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CORRELATION BETWEEN OBSERVED SUPPORTPRESSURE AND ROCK MASS QUALITY

Authors: Bhawani Singh, J. L. Jethwa, A. K. Dube and B. Singh

ABSTRACT

The correlation between rock mass quality and support pressure proposed by Barton etal. (19 !" has pro#en use$ul% e&cept in cases o$ squee'in rock round conditions.)ield data collected systematically $rom *+ tunnel sections indicate a clear need $orcorrection $actors to account hei ht o$ o#erburden and tunnel closure% which do notseem to be adequately accounted $or by the stress reduction $actor. As e&pected% thesupport pressure decrease rapidly with tunnel closure and then increases beyond alimitin closure. That $act that the obser#ed wall support pressure were always close to'ero e&cept in squee'in round conditions has taken care o$ by sli htly modi$yinwall $actors $or ,-wall. A criterion deri#ed $rom the $ield data shows that the squee'in

round conditions would be encountered where the hei ht o$ the o#erburden is reaterthan , 1 /. The data reported therein con$irm the earlier $indin s o$ Barton et al. (19 !"that the support pressure is independent o$ the tunnel si'e.

0 TR234CT02

The reliability o$ a realistic quantitati#e classi$ication system $or estimatin tunnelsupport pressure has increased with the passa e o$ time. 5#er since its de#elopment%the ,-system o$ Barton et al. (19 !" has attracted interest o$ tunnel en ineer. $ield

eolo ists and researchers. 0n spite o$ bein o#erly comprehensi#e and complicated%

this classi$ication method has now $ound acceptance.6ethwa et al. (197*" measured the support pressure by load cells and contact pressurecells in se#eral steel-rib supported tunnel sections throu h both squee'in and elastic

round conditions and compared the measured #alues with those estimated a$ter ,-system. The study brou ht to li ht si ni$icant limitations o$ Barton8s methods $orapplication to tunnel sections under squee'in round conditions. )or e&ample% thesupport pressure is a $unction o$ tunnel closures% which% in turn% depend on the supportsti$$ness. )urthermore% a tunnel at a reater depth is likely to attract hi her supportpressure. The tunnel closure and there$ore the support pressure continues to built up$or a considerable time due to creep o$ the $ailed rock mass. 5mpirical correlationde#eloped in a e$$ort to eliminate the abo#e limitations o$ the ,-system are discussedherein. Because the proposed empirical correlation are based on only *! tunnelsections% there is scope $or re$inement.

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R5C2R30 2) )05:3 3ATA

The $ollowin $ield data were collected;a" Radius o$ tunnel e&ca#ation.b" 3epth o$ tunnel section $rom round le#el.c" 4nit wei ht o$ round o#erlyin the tunnel section.d" , o$ the rock mass around the tunnel section.e" R

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Tunnel Closure

3iametrical de$ormations o$ the tunnel sections were measured by tape e&tensometers%closure meters% and sometimes e#en by simple in#ar tapes.The chan e in tunneldiameter was hal#ed to obtain the radial tunnel closures.

Type o$ Rack

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in which ? is the primary stress #alue. 0t $ollows that a tunnel section e&periencinelastic conditions in a i#en so$t rock mass can encounter squee'in conditions i$ theprimary stress le#el increases due to increase in the tunnel depth or any other reason.This e&plains why phyllites and shales squee'e at one place and present elasticconditions at another% as shown in Tables Al and A* (in the Appendi&". 5quations 1and * can thus be used to predict squee'in conditions in a tunnel% pro#ided that ? andq c are known.

5mpirical Criterion

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#alues o$ !.* and !.! k cm * $or tunnel sections * and !% respecti#ely. Such lar edi$$erences in the measured and predicted support pressures prompted the authors tolook $or possible reasons.

)i ure 1. Criteria $or predictin squee'in round condition.)i ure *. Comparison o$ predicted and obser#ed roo$ support pressures.

Some o$ the data in Table A* that are related to these $our tunnel sections ha#e beenshown in Table 1. 0t can be seen $rom Table 1 that in the cases o$ sections 1 and *% thedi$$erence in support pressure could be the result o$ depth% tunnel closure% tunnelradius% and time o$ obser#ations. Similarly% in tunnel sections / and !% the di$$erencewould be related to tunnel radius and tunnel closures. 0t $ollows that the $ollowin $our$actors mi ht ha#e in$luenced the measured support pressure;

1. Tunnel depth or thickness o$ the o#erburden%*. Tunnel closure%/. Time% and!. Tunnel si'e.

0$ other $actors are unchan ed% the tunnel closures depend on the supportsti$$ness. 0t is di$$icult to estimate the support sti$$ness in the present case% since thesti$$ness o$ back-$ill has to be taken into consideration while estimatin the o#erallsti$$ness o$ a steel rib support system. There$ore% tunnel closure has been used toreplace the sti$$ness o$ a support system (Table /".

Table 1 3etails o$ tunnel sections under squeein round conditions ($rom Table A*"S. o. Tye o$ rock

mass, Tunnel

radiusTunneldepth

Supportpressure

(k sq.cm"

Radialtunnel

2bser#a-tion

(m" (m" ?redict-ed

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? ir E *, ir -1 / 6r (!"

? iw E *, iw -1 / 6r (@"

where

? ir E short-term roo$ support pressure%? ir E short-term wall support pressure%6r E BartonGs oint rou hness coe$$icient%, ir E short term roo$ rock mass quality%, iw E short-term wall rock mass quality.

The #alues o$ , ir and , iw ha#e been taken as @ times , r and , w% where , r % and , w areBartonGs rock mass quality $or roo$ and wall rock% respecti#ely (#alues o$ , r % and , w should be obtained separately $or the roo$ and the wall rock% respecti#ely".

The short term roo$ and wall support pressures were estimated $rom 5qs. ! and @.These #alues were used to calculate correction $actor H$G $or o#erburden or tunnel depth.The correction $actor H$G is de$ined as a ratio o$ measured support pressure to thepredicted support pressure. A relationship o$ $ to tunnel depth is shown in )i ure /.Because the elasto-plastic theory su ests a linear relationship between theo#erburden pressure and the support pressure% a linear relationship has beenattempted in )i ure /.

Accordin to )i ure /% the correction $actor H$ H can be i#en by

$ E 1 I (= - /*+"17++ 1(F"

where = is the thickness o$ o#erburden or tunnel depth in metres.

The data points $or squee'in round appear to su est that the line in )i ure / shouldbe much steeper to represent a natural trend. 0n reality% the di$$erence betweenobser#ed support pressures and proposed line is mainly the result o$ e&cessi#e tunnelclosures% which ha#e been taken into account by another $actor H$ 8 $or squee'in

round condition.

Some may doubt that the correlation proposed in 5q. ! can account $or the method o$construction% the type o$ supports% the primiti#e stresses and tunnel closures. The

instrumented tunnels were constructed by con#entional means% i.e.% drillin andblastin $ollowed by steel ribs. This practice resulted in si ni$icant dama e to the rockmass. There$ore% equation ! is on the sa$e side. 0n the case o$ machine tunnellin %desi ners should reduce the support pressures obtained $rom 5q. ! by perhaps *+ %as there will be reduced dama e to the rock mass.

Another #alid concern is that the $ield data are not su$$icient to pro#e the #alidity o$ theproposed correlation. 0n the opinion o$ the authors% the 0nternational Tunnellin

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Association should compile a data bank $or obser#ed support pressures $rom all partso$ the world and should try to impro#e these correlation.

Ratio o$ >all Support ?ressure to Roo$ Support ?ressure

Barton et al. (19 @" realised that the wall support pressure would be smaller than theroo$ support pressure and there$ore su ested increasin the obser#ed , #alues $orestimatin the wall support pressure% as shown in Table *. The ratio o$ the wall supportpressure ? w to the roo$ support pressure ? r % correspondin to , i-wall% ha#e also beenshown in column / o$ Table *.The obser#ed wall suport pressures $rom some o$ thesquee'in and non squee'in case histories ha#e been plotted in )i . !. 0t can be seenthat the recommendations o$ Barton et al. (19 @".

)i /; Correction $actor $or o#erburden in Barton8s correlation $or short-term roo$support pressure under non-squee'in round conditions.

)i .!; Jariation o$ ratio between wall support pressure and roo$ support pressure withshort term rock mass quality

Table*. >all $actor , i-wall , i % $or estimatin wall support pressure.

Recommendation o$ Barton et al.% 19 @ AuthorGs Recommendation

Ran e o$ , i , i-wall , i ? w ?r Ran e o$ , i , i-wall , i ? w ?r 1 * / ! @ FK+.1 1.+ 1.+ K+.1 1.+ 1.++.1-1+ *.@ +. +.1-@ *.@ +.D1+ @ +.F D@ D1@ +.+-+.!

Correlation between Support ?ressure and Tunnel Closure in Squee'in roundCondition

Jariation o$ the normalised roo$ support pressure with the tunnel closure at the crown isshown in )i . @. The ordinate represents $ r H% which is the correction $actor which is thecorrection $actor $or tunnel closure at the crown. The correction $actor $ r H is i#en as;

$ r H E ?r obsd ?ir . $ ( "

where? r obsd E measured roo$ support pressure%? ir obsd E predicted short term roo$ support pressure% and

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$ E correction $actor $or o#erburden (5q. F".

The data points in )i . @ are taken $rom Table A* and represent ei ht tunnelsections $rom $our di$$erent tunnels. The normalised roo$ support pressure are hi her$or low roo$ tunnel closures. The roo$ support pressures decrease when tunnel closuresincrease and attain minimum #alues when the roo$ closures are appro&imately @ .Such a #ariation is in con$ormity with the round reaction cur#e concept.

)i .@; Correction $actor $or roo$ closure under squee'in round condition (= > /@+, 1 /".)i .F; Correction $actor $or wall closure under squee'in round condition (= > /@+, 1 /".

This trend is repeated in )i .F% which shows the #ariation o$ the normalised wallsupport pressure with the measured tunnel wall closures. The correction $actor $ wH $ortunnel wall closure is i#en as;

$ wH E ?wobsd ?iw (7"

where? wobsd E measured wall support pressure%? iwobsd E predicted short term wall support pressure% and$ E correction $actor $or o#erburden.

Thus% the correction $actors H$ r H and H$ wH are the same as the normalised roo$ and wallsupport pressure% respecti#ely. The recommended #alues o$ these correction $actorsare i#en in Table /.

The #alidity o$ Table / $or squee'in round has been questioned% particularly withre ard to hi hly squee'in or $lowin round. 0t is su ested that the application o$Table / should be restricted to moderately squee'in round by limitin closure to @ %by stren thenin the support system immediately. Serious construction problems mayarise i$ this remedial measure is not $ollowed. 0t is recommended that all such tunnelsections be instrumented.

6ethwa (197!" concluded that the wall support pressure may be si ni$icantly hi herthan the roo$ support pressure in the case o$ parallel tunnels i$ the clear spacin is lessthan the sum o$ the tunnel widths.

Jariation o$ Support ?ressure with Time

A$ter studyin the in$luence o$ the o#erburden and the tunnel closures andincorporatin these in$luences in the correlation between , and support pressure% ithas been possible to study the e$$ect o$ time on the support pressure. )i ure showsthe #ariation o$ the correction $actors H$G o#er time.

)i . ; Jariation in obser#ed support o#er time

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The correction $actors $L $or time are i#en as;

$ r M E ? r obsd ?ir . $G. $GG (9"

$ wM E ? wobsd ?iw . $G. $GG (1+"

where

$ r M E correction $actor $or the in$luence $or the time on the roo$ supportpressure%

$ wM E correction $actor $or the in$luence $or the time on the wall supportpressure%

? r obsd E measured roo$ support pressure%

? wobsd E measured wall support pressure%

$ E corection $actor $or o#erburden (5q. F"% and

$GG E correction $actor $or tunnel closures (Table /".

Table /. Correction $actors $or tunnel closures in squee'in round conditions.

S. o. round Condition Support system Tunnel

Closure( "

$Gw or $Gr

1 on-squee'in(=K/@+, 1 /"

--------- K1 1.+

* Squee'in(=K/@+, 1 /"

Jery sti$$ 1-* D1.7+

/

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$M E lo 9.@ t+.*@

(11"where HtG is the time in months a$ter e&ca#ation o$ the tunnel linin .

Combinin 5qs. 9%1+ and 11% the lon term roo$ and wall support pressures can bei#en as

? r E ? ir .$.$G. lo 9.@ t+.*@ (1*"

? w E ? iw.$.$G. lo 9.@ t+.*@ (1/"

where% ? r and ? w are lon term roo$ and wall support pressures.

Barton et al. (19 @" su ested that the ratio o$ the ultimate to the short term supportpressure is about 1. . 5quation 11% howe#er% su ests the $ollowin relationships;

)i .7; Comparison o$ obser#ed roo$ support pressure with predicted #alues $romauthorsG 5q. 1* (? r E ? ir .$.$G. lo 9.@ t+.*@"

? r E ? ir .$ . $Hlo 9.@ t+.*@ (1*"

? w E ? iw .$. $Hlo 9.@ t+.*@ (1/"

where ? 1 ?+ are lon term roo$ and wall support pressures. Barton et al. (19 @"su ested that the ratio o$ the ultimate to the short term support pressure is about (@" 1 /%

i.e. 1. . 5quation 11% howe#er% su ests the $ollowin relationship;

? $H(lo 9.@ t+.*@

i.e.? 1 ?+ E $ 1H(lo 9.@ t1 +.*@" ( lo 9.@ t+ +.*@" $ +H E 1. @

where ? 1 and ? + are support pressures a$ter t 1 and t + month o$ e&ca#ation.

0n case o$ ri id linin % t 1 and t+ so that the ratio o$ the ultimate support pressure a$ter 1++years to that a$ter one month is i#en by (t + E 1 month and t 1 E1++ years 1**+ months".

? 1 ?+ E (lo 9.@ t 1 +.*@" ( lo 9.@ t+ +.*@" E 1. @

0n other words% the support pressure will increase in 1++ years to 1. @ times thesupport pressure obser#ed a$ter 1 month o$ e&ca#ation. The corrected supportpressures compare well with the obser#ed #alues% as shown in )i ure 7.

This ratio o$ 1. between the ultimate and the short-term support pressure tallies withthe (@"8 su ested by Barton et al. (19 @". =owe#er% the ultimate support pressure $or

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tunnels under squee'in rock conditions may be *-/ times the short-term supportpressure% accordin to 6ethwa (197!".

The ratio o$ the ultimate support pressure to the short-term support pressure% workedout here as 1. % is relati#ely small compared to the ratio o$ */ a$ter 6ethwa (197!"%probably because the period o$ obser#ations reported herein is relati#ely short and thenumber o$ squee'in case histories is small. )urthermore% in special cases o$ solubleor erodible oint $illin s and where seepa e is a serious problem% the lon -term supportpressure may be as hi h as the co#er pressure or F times the short-term supportpressures% whiche#er is smaller. This trend has been indicated $rom a 1+-yearper$ormance study o$ Chhibro-Nhodri under round powerhouse comple& in 0ndia (

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0n a recent study at the under round powerhouse comple& o$ :akhwar dam pro ect in0ndia (, E 7-9 and =E *@+ m"% the obser#ed roo$ support pressures were nearly thesame (i.e.% about +.@ k cm *" $or the Fm wide approach adit% 1!-m-wide e&pansionsur e tank and *1-m-wide powerhouse ca#ern% all e&ca#ated throu h ti htly ointedtraps. These obser#ations should erase all doubts about si'e e$$ect in under roundopenin s.

0t may be noted that rock mass quality , estimated $rom a lar er tunnel would besmaller than that obtained $rom small dri$ts in a similar rock mass. This is due to thepossibility o$ intersectin reater number o$ eolo ical discontinuities in a lar eropenin . Thus% the si'e e$$ect is automatically accounted $or in the estimate o$ ,. Thead#erse e$$ects o$ deterioratin hydro- eolo ical conditions (6 w" should also bedetermined% i$ possible% a$ter a water tunnel is commissioned. 0t would there$ore beunsa$e to obtain , $rom small dri$ts and use it to estimate support requirements $orlar e e&ca#ations.

)or under round e&ca#ations in non dialatant rock masses (schists% slate% etc." withsmooth planes o$ weakness% it is cautioned that Ter'a hi8s concept may still be #alid.

Conclusions

The combined approach o$ $ield instrumentation and quantitati#e classi$ication o$Barton et al. has pro#ed rewardin at this sta e o$ de#elopment o$ rock mechanics.3espite limited $ield data% some practical trends showin the in$luence o$ o#erburden%tunnel closures and time o$ e&ca#ation on the tunnellin condition and the supportpressures ha#e emer ed. 0t would perhaps be hasty to draw any de$inite conclusions$rom these trends howe#er% some tentati#e correlation ha#e been possible. These

correlation are sub ect to re$inement as more $ield data is collected. The $ollowintentati#e conclusions are possible $rom these correlation;

1. Squee'in is likely to occur in a tunnel section where the hei ht o$ o#erburden inmetres e&ceeds /@+ , 1 /.

*. The short-term roo$ support pressure is i#en by the $ollowin correlation;

? r E *.+(@," -1 / .$. $G 6r

where H$ H is the correction $actor $or thickness o$ o#erburden (R" in metres% and $8 is thecorrection $actor $or tunnel closure (see Table /% equal to 1 in non squee'in roundconditions". The-#alue o$ the correction $actor $ is i#en as $ E 1 I (= - /*+"17++ D 1.

)i ure 9. Support pressure #irtually independent o$ tunnel si'e.

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/. 0n squee'in round conditions% the support pressure is si ni$icantly in$luenced bytunnel closures. The correction $actor $G $or tunnel closure #aries $rom +. to 1.7 in thecase o$ a sin le tunnel. The minimum support pressure occurs when the tunnel closureis about @ o$ the tunnel diameter. The support pressure increases rapidly beyondthis limitin closure.

!. The short-term wall support pressure may be obtained $rom the abo#e correlation bysubstitutin , wall % $or ,. 0n eneral% the actual wall support pressure $or the non-squee'in rock conditions is likely to be ne li ible. The short-term #alues o$ ? iw% ?ir depend on ? r (i.e.% @,"% as i#en below;

? iw% ?ir , i

1.+ @, K +.11.+ - +.+ @ K @, K +.1+.+ @, @

@. The ultimate support pressure maybe 1. @ times the short-term support pressure $ortunnel sections under non-squee'in round conditions% e&cept $or cases o$ solubleand erodible oint $illin s with seepa e.

F. The support pressure is independent o$ the tunnel si'e% pro#ided that , is obtained$rom a $ull si'ed openin .

Re$erences

Barton% . :ien% R. and :unde% 6. 19 !. 5n ineerin Classi$ication o$ Rock

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3eere% 3. 4. ?eck% R. B. ashin ton% 3.C.

3ube% A. N. 19 9. eomechanical e#aluation o$ a tunnel stability under )ailin rockconditions in a =imalayan Tunnel. ?h.3. Thesis% 4ni#. o$ Roorkee% 0ndia.3ube% A. N 6ethwa% 6. :. Sin h% B. Sin h% Bhawani and

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4nal% 5. 197/. 3esi n uidelines and roo$ control standards $or coal mines roo$s.?h.3. Thesis% ?ennsyl#ania State 4ni#ersity. Re$er to p. 11/ o$ Rock

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k sq. cm k sq. k sq.k sq. k sq.k sq. k sq- month

cm cmcm cm cm cm

1 2 3 ! 5 F 7 89 1 11 12 13 1! 15

C"i#$o%K"o&$i Tunnel

1%7 to /.! +.1 *F to *.@ to !. * 1.7 to /.+ 1.+ (+.7F" 1.7(*.7" (!./" /%1 1. @ Circular $ibs(*. " +.@+ (/./" (*.!"statae (0.25)

aR,3 E1+-*+, +.+*@+%1+*. /uh E *.7= E *7+(6ethwa eta . 197*"

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!. So$t plastic blackdo do do do 1%+ 1.71.7 ( .9" ( .+" 11.@ 1*.* *FCircular ribs o$

days within thrust#ery hi h capacity

'one% moderatelywere stable.

squee'in .Consequently%

y E *.F!%tunnel closures

R,3 E 1+were likely to be

+ E +.+1F-+.+/low% appro&.

=E *7+ .+-* .

(6ethwa et al. 197*"

irl =ydro Tunnel

@. Jery blocky and+. to 1.@ to 1.* to+.7 to 1.2B 1.1@1.1@ (1.9" (1.*" *.+ *.! 1*Roo$ closure

seamy slates% *./ !.1 1.7 1./considered equal

moderately (1.*" (*.@" (1 @" (1.+"to wall

closure assquee'in .

horseshoe ribsaE1.1% E*.@with in#ert struts

uhla E .Fde$ormed% but not

= E /7+as se#ere as in

, - +./*-+.7*case F.

(6ethwa et al. 197*"

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ab!e A2 ("ontd.).

1 * / ! F

9 1+ 11 1* 1/ 1! is

irl =ydro Tunnel (contd."F. Crushed phyli$tes% *.1 to +.F* to 1.7 to 1.* to1.+ +. 1.7 (1.@" (*.9" 1. !.+* ?eak

hi hly squee'in . #.$ (%.$) 1.F (1" *./ (*.1"1.9 (1.F"

measureda E *@1% m *./

supportR23 E 1+-*@

pressure o$ @q E +. 1 *! +./*

k sq. cmuhla E 1*.!

occurred atu#la E @

hal$ total wall= E *!+

closures when(6ethwa et ad 197*"

horseshoe ribs

with in#ert

budded.

:oictak =ydro Tunnel

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. Crushed shales% *.9 to +.+@@ to /.@ to *.@ to 1.+1.1@ 1.1@ (@.1" (!.F" @.!II @.!II /1@-cm-thick

moderately @.! (!.*" +.** @./ (!.!" @./ (!.+"

shotcrete withsquee'in . (+.1 1"

!-rn-lon rocka L * % E *.

bolts supple-cc

mented withR23 m 1+-*+

circular ribs., E +.+1 1-+.+!!

Squee'inuhla E

occurred e#en= E /++

at = 1F+ m.(6ethwa et al 197*"

Roo$ closure is

considered

equal to wall

closures.

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a E **!% E *.@Jertcal and

R23 E F+% + - +.@

hori'ontaluh E 19+ mm

closures= E /@+

appeared(Sharma 197@"

equal.

See $ootnotes in Table Al $or notations.