ‘A’ HRT Graphic phyllites 0.03 1 15 0.15 4.35 600 2.9 3.23 0.05 0.18 35920. Kaligandaki ‘A’ HRT Graphic phyllites 0.018 1 15 0.09 4.35 600 3.9 3.42 0.05 0.18 38021. Kaligandaki ‘A’ HRT Graphic phyllites 0.023 1 15 0.12 4.35 600 3.2 3.33 0.05 0.18 37022. Kaligandaki ‘A’ HRT Graphic phyllites 0.02 1 15 0.3 4.35 620 4.9 3.36 0.05 0.18 37323. Kaligandaki ‘A’ HRT Graphic phyllites 0.008 1 15 0.16 4.35 620 8.5 6.4 0.09 0.18 40124. Kaligandaki ‘A’ HRT Graphic phyllites 0.009 1 15 0.18 4.35 620 7.7 3.6 0.05 0.18 40025. Kaligandaki ‘A’ HRT Graphic phyllites 0.009 1 15 0.18 4.35 620 8.2 3.6 0.05 0.18 40026. Kaligandaki ‘A’ HRT Siliceous phyllites 0.016 1 15 0.32 4.35 620 4.4 6.3 0.09 0.18 38927. Kaligandaki ‘A’ HRT Graphic phyllites 0.02 1 15 0.1 4.35 620 4.1 3.36 0.05 0.18 37328. Kaligandaki ‘A’ HRT Graphic phyllites 0.025 1 15 0.5 4.35 620 2.5 5.95 0.09 0.18 367

14R.D

.Dwivedietal./Engineering

Geology

168(2014)

9–22

S.no

.

Nam

eof

tunn

elRo

cktype

Referenc

eQ

J rJ n

Na,m

H,m

d=

u/a(%

)J n joint/m

nr

J f

29.

Kaligan

daki

‘A’H

RTGraph

icph

yllites

NEA

(200

2),Pan

thia

ndNilsen

(200

7)0.02

31

150.11

54.35

580

3.7

3.33

0.05

0.18

370

30.

Kaligan

daki

‘A’H

RTGraph

icph

yllites

0.02

51

150.12

54.35

580

1.7

5.95

0.09

0.18

367

31.

Kaligan

daki

‘A’H

RTGraph

icph

yllites

0.02

51

150.12

54.35

550

2.4

5.95

0.09

0.18

367

32.

Kaligan

daki

‘A’H

RTGraph

icph

yllites

0.00

71

150.03

54.35

575

6.0

6.4

0.09

0.18

401

33.

Nathp

aJhak

ri-H

RTQua

rtzmicaschist;s

chistose

quartzites

andam

phibolites

Kum

ar(200

2)0.41

71.5

98.33

35.5

700

3.5

6.1

0.05

0.47

260

34.

Nathp

aJhak

ri-H

RT0.33

31.5

91.66

55.5

700

3.5

8.77

0.05

0.47

273

35.

Nathp

aJhak

ri-H

RT0.33

31.5

91.66

55.5

750

3.5

7.7

0.06

0.47

274

36.

Nathp

aJhak

ri-H

RT0.25

1.5

91.25

5.5

600

3.5

10.99

0.08

0.47

292

37.

Nathp

aJhak

ri-H

RT0.05

61.5

90.55

65.5

850

5.0

8.06

0.05

0.47

343

38.

Nathp

aJhak

ri-H

RT0.03

31.5

90.16

75.5

600

3.0

8.77

0.05

0.47

373

39.

Nathp

aJhak

ri-H

RT0.00

11.5

90.01

95.5

300

6.0

11.63

0.05

0.47

495

40.

Nathp

aJhak

ri-H

RT0.00

31.5

90.05

25.5

400

6.0

10.64

0.06

0.47

453

41.

Nathp

aJhak

ri-H

RT0.19

41.5

90.97

5.5

800

3.5

7.2

0.05

0.47

306

42.

Udh

ampu

rrailtunn

el(T1)

Clay

ston

e,siltyclay

ston

e0.06

251.5

120.31

33.25

300

3.0

9.5

0.06

0.47

340

43.

Udh

ampu

rrailtunn

el(T1)

0.09

381.5

120.46

93.25

312

1.5

9.1

0.06

0.47

327

44.

Udh

ampu

rrailtunn

el(T1)

0.08

332

120.41

73.25

280

1.5

9.7

0.06

0.49

331

45.

Udh

ampu

rrailtunn

el(T1)

0.12

52

120.62

53.25

270

2.2

9.3

0.06

0.49

318

46.

Udh

ampu

rrailtunn

el(T1)

0.06

252

120.62

53.25

285

2.5

9.5

0.06

0.47

340

47.

Udh

ampu

rrailtunn

el(T1)

0.03

131.5

120.31

33.25

280

2.6

9.3

0.06

0.45

348

48.

Udh

ampu

rrailtunn

el(T1)

0.04

172

120.41

73.25

280

2.4

9.3

0.06

0.45

348

49.

Chen

ani–NashriE

scap

eTu

nnel

Siltston

e,siltyclay

ston

e2.28

73.5

125.71

83

727

1.7

5.15

0.05

0.47

221

50.

Chen

ani–NashriE

scap

eTu

nnel

2.42

63.5

126.06

53

736

1.3

5.09

0.05

0.47

218

51.

Chen

ani–NashriE

scap

eTu

nnel

2.90

33.5

127.25

83

733

1.6

4.88

0.05

0.47

209

52.

Chen

ani–NashriE

scap

eTu

nnel

1.65

3.5

124.12

53

690

1.6

5.34

0.05

0.47

229

53.

Chen

ani–NashriE

scap

eTu

nnel

Siltston

e1.51

73.5

123.79

36.5

577

1.8

5.34

0.05

0.45

240

Notations

:HRT

’Headrace

tunn

el;M

G-Minega

llery;M

FSS-

Mod

eratelyfracturedsplin

tery

shales

withclay

coatings.

15R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

The roadway was supported with steel ribs and monitoring wasdone for support pressure and tunnel deformation. A significant move-ment was observed in the 3.5 m wide main roadway. Load cells andclosure studs were installed up to 4 m behind the face. The roadwaydeformation was measured to be 3% (Jethwa, 1981). Support pressurewas observed to be in the range of 0.05–0.20 MPa.

2.7. Tala hydroelectric project

Tala hydroelectric project is situated in South-West Bhutan in East-ern Himalaya. The project lies in the district of Tala and at 3 km down-stream of the existing 336 MW Chukha Hydroelectric project on riverWangchu (Sripad et al., 2007). It has a 22 km long head race tunnel(HRT) of 6.8 m diameter.

The head race tunnel traverses through highly weathered biotiteschist associated with banded gneiss amphibolites and quartzites. Insitu stresses were measured using flat jack technique and ratio of hori-zontal to vertical in situ stresses (k) was determined to be equal to 0.6.

The tunnel was excavated by drill & blast method. While tunnelling,excessive deformation was encountered atmany tunnel sections due tosqueezing behaviour of the poor rock mass present around the tunnelperiphery.

The support system in the tunnel is in the form of steel ribs (ISMB200 or SMB 250 at 0.5 m centre to centre), 5–6 m long rock bolts of25 mm diameter at 2.0 m spacing in combination with 175 mm steelfibre shotcrete as a temporary lining and a final permanent concretelining (Tripathy et al., 2000). Load cells and closure studs were installedup to 3.5 m behind the face. Tunnel deformation and support pressurewere measured to be 2–3.8% and 0.610.94 MPa.

2.8. Kaligandaki “A” hydroelectric project

The Kaligandaki “A” hydroelectric project is located in the LesserHimalaya about 200 km West of Kathmandu. The project is owned byNepal Electricity Authority (NEA), an undertaking of Government ofNepal. The project has an installed capacity of 144 MW and to generatethis energy, water of Kaligandaki river is diverted through a head racetunnel with cross sectional area of about 60 m2.

The project area is located in highly deformed rock formationof the Lesser Himalaya. The rocks of this area are mainly comprisedof Precambrian to lower Palaeozoic shallow marine sediments. Thehead race tunnel mainly passes through highly deformed siliceousand graphitic phyllites that vary in mineral composition and degreeof metamorphism. As a result of tectonic movement, the rock massin the area has been subjected to shearing, folding and faulting. Thephyllites are of poor quality, thinly foliated and highly weathered (NEA,2002). The orientation and dips of joints are highly scattered due toextreme folding and shearing, giving no distinct joint system exceptfor foliation joints. In general, the foliation joints are oriented in SouthEast–North West direction and dip towards South West. The alterationand weathering are considerable and the joints are filled with highlysheared clay, quartz and calcite veins. The maximum rock cover abovethe tunnel is about 600 m and more than 80% of the tunnel alignmenthas overburden exceeding 200 m (Panthi and Nilsen, 2007) (Figure 6).The ratio of horizontal to vertical in situ stresses (k) was determined tobe equal to 0.5.

The head race tunnel was excavated by drill & blast methodand faced severe squeezing due to abovementioned geologicalconditions.

The tunnel was supported with steel ribs at 1 m spacing centre tocentre, 200–250 mm thick reinforced shotcrete and radial bolting.Load cells and closure studs were installed up to 3 m behind the face.Tunnel deformation and support pressure were measured to be 1.4–8.5% and 0.90–1.27 MPa.

Fig. 10. Correction factor for tunnel deformation.After Goel (1994).

16 R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

2.9. Nathpa Jhakri hydroelectric project

Nathpa Jhakri hydro power project is located in the northernstate of Himachal Pradesh (India), on the downstream of Wangtoobridge and derives its name from the names of two villages in theproject vicinity— Nathpa in district Kinnaur and Jhakri in district Shimla.The project was conceived as a run-of-river type hydro power develop-ment, harnessing hydroelectric potential of the middle reaches of theriver Sutlej, one of the principal tributaries of the river Indus in thesouth west Himalayas. The head race tunnel, with 10.15 m diameterand 27394.5 m length, was constructed to carry a design discharge of405 m3/s.

The major rock types of the area are augen gneiss, quartz–biotiteschist, amphibolites and some pegmatite lenses at places. Augen gneissessentially consists of two feldspars, two micas (mainly biotite), gneisswith a porphyro-blastic texture, which at places are mylonitic. Thefoliations are defined by the micaceous layers, which flow aroundthe augens. The elongation direction of the augens defines a strongstretching lineation. The shape of the augens varies from nearlyround to lensoidal at places, showing well drawn out porphyroclasttails. Schistocity of quartz–biotite-schist has a strong dominant char-acter with well-defined quartzose and micaceous layers. The layersare tabular to lensoidal. At places some biotite rich lenses are alsoseen. Strong stretching lineation on the foliation plane is marked.At places the biotite altering to sericite indicated by crumpling andhigh fissility is also noticed. The amphibolites are massive weaklyfoliated with a prominent amphibole lineation, which appears to bea primary igneous flow structure. The quartz, feldspar content is verylow and the rock is especially a biotite rich amphibolite. The amphibo-lites occur as narrow linear belts in the outcrop and generally unparallelto the foliation of the country rocks except at places where they are atan angle to the country rocks. Pegmatite occurs both as concordantand discordant bodies and are commonly associated with the gneisses.These are present as tabular laths. Quartz and feldspar exhibit a graphictexture and show two sets of fractures (Kumar, 2002). There are threesets of joints, two of them are at right angles to each other and thethird, oblique to them is sub-vertical, and resulting in wedge shapedblock or rocks. Foliations were observed dipping with 30°-70°, 40°-75,15°-55°, and 30°-85° towards North-East in various sections of thetunnel. The head race tunnel traverses through augen gneiss, gneiss,quartz mica schist, biotite schist, sericite schist, amphibolites, granitegneiss, and pegmatite (Figure 7). In situ stresses were measured usinghydraulic fracturing technique and ratio of horizontal to vertical insitu stresses (k) was determined to be equal to 1.3.

The excavation of tunnel was carried out through seven adits byheading and bench method and using drill & blast technique. The geo-logical section along the head race tunnel from chainage 15900 m to27394.5 m posed squeezing problems during tunnelling. Large tunneldeformationswere observed due to high ground stresses and poor qual-ity of rock mass between chainage 24438.0 m and chainage 24745.0 m(rock cover of 600 m-700 m) where quartz–mica schist striking sub-parallel to the tunnel was encountered.

The type of support varied with the category of rock mass encoun-tered. Steel ribs have been used to support the squeezing sections ofthe tunnel. Concrete lining of 400–600 mmthickness have been appliedasfinal lining (Kumar, 2002). Load cells and closure studswere installedup to 5 m behind the face. Tunnel deformation and support pressurewere measured to be 3.5%–6% and 0.26–1.02 MPa. This problem wastackled by over excavating the tunnel by 300 mm.

2.10. Udhampur railway tunnel

Indian Railways are linking the Kashmir valley in the State of Jammu& Kashmir through Himalayas, with a broad gauge railway linkwhich isbelow snow line making it an all-weather route. The total route lengthinvolved is 342 km, out of which about 100 km is in tunnels. The rulinggradient is 1 in 100,maximum degree of curvature is restricted to 2.75°.Udhampur–Katra section is the 1st phase of Udhampur–Srinagar–Baramula Rail Link Project which is 25 km long and involves construc-tion of 7 tunnels aggregating to 10 km. Tunnel No. 1 is D-shaped with6.5 mdiameter and 8.25 mheight. It is the longest tunnel of this sectionhaving a length of 3.1 km (Goel et al., 2004).

The tunnel which falls in Shiwalik Group and Pleistocene to re-cent deposits traverses through unconsolidated or poorly consoli-dated sediments with rocks of upper/middle/lower Shiwalik andMurree formations. It passes through thickly bedded, moderatelysoft and sparsely jointed sandstones, sheared claystones and silt-stones. Overburden is comprised of boulders/pebbles in sandy/silty matrix. Claystone/siltstone beds have 3 sets of closely spacedjoints with random joints dipping at 70°. Strike of joints makes anangle of 30° with tunnel axis. In stretch from 270 m to 313 m comprisingof weak rock formation (claystone and siltstone). Q-values of claystoneand siltstone vary between 0.041 and 0.2 and stand up time of approxi-mately 1 day (CIMFR, 2007). In situ stresses were measured using flatjack technique and ratio of horizontal to vertical in situ stresses (k) wasdetermined to be equal to 1.2.

The tunnel was excavated by drill & blast method. Squeezingbehaviour of rock mass was experienced during tunnelling. Steel rib

17R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

supports (ISHB200) were installed at 0.75 m spacing from centre tocentre. Load cells and closure studs were installed up to 3 m behindthe face. Support pressure was observed to be 0.30–0.52 MPa, whereasradial deformation was recorded to be 1.5–3% (CIMFR, 2007).

2.11. Chenani–Nashri tunnel

National Highway Authority of India aims at construction of9.0 km long two lane bidirectional main tunnel with a parallel9.0 km long escape tunnel on new alignment between Chenani andNashri along the existing National Highway (NH)-1A in the state ofJammu & Kashmir (J & K). The longest portion of the alignment is un-derground, with the formation of the Chenani–Nashri tunnel charac-terized by the main tunnel (single-tube, with bi-directional traffic,one lane per direction) and a parallel escape tunnel. Main tunnelwill be a paved carriageway with width of 9.35 m wide and 1.2 mwide footpath each side. The minimum vertical clearance would be5.0 m. The parallel escape tunnel will be 5.00 m wide with the min-imum vertical clearance of 2.5 m. Main tunnel and escape tunnel willbe interconnected at every 300 m for safety reasons. The tunnels arebeing excavated by drill & blast method.

The project area lies in the Western Himalayan region in a sector ofcollisional belt known as sub-Himalayas. This tectonic domain is bound-ed toward south by theHimalayan Frontal Thrust orMain Frontal Thrust(HFT or MFT) and theMain Boundary Thrust (MBT) to the North. Thesemain thrusts as well as most of the belts and units of this NW region ofHimalaya orogen show a regional strike of NWSE to WNW–ESE withmoderate to steep dips either towards north or the south (Facibeniet al., 2011). The rock masses along the project of the Chenani–Nashritunnel belong to the LowerMurree formation. This sedimentary succes-sion is classified as the ‘Lower Tertiary Sediments’ of the ‘Murree Struc-tural Belt’ and bounded on the south by theMain Frontal Thrust and onthenorth by a complex of thrusts regionally referred as theMain Bound-ary Thrust (MBT) that delimited from the metamorphic complex. TheMuree Formation is represented by a sequence of argillaceous and are-naceous rocks that includes a sequence of interbedded sandstone, silt-stone/claystone beds with thickness ranging from a few metres up to10 m (Goel et al., 2012). Rock mass of the area has three sets of joints,i.e., bedding planes dipping at 20–25° towards 150° from North, secondjoint set dipping at 50–75° towards 250–300° fromNorth and third jointset dipping at 65–80° towards 350–90° from North. The strike of jointsmakes an angle of about 22° with tunnel axis on the sections, whichhave been included for analysis. The bands of sandstone, siltstone, andclaystone of varying thickness are frequently encountered during tun-nel excavation. There is no fixed pattern of the bands of these rocks. Infact the bands of mixed rocks, for example, intermix siltstone & sand-stone and intermix siltstone & claystone are also encountered frequent-ly. The uniaxial compressive strengths of freshly obtained rock samplesof sandstone, siltstone and claystone are 70–120 MPa, 25–40 MPa and8–15 MPa respectively.

Squeezing problem was encountered in tunnel sections com-prising siltstone, claystone and intermixed siltstone–claystone. Insitu stresses were measured using flat jack technique and ratio ofhorizontal to vertical in situ stresses (k) was determined to beequal to 1.2.

In these poor rock mass sections, shotcrete with wiremesh (150 -

mm × 150 mm × 6 mm), 4 m long rockbolts of 28 mm diameter at2.5 m × 2.5 m spacing in staggered pattern and lattice girders at2.5 m spacing from centre to centre were used to support the rock inweak sections. Load cells and closure studs were installed up to 5 m be-hind the tunnel face. Deformation of tunnel in claystone and siltstonesections was observed to be 1.3–1.7% in the escape tunnel and 1.5 to2% in the main tunnel. Support pressure was observed to be 0.1–0.25 MPa in the escape tunnel and 0.20–0.25 MPa in the main tunnel(GEODATA, 2011).

3. Parameters considered for development of empirical correlation

The governing parameters like ‘joint factor’ (as a measure of rockmass quality), vertical in situ stress and radius of the tunnel are thegoverning parameters which have been considered for developingthe empirical correlation in the present study for development ofdimensionally correct correlation for prediction of tunnel supportpressure in squeezing ground condition are discussed in the follow-ing sections.

3.1. Joint factor (Jf)

The concept of joint factor was developed by Ramamurthy and hisco-workers (Arora, 1987; Ramamurthy and Arora, 1994; Singh, 1997;Singh et al., 2002; Zhang, 2010). The most significant factors namely,joint frequency, joint orientation and joint strength influencing thestrength of jointed rock mass, have been suitably clubbed together toevolve a single factor called the joint factor, and designated as Jf. Thejoint factor has been defined as:

J f ¼Jn

n � r ð1Þ

where Jn is the joint frequency, i.e. number of joints per metre length inthe direction of loading, n, the joint orientation parameter dependingupon the orientation of the joint with respect to loading direction, andr is the joint strength parameter which depends upon the joint condi-tion (whether clean and rough or filled-up joints), thickness of joint,and joint alteration due toweathering. The joint factor reflects the qual-ity reduction/weakness in the intact rock. The lower the joint factor, thehigher is the strength, i.e. less weak.

Fig. 8(a) depicts a circular tunnel excavated through inclined bed-ding planes. Loading direction on a rock mass element, ‘A’ near thespringing level has been shown by vertical arrows. Enlarged view ofthe element ‘A’ is shown in Fig. 8(b). Joints are shown as apparently dip-ping at an angle of θA°. If tunnel axis makes an angle of α° with strike ofjoints, the apparent dip may be computed as follows:

θA° ¼ tan−1 tanθ° � cosα�� � ð2Þ

where θ° is the true dip of joints. From Fig. 8(b), joint frequency (Jn) iscomputed as follows:In ΔPQR, ∠PRQ = 90°, ∠PQR = 90° − θA° = β,and

Jn ¼ 1000 sinβPR

joints=m length in the loading direction ð3Þ

where PR is expressed in mm.

3.1.1. Joint orientation parameter (n)The strength of jointed rock depends primarily upon the orientation

of the joint with respect to the direction of axial loading. A minimumvalue of strength has been observed when the joints are oriented atan angle of β = 30°–40° (Ramamurthy and Arora, 1994). Similar be-haviour was also observed by Mclamore and Gray (1967), Attwell andSandford (1974) and others. Values of n are presented in Table 1.

3.1.2. Joint strength parameter (r)The joint strength parameter, r was evolved to depict the rough-

ness condition of the joint and is expressed as r = tanϕj where ϕj

is the friction angle of joints at a very low normal stress level(σn → 0). This parameter is determined as the tangent of the frictionangle operating along the joint. For clean joints, the joints can besubjected to a direct shear test at low stress levels and value of ϕj

can be obtained as the secant value of the friction angle. In the ab-sence of actual test, this parameter may be obtained from uni-axialcompressive strength of intact rock material (σci). The suggested

Table 5Coefficient of Accordance of support pressure values estimated from various approaches.

S. no. Name of tunnel Rock type Pobs, MPa PN, MPa (Pobs − PN)2 (Pobs − ΣPobs / n)2 Pu,MPa

(Pobs − Pu)2 Pb,MPa

(Pobs − Pb)2 Ps,MPa

(Pobs − Ps)2

1. Chhibro–Khodri adit Crushed red shales 0.31 0.26 0.00 0.21 1.25 0.89 0.22 0.01 0.40 0.012. Chhibro–Khodri HRT Crushed red shales 1.08 1.02 0.00 0.10 1.16 0.01 1.04 0.00 1.11 0.003. Chhibro–Khodri adit Soft & plastic black clays 0.32 0.39 0.00 0.18 1.19 0.76 0.36 0.00 0.51 0.044. Chhibro–Khodri HRT Soft & plastic black clays 1.15 7.98 46.63 0.18 1.19 0.00 1.07 0.01 1.50 0.125. Giri–Bata HRT Blaini's slates 0.20 0.22 0.00 0.25 0.69 0.24 0.26 0.00 0.16 0.006. Giri–Bata HRT Crushed phyllites 0.17 0.14 0.00 0.28 0.81 0.41 0.37 0.04 0.23 0.007. Loktak HRT MFSS 0.54 0.81 0.07 0.02 3.97 11.78 1.56 1.03 0.50 0.008. Maneri Stage-I HRT Sheared metabasics 0.20 0.21 0.00 0.23 0.92 0.52 0.36 0.02 0.23 0.009. Maneri Stage-II HRT Metavolcanic 0.17 0.14 0.00 0.26 0.36 0.04 0.09 0.01 0.13 0.0010. Maneri Stage-II HRT Sheared metabasics 0.29 0.25 0.00 0.15 0.89 0.35 0.41 0.02 0.28 0.0011. Noonidih Colliery MG Weak coal 0.15 0.10 0.00 0.27 0.58 0.19 0.33 0.03 0.12 0.0012. Tala Hydro HRT AGO (adverse geological occurrences): completely sheared,

highly weathered biotite schist associated with banded gneiss,amphibolites and quartzites in thin bands

0.94 3.05 4.47 0.08 4.05 9.67 1.42 0.23 1.24 0.0913. Tala HRT, Bhutan 0.61 0.86 0.06 0.00 3.48 8.25 1.22 0.38 0.80 0.0414. Tala HRT, Bhutan 0.70 2.52 3.33 0.01 4.26 12.69 1.50 0.64 0.98 0.0815. Tala HRT, Bhutan 0.80 3.53 7.47 0.04 4.26 11.99 1.50 0.49 1.08 0.0816. Tala HRT, Bhutan 0.31 0.29 0.00 0.08 1.80 2.21 0.63 0.10 0.40 0.0117. Kaligandaki ‘A’ HRT Graphic phyllites 0.90 1.60 0.50 0.10 2.52 2.63 1.13 0.05 0.83 0.0118. Kaligandaki ‘A’ HRT Graphic phyllites 1.27 3.37 4.41 0.51 2.72 2.11 1.22 0.00 1.11 0.0219. Kaligandaki ‘A’ HRT Graphic phyllites 1.00 1.50 0.25 0.22 2.49 2.23 1.12 0.01 0.79 0.0420. Kaligandaki ‘A’ HRT Graphic phyllites 1.02 1.80 0.61 0.27 2.96 3.73 1.33 0.09 0.95 0.0121. Kaligandaki ‘A’ HRT Graphic phyllites 0.92 1.75 0.70 0.19 2.72 3.27 1.22 0.09 0.88 0.0022. Kaligandaki ‘A’ HRT Graphic phyllites 1.27 1.54 0.07 0.66 2.85 2.51 1.28 0.00 0.90 0.1423. Kaligandaki ‘A’ HRT Graphic phyllites 1.25 7.65 41.05 0.68 3.87 6.89 1.74 0.24 1.03 0.0524. Kaligandaki ‘A’ HRT Graphic phyllites 1.13 5.36 17.94 0.54 3.72 6.75 1.67 0.30 1.05 0.0125. Kaligandaki ‘A’ HRT Graphic phyllites 1.20 5.88 21.85 0.70 3.72 6.37 1.67 0.22 1.03 0.0326. Kaligandaki ‘A’ HRT Siliceous phyllites 1.15 0.83 0.10 0.66 3.07 3.70 1.38 0.05 1.07 0.0127. Kaligandaki ‘A’ HRT Graphic phyllites 1.07 1.54 0.22 0.58 2.85 3.17 1.28 0.04 0.89 0.0328. Kaligandaki ‘A’ HRT Graphic phyllites 1.27 2.26 0.97 0.98 2.65 1.90 1.19 0.01 0.95 0.1029. Kaligandaki ‘A’ HRT Graphic phyllites 0.97 1.29 0.10 0.52 2.72 3.08 1.22 0.06 0.82 0.0230. Kaligandaki ‘A’ HRT Graphic phyllites 1.27 2.61 1.79 1.09 2.65 1.90 1.19 0.01 0.98 0.0931. Kaligandaki ‘A’ HRT Graphic phyllites 0.95 1.81 0.73 0.57 2.65 2.88 1.19 0.06 0.84 0.01

18R.D

.Dwivedietal./Engineering

Geology

168(2014)

9–22

S.no

.

Nam

eof

tunn

elRo

cktype

P obs,M

PaP N

,MPa

(Pob

s−

P N)2

(Pob

s−

ΣP o

bs/n)

2P u,

MPa

(Pob

s−

P u)2

P b,

MPa

(Pob

s−

P b)2

P s,

MPa

(Pob

s−

P s)2

32.

Kaligan

daki

‘A’H

RTGraph

icph

yllites

1.27

3.55

5.21

1.20

4.05

7.72

1.82

0.30

1.04

0.05

33.

Nathp

aJhak

ri-H

RTQua

rtzmicaschist;S

chistose

quartzites

andam

phibolites

0.26

0.10

0.03

0.01

0.54

0.08

0.39

0.02

0.23

0.00

34.

Nathp

aJhak

ri-H

RT0.32

0.26

0.00

0.03

0.58

0.07

0.42

0.01

0.29

0.00

35.

Nathp

aJhak

ri-H

RT0.32

0.29

0.00

0.04

0.58

0.07

0.42

0.01

0.32

0.00

36.

Nathp

aJhak

ri-H

RT0.32

0.26

0.00

0.04

0.63

0.10

0.47

0.02

0.33

0.00

37.

Nathp

aJhak

ri-H

RT1.02

1.01

0.00

0.82

1.05

0.00

0.77

0.06

0.99

0.00

38.

Nathp

aJhak

ri-H

RT1.00

3.24

5.04

0.83

1.25

0.06

0.91

0.01

1.14

0.02

39.

Nathp

aJhak

ri-H

RT0.99

4.81

14.59

0.86

4.00

9.06

2.93

3.78

1.05

0.00

40.

Nathp

aJhak

ri-H

RT1.02

4.37

11.23

0.82

2.77

3.07

2.03

1.03

1.28

0.07

41.

Nathp

aJhak

ri-H

RT0.60

0.52

0.01

0.34

0.69

0.01

0.51

0.01

0.59

0.00

42.

Udh

ampu

rrailtunn

el(T1)

Clay

ston

e,Siltyclay

ston

e0.30

0.32

0.00

0.05

1.16

0.75

0.44

0.02

0.35

0.00

43.

Udh

ampu

rrailtunn

el(T1)

0.52

0.46

0.00

0.20

1.02

0.25

0.38

0.02

0.37

0.02

44.

Udh

ampu

rrailtunn

el(T1)

0.44

0.44

0.00

0.15

0.79

0.12

0.30

0.02

0.34

0.01

45.

Udh

ampu

rrailtunn

el(T1)

0.35

0.26

0.01

0.09

0.69

0.12

0.26

0.01

0.24

0.01

46.

Udh

ampu

rrailtunn

el(T1)

0.32

0.25

0.01

0.08

0.87

0.31

0.33

0.00

0.35

0.00

47.

Udh

ampu

rrailtunn

el(T1)

0.30

0.34

0.00

0.07

0.88

0.34

0.33

0.00

0.37

0.01

48.

Udh

ampu

rrailtunn

el(T1)

0.30

0.32

0.00

0.08

1.00

0.49

0.37

0.01

0.38

0.01

49.

Chen

ani–NashriE

scap

eTu

nnel

Siltston

e,siltyclay

ston

e0.10

0.28

0.03

0.01

0.15

0.00

0.05

0.00

0.13

0.00

50.

Chen

ani–NashriE

scap

eTu

nnel

0.10

0.30

0.04

0.01

0.15

0.00

0.05

0.00

0.13

0.00

51.

Chen

ani–NashriE

scap

eTu

nnel

Siltston

e0.10

0.26

0.02

0.01

0.14

0.00

0.05

0.00

0.10

0.00

52.

Chen

ani–NashriE

scap

eTu

nnel

Siltston

e,siltyclay

ston

e0.15

0.32

0.03

0.02

0.17

0.00

0.06

0.01

0.15

0.00

53.

Chen

ani–NashriE

scap

eTu

nnel

0.20

0.29

0.01

0.04

0.17

0.00

0.13

0.00

0.14

0.00

Σ((P o

bs−

P est)2

93.26

135.72

9.6

1.25

Σ{(P o

bs−

ΣP o

bs/n)

2}

14.93

Coefficien

tof

Accorda

nce(Ψ

2)=

Σ((P o

bs−

P est)2

/Σ{(P o

bs−

ΣP o

bs/n)

2}

6.25

9.01

0.64

008

Notations

:HRT

—he

adrace

tunn

el;M

G—

minega

llery;M

FSS—

mod

eratelyfracturedsp

lintery

shales

withclay

coatings;P

u,P

N,P

ban

dP s

areestimated

supp

ortp

ressures

usingap

proa

ches

give

nby

Grimstad

andBa

rton

(199

3),G

oel(19

94),Bh

asin

andGrimstad

(199

6)an

dau

thorsrespective

ly;P

est–estimated

supp

ortpressure.

19R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

values of r for various values of σci, the UCS of intact rock, are pre-sented in Table 2.When a joint has gougematerial of sufficient thick-ness to submerge the joint roughness, frictional parameter of gougecontrols the joint strength during shear. Values of friction angle forvarious gouge materials present in a dense state or near the residualstate and the corresponding values of joint strength parameter arepresented in Table 3.

3.2. In situ stresses and uniaxial compressive strength of rock (σci)

Vertical in situ stress has been calculated as follows:

σv ¼ γ � H ð4Þ

where σv, γ and H are vertical in situ stress, unit weight of rock =27 kN/m3 (assumed) and tunnel depth respectively. Values of hori-zontal in situ stress (σh) and σci were taken from the case histories.

3.3. Allowed tunnel deformation, d

If adequate supports are installed in time as it is the practice beingadopted in a conventional method of tunnelling, support pressuredecreases on allowance of deformation in tunnel. Therefore, radial de-formation of tunnel (%) has been considered as one of the governing pa-rameters. This parameter has been determined as follows with the helpof collected data of radius and radial deformation of tunnel:

d ¼ ua� 100% ð5Þ

where d represents the radial tunnel deformation, %, u, the radial defor-mation, m, and a is the radius of the tunnel, m.

4. Dimensionally correct empirical correlation

The ultimate support pressure should increase with in-situstress and decrease with allowed tunnel deformation. Also, a com-petent rock mass will exert a small support pressure and hence alow value of Jf will result in a lower support pressure. Using theabove analogy, an attempt was made to plot the variations of theobserved ultimate support pressure as a function of σv, σh, d, Jf andσci. After several trials, a dimensionally correct expression (Eq. (6))was obtained from Fig. 9 with correlation factor of 0.92, where ratio(10Pobs/σv) has been plotted against Jf3σh

0.1 / {107σci0.1(d0.2 + Jf/ 1434)}.

This plotwas prepared using the data collected from53 tunnel sections atvarious project sites, which is presented in Table 4. Values of estimatedsupport pressure from Eq. (6) have been plotted with the value of ob-served support pressure in Fig. 11.

Ps ¼ 9:23� 10−3σvJ f

3σh0:1

107σ ci0:1 d0:2 þ J f

1434

� �0@

1A

1:7

ð6Þ

where

Ps ultimate support pressure, MPa,Jf joint factor,σv vertical in situ stress (0.027H), MPa,σci uniaxial compressive strength of intact rock, MPa,σh horizontal in situ stress, MPa, andd radial tunnel deformation (%).

5. Comparison with other empirical correlations

For comparing the support pressure predicted on the basis of thecorrelation proposed in this study through Eq. (5), the support pressure

Fig. 11. Comparison of estimated support pressures obtained from various correlationswith observed support pressures.

20 R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

waspredicted using the other available correlations in the literature andthen the comparison made. The other correlations available in the liter-ature are as follows:

5.1. Grimstad and Barton (1993) relation using Q-value

Grimstad and Barton (1993) suggested an empirical approach usingQ-value (Eq. (7)) for estimation of roof support pressure in tunnels. Ac-cordingly, the support pressure is independent of the span or diameterof the tunnel and is given by —

Pu ¼ 0:2ffiffiffiffiffiJn

pJr

Q−1=3 ð7Þ

where Pu is the ultimate roof support pressure, MPa, Jn, the joint setnumber, Jr, the joint roughness number, and Q, the rock quality index.

5.2. Goel (1994) relation using rock mass number (N)

Due to the difficulty in assessment of the stress reduction factor(SRF) required for obtaining the Q-value, Goel (1994) arbitrarily as-sumed stress reduction factor (SRF) = 1 and gave rise to another ex-pression (Eq. (8)) and named it as rock mass number (N).

N ¼ RQDJn

� �JrJa

� �Jwð Þ ð8Þ

where RQD, Jn, Jr, Ja and Jw are rock quality designation, joint set number,joint roughness number, joint alteration number and joint water reduc-tion factor respectively.

Goel (1994) realised the influence of size (diameter/span) of tunnelon support pressure and hence suggested the following empirical corre-lation to predict the support pressure in tunnels for squeezing grounds:

PN ¼ f30

� �10

H0:6a0:1

50N0:33 ð9Þ

where PN represents the ultimate support pressure in squeezing groundcondition in MPa, f, the correction factor for tunnel closure (Figure 10),

H, the depth of tunnel (m), a, the radius of tunnel (m), and N is the rockmass number.

5.3. Bhasin and Grimstad (1996) relation using rock mass quality (Q)

Based on the case studies of Scandinavian tunnels, the data of Singhet al. (1992) and Goel et al. (1995), Bhasin and Grimstad (1996) sug-gested a new correlation for poor quality brecciated rock mass. In thiscorrelation, size of tunnel was taken into consideration as follows:

Pb ¼ 0:04Jr

� D � Q−1=3 ð10Þ

where Pb defines the ultimate roof support pressure, MPa, D, the diam-eter or span of the tunnel (m), Jr, the joint roughness number, and Q isthe rock quality index.

An index called Coefficient of Accordance (COA) has been com-puted for values of support pressure estimated from correlationsgiven by Grimstad and Barton (1993), Goel (1994), Bhasin andGrimstad (1996) and authors' Eq. (6). Values of COA are presentedin Table 5 for comparison of the various approaches. COA (ψ2) is de-fined as follows:

ψ2 ¼ ∑ Pobs−Pestð Þ2

∑ Pobs−∑Pobsn

� �2 ð11Þ

where ψ2 is COA, Pobs is observed support pressure, Pest is estimatedsupport pressure and n is number of data sets. Lower value of COAindicates a better correlation. Values of support pressure estimatedfrom the correlation developed in this study (Eq. (6)) give the leastCoefficient of Accordance (0.08) as compared to other correlations(Table 5). It can therefore be concluded that the proposed correla-tion is definitely an improvement over the other correlations.

In addition to the above method of comparison (Table 5), estimatedvalues of support pressure have also been plottedwith the values of ob-served support pressure in Fig. 11 for comparison. The plot also shows aline AB with 1:1 gradient. If predictions by a given approach are better,the points should lie close to 1:1 line. It is seen that thepredictionsmadeby the proposed approach lie closer to the line AB as compared to theother approaches.

Eq. (7) proposed by Grimstad and Barton (1993) does not involveparameters like diameter or span of tunnel and quantity of allowed de-formation, which are important parameters especially in squeezinggrounds. These parameters have less importance for estimation of sup-port pressure in elastic or non-squeezing ground conditions. Due to thisreason, support pressure values estimated from Eq. (7) (Grimstad andBarton, 1993) and Eq. (10) (Bhasin and Grimstad, 1996) do not hold agood correlationwith the observed support pressure values, thus show-ing COA as 9.09 and 0.64 respectively (Table 5) and the points lie faraway from the line AB in Fig. 11. Eq. (9) proposed by Goel (1994) usesclosure correction to consider the effect of allowed tunnel deformation(Figure 10). The values of correction factors depend upon in-situ stress-es, diameter or span of the tunnel and rock mass quality and hence willvarywith these parameters, whereas values of correction factors as sug-gested in Fig. 10 are constant with respect to the aforesaid parameters.May be due to this reason, the values of estimated support pressurefrom this approach (Eq. (9)) shows a low degree of correlation with ob-served support pressures as the estimated support pressure values havehigh COA of 6.25 (Table 5) and lie very far away from line AB in the plotpresented in Fig. 11. Moreover, all of the abovementioned approachessuffer from the deficiency of not being dimensionally correct. On theother hand, the correlation (Eq. (6)) presented in this study involvesboth the parameters as discussed above and show a very good accor-dance with the observed support pressures, as the estimated values of

21R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

support pressure give very low COA i.e. 0.08 (Table 5) and the corre-sponding points lie very close to the AB line in Fig. 11.

6. Discussion

The proposed correlation (Eq. (6)) for prediction of support pressurein tunnels excavated in squeezing grounds involves tunnel size (diame-ter/span) as one of the parameters which significantly affect the behav-iour of tunnels (Goel et al., 1996; Bhasin et al., 2006). Allowed tunneldeformation is another parameter which plays a very important rolein the mobilisation of the support pressure. The predicted values oncomparisonwith observed support pressures give a very lowCoefficientof Accordance (Table 5 & Figure 11) and a good correlation coefficient of0.92. Eq. (6) uses joint factor as a measure of rock mass quality whichtakes into account the anisotropy of rock mass strength in a realisticway. In addition to this, Eq. (5) involves horizontal in situ stress and uni-axial compressive strength of intact rock. On the other hand, Eq. (7)does not involve the above stated four parameters and therefore thepredictions using this equation are not reliable for squeezing groundsand hence the values of estimated support pressure fit with observedsupport pressure values with a poor Coefficient of Accordance (Table 5& Figure 11). Approach suggested by Bhasin and Grimstad (1996) is amodification of the approach suggested by Grimstad and Barton(1993) in which tunnel size was introduced as a new parameter(Eq. (10)). However, Eq. (10) did not involve allowed tunnel closure,σh and σci as parameters and the values of predicted support pressureusing this approach were found to fit with the observed values of sup-port pressure with COA of 0.64 (Figure 11) i.e. the prediction is muchbetter than that of Eqs. (7) and (8) which use both tunnel size andallowed tunnel closure by introducing a correction factor, f and the pre-dicted values fit with very low accordance with the observed values ofsupport pressure (Figure 11).

7. Conclusions

The estimated values of support pressure using correlations(Eqs. (7), (9) & (10)) were found to fit with the observed values of sup-port pressure with values of Coefficient of Accordance of 9.09, 6.25 and0.64 respectively (Table 5 & Figure 11). The dimensionally correct em-pirical correlation (Eq. (6)), which has been proposed in the presentstudy on basis of data of 53 different tunnel sections, shows a goodaccordance with the observed values of support pressure (Table 5& Figure 11) and gives a correlation coefficient of 0.92 (Figure 9).Eq. (6) is therefore a better correlation than the existing correlationsfor squeezing ground conditions. The concept of joint factor takesinto account anisotropy of rock mass strength in a realistic way andinvolves few parameters (only three) which can be easily assessedin the field and hence Eq. (6) is recommended for use in practicefor estimation of support pressure in tunnels which are excavatedin squeezing ground.

The developed correlation (Eq. (6)) is valid for dry tunnels excavatedby drill & blast method in squeezing ground conditions (where tunneldeformation is larger than 1% of opening size). In the analysis, equiva-lent radius, Req has been taken into consideration, which is computedusing expression: Req = (A / π)0.5 for non-circular openings, where Ais a cross-sectional area of tunnel. In addition to this, minor influenceof schistosity has also not been considered in the analysis.

References

Arora, V.K., 1987. Strength and Deformation Behaviour of Jointed Rocks. Ph. D. Thesis IIT,Delhi, India.

Attewell, P.B., Sandford, M.R., 1974. Intrinsic shear strength of a brittle anisotropic rock—I:experimental and mechanical interpretation. Int. J. Rock Mech. Min. Sci. Geomech.Abstr. 11 (11), 423–430.

Barla, G., 1995. Squeezing rocks in tunnels. ISRM News J. 2 (3/4), 44–49.

Barla, G., Bonini, M., Semeraro, M., 2011. Analysis of the behaviour of a yield-controlsupport system in squeezing rock. Tunn. Undergr. Space Technol. 26, 146–154.

Bhasin, R., Grimstad, E., 1996. The use of stress–strength relationships in the assessmentof tunnel stability. Tunn. Undergr. Space Technol. 11 (1), 19–98.

Bhasin, R., Magnussen, A.W., Grimstad, E., 2006. The effect of tunnel size on stability prob-lems in rock masses. Tunn. Undergr. Space Technol. 21, 405.

Cantieni, L., Anagnostou, G., 2009. The interaction between yielding supports and squeez-ing ground. Tunn. Undergr. Space Technol. 24, 309–322.

Choudhari, J.B., 2007. Closure of Underground Opening in Jointed Rocks. Ph. D. ThesisDept. of Civil Engg., IIT Roorkee, Roorkee, India.

CIMFR, 2007. Instrumentation, Evaluation and Design of Support System in Tunnels ofUdhampur–Katra Rail Link Project. Internal Report. Central Institute of Mining andFuel Research, Dhanbad, India (GC/MT/R/2/2006-07).

Dube, A.K., 1979. Geomechanical Evaluation of Tunnel Stability under Failing Rock Condi-tions in a Himalayan Tunnel. Ph.D. Thesis Deptt. of Civil Engg., University of Roorkee,Roorkee, India.

Facibeni, L., Palomba, M., Carrieri, G., Russo, G., Guvenc, A.H., 2011. Critical aspects in thedesign of the Chenani–Nashri tunnel. Proc. of 3rd Indian Rock Conference-INDOROCK2011, ISRMTT Roorkee Chapter Roorkee, Oct. 13–15, Roorkee, India.

GEODATA, 2011. Rehabilitation, strengthening and four laning of Chenani to Nashrisection of NH-1A including 9 km long tunnel (2 lanes) with parallel escape tunnelin the state of Jammu & Kashmir. Base line Geological Report Submitted to ITNL,India (I1007-GDE-ENG-RPT-GE-0003 Rev B).

Goel, R.K., 1994. Correlations for Predicting Support Pressures and Deformations inTunnels. Ph.D. Thesis Deptt. of Mining Engg., Visvesvaraya Regional College ofEngineering, Nagpur University, Nagpur, India.

Goel, R.K., Jethwa, J.L., Singh, B., 1988. Case history of Maneri–Uttarkashi power tunnel.Proc. of 2nd Int. Conf. on Case Histories in Geotechnical Engineering, St. Louis, USA,June 1–5.

Goel, R.K., Jethwa, J.L., Paithankar, A.G., 1995. Indian experiences with Q and RMR system.Tunn. Undergr. Space Technol. 10 (1), 97–109.

Goel, R.K., Jethwa, J.L., Dhar, B.B., 1996. Effect of tunnel size on support pressure. Int.J. Rock Mech. Min. Sci. Geomech. Abstr. 33 (7), 749–755.

Goel, R.K., Swarup, A., Dwivedi, R.D., Mishra, S., 2004. Case history of a railway tunnel.Proc of Need for Accelerated Underground Construction Issues & Challenges (Tunnel-ling Asia '2004), Dec 14–17, New Delhi, India, pp. 14–17.

Goel, R.K., Dwivedi, R.D., Viswanathan, G., Rathore, J.S., 2012. Challenges of design andconstruction of a highway tunnel through mixed geology in Himalayas. Proc of 7thAsian Rock Mechanics Symposium, Oct 15–19, Seoul, Korea.

Grimstad, E., Barton, N., 1993. Updating the Q-system for NMT. Proc. Int. symp. OnSprayed Concrete — Modern Use of Wet Mix Sprayed Concrete for UndergroundSupport, Fagernes. Norwegian Concrete Assn, Oslo, pp. 46–66.

Jain, M.S., Andotra, B.S., Sondhi, S.N., 1975. Note on Geological Features of the Chhibro–Khodri Tunnel and Occurrences of Subathu Shales. Unpubl. Rep. of Geological Surveyof India.

Jain, M.S., Jaitle, G.S., Sondhi, S.N., Rajagopalan, G., 1976. Geotechnical note on the alterna-tive alignments between Heena and Tiloth adits, Memo. XIV Meeting, Board of Con-sultants, Maneri Stage I Project.

Jethwa, J.L., 1981. Evaluation of Rock Pressures in Tunnels through Squeezing Ground inLower Himalayas. Ph. D. Thesis University of Roorkee, Roorkee, India.

Jethwa, J.L., Singh, B., Singh, Bhawani, Mithal, R.S., 1980. Influence of geology ontunnelling conditions and deformational behaviour of supports in the faultedZones — a case history of Chhibro–Khodri tunnel in India. Eng. Geol. 16 (3/4),291–318.

Kovári, K., 1998. Tunnelling in squeezing rock. Tunnel 5, 12–31.Kovari, K., Amberg, F., Ehrbar, H., 2000. Mastering of squeezing rock in the Gotthard Base

tunnel. Tunnels Tunn. Int. 234–238.Kumar, N., 2002. Rock Mass Characterization and Evaluation of Supports for Tunnels in

Himalaya. Ph. D. Thesis Dept. Of Civil Engg., IIT Roorkee, Roorkee, India.Malhotra, V.K., Tyagi, G.D., Sharma, K.S., 1982. NATM for Tunnel Boring at Loktak H. E. Pro-

ject. Proc. of Sym. on Tunnelling, 52nd Session of the Central Board of Irrigation &Power, New Delhi, India, pp. 35–58 (June).

Mclamore, R., Gray, K.E., 1967. The mechanical behaviour of anisotropic sedimentaryrocks. Trans. Am. Soc. Mech. Eng. Ser. B 89, 62–79.

Nepal Electricity Authority (NEA), 2002. Project completion report. Geology andGeotechnical. Kaligandaki “A” Hydroelectric Project, Syanga, Nepal, vol. IV-Aand V-C.

Panthi, K.K., Nilsen, B., 2007. Uncertainty analysis of tunnel squeezing for two tunnel casesfrom Nepal Himalaya. Int. J. Rock Mech. Min. Sci. 44 (1), 67–76.

Ramamurthy, T., Arora, V.K., 1994. Strength prediction for jointed rocks in confined andunconfined states. Int. J. Rock Mech. Min. Sci. 31 (1), 9–22.

Selmer-Olsen, R., Broch, E., 1977. General design procedure for underground openings inNorway. In: Bergman, S.M. (Ed.), Proc. of Int. symp. ROCKSTORE, 77. Oxford, Stock-holm Pergamon, pp. 219–226.

Shome, S.K., Andotra, B.S., Jain, M.S., 1973. Review of failure patterns in the stage II tunnelsof Yamuna hydroelectric scheme, Dehradun District. Proc. of Symp. Rock Mech. andTunnelling Problems, 1. Kurukshetra University, pp. 70–79.

Singh, M., 1997. Engineering Behaviour of Jointed Model Materials. Ph.D. Thesis IIT, NewDelhi, India.

Singh, B., Goel, R.K., 2006. Tunnelling in Weak Rocks. In: John (Ed.), Elsevier Ltd., TheBoulevard, Langford, Kidlington, Oxford (UK).

Singh, B., Jethwa, J.L., Dube, A.K., Singh, B., 1992. Correlation between observedsupport pressure and rock mass quality. Tunn. Undergr. Space Technol. 7(1), 59–74.

Singh, M., Rao, K.S., Ramamurthy, T., 2002. Strength and deformational behaviour of ajointed rock mass. Rock Mech. Rock. Eng. 35, 45–64.

22 R.D. Dwivedi et al. / Engineering Geology 168 (2014) 9–22

Sripad, S.K., Raju, G.D., Singh, Rajbal, Khazanchi, R.N., 2007. Instrumentation of under-ground excavations at Tala hydroelectric project in Bhutan. In: Singh, Rajbal, Sthapak,A.K. (Eds.), Proc. of International Workshop on Experiences and Construction of TalaHydroelectric Project Bhutan, 14–15 June, New Delhi, India, pp. 269–282.

Terzaghi, K., 1946. Rock defects and loads on tunnel supports. Rock tunnelling with steelsupports. In: Proctor, R.V., White, T.L. (Eds.), Commercial Shearing and StampingCompany, Youngstown, OH.

Tripathy, P.K., Kapadia, H., Kumar, S., 2000. Use of alkali free accelerators in Tala hydro-electric project. In: Kaushish, S.P., Ramamurthy, T. (Eds.), Proc. of Tunnelling Asia‘2000’, 26–29 Sep., New Delhi, India, pp. 292–295.

Varshney, R.S., 1988. Tunnelling in squeezing rocks. Int. Symp. on Tunnelling for WaterResources and Power Project. Jan 19–23. New Delhi, India, pp. 34–47.

Zhang, L., 2010. Estimating the strength of jointed rock masses. Rock Mech. Rock. Eng. 43(4), 391–402.