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Structural Equivalency Lecture 10

Structural Equivalency Lecture 10. Subbase Thickness, inches LTE=10% DC-10 Gear k=100 Subbase E=1x10 6 psi h- Varies LTE=10% 0510152025 25 20 15 10 5

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  • Structural EquivalencyLecture 10

  • Subbase Thickness, inchesLTE=10%DC-10 Gear k=100 Subbase E=1x106 psi h- VariesLTE=10%05101520252520151050182124Subgrade Stress, psi

  • Conventional Plate Theory Single Placed Layer1) Regard the base as contributing exclusively to the stiffness of the subgrade kcomposite Based of PCA tests (1950s) Volumetric approach Backcalculation- matching Defl. BasinBasin Area

  • h1E1h2E21kheEeek

  • Slab Action: - Value

  • Equivalent Thicknesshe-p Equivalent Thicknessm Measured Valuekb Back-calculatedEc Based on Cores

  • Unbonded Layers No separation during bending

  • Bonded System

  • unbonded or bondedTandemDualTridemTied or Extended ShoulderDoWLslab = 0 or f

  • Bending Moment

  • Bending Moment - with Subbase

  • Bending Stress - with Subbase

  • Partially Bonded Systemcee-phche-pTransformed Section

  • Summary

    Where

    e=

    P= Applied FWD load (F)

    a, b, c= 0.0006, 0.0403, and -0.0002 (for FWD plate loading)

    hc= Concrete slab thickness (L)

    v= Load induced vertical pressure (FL-2) ( 0.7 psi)

    _1146672016.unknown

    Chart1

    1.1071937801

    1.7125512339

    -0.4302859577

    -0.2561638204

    0.0637509206

    0.2307404555

    0.1520043536

    -0.8633870713

    -1.2408466027

    -1.8700281819

    4.6581773297

    -1.5682508522

    -0.3368244409

    0.7890599638

    -0.192431426

    1.0456929578

    0.1751957652

    0.1020538782

    0.401027312

    0.946589035

    -0.5760740767

    -1.707725109

    0.7727929208

    0.7768850624

    1.0619293039

    -0.8762986917

    -0.4339394865

    0.1937588334

    0.7387563676

    0.8293533275

    1.6424611998

    -0.2706708579

    0.639199727

    0.6837678868

    -0.211252843

    0.3085207633

    -0.133223681

    0.296426277

    0.6233696645

    -0.0958034333

    0.3670125833

    -0.0058867493

    1.1176662439

    -0.6086990662

    -0.2158787744

    1.2148897389

    0.2643242189

    0.3370625034

    0.3167859064

    0.8971792358

    0.9852085587

    0.4393603038

    0.535428831

    0.4442017109

    -0.2071863481

    -1.2533426482

    1.0031056987

    1.2944192948

    0.960979392

    -0.1387896447

    0.9896643074

    0.4515456279

    1.0152164626

    1.0931757631

    ln(mu)

    ln(-ln(x))

    SLABS CL_WEST

    3.09144135271.903676997610.6

    3.57149043952.35216779119.7

    3.7261697572.616984208419.9

    3.79762902622.6374941865

    4.47182678992.604861281625.6

    4.33488520682.621696896715.9

    3.61694485112.44826223336

    3.38700253842.23575525856.4

    3.58870606362.72671290768.1

    3.4228081212.508317610929

    4.0638227582.930821709518.6

    3.56680870492.7678436367

    4.03802707253.2850152936

    3.70849924062.6264682813

    4.11761316562.4067737725

    3.3110823962.0893460126

    5.1683287933.3627574429

    3.85032966432.4227924299

    3.36882694722.3407379772

    3.43081349162.3194233289

    3.41286939952.278505695

    3.84600260252.4197356371

    3.49953736162.2076970171

    3.00317002162.1318799032

    3.38227998572.5664995819

    3.72996591952.4477904025

    3.61157204632.2725559047

    3.90234338572.4610255814

    3.50125520292.4914593014

    3.41331701472.5387606853

    3.30904218362.1564544293

    3.20495988182.0403158757

    3.40129821242.2278045278

    3.36311531482.0482131379

    3.1909189952.2166607249

    3.36291863621.946095804

    2.90302326231.883042234

    3.12241560841.8481325062

    3.02261237132.0532613579

    3.07480836291.8448849315

    3.09787171121.8902269023

    2.82991274741.8751398327

    2.8558430061.9797140366

    2.91685135671.8738000031

    3.22273990391.9488544085

    4.51553786672.496167006

    3.38206630472.2222221943

    3.2576734112.1045146713

    2.96094905562.0298330199

    3.15648345862.0484553229

    3.77658927822.214918626

    2.83648127091.9393193396

    3.63796499162.0966167473

    3.59812076452.1509427238

    3.9108004562.2986354199

    3.82480325532.1842391044

    4.71927596052.4131556087

    4.58948028582.5237268472

    3.12805283281.9726458862

    3.77862422562.2361175264

    3.86188570962.4188691773

    3.22780844932.2139458979

    3.60251908211.9540654705

    3.26996203162.1863117417

    2.97608432311.9870264275

    3.35496525322.1531868118

    3.33206576012.1368681254

    3.22018695192.0852028767

    3.52184656442.2301931862

    3.27337940772.0023331119

    3.62188293662.1048639695

    3.62963981272.3186646502

    4.06368737552.4480043868

    3.34017163852.0777443634

    3.03186352211.9021829101

    3.53343942362.0871093274

    3.77459730792.1109122496

    3.36883674241.8736270572

    3.38641244112.0071151714

    3.28749598022.2110591472

    3.25148561042.5974511076

    3.54375799232.2815976083

    3.00715218441.6356469586

    4.02242072051.9960884923

    4.09109623892.1949712639

    4.24702011832.5244524931

    4.30543117322.4936894875

    4.18474911212.5521802321

    4.09379618692.2995380497

    4.62829044492.4484481648

    4.22278036532.9466084462

    4.47424990842.3241527398

    3.99055305432.0156364719

    3.75359919472.1081858827

    3.60524627471.9994612307

    3.74563176012.0925317542

    3.90256912072.2944237407

    4.04920852742.1121826083

    3.65439584442.1532981942

    4.14012078942.4591693668

    3.48987405682.0314193346

    3.62879113932.2164492437

    4.19200195272.4384169015

    3.52821544462.14806045

    3.80126576772.167748721

    3.58675658132.268546933

    3.74588562242.0799256303

    2.77021668071.7084612082

    3.06128568281.8707857348

    2.79449701011.7606354959

    3.20045919121.7643559369

    3.39168260641.9174862521

    3.43999004421.8380842457

    3.4757526351.9194455644

    3.28044736511.8568569109

    2.8860176391.7076434901

    2.64609834971.4544157493

    2.93842559721.6369774019

    3.1658051031.7541675045

    2.97705477531.7426661013

    3.14764933051.8844481802

    2.93360479881.7362150607

    &L&7P:/CIVIL/PROJECTS/2003/03-128GH-0/&F

    15L END

    33R END

    TDZ

    'WD'

    'WG' & 'WH'

    'WJ' & 'WK'

    'WL'

    'WM'

    TDZ

    ND1

    ND7

    CBR

    STATION (FEET)

    DEFLECTION (MILS [.001 IN])

    FIELD CBR VALUES

    JOINTS CL_WEST

    6.38112215272.3136711975

    6.20162004182.5832582228

    6.69820928683.0058447069

    6.49414265023.095247508

    4.70138461642.3334711357

    4.95618076682.3499894744

    5.67368499432.8804859749

    8.3060953272.639991431

    5.66141145052.7503686872

    11.21554437182.2593764121

    12.83387531892.7690924715

    7.3262527733.2953810092

    6.45022983633.1081924324

    14.86285205992.3581978108

    4.66850844542.6611421209

    5.70272646582.825949917

    4.21772587382.1385655082

    14.057949842.8283505978

    5.50304920363.0090068451

    3.91131925672.3943120333

    4.19123917972.4387078692

    4.13437654172.3082057265

    5.57434120342.7359361372

    4.32645211062.2131118322

    4.99645705772.2711168444

    7.29326299082.9797378733

    7.21465004543.0267266302

    5.84317389592.6559883781

    5.36087858442.9369167166

    7.72631595013.2315788771

    6.92173199532.9106242144

    14.35330913222.2496357433

    5.60249301062.1257047208

    5.18119760312.3839277315

    5.3843572332.126946739

    4.51035265452.2088081587

    5.61524692182.3306876106

    3.95899612862.1385649313

    4.52666287892.1194202267

    4.2945688662.1518823584

    3.22607526311.9173057288

    3.22387035111.9120295113

    4.4110875422.1088497669

    4.29942420262.2456812996

    3.42835270021.9491142055

    3.18590031791.8547441644

    3.60267141292.0055174763

    7.82066661862.8746757798

    5.06342151952.5471795696

    4.29824886562.0425561724

    4.96872560562.1096265326

    4.73630124392.1200583734

    6.97255929212.4127917792

    4.64222058452.2413955781

    5.01020259442.2318175627

    3.83521719932.062416542

    5.11039623172.5453324951

    6.19459803652.940869677

    4.61398068272.478070739

    4.18783612282.1997644733

    5.48063900452.4766461828

    4.18303830472.1714199233

    3.84936609942.0517848626

    4.05501414182.3678914868

    3.72003050431.9995164847

    4.11451229232.2665550697

    4.17618371472.1672809899

    4.58896667962.0724367737

    5.08886120362.2731970318

    4.92808580242.2889547917

    4.77257476222.1701542381

    4.56769665972.4838596352

    5.15951742252.2112217835

    4.74780204952.1564089993

    3.9953311272.1368289769

    4.62700823012.3427891835

    4.25558601662.239782114

    4.26192962822.1807536617

    2.8742117351.927719107

    3.91827597532.1515533499

    10.96401994662.1354878737

    5.22308776242.6656437265

    3.29349106241.8819949098

    4.47622025872.2381101293

    6.45754551282.3350484476

    4.88126180482.6343313352

    5.04198231742.5930196528

    7.39023795682.5569599598

    4.59507780812.354077964

    4.87094070392.5499584177

    12.72678067341.7288424739

    4.2832435022.2687964382

    4.25707779042.1388715987

    5.86939041672.1830013032

    3.57608555491.8967083782

    4.93256719442.0292208288

    7.07925392282.4160195411

    4.5693912652.1207711957

    3.89088951372.1627549921

    6.64361377912.6406792616

    3.16984902891.911097157

    4.5795516562.3830245268

    5.90037735992.0701479024

    3.93618356692.1879317388

    4.19581870022.2876957047

    5.60549763882.242199105

    3.98179764512.213258977

    3.73504934721.9140835408

    5.13927094112.0223501556

    3.21823796761.7752216828

    3.59816975681.8614808256

    5.45380943691.9528482723

    3.15791633321.8362323464

    3.84552776452.065190823

    4.58878607941.9337709828

    3.44620598971.8110692553

    2.97528550651.5209125702

    4.46134801761.6161498443

    3.28919985621.7278707289

    3.12588507481.7500910645

    3.99054109861.6627253476

    3.05209039421.7206413777

    15L END

    33R END

    ND1

    ND7

    STATION (FEET)

    DEFLECTION (MILS [.001 IN])

    RUNWAY 15L-33R (CENTERLINE-WEST) JOINTS - NORMALIZED TO 50,000 LBF

    CBRs

    CBRBore HoleStationCBR @0.1

    12200010.6

    24300019.7

    36390019.9

    48

    59630025.6

    611780015.9

    71386806

    81495006.4

    91597008.1

    10171095029

    11191270018.6

    1220WD25.1

    1321WG23.7

    1424WM17.2

    15L_SOUTH_MAIN KLOTZ

    DistStationStressForce (LBF)N=50,000 LBFD1D2D3D4D5D6D7ND1ND2ND3ND4ND5ND6ND7SlabPositionSurfaceTemperatureAirTemperatureTimeBasin AreaRRSd*0dyn k0.00060.0403-0.0002seheeff sigmaUB sigmaIF ShearmuxLn(-ln(x))ln(mu)

    01000+561614600.813.803.143.092.882.782.592.343.092.552.512.342.262.111.90Center55.049.712/28/03 11:04 PM55.4272.2001785660.1244849841474.75767709140.82631582741.89785964841.867694039220.57271.2462472496291.023814851834.322815.460.051.112.74

    1001100+528578190.864.133.493.213.072.952.772.723.573.022.782.652.552.402.35Center55.349.412/28/03 11:13 PM54.9670.88485661670.1244682324401.02613442370.845036356220.029676374he-u1.852327142120.07265.7948157473273.78302768399.40230.000.001.71

    2001200+527577000.874.303.813.863.593.453.113.023.733.303.343.112.992.692.62Center55.349.612/28/03 11:19 PM59.9485.71200428640.1246183605262.67088515410.886046514531.1988394088he-b1.98548423725.86171.3294538989273.2195604702179.259080.750.52-0.434.39

    3001300+504551660.914.193.753.583.433.313.122.913.803.403.243.113.002.832.64Center55.449.112/28/03 11:24 PM59.4084.02046107740.124604798256.4032948190.894988054611.16916303481.974737005525.18171.8124951969261.220610962159.829972.000.46-0.264.28

    4001400+513562410.895.034.443.973.703.413.172.934.473.953.533.293.032.822.60Center55.249.612/28/03 11:30 PM54.0868.42716161580.1244345763334.23512073950.88270375191.821759323819.15279.3629317909266.3109230524-38.41000.000.00

    5001500+528577870.875.014.804.414.063.723.343.034.334.153.823.513.222.892.62Center54.949.312/28/03 11:37 PM58.3280.73653519760.1245762385254.76956494930.95808382661.950604745323.88197.7181861721273.6315021147139.788062.970.340.064.14

    6001600+535586130.854.243.743.503.353.213.052.873.623.192.992.862.742.602.45Center55.049.712/28/03 11:42 PM57.7579.01225908240.1245599405323.32664624770.88207552161.93620662423.20210.8601547765277.5427558698124.477056.070.280.234.03

    7001700+547599350.834.063.593.503.233.012.932.683.392.992.922.692.512.442.24Center54.949.212/28/03 11:48 PM58.0279.82103011740.124567704345.967888350.88423644451.943108143923.52210.587256318283.8026559476135.836861.190.310.154.11

    8001800+519568450.884.083.673.493.443.333.263.103.593.233.073.032.932.872.73Center55.149.412/28/03 11:53 PM61.1289.40731044510.1246455921246.99334177270.89950983942.004981178727.36152.3030623921269.1709681712198.550689.440.66-0.864.49

    9001900+524574090.873.933.693.483.353.283.072.883.423.213.032.922.862.672.51Center55.049.812/28/03 11:59 PM61.9191.94153640550.1246625662247.34889651650.93893129262.015194693828.39143.493794905271.8416063284212.989195.940.75-1.244.56

    10002000+488533980.944.344.264.033.783.573.343.134.063.993.773.543.343.132.93Center54.949.512/29/03 12:04 AM62.8194.8627247290.1246806165182.05306056850.98156683852.02378049829.60123.3107554164252.8488232634209.376894.310.86-1.874.55

    11002100+480525680.953.753.903.653.433.273.092.913.573.713.473.263.112.942.77Center54.849.012/29/03 12:09 AM66.14106.12058522620.1247378769163.24530941781.04000002542.024943862934.3890.0678007433248.9186288121234.0851105.441.284.66

    12002200+485531200.944.293.933.743.673.593.503.494.043.703.523.453.383.293.29Center54.749.312/29/03 12:14 AM62.4393.64424332430.1246732737187.02515958310.91608388422.020614144429.10126.7727882362251.5324448809203.858791.830.81-1.574.52

    13002300+494540650.924.013.673.453.253.143.002.843.713.393.193.012.902.772.63Center54.849.512/29/03 12:19 AM59.6684.81602186430.1246112682252.53381013230.91521193691.979934168225.50164.6367208294256.0071843465162.120073.030.49-0.344.29

    14002400+472517290.974.263.543.313.162.942.722.494.123.423.203.052.842.632.41Center54.649.212/29/03 12:24 AM53.6567.2203086180.1244168234345.91280888730.83098586191.805864459218.70267.0865642804244.9458177945-59.79180.000.00

    15002500+516564770.893.743.253.092.902.692.492.363.312.882.742.572.382.202.09Center54.549.512/29/03 12:29 AM56.0574.01951964480.1245068388387.61655117120.86898401881.88780878421.27235.7619611364267.428424125359.285626.710.110.793.28

    16002600+478523380.965.415.014.694.444.183.903.525.174.794.484.243.993.733.36Center54.749.312/29/03 12:34 AM59.1983.37952341410.1245994631181.49486517880.9260629151.970365808624.92165.9993457105247.8295387834147.160466.290.44-0.194.19

    17002700+454497361.013.833.323.142.932.702.512.413.853.343.162.952.712.522.42Center54.649.612/29/03 12:38 AM55.5272.48213522830.1244884684306.08363165730.86684073091.870898064220.68217.6068272711235.508615937431.766114.310.061.052.66

    18002800+497544700.923.673.343.042.972.752.512.553.373.072.792.732.522.302.34Center54.549.612/29/03 12:43 AM57.9479.58174098570.1245654293318.01626334240.91008170161.941093462123.42192.7238545147257.9249298317121.194354.590.300.184.00

    19002900+472517370.973.553.212.842.912.702.582.403.433.102.742.812.612.492.32Center54.649.612/29/03 12:48 AM58.1980.33851268620.1245725605291.0576036780.90422544221.947386737123.72179.070548473244.9836991868121.778354.860.330.104.00

    20003000+467511300.983.493.132.812.662.642.482.333.413.062.752.602.582.432.28Center54.350.412/29/03 12:52 AM57.1877.31807015230.1245429598312.11403240790.89684817491.920901432722.54193.3447296582242.109448545991.973641.430.220.403.72

    21003100+464508320.983.913.323.092.942.782.482.463.853.273.042.892.732.442.42Center54.550.212/29/03 12:57 AM54.6169.91092396560.124455277336.55097702430.84910482361.840502777919.71240.9097495367240.6983666827-7.87620.000.00

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    54.708739051181.1433667914293.03596750330.863935779819.9821.020.12

    THE DATA BELOW REPRESENTS TESTING AT THE JOINTS8.913920157486.86075667433.3626.770.18

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    4121412+517565960.885.614.763.983.423.052.922.664.964.213.523.022.692.582.35Approach Edge55.249.912/28/03 11:35 PM47.625668305143.73863755820.848484869110.29

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    6121612+508556820.909.255.064.583.773.903.392.948.314.544.113.393.503.042.64Approach Edge55.149.212/28/03 11:45 PM34.761081489420.74487716820.54702702083.81

    7121712+483529020.955.994.974.283.833.393.202.915.664.704.053.623.203.022.75Approach Edge54.950.412/28/03 11:51 PM48.320536079645.21617320110.829716190310.76

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    9121912+447489331.0212.564.033.413.223.092.852.7112.834.123.483.293.162.912.77Approach Edge54.949.312/29/03 12:01 AM23.15445795277.10026417660.32085987860.91

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    20123012+492539380.934.463.723.333.082.892.672.494.133.453.092.862.682.482.31Approach Edge54.249.812/29/03 12:55 AM51.565022198652.43463231380.834080716813.11

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    26123612+454497121.015.334.544.063.713.383.152.925.364.574.083.733.403.172.94Approach Edge54.550.112/29/03 1:25 AM51.703565811652.75458697030.85178236913.21

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    28123812+444486151.036.734.613.913.603.453.212.836.924.744.023.703.553.302.91Approach Edge54.350.512/29/03 1:38 AM42.008916358932.68169841660.68499258856.98

    29123912+432473411.0613.593.212.942.672.472.402.1314.353.393.112.822.612.532.25Approach Edge54.450.112/29/03 1:44 AM19.02869794763.87276918840.23620310820.41

    30124012+507555110.906.224.163.623.062.882.762.365.603.753.262.762.592.492.13Approach Edge54.649.412/29/03 1:50 AM40.070739714729.23234210790.66881028746.01

    31124112+475520150.965.393.703.293.072.812.542.485.183.563.162.952.702.442.38Approach Edge54.650.312/29/03 1:54 AM43.068646239834.64711485220.68645642667.54

    32124212+545597100.846.433.553.253.192.802.812.545.382.972.722.672.342.352.13Approach Edge54.149.812/29/03 1:59 AM37.483670922424.92083605340.55209954084.86

    33124312+541593080.845.353.903.513.143.202.982.624.513.292.962.652.702.512.21Approach Edge56.752.112/29/03 3:09 AM46.463552572441.32151757570.72897199349.54

    34124412+507555630.906.243.983.653.353.052.822.595.623.583.283.012.742.542.33Approach Edge56.852.512/29/03 3:14 AM40.894233991230.67495942740.6378205886.41

    35124512+517565800.884.483.553.243.032.802.692.423.963.142.862.682.472.382.14Approach Edge56.850.712/29/03 3:18 AM50.249999121949.44548553290.792410700312.12

    36124612+523573270.875.193.803.413.072.842.642.434.533.312.972.682.482.302.12Approach Edge56.751.812/29/03 3:22 AM45.248554535738.86661078920.73217724678.79

    37124712+496543710.924.673.332.942.702.632.592.344.293.062.702.482.422.382.15Approach Edge56.751.412/29/03 3:27 AM45.468950141439.30644055060.71306207058.93

    38124812+548599800.833.873.192.942.722.562.392.303.232.662.452.272.131.991.92Approach Edge56.951.412/29/03 3:31 AM52.356591035654.27561588280.824289444813.73

    39124912+532583150.863.763.212.932.752.592.452.233.222.752.512.362.222.101.91Approach Edge56.651.712/29/03 3:35 AM54.01595857358.23654899460.8537234815.08

    40125012+496542950.924.793.503.172.882.792.692.294.413.222.922.652.572.482.11Approach Edge56.451.312/29/03 3:39 AM46.521922065941.44131143910.73068894119.58

    41125112+476521000.964.483.503.132.962.752.552.344.303.363.002.842.642.452.25Approach Edge56.451.712/29/03 3:43 AM49.017857764446.7231968260.781249996711.24

    42125212+525574620.873.943.283.032.732.562.542.243.432.852.642.382.232.211.95Approach Edge56.151.012/29/03 3:47 AM52.477157019454.55877036470.832487290313.82

    43125312+514563420.893.593.212.932.742.562.232.093.192.852.602.432.271.981.85Approach Edge56.051.012/29/03 3:52 AM55.186632407961.11378990840.894150516216.08

    44125412+503550980.913.973.393.042.782.582.402.213.603.082.762.522.342.182.01Approach Edge56.050.512/29/03 3:56 AM52.231739988553.98316375680.853904353713.63

    45125512+472516580.978.086.005.184.564.003.462.977.825.815.014.413.873.352.87Approach Edge56.251.312/29/03 4:01 AM42.660890465133.88422890820.74257420547.32

    46125612+443484851.034.913.543.113.172.932.692.475.063.653.213.273.022.772.55Approach Edge55.850.512/29/03 4:05 AM46.753566178841.91840269040.72097761149.73

    47125712+514563020.894.843.623.242.942.652.422.304.303.212.882.612.352.152.04Approach Edge55.550.512/29/03 4:09 AM45.719007260539.80840494520.74793383719.08

    48125812+493540380.935.373.603.222.932.762.492.284.973.332.982.712.552.302.11Approach Edge55.650.712/29/03 4:13 AM42.0670393132.78804010370.6703910587.01

    49125912+506554230.905.253.733.343.042.812.592.354.743.373.012.742.542.342.12Approach Edge55.350.712/29/03 4:17 AM44.137137627636.6856303730.71047608428.14

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