Disclosure to Promote the Right To Information

Whereas the Parliament of India has set out to provide a practical regime of right to information for citizens to secure access to information under the control of public authorities, in order to promote transparency and accountability in the working of every public authority, and whereas the attached publication of the Bureau of Indian Standards is of particular interest to the public, particularly disadvantaged communities and those engaged in the pursuit of education and knowledge, the attached public safety standard is made available to promote the timely dissemination of this information in an accurate manner to the public.

इंटरनेट मानक

“!ान $ एक न' भारत का +नम-ण”Satyanarayan Gangaram Pitroda

“Invent a New India Using Knowledge”

“प0रा1 को छोड न' 5 तरफ”Jawaharlal Nehru

“Step Out From the Old to the New”

“जान1 का अ+धकार, जी1 का अ+धकार”Mazdoor Kisan Shakti Sangathan

“The Right to Information, The Right to Live”

“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता है”Bhartṛhari—Nītiśatakam

“Knowledge is such a treasure which cannot be stolen”

“Invent a New India Using Knowledge”

है”ह”ह

IS 4880-4 (1971): Code of practice for design of tunnelsconveying water, Part 4: Structural design of concretelining in rock [WRD 14: Water Conductor Systems]

IS : 4880 ( Part IV ) ·1971("••fftrmed 1"5)

Indian Standard

CODE OF PRACTICE FORDESIGN iN TUNNELS CONVEYING WATER

PART IV STRUCTUML DESIGN OF CONCRETEUNINGINROCK

(Scrond Reprint OCTOBER 1998

UOC~24.196 : 624.191.1

C Copyright 1971

BUREAU OF INDIAN STANI)ARDSMANAK BHAVAN. 9 BAHADUR SUAH ZAFAR MARG

NEW DELIII 110002

Gr 7 November 1971

18:__ (Part IV)-1t71

Indian StandardCODE OF PRACTICE FOR

DESIGN OF TUNNELS CONVEYING WATERPART IV STRUCTURAL DESIGN OF CONCRETE

LINING IN ROCK

Water Conductor Systems Sectional Committee, BDC 58

ChaitmanSHRI P. M. MANE

Ramalayam, Pedder Road, Bombay 26

M""bns R'fJ1IJ1RlmiSRIU N. M. CBAKBAVORTY Damodar Valley Corporation, DhanbadCRIBI' CONSTRUCTION ENGINEER Tamil Nadu Electricuy Board, Madras

SUPJ:SJNTBNDINO ENGINEER

( TEOHNICAL/CIVIL ) ( AII,,1I411 )CUIKI' EKQINEKR (CIVIl,) Andhra Pradesh ~tatt. Electricity Board, Hyderabad

SUPEIUNTENDUfG ENGINBER(CIVIL ANI> INVE8TIGATION

CIRCLE) (Alt",.al,)CRIBI' ENOINI.BB ( CIVIL) Kerala State Electricity Board, TrrvandrumDEPUTY DIRECTOR ( DAMS I ) <Antral Water & Power Commission, New DelhiD,BBoToa Irrrganon & Power Research Institute. AmrHsar

DB GA11NDKR SINO H ( A/lerna")Saar D. N. DUTTA Assam Stare Electrrcity Board, ShillongSHRI O. P. DUTTA Beas Project, Nangal Township

SHRJ J. S. SINGHOTA( Alttrnau)SSRI R. G. GANDHI The Hmdustan Construction Co Ltd, Rombay

SHRl M. S. DEWAN ( AI,,,nat,)SHIU K. C. GH08AL Alokudyog Cement Service, New Delhi

SHRI A. K. BT8WA8 ( Altmlnll )StlRI B. S. KAPRRl Irrigation & Power Department, Government of

Maharashtra

Geological Survey of India, CalcuttaMinistry of Irrigation & PowerPatel Engmeermg Co Ltd, Bombay

Alt"nat, )Gammon India Private Ltd, BombayR. J. Shah & Co Ltj, BombayPublic Work! & Electrrcuv Department, Government

of MysoreSUR1 S. G. BALAKUNDRY (AltmatJtI)

SURI R. S. KALE ( Alternat« )SaRI V. S. KRI8JtNASWAMY

SHIU K. S. S. MURTHYSURJ Y. G. PATEl.

SHRI C. K. CUOXSUI (

SURI P. B. PATIL

SaRI A. R. RA10RUR8Hftl G. S. SHIVANNA

( Conh,,,"d 0" /NI" 2 )

n lJ I~ .: A [J () F f N I) I A N S 'r A N I) i\ I( I> ~

MANAK BHAVAN, 9 BAIIAlJlJl{ SIIAl1lAI ;\1{ M!\I{(,NbW DFLIII 110002

IS:_O (Part IV)-1971

( Co,.tmued from pail 1 )

MtmlJ"s

SECRE'rl\R.Y

Snnr J. E. \7 AZ

SURI]. WALT~R ( Alternate )Sit m D. AJJ'rH A SIMBA,

Director ( C1V Engg )

RfJ()rfSmtlng

Central Board of In igarion & Power , New DelhiPublic \\'orkc; Dep.u trrrent, Governrnpnt of Tamil

Nadu

:~"rrtI117 ~

Su nt HIMLf,~H KVMAH

Assistan: Du i r tor \ Civ Engg j, lSI

Panel for Design of Tunnels, Bl)C 58 . PI

SUkJ C. K. ClIOI\SHI

M,mbr,s

11EPl'rY Dnu-oroa ( I)AM8 J'Hlc.l o. P. (;LPTA

SURI It S. KAPRE

Patel Engmeer mg Co Ltd, RUInhav

Central Water & Power Comrmssron. New nt,UUI (f1~at1nn Depai trucnt , Govr rnment of Uttar

PC&i.dt·shIrri~atlntj & PO\\f'r nppartnlent, Government of

Mahar..ashn aSHIU R. S. KAJllt ( Alt61'natt)

SHIH V. S. KRINHNA8WAMY Geological Survey of India, CalcuttaSHUJ A. R. RAH.'HIj}~ R.J. Shah & Co Ltd, BombaySnRI J. S. SINOUOTA Beas Project, Nangal Township

SHIH o. R.. MEHTA (Alt,rnat,)SHRI J. E. VAZ PUbJH..: ,,york, Department, Government or Tamil

Nadu

2

AMENDMENT NO. 1 JUNE 1986TO

IS:4SS0(Part 4)-1971 CODE or PRACTICE FOR DESIGNOF TUNNELS CONVEYING WATER

PART 4 STRUCTURAL DESIGN OF CONCRETE LINING IN ROCK

(Page 24. ctause D-2.1, tine 1) - Substitute thefollowing tor the existing line:

tm1, ~ • Poisson's number of rock and concreterespectively.'

(Page 24~ ctause D-2.1~ lines 13 and 14) ­Substitute the following in the existing lines:

'a = internal radius of the tunnel; and

b = e~crnal radius of the lining up to A-line.'

(BDC 58)

Punted at New India Prm11nr Press, Khmll\. Im11~

AMENDMENT NO.2 JANUARY 2008TO

IS 4880 (PART 4) : 1971 CODE OF PRACTICE FOR.DESIGN IN TUNNELS CONVEYING WATER

PART 4 STRUCTURAL DESIGN OFCONCRETE LINING IN ROCK

(Page S, clause 3.1) - Substitute ~IS 456 : 2000·' for 'IS 456 : 1964*'.

(Page 9, clause 6.1) - Substitute 'IS 456 : 2000·' for 'IS 456 : 1964·'.

(Pages 5 and 9, footnote marked *) - Substitute the following for theexisting footnote:

'Plain and reinforced concrete - Codeof practice(fourth revISIon) 1

(WRD 14)

Reprography Unit,BIS.NewDelhi, India

IS z4880 ( Part IV )·1971

Indian StandardCODE OF PRACTICE FOR

DESIGN OF TUNNELS CONVEYING WATERPART IV STRUCTURAL DESIGN OF CONCRETE

LINING IN ROCK

o. }/ ORE W 0 R D

0.1 Thi- Indian Standard ( Part IV) wac; adopted by the Indian StandardsInstitution on 15 March 1971) after the draft finalized by tho \Vater Con­ductor Systems Sectional Committee had been approved hy the CivilEngiueer ing Division Council.

0.2 \Vater conductor system occasionally takes the form of tunnels throughhigh ~round or mountains, in ru~~ed terrain where the cost of surface pipelille or canal is excessive and elsewhere a" convenience and economydictates. This standard, which is br-ing published in parts, is intended tohelp engineers in design of tunnels conveying water. This part lays downt h(\ criteria for structural design of concrete linins; fc)l' tunnels in rock,covel ilH.~ reromrnended methods of design. However, in view of thecomplex nature of the subjP'-'t. it is not possible to cover each and everypossible situation in the standard and many times a departure from thepractices recommended in this standard may be considered necessary tomeet the requirements of a project or site for which descretion of thedesigner would he required.

0.3 'This standard is one of a series of Indian Standards on tunnels.(see page 28).

0.4 Othr r parts of this standard are as follows:

Part I General designPart II Gcomett ic designPart III Hydraulic designPart V StJ uctural design of concrete lining in soft strata and soilsPart \'1 Tunnel supports

0.5 For the purpose of deciding whether a particular requirement of thisstandard is complied with, the final value, observed or calculated, express­ing the result of a lest or analysis, shall be rounded ofTin accordance withIS: 2·1960·. The number of significant places retained in the rounded offvalue should be the same as that of the specified value in this standard.

• Rules for rounding ofTnumerical values ( rlvutd ).

3

IS. 4880 ( Part IV) .1971

1. SCOPE

1.1 This standard (Part IV) covers criteria for structural design of plainand reinforced concrete lining for tunnels and circular shafts in rockmainly for river valley projects.

NOTI:- The provlsions may, nevertheless, be used (or design or any other type oftunnel, like railway or roadway tunnel. provided that all the factors peculiar to suchprojects which may affect the design are taken into account.

1.2 This standard, however, does not cover the design of steel and pres­tressed concrete linings, tunnels in swelling and/or squeezing type of rocks,soils or clays and cut and cover sections

2. TERMINOLOGY

2.0 For the purpose of this standard, the following definitions shall apply.

2.1 Millimam Eseavadoll Line ( A.Liae ) - A line within which nounexcavated material of any kind and no supports other than permanentstructural steel supports shall be permitted to remain (see Fig. 1).

8-LINE

UNSUPPORTED SUPPORTEDSECTION SECTION

CIRCULAR SECTION

B-LINE

B-LINt

A-LlNE~ SOLIiJ=~~~ PERMANENT SUPPORTS

SECTION XX B·lINEPERMANENT

SUPPORT

~

UNSUPPORTED SUPPORTEDSECTION SECTION

HORSE-SHOE SECT~N

FIG. 1 TYPICAL SECTIONS Olf CONCRETE LIlUD TUNNELlSUO\\'INO A- AND B-LINEI

4

IS 14880 (Part IV) .1971

2.2 Pay Llae (B-Lllle) - An assumed line (beyond A-line) denotingmean line to which payment of excavation and concrete lining is madewhether the actual exca vation falls inside or outside it.

2.3 Cover - Cover on a tunnel in any direction is the distance from thetunnel soffit to the rock surface in that direction. However, where thethickness of the overburden is sizable its equivalent weight may also bereckoned provided that the rock cover is more than three times thediameter of the tunnel.

3. MATERIAL

3.1 Use of plain and reinforced concrete shall generally conform toIS:456-1964·.

f. GENERAL

4.1 Structural design of tunnel lining requires a thorough study of thegeology of rock mass, the effective cover, results of in .fitu tests for modulusof elasticity, poissons ratio, state of stress and other mechanical charac­teristics of the rock. It is preferable to make a critical study of thesefactors which may be dene in pilot tunnels, test drifts, during actualexcavations or by other exploratory techniques. The assessment of rockload on the lining and portion of the internal pressure which should beassumed to be transmitted to the rock mass, will have to be done bythe designer on the basis of the results of these investigations.

4.2 It is essential for the designer to have fairly accurate idea of 'heseepage, and the presence or absence of ground water underlressure li~lyto be met with. Where heavy seepage of water is anticipate ,the designershall make provisions for grouting with cement and/or chemicals ~ orextra drainage holes, and also consider the feasibility of providing steellining, if necessary. It is recommended that such designs of alternateuse of steel lining be made along with the design of plain or reinforcelining so that a design is readily available should the construction per­sonnel require it when they meet unanticipated conditions.

4.3 The portions of a tunnel which should be reinforced and the amountof reinforcement required depends on the physical features of the tunnel,leological factor. and internal water pressure, For a free-flow tunnelnormally no reinforcement need be provided, However, reinforcement,hall be provided where required to resist external loads due to uDstableground Or grout or water pressures. Pressure tunnels with high hydro­static loads shall have lining reinforced sufficiently to withstand burstingwhere inadequate cover or unstable supporting rock exists.

"Code or practice for plain aDd reinforced concrete ( SIe."d "Dis..,. ).

5

15,4880 (Part IV)-!971

4.3.1 The provision of reinforcement in the tunnel lining compl icates 'theconstruction sequence besides requiring a thicker lining. The use ofreinforcement should, therefore, he restricted, as much as possible consistentwith the safety of lining. For free Row tunnels it is recommended that asfar as possible, no reinforcement should be provided to resist external loads.Such loads should be resisted and taken care of by steel supports and/orprecast concrete rings.

4.3.2 A pressure tunnel should ordinarily be reinforced wherever thedepth of cover is less than the internal pressure head. The final choicewhether reinforcement should he provided or not would be guided by thegeological ~et up and economics.

4.3.3 For design of junctions and transitions for tunnels detailed struc­tural analysis shalJ be made. Such transitions are difficult to construct inthe restricted working space in tunnels, and the designer shall keep in viewthis aspect and propose structures which are easy for construction.

~.3.t An adequate amount of both longitudinal and circumferentialreinforcement in addition to steel supports may be provided, if required,near the portals of both pressure and free-flow tunnels to resist loadsresulting from loosened rock headings or from sloughing of the portalcuts.

4.4 If the seepage of water throug-h the 1ining is likely to involve heavy lossof water and the structural stabilitv of the rock mass around the tunnel islikely to be affected adversely· or' might lead to such situation as to bedamaging to the tunnel or adjoining structures, steel lining shall beprovided. Where rock cover is less than that specified in 4.5 and 4.5.1 orwhere the cavitation of lining is expected due to the high velocity of wateror eros-ion is expected the provision of a steel 1iner shall be considered.

4.5 Where the rock is relatively impervious and the danger of blowoutexists, the vertical cover shall be greater than the internal pressure head inthe tunnel. In other cases the weight of the rock over the tunnel shall begreater than the internal pressure.

NOT. - The conventional practice ill to provide a vertical cover equal to tbe inter.nat water pressure head (H). Recent trend, however, is to provide lesser cover \ atlow u 0·5 H) depending upon the nature of the rock,

4.5.1 For tunnels located near mountain slopes, the lateral cover ratherthan the vertical cover may be the governing criteria many times. Inluch easel the effective vertical cover equivalent to the actual lateralcover shall be found out, by drawing a profile of the ground surface(perpendicular to the contour lines) and fitting the curve shown in Fig. 2!n such a ~'ay that it touches the ground surface, The vertical distance

6

(S: 4880 (Part IV ) ·1971

marked' C,,' shall he designated as the effective vr-rt leal (·nv.~r and shallbe greater than the internal prpssure head in the tunnel. This method ofestimating the effective cover shall not hold good where joints. stratification,faults, etc, in the rock arc adversely located to inva lida te the assumption thathorizontal cover is half as effective as the vertical rover on the basis ofwhich the curve of Fi~. 2 is drawn. In such cases special analysis shallhe made for determining the stability of the rock mass around the tunnel.

-----CH = ~R

VERTICAL COVER GOVERNS

>u

CHHORIZONTAL COVER GOVERNS

I>

1..+---_____

.....---CH-~.JDIAGONAL COVER GOVERNS

Flo. 2 E~TIMATION OF EFFECTIVE COVJ:o:R

5. LOADING CONDITIONS

5.1 General-Design shan be based on the most adverse combination ofprobable load conditions, but shall include only those loads which havereasonable probability of simultaneous occurrence.

5.2 Load CODditioa8 - The design loading applicable to tunnel liningsshall be classified as C Normal' and 'Extrf'lne' design loading conditions.Design shall be made for' Normal' loading conditions anti shall he checked

7

18,4880 (Part IV).1971

for safety under 'Extreme' loading conditions (set Appendix A). Thedesign loading shall be as follows:

a) External Rork 140ad (set 7.4.2)

h) Self Load of Lining

c) DesiR1Z External J1'ater Pressure (see 7.4.'):

1) Normai design loading conditions - The maximum loading obtain­ed from either maximum steady or steady state conditionwith loading equal to normal maximum ground water pressureand no internal pressure, or maximum difference in levelsbetween hydraulic gradient in the tunnel, under steady stateor static conditions and the maximum down surge undernorma) transient operation.

2) Extrenu dt.riRn loading conditions - Loading equal to themaximum difference in levels between the hydraulic gradientin the tunnel under static conditions and the maximum downSUI ge under extreme transient operations or the differencebetween the hydraulic gradient and the tunnel invert level incase of tunnel empty condition.

d) D,.rign Internal Wall' Pressure:

I) Normal dfs;gn loading conditions - Maximum static conditionscorresponding to maximum water level in the head pond, orloading equal to the difference in levels between the maximumupsurge occurring under normal transient operation and thetunnel invert.

2) Ext"m, design loadinR ,ondilions- Loading equal to thedifference between the highest level of hydraulic gradient inthe tunnel under emergency transient operation and theinvert of the tunnel.

e) Grout Pressures (SI' 7.4.f )

f) Oth« Loads - Pressure transmitted from buildings and structures onexternal surface' lying within the area of subsidence and non­permanent loads, such as weight of vehicles moving in the tunnelor on the surface above it, where applicable.,

5.3 The loading conditions vary from construction stage to operation stageand from operation stage to maintenance stage. The design shall bechecked for all probable combination of loading conditions likely to occurduring aU these stages.

a

IS: 4880 (Part IV) .1971

8. STRESSES

6.1 For design of concrete lining, the thickness of concrete up to A-line shallbe considered. The stresses for concrete and reinforcement shall be inaccordance with IS: 456-1964* for design of lining for condition of normalload.

6.1.1 For extreme conditions of loading, the stresses in accordancewith 6.1 shall be increased by 331 percent.

7. DESIGN

7.1 The design of concrete lining for external loads may be done byconsidering it as an independent structural member (see 7.4). The designof concrete lining for internal water pressure may be done by consideringthe lining as a part of composite thick cylinder consisting of peripheralconcrete and surrounding rock mall subjected to specific boundaryconditions (lit 7.5 ).

NOTE - To eDlure the validity or the aaumption rhat lining i. a part of compoaitethick cylinder in the latter case adequate measures shall be taken, sucb u p....urepuling or the rock mall ••rouodiDI the tunnel.

7.2 Tldeluaen of LIaba*- The thickness of the lining shall be deaignedsuch that the stresses in it are within permissible limits when the lIlostadverse load conditions occur. The minimum thickness of the lining will,however, be governed by .-equirements of construction. It is recommend­ed that the minimum thickness of unreinforced concrete lining be 15) cmfor manual placement. Where mechanical placement is contemplated thethicknesa of the lining shall be 10 designed that the slick line can be .ilyintroduced on the top or the shutter without being obstructed by steelsupports. For a 15-mm slick line a clear space of 18 em is recommencled.For reinforced concrete lining. a minimum thickness of 30 COl isrecommended, the reinforcement, however, being arranged in the crownto allow for proper placement of Ilick line.

7.2.1 However, for preliminary design of lining for tunnele in reasonably.table rock, a thickness of lining may be ...umed to be 6 em per metreof finilhed diameter of tunnel.

Nor. - MiDimum thicb_ or tiD.,... Dec:eIIU')' from structural coDlid....tioaI. 8MJId be provided since thin liainp are more S.ibl. and abed oft' loada to theabuImeaIL

7.1 Where .tructurallteelsupports are used, they shall be considered .1reinforcement only if it i. paumle to make them effective u reinforcementby uae of hilb teDlUe boltl at the joina or by welding the joint.. A

ecode of practice lor plaia aacI reiDlorced concrete(~ fWIisiM ).

9

1114880 (Part IV) ·1971

minimum cover of 15 em shan be provided over the inner flange' of 'steelsupports and a minimum cover of 8 em over the reinforcement bars.

NOTE - Welding of joints in soft strata tunnels may not be possible, and it rna)become necessary to embed the steel supports partly or fully in primary concreteimmediately after erection. Welded joints should, therefore, be avoided.

7.4 De8ip Cor Esternal Loads - The lining may be considered as anindependent structural element assuming that it deflects under the activeexternal loads and its deflection is restricted by the passive resistancedeveloped in the surrounding rock mass. At any point on the perifery ofthe lining this may be stated by the following equation:

~/J = D.r + lie + ~w - {j,y

where

~p == deflection due to passive resistance;~, :III: deflection due to rock load;

~e = deflection due to self weight of lining and the watercontained in it;

~w = deflection due to the external water pressure, if any; and

!iy = yield ofsurrounding rock mass due to abutting of the liningagainst it.

7.4.1 The following loads and reactions are involved in the design oflining:

a) Rock load (st, 7.4.2) ;b) External pressure of water, if any (s" 7.4.3) ;

c) Grout pressure, if any (s" 7.4.4) ;d) Self weight of lining;

e) Weight of water contained in the tunnel;I ) Reaction due to active vertical loads (see 7.4.5) ; and

g) Lateral passive pressure due to the deformation of lining (st, 7.f.6 ).NOTE - As compared to the other loads, the self weight and the weight of water

contained in the tunnel are small. These load. are Dot dilcuseed in detail. However,the formulae for calculating bending moment, thrust, radial shear and horizontal andvertical deflections caused by self load and the weilbt of water contained in theconduit are given in Appendix o.7.4.2 Rock Loatl- Rock load acting on the tunnel varies depending

upon the type and mechanical characteristics of rock rna.. pre-existingstrellel,in tile rock mass and the width of the excavation. The rock loadis also affected by ground water conditions which may lubricate the jointsin rock and cause greater load than when the material is dry.

10

IS 14880 ( Part IV) ·1971

The existing stresses and their distribution after tunnelling has a greateffect on the development of load on tunnel lining. The redistribution maytake considerable time to reach an equilibrium condition. Wherever itis felt that rock loads are likely to develop excessively it is advisable toprevent the movement of rock oy immediately supporting it by shotcretingand/or steel supports and primary lining. Where weak rocks aresupported by steel rib supports, much of the rock load would be takenby the supports and the lining would take the load developed after itsplacement. There may also be redistribution of stresses in supports dueto deformation of the lining. A reasonable approach is to determine thediametral changes in the supported section with respect to time beforeconcreting to estimate the extent of deformation that has already takenplace. This investigation may be conveniently done in an experimentalsection of the tunnel or pilot tunnel with proper instrumentation.

In major tunnels, it is recommended that as excavation proceeds loadcell measurements and diametral change measurements are carried out toestimate the rock loads. In rocks where the loads and deformations do notattain stable values) it is recommended that pressure measurements shouldbe made using flat jack or pressure cells.

7.4.2.1 In the absence of any data and investigations, rock loads maybe assumed to be acting uniformly over the tunnel crown alt ShOWD inFig. 3 in accordance with Appendix B. However, Appendix B may betaken as an aid to judgement by the designer. l

UNIFORM VERTICAL~ ROCtcLOAO

UNIFORM VERllCALREACTION DUE TO_fiGHT 0" UNtNG

TRIANGULAR PASSlvlPRESSURE

UNIFORM VERTICAl.REACTION FOR

CONTA'NED WATER

UNIfORM vERTICAL REAC110NFOR ROC Ie ~OAO

FlO. 3 EXTERNAL LoADI ON LINING

7.4.3 Exter"al '1'attrPr,ssure - Lining shall be designed for external waterpressure, if any. However, in areas where drainage holes are provided,lining shall not be designed for external water pressure (se, 8.1). For

1J

11•.- (Part IV )-1971

conditions of loading for external water pressure reference may' be madeto 5.2. For design of lining for external water pressure where effectivepressure grouting has been done, the water pressure may beassumed to acton the whole grouted cylinder which may be taken as a structural elementfor computing the stresses and deformation of lining.

7.4.4 Gro.d P,ess",tJo-The lining shall be checked for stresses developedin it at the pressure on which grouting is done and it shall be ensured thatthe stresses arc within the limits depending on the strength attainedby concrete by then (see 9.1 and 9.2).

7.4.5 Vertical Reaction» - Reactions due to the vertical loads may beassumed, reasonably, to be vertical and uniformly distributed on the invertof the lining as shown in Fig. 3.

NOTE - In fact, these reactions, may, however, not be uniform depending uponthe foundation conditions. Nevertheless, with the uncertainties involved in thede"isn of tunnels, the assumption may not giv() far out results, Moreover, normally,uniform reaction' would give more critical condition.

7....6 Lateral Passive Pressure - The lateral passive pressure may beestimated either by considerinz the lining as a ring restrained by elasticmedium with a suitable modulus of deformation or by restricting themaximum deflection of the Jining at the horizontal diameter to an assumedvalue (depending upon the yield of the surrounding rock mass) bythe lateral passive pressure. The latter method is discussed in detailin 7.~.6.1 for design of circular linings. For design of non-circular liningsthe former method shall only be used.

7.4.6.1 For analyzing a circular lining, the designer will have to assumethe maximum deflection to be permitted along the horizontal central axisof the tunnel. This value of horizontal deflection will consist of the yieldof the rock mass surrounding the tunnel (Sft Note 2). It may be assumedthat any further deflection of the lining is restricted to this value bv thelateral Passive resistance of the surrounding rock mass in a pattern given infig. 3. The design shall be such that the maximum value of the passiveresistance is within the maximum permissible values.

NOTID 1 - For a circular lining the deflection is outward in a Ion", ext~ding

approximately from 450 above the horiaontal diameter to the invert as the invert moveup. The maximum value iI near horizontal diameter. On the above consideration andneglectm. the effect of vertical translation of the lining, the lateral rock restraint mayhe ..umed to have approximately a straiulular distribution as shown in Fig, 3. ThevfTticatl translation or the lininf( would cause • shifting of the point of maximumintensity llillhtly below the horizontal diameter and restrlction of the upper limit to ana nile lli,btly lea than 45~, Inn tilt' e1Tt'ft of vertical translatiun woula be small andcan be negleeted. The passive vrf'ASures would, in fact, bealso radial to the surfae«hut in view of the fact that the deflections would be mostly in horizontal direction andvertiaal deftections would besmall, it may be alluJned lO act in horizontal dlrecrion,

12

IS: 4880 (Part IV) ·1971

NOTE 2 - The rork mass surrounding the tunnel yields due to the bearing pressureor lining against it. This yield may be due to closing up of JOInts and fractures in therock ma'I and also due to its elastic or plastic deformation. The value of viold takenfor design should be based on the experiments carried out In the test sections ( se« 4.1 ) .

At Bhakra Dam, rock deflection tests indicated yit'Jd of either face m poor shatteredrock as ),25 mm under a stress of 54 kg! em l • However, a total deflection of 3'8 mmwas assumed in the design of lining though actual bearing pressure on the rock wasanticrpated to be much I.·",,,. Experimenta on (;arrison Darn tunnels, in clay shale ofinternal diameter B·A m and lining thickness of 0'9 01 indicated deflection of eitherface of Ijnin~ at horizontal diameter to range between 3 to 4 min. In design ofRamganga Dam tunnel .. outer deflection of either face of Itning at horizontal diameterwas assumed to be 3·8 mm.

7.4.6.2 Formulae for determining the value, of horizontal deflection;vertical deflection, bending moments, normal thrust, radial shear for thevarious circumferential points on a circular Iininz are givpn in Appendix Cconsidering the invert as the reference point for various loads excepting theinternal pressure. In derivation of these values the pattern of verticalreaction and passive pressure has been assumed in accordance with 7.4.5and 7.4.6 as shown in Fig. 3.

1.4.7 For non-circular lining model tests are recommended to determinethe stress distributions. However, the design may he done assuminguniformly distributed loads as in the rase of circular tunnels, and using thesame distribution for passive pressures. The design of such indeterminatesections may be done by istandard methods and is not covered by thisstandard.

7.5 De.111I For laternal Water Pressure - Lining shall be consideredas a part of composite thick cylinder consisring of peripheral concrete andsur-rounding rock mass subjected to specified boundary conditions. ,

NOTF. - This method suffers from uncertainties of external loads, material propertu«and indeterminate tectonic forces. In this method the rock surrounding the tllnneh isassumed to have reasonably uniform characteristics and strength and that effecu. copressure grouting has been done to validate the assumption that concrete lining andsurrounding rock behave as a com posite cylinder. I he grout fills the cracks in 'therock and thus reduces its ability to deform inelastically and increases the modulus ofdeformation. I r the grout pressures are high enough to cause .uffici~nt prestress inthe lining the effect of temperature and drying shrinkage and inelastic deformationmight be completely counteracted.

7.5.1 For analysing a circular lining the method given in Appendix Dmay be adopted. The design shall be such that at no point in the liningand the surrounding rock the stresses exceed the permissible limits.

If the rock is very good, and cracking of lining is not otherwise harm­ful, cracking of the lining may be permitted to some extent. In that case,tangential stress in concrete lining will be absent and corresponding ly,tangential stress in rock will increase.

13

IS I 4880 (Part IV) -1971

If the rock is not good, tensile stress in concrete may exceed' theallowable limit and in such a case, reinforcement may be provided.Reinforcement however, is not capable of reducing the tensile stresses toa considerable extent. By suitable arrangement, it will help to distributethe cracks on the whole periphery in the form of hair cracks which are notharmful because they may get closed in course of time, or at least they willnot result in serious leakages.

7.5.2 For analyzing non-circular linings, the stress pattern may bedetermined by photo-elastic studies.

8. GROUND WATER DRAINAGE HOLES8.1 Drainage holes may be provided in other than water conveying tunnelsto relieve external pressure, if any t caused by seepage along the outside ofthe tunnel lining. In free flow tunnels drainage holes may be provided inthe crown above the full supply level. In case of pressure tunnels, if theexternal water pressure is substantially more than the internal water pres­sure, drainage holes may be provided in the crown. However, when themountain material is likely to be washed into the tunnel through suchdrainage holes they shall not be provided.

8.1.1 The arrangement of drainage holes depends upon the site condi­tions and shall be decided by the designer. A recommended arrangementis described below:

At successive sections; one vertical hole drilled in the crown alter­nating with two drilled horizontal holes one in each side wallextending to a depth of at least 15 em beyond the back of the lining.

8.1.2 If the flow through the tunnel is conveyed in a separate pipe, thehorizontal holes shall be drilled near the invert.

9. GROUTING9.1 BacY11 Grouting-Backfill grouting shan be done at a pressurenot exceeding 5 kg/em' and shall be considered as a part of concreting..It shall he done throughout the length of the concrete lining not earlierthan 21 days after placement after the concrete in the lining has cooled off.However, stresses developed in concrete at the specified grout pressure maybe calculated and seen whether they are within permissible limits depend­ing on the strength attained by concrete by then. The grout pressure men­tioned above is the pressure as measured at the grout hole.

NOTE - BacidiU 8routin~ lerVftl to fill aU voids and CAyities between concrete linin.and rock.

9.2 Pre••are Groutilll- Pressure grouting shall be done at a maximumpracticable pressure consistent with the strength of lining and safetyagainst uplift of overburden. The depth of grout holes shall be at leastequal to the diameter of the tunnel.

NoT. 1 - Pressure f(1'outinl consolidates the surroundinl rock and filii any gaplcaused by .hrinkagel of concrete. Thillfoutin. is normally specified where linin. is

14

IS14880(Part IV) -1971

reinforced, to improve the rock quality and, therefore, to increase the resistance ofrock to carry internal water pressure, As a rule of thumb a grout pressure of I·Stimes the water pressure in the tunnel may be used subject to the conditions thatsafety against uplift of the overburden is ensured. Grout pressures of up to 5 to 10times the water pressure In the tunnel have been used in Italy.

NOTE 2 - It is advantageous to provide a grout curtain by means of extensive deepgrouting at the reservoir end of the tunnel to reduce loss of water due to seepage.

9.3 Pattera or Holes for Grouting-For small tunnels, rings of groutholes, may be spaced at about 3 m centres, depending upon the nature of therock. Each ring may consist of «)ur grout holes distributed at about 900

around the periphery, with alternate rings placed vertical and 450 axes.

APPENDIX A( Clause 5.2)

BASIC CONDITIONS FOR INCLUDING THE EFFECT OFWATER HAMMER IN THE DESIGN

A-I. The basic conditions for including effect of water hammer in thedesign of tunnels or turbine penstock installations are divided into normaland emergency conditions with suitable factors of safety assigned to eachtype of operation.

A-2. NORMAL CONDmONS OF OPERATIONSA-2.1 The basic conditions to be considered are as follows:

a) Turbine penstock installation may be operated at any head be­tween the maximum and the minimum values of forebay watersurface elevation.

b) Turbine gates may be moved at any rate of speed by action ofthegovernor head up to a predetermined rate, or at a slower rate- bymanual control through the auxiliary relay valve.

c) The turbine may be operating at any gate position and be requjredto add or drop any or all of its load.

d) If the turbine penstock installation is equipped with any of thefollowing pressure control devices it will be assumed that thesedevices are properly adjusted and function in all manner for whichthe equipment is designed.1) Surge tanks,2) Relief valves,3) Governor control apparatus,4) Cushioning stroke device, and5) Any other pressure control device.

e) Unless the actual turbine characteristics arc known, the effectivearea through the turbine gates during the maximum rate of gatemovement will be taken as a linear relation with reference to time.

15

IS: 4880 (Part IV). ]971

f) ThE' water hammer effects shall be computed on the basis of gover..nor head action for the governor rate which is actually set on theturbine for speed regulation. If the relay valve stops are adjustedto give a slower governor setting than that for which the governoris desizned this shall be determined prior to proceeding with thedesign of turbine penstock installation and later adhered to at thepower plant so that an economical basis for designing the penstockscroll case, etc, under normal operating conditions may beestablished.

g) In those instances, where due to higher reservoir elevation, it isnecessary to set the stops on the main relay valve for a slower rateof gate movement, water hammer effects will be computed for thisslower rate of gate movement also,

h) The reduction in head at various p iints along the penstock will becomputed for rate of gate opening which is actually set in the gover­nor in those cases where it appears that the profile of the penstock isunfavourable. This minimum pressure will then be used as a basisfor normal design of the penstock to ensure that sub-atmosphericpressures will not cause a penstock failure due to collapse.

j) I f a surge is present in the penstock system, the upsurge in thesurge tank will be computed for the maximum reservoir level con­dition for the rejection of the turbine flow which corresponds tothe rated output of the generator during the gate traversing timewhich is actually set on the governor.

k) The downsurge in the surge tank will be computed for minimumreservoir level condition for a load addition from speed-no-load tothe full gate position during the gate traversing time which isactually set on the governor.

A-3. EMERGENCY COND ITIONSA-3.1 The basic conditions to be considered as an emergency operationare as follows:

a) The turbine gates may be closed at any time by the action of thegovernor head. manual control knob with the main relay valve orthe emergency solenoid device.

b) The cushioning stroke will be assumed to be inoperative.c) I ra relief valve is present, it will be assumed inoperative.d) The gate traversing time will be taken as the minimum time for

which the governor is designed.e) The maximum head including water hammer at the turbine and

along the length of the penstock will be computed for the maxi­mum reservoir head condition for final part gate closure to the

. i he maxi ,,2£ dzero gate posu on at t e maximum governor rate In -a- secon s,

Where 'L' is length of penstock and 'a· wave velocity.

16

IS : 4880 ( Part IV )-1971.f) If a surge tank is present in the penstock system, the upsurge in

the tank will be computed for the maximum reservoir head condi­tion for the rejections of full gate turbine flow at the maximum ratefor which the governor is designed. The downsurge in the surgetank will be computed for the minimum reservoir head conditionfor full gate opening from the speed-no-load position at the maxi­mum rate for which the governor is designed. In determiningthe top and bottom elevations of the surge tank nothing willbe added to the upsurge and down surge for this emergencycondition of operation.

A-4. EMERGENCY CONDmONS NOT TO BE CONSIDERED ASA BASIS FOR DESIGN

A-f.l The other possible emergency conditions of operation are thoseduring which certain pieces of control are assumed to malfunction in themost'[unfavourable manner. The most severe emergency head rise in aturbine penstock installation occurs from either of the two following condi­tions of operation:

a) Rapid closure of turbine gates in less than 21. 5, when the flowa

of water in the peastock is maximum.

b) Rhythmic opening and closing of the turbine gates when a corn-

I f · · c. d i 41Jplete eye e 0 gate operation IS perrorrne In - s.a

Since these conditions of operation require a complete malfunctioning,of the governor control apparatus at the most unfavourable moment, theprobability of obtaining this type of operation is exceedingly r(\m<\te.Hence, the conditions shall not 1,•• used as a basis for design, However,after the design has been establi-hed from other considerations it is deiir­able that the stresses in the lUI bine scroll case penstock and pressurecontrol devices he not in exec-s of the ultimate bursting strength or t wist­ing strength of structures for these emergency conditions of operation.

APPENDIX B( Clause 7.4.2.1 )

ROCK LOADS ON TUNNEL LINING

B-1. SCOPE

8-1.1 This appendix contains recommendations for evaluating rock loadson tunnel lining.

J7

IS I ~880 (Part IV) .1971

....2. LOAD DISTRIBUTION8-2.1 Rock load may be assumed as an equivalent uniformly distributedload over the tunnel soffit over a span equal to the tunnel width or diameteras the case may be.

11-3. LOAD11-3.1 Rock loads may be estimated by any of the methods given in 8-3.1.1to 8-3.1.3_

B-3.I.l Rock load at depths less than or equal to 1·5 (B + H,) may betaken as equal to depth of actual rock cover where B is the width andH, is the height of the tunnel opening. In case of circular tunnels BandHe both will be equal to the diameter of tunnel D.

Rock load (H",) on the roof of support in tunnel with width Bandheight H, at depth of more than 1-5 (B+H,) may be assumed to beaccording to Table I.

11-3.1.2 Rock load may also be worked out using Fenner's ellipse (seeFig. 4 on P 21 ) by the following equation:

hQ= T(m-2)

wherea == main axis of ellipse of rock load,b == tunnel diameter ( excavated), and

m.. inverse of poissons ratio for rock (which usually varies from2 to 7 ).

The weight of rock in the shaded portion may be taken as rock load andmay be considered as uniformly distributed on the diameter of tunnel.

NOTK- The above treatment a'llIm~ the rock to be bcmogeneous and to behavewithin elastic range. It has also limited application .1 it does not rive .n~· rock loadsfor value of poissolls ratio equal to 0·25 and above. It does not &lao take intoconaideration the Itrength and characteriltiCi of rock.

8-3.1.3 The rock load according to the Russian practice depends uponthe degree of rock firmness. The rock load may be taken .a that for rockarea enclosed by a parabola starting from intersection points of the ruptureplanes with horizontal length drawn to the crown of the tunnel section.The d imensiona of the parabola are given below (se, FiS. 5 on P 21 ):

B".... 27B == b+2 m tan (45° - ;/2 )

where", - the angle of repose of the soil,f ... the strength factor after Protodyakonov (1M Table 2 ).

In the case of circular tunnels,B == D [ 1 + 2 tan (45° - ;/2 ) ]

whereD = diameter of the tunnel.

18

IS: 4880 ( Part IV ).1971

TABLE 1 ROCK LOAD(Claus, B-3.1.1 )

2. Hard stratified or schis- 0 to 0·50 Btose

ROOK CONDITION

1. Hard and intact

ROOK LOAD H"m

Zero

REMARKS

Light lining required only ifspall ing or popping occurs

Light support

3. Mas s i v e. moderately 0 to 0'25 Bjointed

4. Moderately blocky and 0'25 B to O'35 ( B + H, )seamy

Load may change erraticallyfrom poin t to point

No side pressure

5. Very blocky and seamy

6. Completely crushed butchemically intact

(0'35 to 1'10) (B + He )

1-10 ( B + II, )

Little or no side pressure

Considerable side pressure. Soften­ing effect of seepage towardsbottom of tunnel. Requireseither cont inuous support forlower ends ot ribs or circularribs.

Up to 80 In irrespect ive Circular ribs required. In extremeof value of ( B +H. ) cases use yielding support

7. Squeezing rock, mode- 0'10 to 2·10) (B+Ht ) 1rate depth 1Heavy side pressure. Invert

struts required. Circular fibs8. Squeezing rock, great (2*10 to 4·50) (B+ lIe) are recommended.

depth

9. Swelling rock

Non I - The above Table has been arrived on the basis of observation and behavieurof supports in Alpine tunnels where the load was derived mamlv on loosening type ofrock. i

NOTE 2 - The roof of the tunnel is assumed to be located below the water tattle.If it is located permancntlv above the water table, the values given for types 4 to 6mav be reduced by fifty percen t.

NOTR 3 - Some of the most common rock formations contain layers of shale. In anunweathered state, real shale. are no worse than other stratified rocks. However,the term shale is often applied to firmly compacted clay sedrmems which have not yetacquired the properties of rock. Such 10 called shales tnay behave in the tunnellikesqueezing or even swelling rock.

NOTBl 4 - If rock formation consists of sequence of horizontal layers of sand atoneor lime stone and of immature shale. the excavation of the tunnel i. commonlyassociated with a gradual compression of the rock on the both sides of the tunnel,involving a downward movement of the roof. Furthermore, the relatively low resis­tance against slippage at the boundaries between the so called shale and rock i. likelyto reduce very considerably the capacity of rock located above the roof to bridge.Hence, in such rock formations, the roof pressure nlay be as heavy as in a very blockyand seamy rock.

19

1814880 (Part IV)-19'.

TABLB 2 STRENGTH FACTORS( CllUU' B-3.1.3)

C.T" 8THBMOTH DJINOTATION OJ' ROCK UNIT CaU'HIlfO STIl-Q01\Y GBA-DE ( SOIL) W.cIQBT STRENGTH ItNQT.

FAOTOS(kl/ml ) (kg/cm' ) I

I Highest Solid, danae quartizite, basalt 2800·3000 2000 20and other solid rocks ofexceptionally high strength.

II Very high Solid. granite, ~uartzporphyr, 2600-2700 1500 15silica abale. ighly rea••tiveMndltones and limestone••

III Hilb Granite and alike, very 2500-2600 1000 15r e s i s t i v e la nd aDdlimestones. Quartz. Solidconglomerates.

IlIa Hilh Limestones, weathered tranite. 2500 800 8Solid .ndltone, mar Ie.

IV Moderately Normal .ndatone. 2400 60Q 6atroDI

IV. Moderately Sandltone ahales. 2300 500 5Itronl

V Medium Clay..ha1es. Sand anti Lime- 2400·2100 400 f.tODel of smaller resistanee.LOGIe conglomerates.

v. Medium Various .hales and Ilat•• 2400-2800 !OO SDenae marl.

VI Mod...tely Loose lbale and very 100M 2200-2600 200..150 210018 Iimeatone, Iypaum, frozen

Mound. common marl.oc~ and.tone cemented

IJ"ave and boulden, ItoneyRround.

VIa Mod..'ely Gravelly sround. Bloeky aDd 2200·2400 1'5IooIe fiuured shale, compreued

boulders and .....veI, hardclay.

VII LooIe Dense day, Cob_IV. hal.... 2000·2200 11»Clayey Found.

VIla Looee LOGIe loam, lotti, ....v... 1100-2000 0'8VIII Soil, Soil with v...wioD peat, .a 1600-1800 0-6

loam. wet MIld.IX Granular Sand. fine .....I t upfill. l4CJO.1600 0-5

lOiltX Plutie: Snty IJ'OUftdt modified lOOlel 0-3

toila and other IOU, iD liquidcondition.

20

IS r f880 (Part IV ).1971

The load may be taken as uniformly distributed over the diameter ofthe tunnel.

NOTJC - The above is applicable when the dlstanee between the vertex of thepressure parabola from the bottom of the weak layer or from the ground surface isnot letl than Ia. However t where this condition is not fulfilled the total value of rockload may be assumed.

bFlo.15 ASSUMED ROCK LOAD

ON A CIRCULAR CAVITY

Flo. 4 FENNtR'S Et.LIP8B

APPENDIX C( Note Under Claus« 7.4.1 and Clause 7.4.6.2 )

FORMULAE FOR VALUES OF BENDING MOMENTS,NORMAL THRUST, RADIAL SHEAR, HORIZONTAL AND-

VEltTlCAL DEFLECTIONc.t. The values of bending moment, normal thrust, radial shear andhorizontal and vertical deflection for the loading pattern shown in Fig. 3are given in Tables 3 to 7.0.2. For purpose of this appendix, the following notations shall apply:

E =- Young's modulus of the lining material,J == moment of inertia of the section,

K := intensity of lateral triangular load at horizontal diameter,P - total rock load on mean diameter t

, == internal radius of tunnel,R == mean radius of tunnel lining,t == thickness of lining,

W == unit weight of water,W, - unit weight of concrete, and~ == angle that the section rnak(l5 with the vertical diameter at the centre

measured from invert.

11

IS: 4880 (Part IV) -1971

C-3. For the purpose of this appendix, the following sign conventions shailapply:

a) Positive moment indicates tension on inside face and compressionon outside face;

b) Positive thrust means compression on the section;

c) Positive shear means that considering left half of the ring the sumof all the forces on left of the section acts outwards when viewedfrom inside;

d) Positive horizontal deflection means outward deflection withreference to centre of conduit; and

e) Positive vertical deflection means downward deflection.

TABLE 3 VALUES OF BENDING MOMENTS( Claus, C- ) )

tP UNIJ'ORM VBRTICA L CONVUIT CO;:iTAINED LATERALLOAn WRIGHT WATKR PRE8SUUE

0 + 0-1250 PR + 0-440 6 We t R' + 0·2203 W,' R - 0'1+34 KR'n

Zero - 0'033 4 We I JlI - 0'0167 W,I R - 0'0084 KRI4"n

- 0'125 0 PR - 0-392 7 J1'e t RI - 0'196 3 Ji' " R + 0'165 3 KRI"231r

Zero +0'033 4 J1'c t RI +0'016 7 W,! R - 0'018 7 KRIT1r + 0-125 0 PR '1- 0·314 8 W" t R' + 0·172 4 W ,. R - 0-129 5 'LR'

TABLE f VALUES OF NORMAL THRUST(Clauu C·l )

t/J UNlroR~1 VII:BTIOAL CONDUIT CON'rAINED

LOAD WEIGHT WA'rltR

0 Zero + O'1667 We t R - 1'4166 W,t1f + 02500 P + 1-1332W,tR - 0-7869W,'T~ + 0'500 0 P + I-S708WotR - 0'2146 W,'23n + 0-2500 P + 0'437 6 Wo , R - 0,4217 W,'-..-'If Zero -0'1667 ~V.' R - 0-5834W,'

22

LATRRALPIUt8SURE

+ 0'4754 KR

+ 0'3058 KR

Zero

+ 0'2674 KR

+0'3782 KR

IS: 4880 (Part IV )-1971

TABLE 5 VALUES OF RADIAL SHEAR

( Clause c-i )

tp UNI:rORM VBRTt~AL CONDUIT CONTAINED LATERALLOAD \'\'js.lOUT WATER PRS8SUBS

0 Zero Zero Zero Zero1'f

-0-2500 P - 0'897 6 ~l'c t R"4 - 0·448 8 W,' + 0'3058 KR

7tZero + 0' 166 7 K e t R + 0'083 3 ~v ,.2 - 0'0246 KR

31t + 0-2500 P + 0 673 2 J¥o t R + 0-SS6 6 H',' - 0-267 4KRT1r Zero Zero Z~ro Zero

TABLE 6 VALVES OF HORIZONTAL DEFLECTION( G~QUJI C-I )

~ UNrroRIII VSWflOAL CONI>UIT CONTAINltD LATERALLO/.D WKIOHT \VATlI:U, PaEil8URE

0 Zero Zero Zero Zero

~PH' ... 0-050 40 !!oll~ ( W,tRI KRt

4- + 0'01473 ET EI + 0'02520-EI - - 0-01750 --,-/

~ PR.' +0'130 90 WoIR4 + 0-065 45 W,IR' KR4-~- + 0-041 67 £1- E/ EI - 0-05055 7/-

31T PRI + 0042 16H'rtR' 0021 08 Wr2R3

- 0 010 241f.- + 0-Ot473 -rT bJ + £1

'It Zero Zero Zero Zero

•

TABLE 7 VALVES OF VERTICAL DEFLECTION( Claus, C·l )

t1J UNIfORM VERTICAL COSDUIT CONTAINltD LA Tl;}C,AL

LOAD WRHHiT "'VATER PKh.~SUJUI

0 llerQ Zero Zero Zero

11' PR' + 0'092 79 ~ol~' + 0'046 40 H~:' _ 00:31 i6 IfR·4 + 0'02694 Ei EI El~ PH' 0'139 17WetR· o '( sa W',"R3 _ 0-04'-1 9'> It~.2 + 0'0+167 £1 + El + -UtiJ:> EI ~ . iiI

3ft .. PR3 O'lS- 35 JVctR· 0'092 68 !V,IR~ _ 0'068 10 K~.- + 0'056 40 iiI + J EJ + El EJ

Tt + 0'083 33 PRJ +O'26180~ + 0-130 90 ~~~IR' _ 0'0)7 39 ,-oR'£1 ~l .t'l

23

1814180 (Part IV)-1971

APPENDIX D(Clause 7.5.1 )

BASIC EQ,UATIONS FOR ANALYSIS OF TUNNEL LININGCONSIDERING IT AND THE SURROUNDING ROCK AS A

COMPOSITE CYLINDER

1).1. SCOPE

1).1.1 This appendix contains basic equations for calculating radial andtangential stresses in concrete lining and the surrounding rock rna••considering both as parts of a composite cylinder.

D-2. NOTATIONS

1).2.1 For this appendix the following notations shall apply:

p .. internal hydrostatic pressure (negative compression);Gtl, Gtl, a'. = tangential stress in rock, concrete and steel respectively;arh Gr', 0"1 == radial stress in rock, concrete and steel respectively;

E, Ell E, - modulus of elasticity of rock, concrete And steelrespectively;

mt, m. = poission's ratio of rock, and concrete respectively;Uh U1, V. =s radial deformation in rock, concrete and steel

respectively;~ :as radius of element;

B 6f C,etc = integration constants;A, == areas of reinforcement per unit length of tunnel;a == internal diameter of the tunnel; and

b - extemal diameter of the lining up to A·line.

0-3. BASIC EQ,UATIONS

1).3.1 Plaia eeaaeat Coacrete Liala. Co.eWerial tlaat It I. DotCrack..

• ) Btlne EfJUalioftl:

cr,- m~~1 [B(m+I)- ~ (m-I) ]

cr,- m~!i [B(m+l)+-~-(m-I) ]

u- B~+C/~

24

b) Limit Conditions and Constants:1) When x == 00

2) When % c:: b,3) When x= b,

4) When x :=b,

arl = 0O"rJ -= a,1a,) = -pU, ==l/l

IS:~880 (Part IV )-1971

C'l - 0

D-3.2 Plaia CemeDt Coaerete LiDla, Coa.ldenal that it i. Craeked

a) Basic Equations for Rock:

ml EJ [ c. ]a,l:::: m,. _1 B1 ("'1 + 1) - ~t2- (ml - 1)

ml E1 [B C1 ]an = I 1 1 (ml + 1) (ml - 1)ml - t:!

b) For Concrete:a. (a,t) x = a

ar. = x

CJtl =s 0 (since concrete does not take any tangen tial stress )

c) Limit Conditions:1) \Vhen x = 00

2) When x = b,3) When x = a,

d) Constants are calculated a :B) =-0

C(J0 bop (ml + 1)

l-mlEl

( 0'1) X =- tJ~== -p

D.3.3 PlaiD Cemeat COllcrete Lillia, Co.8ideriD' that It J.Cracked aDei SarrouacliD. Rock alao i. Cracked for a DlstaQCeEqual to Radius Beyoad whlcb Rock i. Mal.lve aDd UDcrackeci

a) For Contretl:ao (art) :r _ (J

a,3 == x

au ==0b) For Crackrd Rotk:

a. ( a,l) II: _ tJ

aeal'= ----­x(lU' .. 0

NOTE - Symbol ar1' and all' refer to cracked sone of rock.

25

18.4880 (Part IV )..1971

c) For Surrounding Uncracked Rock:

m1E1 [0"1 = --mil '-:-1 B1 (rna + 1) -

O't} = ffll Hl [B1 (ml + 1) +,,/'1 -- 1

d) Limit Conditions:

1) Atx=oo2) At ,," =.Y,

3) At x = b,4) Atx=a,

tJ"l .:::;.- 0,

0"1 = (1"'1

0"2 :::::: (1'1'

0'''2 = -p

D-3.4 Reinforced Cement Concrete Lining Considering that it isDot Cracked

a) Basic Equations:

"I E [ C1 ]0, = ---~ B (m -t- 1) - -- (m - 1)"1 2 - I x 2

m l~ [ C1 ]ar >: --- --- B (nz ~t· 1) I -- - (In - 1 )rf1 2 -- I x 2

U -: B» + 0/"(

E 3 C2t1(a= - - - (B2fl + -----)

a a

1~:3A ..\ ( B ()2 )Ct'S = --.- :Il +(12 a

b) Limit Conditions and Constants:

1) At y := oo

2) At x = b..

3) At x ==- (/,

4) At.\ - h,

art .z; 0

(1rl =:;:- (J"l

f1,2 -- 0' ..3 = -- f'i, = ['2

(') Constants are given by:

(:1 ~ Blb t -to OJ

C2

== {'r (m!j- l_llB'Z _ {_~!n12 (,nl t I )2 1c.J~1nl) \ m ~ + I ) ~ E1,n1 ( m2 - 1) ~

~J~21112 l~"aA, ~ ~ E 2" l l - + E3 1'1 , ~ C- P== B. -- - -. ~. ~- •,n~-1 a as ( ,ns - I ) a l

26

IS ,4880 (Part IV ).1971

D-3.5 Reinforced Cement Concrete Lining Considering that itI. Cracked and that Becau8e of Radial Cracks it CaDDot TakeTangential Tensile Stres8

Basic Equations

For rock

For concrete

t'jf1 == ()a (C1 ,) ) r _ "

O'r2 = -~

x

For Steel

c: \ crr2) X-It

F~• log hill

a.a,)0'13 := A,

E3A~ ( ·B C f )ar' -:: X - a 1 + If aa

U, a2 a r J)s = I. ... A

na •

Con.tants

27

8UREAU OF INDIAN STANDARDS

"..~MInIk -.;~I 8IhacU Shih zaw Marg, Nl!W DELHI 110002~: SIS 0111, S2S1375,32S 1402,.: "11I2l4Ol2,8111_,1111 S23t3I2

323 78 173378682eo.a

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TIIIphone..77 00 S2

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.,."." 0IIIHtI:•P\IIhp8k', NwmohllMd Sh8Ikh M_g,~, AHMEDABAD 380001*~ ....tMI At.., 1.t St8glI, 88ng11ore ·1Umkur Road.

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