E n M m s h

1300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 55001300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5500

sc mr sr grpo MPa ri

D

0.689789490513517 0 0.00280513 1.993295881 1.374955 0.8326666971 -0.59990.689789490513517 0.25 0.00280513 1.365915661 0.942194 0.8326666971 -0.59990.689789490513517 0.75 0.00280513 1.035760376 0.714457 0.8326666971 -0.59990.689789490513517 1.25 0.00280513 0.856102845 0.590531 0.8326666971 -0.59990.689789490513517 1.75 0.00280513 0.733292575 0.505818 0.8326666971 -0.59990.689789490513517 2.25 0.00280513 0.641398758 0.44243 0.8326666971 -0.59990.689789490513517 2.75 0.00280513 0.569055761 0.392529 0.8326666971 -0.59990.689789490513517 3.25 0.00280513 0.510185549 0.351921 0.8326666971 -0.59990.689789490513517 3.75 0.00280513 0.461136761 0.318087 0.8326666971 -0.5999

N= (2/(mr*sc))*((mrscpo+s

rsc2- mrsc

2M)0.5)pi ue/re re/ri re sre= po-scM

R = 1.1 D K L B

K/L

-0.827671719 -0.659939665 0.02229083026451 -1.53207500856882 -0.0145494 0.0201596942968165-0.374155814 -0.659939665 0.01046719885509 -1.44808475053081 -0.0072283 0.0128385617745597-0.042159129 -0.659939665 0.00601868052609 -1.65398080109979 -0.0036389 0.009249162270080320.1864206737 -0.659939665 0.00411182465732 -1.69980411844226 -0.002419 0.008029255466147620.3722185815 -0.659939665 0.00301673582743 -1.70424578774607 -0.0017701 0.007380385900523550.5328759964 -0.659939665 0.00230801663681 -1.69319413698019 -0.0013631 0.006973370354002510.6764703748 -0.659939665 0.00181673823181 -1.67573969793927 -0.0010841 0.00669439742323140.8075031312 -0.659939665 0.00146028966908 -1.65575756215877 -0.0008819 0.006492202901352310.9287878288 -0.659939665 0.00119300481142 -1.63507382418455 -0.0007296 0.00633988995827037

R = 2D ln re/ri eav

if re/ri < √3 if re/ri > √3 [2(ue/re)(re/ri)2] {[(re/ri)2-1][1+(1/R)]} (2(1+n)Msc)/E)-eav

174.89563

45.47548

17.19036

13.25301

10.59730

7.94415

5.29355

2.64550

0.000000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.832666697140071

Required support line curve

ui/rio

pi/p

o

X A

1.37957898102703 0.08009907134 0 0.03081917985943140.62365003500858 0.02395323327 0 0.00820046547823916

0.0702716396110805 0.00992249718 0 0.00311578150983327-0.310729528429998 0.00588473833 0.00240384615384615 0-0.620421018972965 0.00396856635 0.00192307692307692 0-0.888207857028329 0.00286879133 0.00144230769230769 0

-1.127553701085 0.00216780963 0.000961538461538462 0-1.34596159444995 0.00168985091 0.000480769230769231 0-1.54812123781856 0.00134815929 0 0

For picr = po - Msc < pi For pi < picr = po - Msc

2N-(4/mrsc)*(mrscpi+srsc

2)0.5 B *eX ui/rio = ((1+n)/E)*(po-pi) ui/rio = {1- [(1- eav)/(1+A)]0.5}

174.89563

45.47548

17.19036

13.25301

10.59730

7.94415

5.29355

2.64550

0.000000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.8326666971400710.832666697140071

Required support line curve

ui/rio

pi/p

o

Roof Sidewalls Floor

-36657.500303 0 36657.5003029969 5674.89563 0.03179920529 174.89563-36660.31870488 0.06666667 36660.4520382151 5545.47548 0.00826826913 45.47548-36661.70362252 0.2 36662.1036225195 5517.19036 0.00312551995 17.19036-36662.3964617 0.33333333 36663.0631283655 5513.25301 0.00240963855 13.25301

-36662.82788326 0.46666667 36663.7612165889 5510.5973 0.00192678227 10.59730-36663.11713252 0.6 36664.3171325179 5507.94415 0.00144439095 7.94415-36663.31647544 0.73333333 36664.783142108 5505.29355 0.00096246391 5.29355-36663.45386247 0.86666667 36665.1871957991 5502.6455 0.00048100048 2.64550-36663.54608472 1 36665.546084725 5500 0 0.00000

rio= ri+ui= ri/(1-ui/rio)

ui/ri = (ui/rio)/(1-(ui/ri

))ui

{pi+gr(re-ri)}/po pi/po {pi-gr(re-ri)}/po

SUPPORT INTERACTION ANALSIS OF CIRCULAR TUNNEL

E n M m s h

1300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5500 0.689789490513517 0 0.00280513 1.99329588141300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5501 0.689789490513517 0.2 0.00280513 1.42152151671300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5502 0.689789490513517 0.4 0.00280513 1.23577468261300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5503 0.689789490513517 0.6 0.00280513 1.10987727571300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5504 0.689789490513517 0.8 0.00280513 1.01375989451300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5505 0.689789490513517 1 0.00280513 0.93600032481300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5506 0.689789490513517 1.2 0.00280513 0.87084682321300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5507 0.689789490513517 1.4 0.00280513 0.81494251621300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5508 0.689789490513517 1.6 0.00280513 0.7661376721300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5509 0.689789490513517 1.8 0.00280513 0.72296417021300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5510 0.689789490513517 2 0.00280513 0.68437074931300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5511 0.689789490513517 2.2 0.00280513 0.64957671841300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5512 0.689789490513517 2.4 0.00280513 0.61798530691300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5513 0.689789490513517 2.6 0.00280513 0.58912946781300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5514 0.689789490513517 2.8 0.00280513 0.56263646291300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5515 0.689789490513517 3 0.00280513 0.53820386961300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5516 0.689789490513517 3.2 0.00280513 0.51558282611300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5517 0.689789490513517 3.4 0.00280513 0.49456602691300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5518 0.689789490513517 3.5 0.00280513 0.48460358541300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5519 0.689789490513517 3.6 0.00280513 0.47497892671300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5520 0.689789490513517 3.7 0.00280513 0.46567427521300 0.25 0.041676 70 0.1 0.5 0 0.001 25 150 3.75 5500 0.689789490513517 3.75 0.00280513 0.4611367608

sc mr sr grpo MPa ri

N= (2/(mr*sc))*((mrscpo+

srsc2- mrsc

2M)0.5)pi ue/re re/ri

AVAILABLE SUPPORT CURVE

1/Ks Ps max ui/ri pi

0.0257 0.1566 0 0.0222 0.0308 0 To find 1/Ks Available 0.0354 0.0082 0.25 Steel spacing, s s 1.5

0.106201 0.0031 0.75 Es 2E+050.0024 1.25 As 0.00430.0019 1.75 Is 3E-050.0014 2.25 W 0.10590.0010 2.75 X 0.20230.0005 3.25 tB 0.250.0000 3.75 ri 5.5 in radians Sin cos

ɵ 11.25 0.196349540849362 0.195 0.98

0.005041 Pi 0 250

0.02218 Ps max 0.15664 0.005

0.02218 0.15664 3.5

0.03 0.15664 10000

Uie Uiemax

Uio sys

Uiemax Uio

P0

EB

D

R = 1.1 D K L B X

K/L

1.374955 0.8326666971 -0.5999 -0.8276717192 -0.659939665 0.02229083026451 -1.53207500856882 -0.01454944 0.0201596942968165 1.379578981027030.980551 0.8326666971 -0.5999 -0.4220347621 -0.659939665 0.01133677641595 -1.39785323093599 -0.00811013 0.0137203899229409 0.7034555772442220.852424 0.8326666971 -0.5999 -0.254014433 -0.659939665 0.00856764164564 -1.54809366716348 -0.00553432 0.0111445737042574 0.423396093559520.765582 0.8326666971 -0.5999 -0.1250879 -0.659939665 0.00691086843207 -1.62148971637131 -0.00426205 0.00987230523318054 0.2084988934887950.699281 0.8326666971 -0.5999 -0.0163978049 -0.659939665 0.00576571163927 -1.66209776854667 -0.00346894 0.00907919286572879 0.02733217346140830.645643 0.8326666971 -0.5999 0.0793600912 -0.659939665 0.00491512655975 -1.68518425976815 -0.00291667 0.00852692646132316 -0.1322789110098740.600701 0.8326666971 -0.5999 0.1659318466 -0.659939665 0.00425467361382 -1.69780083279141 -0.00250599 0.00811624735580738 -0.2765783613946150.562139 0.8326666971 -0.5999 0.245542792 -0.659939665 0.00372594687068 -1.70373086121403 -0.00218693 0.00779719030671537 -0.4092754009727970.528474 0.8326666971 -0.5999 0.3196428532 -0.659939665 0.00329303496088 -1.7052035742629 -0.00193117 0.00754142457730349 -0.5327867939079950.498693 0.8326666971 -0.5999 0.3892391522 -0.659939665 0.00293235303296 -1.70361981865915 -0.00172125 0.00733150483728451 -0.6487912303214050.472072 0.8326666971 -0.5999 0.4550649685 -0.659939665 0.00262763830455 -1.69990212171463 -0.00154576 0.00715601494032982 -0.758510954272360.448071 0.8326666971 -0.5999 0.5176738688 -0.659939665 0.00236724718012 -1.69467992233329 -0.00139687 0.0070071261374576 -0.862868661298518

0.42628 0.8326666971 -0.5999 0.5774959192 -0.659939665 0.00214258966214 -1.68839464199739 -0.00126901 0.00687926633832942 -0.9625811940494450.406375 0.8326666971 -0.5999 0.634873129 -0.659939665 0.00194717147542 -1.68136261002931 -0.00115809 0.00676834769007457 -1.058218619853140.388101 0.8326666971 -0.5999 0.6900827979 -0.659939665 0.00177598156929 -1.67381442754251 -0.00106104 0.00667129486349093 -1.150243147107670.371247 0.8326666971 -0.5999 0.7433534604 -0.659939665 0.0016250859589 -1.66592048939041 -0.00097549 0.00658574465931915 -1.239035701804870.355644 0.8326666971 -0.5999 0.7948761094 -0.659939665 0.00149135004452 -1.6578080336721 -0.00089959 0.00650984786902153 -1.324914634104220.341146 0.8326666971 -0.5999 0.8448123008 -0.659939665 0.00137224376561 -1.64957282351043 -0.00083188 0.00644213460889359 -1.408149228721640.334274 0.8326666971 -0.5999 0.8692294175 -0.659939665 0.00131751616427 -1.64543256973214 -0.00080071 0.00641096747680422 -1.448848143719160.327635 0.8326666971 -0.5999 0.8933001394 -0.659939665 0.00126570177677 -1.64128732666889 -0.00077116 0.00638142039843606 -1.488969681375510.321217 0.8326666971 -0.5999 0.9170388037 -0.659939665 0.00121659828714 -1.63714346856192 -0.00074312 0.00635337893712445 -1.528537738972840.318087 0.8326666971 -0.5999 0.9287878288 -0.659939665 0.00119300481142 -1.63507382418455 -0.00072963 0.00633988995827037 -1.54812123781856

re sre= po-scM

R = 2D ln re/ri eav

if re/ri < √3 if re/ri > √3 [2(ue/re)(re/ri)2] {[(re/ri)2-1][1+(1/R)]} (2(1+n)Msc)/E)-eav2N-(4/

mrsc)*(mrscpi+srsc2)0.5

pi/p

o

ui

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

side wall

Roof

Floor

Available support curve

A Roof Sidewalls Floor

0.08009907134 0 0.0308191798594314 -0.0367 0.0000 0.0367 5674.89563 0.03179920529 174.895630.02772511328 0 0.00958888490890042 0.0167 0.0533 0.0900 5554.25915 0.00968172183 53.259150.01701931388 0 0.00566243197046223 0.0700 0.1067 0.1433 5533.33212 0.0056946777 31.332120.01216097774 0 0.0039096548451022 0.1233 0.1600 0.1967 5524.59928 0.00392500024 21.599280.00933076934 0 0.00290804990348414 0.1766 0.2133 0.2500 5520.05259 0.00291653132 16.052590.00747041135 0.00264423076923077 0 0.2300 0.2667 0.3034 5519.59508 0.00265124126 14.595080.00615515251 0.00245192307692308 0 0.2833 0.3200 0.3567 5519.53347 0.00245794978 13.533470.00517835817 0.00225961538461538 0 0.3366 0.3733 0.4100 5519.47188 0.00226473281 12.471880.00442656685 0.00206730769230769 0 0.3900 0.4267 0.4634 5519.41032 0.00207159031 11.410320.00383201036 0.001875 0 0.4433 0.4800 0.5167 5519.34878 0.00187852223 10.348780.00335161493 0.00168269230769231 0 0.4966 0.5333 0.5701 5519.28726 0.00168552853 9.287260.00295665626 0.00149038461538462 0 0.5499 0.5867 0.6234 5519.22577 0.00149260918 8.225770.00262723199 0.00129807692307692 0 0.6033 0.6400 0.6767 5519.1643 0.00129976412 7.164300.00234911432 0.00110576923076923 0 0.6566 0.6933 0.7301 5519.10285 0.00110699331 6.102850.0021118637 0.000913461538461538 0 0.7099 0.7467 0.7834 5519.04143 0.00091429671 5.04143

0.00190764922 0.000721153846153846 0 0.7632 0.8000 0.8368 5518.98003 0.00072167428 3.980030.00173048454 0.000528846153846153 0 0.8166 0.8533 0.8901 5518.91866 0.00052912598 2.918660.00157571749 0.000336538461538461 0 0.8699 0.9067 0.9434 5518.85731 0.00033665176 1.857310.00150555567 0.000240384615384615 0 0.8965 0.9333 0.9701 5519.32676 0.00024044241 1.326760.00143968023 0.000144230769230768 0 0.9232 0.9600 0.9968 5519.79612 0.00014425157 0.796120.0013777463 4.80769230769221E-05 0 0.9499 0.9867 1.0235 5520.2654 4.8079235E-05 0.26540

0.00134815929 0 0 0.9633 1.0000 1.0367 5500 0 0.00000

For picr = po - Msc < pi For pi < picr = po - Msc

rio= ri+ui= ri/(1-ui/rio)

ui/ri = (ui/rio)/(1-(ui/r

i))ui

B *eX ui/rio = ((1+n)/E)*(po-pi) ui/rio = {1- [(1- eav)/(1+A)]0.5} {pi+gr(re-ri)}/po pi/po {pi-gr(re-ri)}/po