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Page 1
Note 1: Click CTRL+ on our keboard before usin this sreadsheet in EXCEL97.
Note 2: Due to different monitor, EXCEL, and fonts caabilities on different com uters, the text on some of the
sheets ma be truncated. It ma be necessar to unrotect the sheet and resize some of the columns.
Note 3: This sreadsheet needs to be coied to the hard drive to be used. It cannot be run off a flo drive.
Note 4: Fiures accom anin the text are scanned into the sreadsheet. For clarit of these fiures it ma be
useful to print these pages and use the printed figures.
I. Input Sheet - General Information
l The general information section requests information about the agency. Thisinformation is not required for the analysis, but the information entered heremay be displayed on the "Results" sheet.
II. Input Sheet - Design Information
l All design inputs are required except sensitivity analysis.
No default values are used.l Information can be retrieved from the "Saved Data" sheet using the "Retrieve Data"button. The existing data can be replaced or saved as a new set using the
"Save Data" button.Clicking on the "Retrieve Data" button opens the "Saved Data" sheet. Select the
appropriate row to be retrieved and click on the "Export" button.If the retrieval is successful, the data are retreived. Changes can be made and savedas a new data set using a different value for the search ID. The data can alsobe overwritten using the same search ID. The search value can be text, numbers, or acombination of the two that uniquely identifies the data (example: Project Numbers).This feature can also be used to save a default set of values.
Using the "Clear All" ID to retrieve the "Clear All" data set clears all the data inthe spreadsheet.
l Design information such as initial and terminal serviceability, concrete properties, baseproperties, and reliability and standard deviation can be input in the appropriate cells.Table 14 provides help for estimating base property values.
Climatic properties such as wind, temperature, and precipitation, which are required forpositive temperature differential calculation, can be estimated using the table of climaticproperties for major cities provided in table 15.
A pavement type can be selected by clicking the option buttons provided. For JPCP andJRCP, the joint spacing needs to be entered in ft in the space provided. Thisautomatically calculates the effective joint spacing to be used in design.
l Edge support can also be selected using the option buttons provided. Thisautomatically calculates the edge support factor to be used in design.
l A first run MUST be performed using design inputs for all variables and using anestimated effective subgrade k-value. This determines an approximate slab thicknessfor the inputs provided. The user can then navigate to the seasonal k-value calculationsheet (and, if necessary, the "Fill/Rigid Layer" sheet) to calculate the k-value adjusted for
the effects of season and presence of fill section or rigid layer beneath the pavement.
(The approximate slab thickness obtained from the first run is used in calculating the damageduring different seasons of the year.)Approximately 3 to 4 iterations will be required (i.e., after a first run with a trial k-value,
a trial thickness is obtained). The "Calculate seasonal k-value" button can then be used tocalculate a seasonally adjusted k-value. This is exported back to the "Input Form" sheet.The slab thickness is calculated again using the new k-value. This changes the seasonaladjusted k-value and the procedure need to be repeated again. This is done till the
change in thickness does not change the seasonally adjusted k-value.Detailed information on k-value is provided in the "k-Value Information" Sheet.
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Page 2
l A traffic calculation should be performed before the first run. This will result in
a more appropriate slab thickness for the seasonal k-value computation.l After all the design information has been entered, clicking on the "Calculate" button
displays the design thickness at the bottom of the Input Form.The above calculation is performed in the "Calculation Sheet" sheet. The "Calculation Sheet"also provides the design traffic for slab thicknesses varying from 7 in to 15 inches, in incrementsof 0.5 in. The next row is not locked, to enable the user to change any variable and
observe its effects on the design traffic. The last row is locked and represents the thicknessfor the traffic and other inputs provided by the user in the Input Form.
l Sensitivity analysis can also be performed from the Input Form. A desired thicknesscan be input, or the calculated thickness for the input design variable can be imported.The sensitivity analysis produces a graph on a sheet labeled "Sensitivity (Other)."The sensitivity for thickness vs. traffic is created automatically on the"Sensitivity (Thickness)" sheet.The actual data for the sensitivity analysis is contained in a sheet called "Sensitivity Sheet;"
this sheet is hidden.l The Input Form also contains a link to the "Faulting Check" sheet for JRCP andJPCP. For CRCP, the "Faulting Check" sheet and the "Corner Break Check" sheetremain hidden.
l Red dots or flags at the top right corners of cells indicate that a note is attached to that cell.
This note can be read by moving the mouse over that cell.NOTE: This spreadsheet was created in Excel95. Due to compatibility problems with Excel97,
the larger notes are partially cut off (because Excel97 displays notes with fixed sizes as default).To see the entire note, a macro is written in this spreadsheet to change the size of notesthat are bigger than the comment box (The notes in Excel97 are now called comments).However, the user must run this macro by pressing "ctrl+j" each time the spreadsheet is
opened in Excel97. This command does not affect spreadsheets in Excel95.l Certain cells are locked to prevent accidental erasure. Cells can only be locked when the
sheet is also protected, so some sheets are protected. To unprotect a sheet, go to Toolson the menu, select Protection and select Unprotect Sheet. This creates the potentialfor accidental erasure, so it is useful to keep the sheet protected. To reprotect thesheet, select Tools, Protection, Protect Sheet and select OK without entering a password.
The workbook should not be protected because some of the Excel basic programs (macros)need the workbook to be unprotected to be executed.For the same reason, the "Sensitivity Sheet" (which is hidden) and the "Saved Data"sheet should not be protected. Hidden sheets can be viewed by using Format, Sheet, Unhide,or Edit, Sheet, Unhide from the menu.
III. Faulting Check Sheet
l For jointed pavements, the Input Form links to the "Faulting Check" sheet. All cells
need to be input in this sheet. The cells that do not need to be input are hidden usingthe outlining ("+") at the left of the sheet. To observe the values at this location, the sheet hasto be unprotected and the "+" clicked.
Each time a cell value is changed, the "Calculate" button needs to be clicked to calculatefaulting, which is displayed at the bottom of the sheet. This is then compared with the criteriaset at the bottom of the sheet to "PASS" or "FAIL" the design.The criteria can be changed by changing the values in the criteria table.
l The doweled and nondoweled sheets are designed independent of each other to providethe user control over the individual design. For example, the user may decide to provide
l While making a one-on-one comparison between the faulting check for the doweled andnondoweled designs, the user needs to ensure that all values are comparable.
l Corner break checks need to be performed only for nondoweled pavements. This sheet
edgedrains for the nondoweled design, which will change the drainage coefficient, Cd.
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Page 3
can be accessed by clicking on the "Corner Break Check" button.
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Page 4
Table 14. Modulus of elasticity and coefficient of friction for various base types.
Base Type or
Interface Treatment
Modulus of
Elasticity
(psi)
Peak Friction Coefficient
low mean high
Fine-grained soil 3,000 - 40,000 0. 1.3 !.0
"and 10,000 - !,000 0. 0.# 1.0
$ggregate 1,000 - 4,000 0.% 1.4 !.0
&olyet'ylene s'eeting $ 0. 0. 1.0
*i+e-stabilied clay !0,000 - %0,000 3.0 $ .3
e+ent-treated gravel (00 ") / 1000 #.0 34 3
$sp'alt-treated gravel 300,000 - 00,000 3.% .# 10
*ean concrete it'out
curing co+pound
(00 ") / 1000 3
*ean concrete it' single
or double a2 curing
co+pound
(00 ") / 1000 3. 4.
otes " co+pressive strengt', psi
*o, +ean, and 'ig' +easured pea5 coefficients of friction su++aried fro+ various references
are s'on above.
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Page 5
6dge7rains
&recip.*evel
Fine-8rained "ubgrade oarse-8rained "ubgrade
onper+eable
9ase
&er+eable
9ase
onper+eable
9ase
&er+eable
9ase
o :et 0.%0-0.;0 0.#-0.; 0.%-0.; 0.;0-1.00
7ry 0.;0-1.10 0.;-1.10 0.;0-1.1 1.00-1.1
day (30 +>day) or unifor+ity coefficient (u) .3. :et cli+ate &recipitation ! in>year (3 ++>year)=
7ry cli+ate &recipitation ! in>year (3 ++>year).4. "elect +idpoint of range and use ot'er drainage features (ade?uacy of cross slopes, dept' ofditc'es, presence of daylig'ting, relative drainability of base course, bat'tub design, etc.) to ad@ust upardor donard.
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Page 6
Table 1. Mean annual te+perature, precipitation, and ind speed for selected A.". cities.
*ocation Mean$nnualTe+perature,
BF
Mean$nnual&re
cipitation,
in
Mean$nnual:ind"peed,+p'
*ocation Mean$nnualTe+perature,
BF
Mean$nnual&re
cipitation,
in
Mean$nnual:ind"peed,+p'
*ocation Mean$nnualTe+perature,
BF
Mean$nnual&re
cipitation,
in
Mean$nnual:ind"peed,+p'
$*$9$M$ C$"$" DC*$EDM$
9ir+ing'a+ !.! !.! %.! Tope5a 4.1 !#. 10.1 D5la'o+a ity ;.; 30.; 1!.
Mobile %. 4. ;.0 :ic'ita .4 40.1 1!.3 Tulsa 0.3 3#.# 10.4
Montgo+ery %. 4;.! .% C6TAC< D68D
$*$"C$ *e2ington 4.; 4.% %.1 Medford 3. 1;.# 4.#
$nc'orage 3.3 1.! .; *ouisville .! 43. #.3 &ortland 3.0 3%.4 %.;
Fairban5s !.; 10.4 . *DAG"G$$ "ale+ !.0 40.4 %.0Cing "al+on 3!.# 1;.3 10.# 9aton ouge %. .# %.% &6"
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Page 7
"avanna' .; 4;.% %.; $lbany 4%.3 3.% #.; orfol5 ;. 4.! 10.
E$:$GG 9uffalo 4%. 3%. 1!.1 ic'+ond %.% 44.1 %.
Eilo %3. 1!#.! %.1 e
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Rigid Pavement Design - Based on AASHTO Supplemental Guide
I. General
Agency:INCOStreet Address:City:SOROAKOState:
Project Number:35391 ID: INCO
Description:Ramp Access Road
Location:Soroako
II. Design
ServiceabilityInitial Serviceability, P1: 4.5 Joint Spacing:
Terminal Serviceability, P2: 2.526.2 ft
PCC Properties
725 psi JRCP
3,500,000 psi
Poisson's Ratio for Concrete, m: 0.15 Effective Joint Spacing: 314.964in
Base Properties
1,000,000 psi
9.8 inSlab-Base Friction Factor, f: 1.4
Reliability and Standard Deviation
Reliability Level (R): 90.0 % Edge Support Factor: 0.94
0.30
Climatic Properties Slab Thickness used for
Mean Annual Wind Speed, WIND: 45.0 mph Sensitivity Analysis: 15.40 in
Mean Annual Air Temperature, TEMP: 86.0
Mean Annual Precipitation, PRECIP: 25.4 in
Subgrade k-Value
200psi/in
Design ESALs
11.3million
Calculated Slab Thickness for Above Inputs: 15.40in
Reference:LTPP DATA ANALYSIS - Phase I: Validation of Guidelines for k-Value Selection and Concrete
Pavement Performance Prediction
-ay ean ouus o upture,c:
astic ouus o a,c:
astic ouus o ase,b:
esgn cness o ase,b:
vera tanar eviation,0:
oF
Pavement Type, Joint Spacing (L)
PCP
RCP
CRCP
Edge Support
Conventional 12-t !ide tra"c lan
Conventional 12-t !ide tra"c lane # tied P
2-t !idened $la% !&conventional 12-t tra"
Sen$itivity 'naly$i$
odulu$ o Ruptur Ela$tic odulu$ (Sla
Ela$tic odulu$ (a$e a$e T*ic+ne$$
+-alue oint Spacing
Relia%ility Standard eviation
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Rigid Pavement Design - Based on AASHTO Supplemental Guide
Results
Project #35391
Description:Ramp Access Road
Location:Soroako
Slab Thickness Design
Pavement Type JRCP18-kip ESALs Over Initial Performance Period (million) 11.25 million
Initial Serviceability 4.5Terminal Serviceability 2.528-day Mean PCC Modulus of Rupture 725 psiElastic Modulus of Slab 3,500,000 psiElastic Modulus of Base 1,000,000 psi
Base Thickness 9.8 in.Mean Effective k-Value 200 psi/inReliability Level 90 %
Overall Standard Deviation 0.3
Calculated Design Thickness 15.40 in
Temperature Differential
Mean Annual Wind Speed 45 mph
Mean Annual Air Temperature 86Mean Annual Precipitation 25.4 in
Maximum Positive Temperature Differential 28.53
Modulus of Subgrade Reaction
Period Description Subgrade k-Value, psi
eerence: - ase : a aon o u enes or -aue eecon an oncree
Pavement Performance Prediction
oF
oF
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Seasonally Adjusted Modulus of Subgrade Reaction 165 psi/in
Modulus of Subgrade Reaction Adjusted for Rigid Layer
and Fill Section 0 psi/in
Traffic
Performance Period 20 yearsTwo-Way ADT 64
Number of Lanes in Design Direction 1Percent of All Trucks in Design Lane 100%Percent Trucks in Design Direction 100%
Vehicle Class Percent of Annual Initial Annual Accumulated
ADT Growth Truck FactorGrowth in18-kip ESALsTruck Factor (millions)
1 100.0% 4.0% 16.3 11.25
Total Calculated Cumulative ESALs 11.25 million
Faulting
Doweled
Dowel Diameter 1.26 in
Drainage Coefficient 0.90
Average Fault for Design Years with Design Inputs inCriteria Check
Nondoweled
Drainage Coefficient 0.9
Average Fault for Design Years with Design Inputs inCriteria Check
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Calculation Sheet
Page 11
D Design Traffic L E l F Term1 Term2 Term3 Term4(in) MESALs in in
7.0 0.27 315 0.94 26.75 1.42 -1.94 0.60 1.08 -0.21
7.5 0.20 315 0.94 28.17 1.39 -1.94 0.61 1.03 -0.19
8.0 0.19 315 0.94 29.56 1.37 -1.94 0.62 0.98 -0.18
8.5 0.20 315 0.94 30.94 1.34 -1.94 0.63 0.93 -0.17
9.0 0.24 315 0.94 32.29 1.31 -1.94 0.64 0.89 -0.16
9.5 0.29 315 0.94 33.63 1.29 -1.94 0.64 0.86 -0.15
10.0 0.37 315 0.94 34.95 1.26 -1.94 0.65 0.83 -0.15
10.5 0.49 315 0.94 36.25 1.23 -1.94 0.66 0.80 -0.14
11.0 0.66 315 0.94 37.54 1.20 -1.94 0.67 0.77 -0.13
11.5 0.90 315 0.94 38.81 1.18 -1.94 0.68 0.74 -0.13
12.0 1.23 315 0.94 40.07 1.15 -1.94 0.68 0.72 -0.12
12.5 1.69 315 0.94 41.32 1.12 -1.94 0.69 0.70 -0.12
13.0 2.34 315 0.94 42.55 1.09 -1.94 0.70 0.68 -0.11
13.5 3.25 315 0.94 43.77 1.07 -1.94 0.70 0.66 -0.11
14.0 4.51 315 0.94 44.98 1.04 -1.94 0.71 0.64 -0.10
14.5 6.27 315 0.94 46.18 1.01 -1.94 0.72 0.63 -0.10
15.0 8.71 315 0.94 47.37 0.99 -1.94 0.72 0.61 -0.10
11.00 0.66 315 0.94 37.54 1.20 -1.94 0.67 0.77 -0.13
15.40 11.31 315 0.94 48.30 0.96 -1.94 0.73 0.60 -0.09
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Calculation Sheet
Page 12
Term5 Term6 Term7 log b b TD L Epsi psi in
0.76 -0.15 -0.74 -0.60 0.2523 24.46 57.1 547.5 180 1.00
0.72 -0.16 -0.66 -0.60 0.2513 24.96 61.2 583.8 180 1.00
0.69 -0.16 -0.60 -0.60 0.2487 25.40 63.2 593.9 180 1.00
0.66 -0.17 -0.55 -0.61 0.2449 25.78 63.7 586.4 180 1.00
0.63 -0.17 -0.50 -0.62 0.2404 26.12 63.2 567.8 180 1.00
0.61 -0.18 -0.47 -0.63 0.2356 26.43 62.1 542.5 180 1.00
0.58 -0.18 -0.43 -0.64 0.2305 26.70 60.7 513.3 180 1.00
0.56 -0.18 -0.40 -0.65 0.2254 26.95 59.0 482.5 180 1.00
0.54 -0.19 -0.37 -0.66 0.2202 27.17 57.1 451.4 180 1.00
0.53 -0.19 -0.35 -0.67 0.2152 27.38 55.2 420.8 180 1.00
0.51 -0.20 -0.33 -0.68 0.2104 27.57 53.3 391.3 180 1.00
0.49 -0.20 -0.31 -0.69 0.2056 27.74 51.4 363.1 180 1.00
0.48 -0.20 -0.29 -0.70 0.2011 27.90 49.5 336.6 180 1.00
0.47 -0.21 -0.27 -0.71 0.1968 28.05 47.7 311.7 180 1.00
0.45 -0.21 -0.26 -0.72 0.1926 28.19 45.9 288.4 180 1.00
0.44 -0.22 -0.25 -0.72 0.1886 28.32 44.2 266.8 180 1.00
0.43 -0.22 -0.23 -0.73 0.1848 28.44 42.6 246.7 180 1.00
0.54 -0.19 -0.37 -0.66 0.2202 27.17 57.1 451.4 180 1.00
0.42 -0.22 -0.23 -0.74 0.1819 28.53 41.3 231.8 180 1.00
l
t'
oF
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Calculation Sheet
Page 13
l F Term1 Term2 Term3 Term4 Term5 Term6 Term7 log bin
32.65 1.10 -1.94 0.49 0.51 -0.17 0.09 -0.18 -0.23 -1.44
34.39 1.10 -1.94 0.50 0.48 -0.16 0.09 -0.19 -0.21 -1.44
36.09 1.09 -1.94 0.51 0.46 -0.15 0.08 -0.20 -0.19 -1.43
37.77 1.08 -1.94 0.51 0.44 -0.14 0.08 -0.20 -0.17 -1.43
39.43 1.08 -1.94 0.52 0.42 -0.13 0.08 -0.21 -0.16 -1.43
41.06 1.07 -1.94 0.53 0.40 -0.13 0.07 -0.21 -0.15 -1.43
42.67 1.07 -1.94 0.53 0.39 -0.12 0.07 -0.22 -0.14 -1.43
44.26 1.06 -1.94 0.54 0.37 -0.11 0.07 -0.22 -0.13 -1.43
45.83 1.05 -1.94 0.55 0.36 -0.11 0.07 -0.23 -0.12 -1.43
47.38 1.05 -1.94 0.55 0.35 -0.10 0.06 -0.23 -0.11 -1.43
48.92 1.04 -1.94 0.56 0.34 -0.10 0.06 -0.24 -0.10 -1.43
50.44 1.03 -1.94 0.56 0.33 -0.10 0.06 -0.24 -0.10 -1.43
51.95 1.03 -1.94 0.57 0.32 -0.09 0.06 -0.25 -0.09 -1.43
53.44 1.02 -1.94 0.58 0.31 -0.09 0.06 -0.25 -0.09 -1.43
54.92 1.02 -1.94 0.58 0.30 -0.08 0.05 -0.26 -0.08 -1.43
56.38 1.01 -1.94 0.59 0.29 -0.08 0.05 -0.26 -0.08 -1.43
57.83 1.00 -1.94 0.59 0.29 -0.08 0.05 -0.27 -0.07 -1.44
45.83 1.05 -1.94 0.55 0.36 -0.11 0.07 -0.23 -0.12 -1.43
58.97 1.00 -1.94 0.59 0.28 -0.08 0.05 -0.27 -0.07 -1.44
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Calculation Sheet
Page 14
b TD L1 L2 log R G Y log Wpsi psi kips
0.0362 6.16 284.6 384.1 18 1 6.58 -0.176 1.37 6.45
0.0367 6.69 258.9 353.9 18 1 6.77 -0.176 1.22 6.63
0.0370 7.15 236.6 326.4 18 1 6.96 -0.176 1.14 6.80
0.0373 7.56 217.0 301.6 18 1 7.13 -0.176 1.09 6.97
0.0374 7.92 199.7 279.2 18 1 7.29 -0.176 1.06 7.13
0.0375 8.24 184.4 258.8 18 1 7.45 -0.176 1.04 7.28
0.0375 8.53 170.9 240.4 18 1 7.60 -0.176 1.03 7.42
0.0375 8.79 158.8 223.7 18 1 7.74 -0.176 1.02 7.57
0.0375 9.03 147.9 208.5 18 1 7.87 -0.176 1.01 7.70
0.0374 9.25 138.2 194.7 18 1 8.00 -0.176 1.01 7.83
0.0373 9.45 129.4 182.1 18 1 8.13 -0.176 1.01 7.95
0.0372 9.64 121.4 170.6 18 1 8.25 -0.176 1.00 8.07
0.0371 9.81 114.2 160.1 18 1 8.37 -0.176 1.00 8.19
0.0370 9.96 107.6 150.4 18 1 8.48 -0.176 1.00 8.30
0.0369 10.11 101.5 141.5 18 1 8.59 -0.176 1.00 8.41
0.0367 10.25 96.0 133.3 18 1 8.69 -0.176 1.00 8.52
0.0366 10.37 90.9 125.8 18 1 8.79 -0.176 1.00 8.62
0.0375 9.03 147.9 208.5 18 1 7.87 -0.176 1.01 7.70
0.0365 10.47 87.2 120.2 18 1 8.87 -0.176 1.00 8.69
l
t
oF
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Calculation Sheet
Page 15
log W'W'(50%) ZMESALs MESALS
5.82 0.66 1.282 0.27 5.44
5.69 0.50 1.282 0.20 5.31
5.66 0.46 1.282 0.19 5.28 -14.711
5.69 0.49 1.282 0.20 5.31 4.336
5.76 0.57 1.282 0.24 5.37
5.85 0.71 1.282 0.29 5.46 0.941
5.96 0.90 1.282 0.37 5.57 0.632
6.08 1.19 1.282 0.49 5.69
6.20 1.60 1.282 0.66 5.82
6.34 2.17 1.282 0.90 5.95
6.47 2.98 1.282 1.23 6.09
6.61 4.10 1.282 1.69 6.23
6.75 5.68 1.282 2.34 6.37
6.90 7.87 1.282 3.25 6.51
7.04 10.93 1.282 4.51 6.65
7.18 15.19 1.282 6.27 6.80
7.32 21.12 1.282 8.71 6.94
6.20 1.60 1.282 0.66 5.82
7.44 27.41 1.282 11.31 7.05 15.3959385782 15.39593858
W18 R
log W18 RD = A
0+ A
1log W
18 R
A0=
A1=
R2=
Stand Err of X =
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0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
Sensitivity Analysis (Standard Deviation)
Standard Deviation
DesignTraffic,MESALs
Modulus of
Rupture = 725 psi
Elastic Modulus of
Concrete =
3,500,000 psi
Elastic Modulus of
Base = 1,000,000
psiBase Thickness =
9.843 in
k-Value of
subgrade = 200
psi/inJoint Spacing =
26.247 ft
Reliability = 90 %
Standard
Deviation = 0.2 to
0.6Slab Thickness =
15.4 in
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7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0
0.10
1.00
10.00
Sensitivity Analysis (Thickness)
Slab Thickness, in
DesignTraffic,MESALs
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Faulting
DOWELED PAVEMENT NONDOWELED PAVEMENT
Dowel Diameter: 1.26 in
1,500,000 psi/in
29,000,000 psi
ALPHA: 0.000006
TRANGE: 86.0 Days90: 17 days
e: 0.00015strain
D: 15.40 in D: 15.40 in
P: 9,000 lbf
T: 0.45
FI: 91 FI: 91
CESAL: 11.25 million CESAL: 11.25 millionAge: 20.0 years Age: 20.0 years
0.90 0.90
Faulting (doweled) Faulting (nondoweled)
in in
Faulting Check Faulting Check
Recommended critical mean joint faulting levels for design (Table 28)
Joint Spacing Critical Mean Joint Faulting
< 25 ft 0.06 in
> 25 ft 0.13 in
Kd:
Es:
/oFoF
oF-days oF-days
Cd: C
d:
a$e&Sla% .rictional Re$traint
Sta%ili/ed a$e
'ggregate a$e or LC !& %ond %rea+er
a$e Type
Sta%ili/ed a$e
0n$ta%ili/ed a$e
a$e Type
Sta%ili/ed a$e
0n$ta%ili/ed a$e
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Note: Joint load position stress checks need to be performed only for nondoweled pavements
Only two numbers need to be entered in this sheet:
Temperature gradient
Tensile stress at top of slab
Step 1:
Total Negative Temperature Differential
Slab Thickness: 15.40in
Total Negative Temperature Differential: 9.1
Construction Curling and Moisture Gradient Temperature Differential
Enter temperature gradient: (enter positive value from below)
For temperature gradient use:
Wet Climate: (Annual Precipitation >= 30 in or
Thornthwaite Moisture Index > 0)
Dry Climate: (Annual Precipitation < 30 in or
Thornthwaite Moisture Index < 0)
Total Effective Negative Temp. Differential: 9.1
Step 2:
Use one or more of the following charts to estimate the tensile stress at top of slab.
Note that the charts show the variation of tensile stress with negative temperature differential
for slab thicknesses ranging from 7 to 13 in. These are plotted for a base course thicknessof 6 in. The six charts represent three k-values (100, 250 and 500 psi/in) and two values for the
elastic modulus of the base (25,000 psi and 1,000,000 psi). Use judgment to
extrapolate the value of the tensile stress at the top of the slab from these charts.
Enter Tensile Stress at Top of Slab: psi (use charts below)
oF
oF/in
0 to 2oF/in
1 to 3oF/in
oF
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Step 3:
Compare the above tensile stress with the maximum tensile stress at the bottom of the slab for
which the slab is designed. For the given inputs and the above thickness, this value is
232 psi
The slab is designed for a tensile stress of 232psi.
If the tensile stress at the top of the slab (obtained from the charts below and entered above) is
less than the design stress, the design is acceptable. If the check fails, new inputs have to be provided.
Corner Break Check:
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NOTE: The k-value used in this design procedure is not a composite k, as in the original AASHTO
design procedure. The k-value to be input in the "Input Form" and in the "Seasonal k-Value" sheet
is the actual subgrade soil modulus of subgrade reaction.
The k-value input required for this design method is determined using the following steps:
Step 1. Select a subgrade soil k-value for each season, using any of the three following methods:
(a) Correlations with soil type and other soil properties or tests.
(b) Deflection testing and backcalculation (recommended).
(c) Plate bearing tests.
Detailed information for Step 1 is included below.
Step 2. The "Seasonal k-Value" Sheet can then be used to determine a seasonally adjusted
effective k-value.
Step 3. This seasonally adjusted effective k-value can then be adjusted for the effects of
a shallow rigid layer, if present, or an embankment above the natural subgrade using the
"Fill/Rigid Adjustment" sheet.
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Method A -- Correlations.Guidelines are presented for selecting an appropriate k-value based
on soil classification, moisture level, density, California Bearing Ratio (CBR), or Dynamic Cone
Penetrometer (DCP) data. These correlation methods are anticipated to be used routinely for
design. The k-values obtained from soil type or tests correlation methods may need to be
adjusted for embankment above the subgrade or a shallow rigid layer beneath the subgrade.
The k-values and correlations for cohesive soils (A-4 through A-7): The bearing capacity of
cohesive soils is strongly influenced by their degree of saturation (Sr, percent), which is a function
of water content (w, percent), dry density (g, lb/ft3
), and specific gravity (Gs):
Recommended k-values for each fine-grained soil type as a function of degree of saturation are
shown in Figure 40. Each line represents the middle of a range of reasonable values for k. For
any given soil type and degree of saturation, the range of values is about + 40 psi/in [11 kPa/mm].
A reasonable lower limit for k at 100 percent saturation is considered to be 25 psi/in [7 kPa/mm ].
Thus, for example, an A-6 soil might be expected to exhibit k-values between about 180 and 260
psi/in [49 and 70 kPa/mm] at 50 percent saturation, and k-values between about 25 and 85 psi/in[7 and 23 kPa/mm] at 100 percent saturation.
Two different types of materials can be classified as A-4: predominantly silty materials (at least 75
percent passing the #200 sieve, possibly organic), and mixtures of silt, sand, and gravel (up to 64
percent retained on #200 sieve). The former may have a density between about 90 and 105 lb/ft3
[1442 and 1682 kg/m3
], and a CBR between about 4 and 8. The latter may have a density
between about 100 and 125 lb/ft3
[1602 and 2002 kg/m3
], and a CBR between about 5 and 15.
The line labeled A-4 in Figure B-4 is more representative of the former group. If the material in
question is A-4, but possesses the properties of the stronger subset of materials in the A-4 class,
a higher k-value at any given degree of saturation (for example, along the line labeled A-7-6 in
Figure 40) is appropriate.
Recommended k-value ranges for fine-grained soils, along with typical ranges of dry density and
CBR for each soil type, are summarized in Table 11.
The k -values and correlations for cohesionless soils (A-1 and A-3):The bearing capacity of
cohesionless materials is fairly insensitive to moisture variation and is predominantly a function of
their void ratio and overall stress state. Recommended k-value ranges for cohesionless soils,
along with typical ranges of dry density and CBR for each soil type, are summarized in Table 11.
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Figure 40. The k-value versus degree of saturation for cohesive soils
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Table 11. Recommended k-value ranges for various soil types.
AASHTO
Class
Description Unified
Class
Dry
Density
(lb/ft3)
CBR
(perce
nt)
k Value
(psi/in)
Coarse-grained Soils:
A-1-a, well graded
gravel GW, GP
125 - 140 60 - 80 300 - 450
A-1-a, poorly graded 120 - 130 35 - 60 300 - 400
A-1-b coarse sand SW 110 - 130 20 - 40 200 - 400
A-3 fine sand SP 105 - 120 15 - 25 150 - 300
A-2 Soils (granular materials with high fines):
A-2-4, gravelly silty gravel GM 130 - 145 40 - 80 300 - 500
A-2-5, gravelly silty sandy gravel
A-2-4, sandy silty sand SM 120 - 135 20 - 40 300 - 400
A-2-5, sandy silty gravelly sand
A-2-6, gravelly clayey gravel GC 120 - 140 20 - 40 200 - 450
A-2-7, gravelly clayey sandy gravel
A-2-6, sandy clayey sand
SC 105 - 130 10 - 20 150 - 350
A-2-7, sandy clayey gravelly
sand
Fine-grained Soils:
A-4
silt
ML, OL
90 - 105 4 - 8 25 - 165 *
silt/sand/
gravel mixture
100 - 125 5 - 15 40 - 220 *
A-5 poorly graded
silt
MH 80 - 100 4 - 8 25 - 190 *
A-6 plastic clay CL 100 - 125 5 - 15 25 - 255 *
A-7-5 moderately plastic
elastic clay
CL, OL 90 - 125 4 - 15 25 - 215 *
A-7-6 highly plasticelastic clay
CH, OH 80 - 110 3 - 5 40 - 220 *
* k-value of fine-grained soil is highly dependent on degree of saturation. See Figure 40.
These recommended k-value ranges apply to a homogeneous soil layer at least 10 ft [3 m] thick. If an
embankment layer less than 10 ft [3 m] thick exists over a softer subgrade, the k-value for the underlying
soil should be estimated from this table and adjusted for the type and thickness of embankment material
using Step 3. If a layer of bedrock exists within 10 ft [3 m] of the top of the soil, the k should be adjusted
using Step 3. 1 lb/ft3=16.018 kg/m
3, 1 psi/in = 0.271 kPa/mm
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The k-values and correlations for A-2 soils:Soils in the A-2 class are all granular materials
falling between A-1 and A-3. Although it is difficult to predict the behavior of such a wide variety of
materials, the available data indicate that in terms of bearing capacity, A-2 materials behave
similarly to cohesionless materials of comparable density. Recommended k-value ranges for A-2
soils, along with typical ranges of dry density and CBR for each soil type, are summarized in
Table 11.
Correlation of k-value to California Bearing Ratio:Figure 41 illustrates the approximate range
of k-values that might be expected for a soil with a given CBR.
Correlation of k-values to penetration rate by Dynamic Cone Penetrometer:Figure 42
illustrates the range of k-values that might be expected for a soil with a given penetration rate
(inches per blow) measured with a Dynamic Cone Penetrometer. This is a rapid hand-held testing
device that can be used to quickly test dozens of locations along an alignment. The DCP can also
penetrate AC surfaces and surface treatments to test the foundation below.
Assignment of k-values to seasons.Among the factors that should be considered in selecting
seasonal k-values are the seasonal movement of the water table, seasonal precipitation levels,
winter frost depths, number of freeze-thaw cycles, and the extent to which the subgrade will be
protected from frost by embankment material. A "frozen" k may not be appropriate for winter,
even in a cold climate, if the frost will not reach and remain in a substantial thickness of the
subgrade throughout the winter. If it is anticipated that a substantial depth (e.g., three feet or
more) of the subgrade will be frozen, a k-value of 500 psi/in [135 kPa/mm] would be an
appropriate "frozen" k.
The seasonal variation in degree of saturation is difficult to predict, but in locations where a water
table is constantly present at a depth of less than about 10 ft [3 m], it is reasonable to expect that
fine-grained subgrades will remain at least 70 to 90 percent saturated, and may be completely
saturated for substantial periods in the spring. County soil reports can provide data on the
position of the high-water table (i.e., the typical depth to the water table at the time of the year that
it is at its highest). Unfortunately, county soil reports do not provide data on the variation in depth
to the water table throughout the year.
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Figure 41. Approximate relationship of k-value range to CBR.
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Figure 42. Approximate relationship of k-value range to DCP penetration rate.
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Method B Deflection Testing and Backcalculation Methods.These methods are suitable
for determining k-value for design of overlays of existing pavements, for design of a reconstructed
pavement on existing alignments, or for design of similar pavements in the same general location
on the same type of subgrade. An agency may also use backcalculation methods to develop
correlations between nondestructive deflection testing results and subgrade types and properties.
Cut and fill sections are likely to yield different k-values. No embankment or rigid layer adjustment
is required for backcalculated k-values if these characteristics are similar for the pavement being
tested and the pavement being designed, but backcalculated dynamic k-values do need to be
reduced by a factor of two to estimate a static elastic k-value for use in design which is required in
this catalog.
An appropriate design subgrade elastic k-value for use as an input to this design method is
determined by the following steps:
1. Measure deflections on an in-service concrete or composite (AC-overlaid PCC) pavement
with the same or similar subgrade as the pavement being designed.
2. Compute the appropriate AREA of each deflection basin.
3.Compute an initial estimate (assuming an infinite slab size) of the radius of relative stiffness, l.
4.Compute an initial estimate (assuming an infinite slab size) of the subgrade k-value.
5. Compute adjustment factors for the maximum deflection d0and the initially estimated l to
account for the finite slab size.
6.Adjust the initially estimated k-value to account for the finite slab size.
7.Compute the mean backcalculated subgrade k-value for all of the deflection basins
considered.
8.Compute the estimated mean static k-value for use in design for the specific season during
the testing.
9.Determine the effective seasonally adjusted elastic k-value considering the factors discussed
above.
These steps are described below, with the relevant equations for bare concrete and composite
(asphalt concrete over concrete slab) pavements given for each step.
Measure deflections.Measure slab deflection basins along the project at an interval sufficient to
adequately assess conditions. Intervals of 100 to 1000 ft [30 to 300 m] are typical. Measure
deflections with sensors located at 0, 8, 12, 18, 24, 36, and 60 in [0, 203, 305, 457, 610, 915, and
1524 mm] from the center of the load. Measure deflections in the outer wheel path. A heavy-load
deflection device (e.g., Falling Weight Deflectometer) and a load magnitude of 9,000 lbf [40 kN]
are recommended. ASTM D4694 and D4695 provide additional guidance on deflection testing.
d
d12+
d
d18+
d
d9+
d
d6+
d
d5+
d
d6+4=AREA
603624181287
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Compute AREA.For a bare concrete pavement, compute the AREA7of each deflection basin
using the following equation:
where d0=deflection in center of loading plate, inches
di= deflections at 0, 8, 12, 18, 24, 36, and 60 in [0, 203, 305, 457, 610, 915, and 1524
mm] from plate center, inches
For a composite pavement, compute the AREA5of each deflection basin using the following
equation:
d
d12+
d
d18+
d
d9+
d
d6+
d
d5+
d
d6+4=AREA
0
60
0
36
0
24
0
18
0
12
0
87
d
d12+
d
d18+
d
d9+
d
d6+3=AREA
12
60
12
36
12
24
12
185
Estimate l assuming an infinite slab size.The radius of relative stiffness for a bare
concrete pavement (assuming an infinite slab) may be estimated using the following equation:
The radius of relative stiffness for a composite pavement (assuming an infinite slab) may be
estimated using the following equation:
Estimate k assuming an infinite slab size.For a bare concrete pavement, compute an
0.698-
289.708
AREA60
=
7
2.566
est
ln
0.476-
158.40
AREA48
=
5
2.220
est
ln
( )est2
0
*0
estd
dP=k
[26]
[27]
[28]
[30]
[29]
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na esmae o e -vaue usng e oowng equaon:
where k = backcalculated dynamic k-value, psi/in
P = load, lb
d0= deflection measured at center of load plate, inch
lest = estimated radius of relative stiffness, inches, from previous step
d0
*= nondimensional coefficient of deflection at center of load plate:
( )est2
0
*0
estd
dP=k
( )[ ]e0.1245=d
e0.14707-*0
est-0.07565
For a composite pavement, compute an initial estimate of the k-value using the following equation:
d12= deflection measured 12 in [305 mm] from center of load plate, inch
lest = estimated radius of relative stiffness, in, from previous step
d12*= nondimensional coefficient of deflection 12 in [305 mm] from center of load plate:
Compute adjustment factors for d0and l for finite slab size.For both bare concrete and
composite pavements, the initial estimate of l is used to compute the following adjustment factors
to d0and l to account for the finite size of the slabs tested:
( )est2
12
*12
estd
dP=k
( )[ ]e0.12188=d e
0.79432-*12
est-0.07074
e1.15085-1=AF
L0.71878-
d est
0.80151
0
e0.89434-1=AF
L0.61662-
est
1.04831
where, if the slab length is less than or equal to twice the slab width, L is the square root of the
product of the slab length and width, both in inches, or if the slab length is greater than twice the
L*2=L,L*2>Lif
LL=L,L*2Lif
!
!!
[32]
[33]
[31]
[34]
[36]
[35]
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width, L is the product of the square root of two and the slab length in inches:
Adjust k for finite slab size.For both bare concrete and composite pavements, adjust the
initially estimated k-value using the following equation:
Compute mean dynamic k-value.Exclude from the calculation of the mean k-value any
unrealistic values (i.e., less than 50 psi/in [14 kPa/mm] or greater than 1500 psi/in [407 kPa/mm]),
as well as any individual values that appear to be significantly out of line with the rest of the
values.
L*2=L,L*2>Lif
LL=L,L*2Lif
!
!!
AFAF
k=kd
2
est
0
Compute the estimated mean static k-value for design.Divide the mean dynamic k-value by
two to estimate the mean static k-value for design.
A blank worksheet for computation of k from deflection data and example computations of k from
deflection basins measured on two pavements, one bare concrete and the other composite, are
given in Table 12.
Seasonal variation in backcalculated k-values.The design k-value determined from
backcalculation as described above represents the k-value for the season in which the deflection
testing was conducted. An agency may wish to conduct deflection testing on selected projects in
different seasons of the year to assess the seasonal variation in backcalculated k-values for
different types of subgrades.
[37]
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Table A2. Determination of design subgrade k-value from deflection measurements.
BARE CONCRETE PAVEMENT
Step Equation Calculated Value Example
d0
d8
d12
d18
d24
d36
d60
______________
______________
______________
______________
______________
______________
______________
0.00418
0.00398
0.00384
0.00361
0.00336
0.00288
0.00205
AREA7 [26] 45.0
Initial estimate of l [28] 40.79
Nondimensional d0*and initial estimate of k
[31][30]
0.1237160
Afd0
AFl
[34]
[35]
0.867
0.934
Adjusted k [37] 212
Mean dynamic k 212
Mean static k for design 106
Table 12.
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COMPOSITE PAVEMENT
Step Equation Calculated Value Example
d12
d18
d24
d36
d60
______________
____________________________
______________
______________
0.00349
0.003320.00313
0.00273
0.00202
AREA5 [27] 37.8
Initial estimate of l [29] 48.83
Nondimensional d12*
and initial estimate of k
[33]
[32]
0.1189
128
Afd0
AFl
[34]
[35]
0.823
0.896
Adjusted k [37] 195
Mean dynamic k 195
Mean static k for design 97
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Method C -- Plate Bearing Test Methods.The subgrade or embankment elastic k-value may
be determined from either of two types of plate bearing tests: repetitive static plate loading
(AASHTO T221, ASTM D1195) or nonrepetitive static plate loading (AASHTO T222, ASTM
D1196). These test methods were developed for a variety of purposes, and do not provide explicit
guidance on the determination of the required k-value input to the design procedure describedhere.
For the purpose of concrete pavement design, the recommended subgrade input parameter is
the static elastic k-value. This may be determined from either a repetitive or nonrepetitive test on
the prepared subgrade or on a prepared test embankment, provided that the embankment is at
least 10 ft [3 m] thick. Otherwise, the tests should be conducted on the subgrade, and the k-value
obtained should be adjusted to account for the thickness and density of the embankment, using
the nomograph provided in Step 3.
In a repetitive test, the elastic k-value is determined from the ratio of load to elastic
deformation (the recoverable portion of the total deformation measured). In a nonrepetitive test,
the load-deformation ratio at a deformation of 0.05 in [1.25 mm] is considered to represent the
elastic k-value, according to extensive research by the U.S. Army Corps of Engineers.
Note also that a 30-in-diameter [762-mm-diameter] plate should be used to determine the
elastic static k-value for use in design. Smaller diameter plates will yield substantially higher k-
values, which are not appropriate for use in this design procedure. An adequate number of tests
should be run to ensure coverage over the project length. The mean of the tests becomes the
static elastic k-value for the season of testing. This value is then used to determine the effective
seasonally adjusted elastic k-value considering the factors discussed above.
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Season Number of MonthsSubgrade k-Value, Relative Damage
psi/in millions in the Season
21.72 0.000019.19 0.0000
23.12 0.0000
22.31 0.0000
Total: 0 Mean Damage:
Seasonally Adjusted Subgrade k-Value (psi/in): 165
W18,
W18
:
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Adjustment for the Effects of Embankment and/or Shallow Rigid Layer:
The seasonally adjusted subgrade k-value is to be adjusted using the following nomograph if:(a) fill material will be placed above the natural subgrade, and/or(b) a rigid layer (e.g., bedrock or hardpan clay) is present at a depth of 10 ft or less beneath
the existing subgrade surface.
Note: The rigid layer adjustment should only be applied if the subgrade k was determined on the basis of soil type or similar correlations. If the k-value was determined from nondestructive deflection testing or from plate bearing tests, the effect of a rigid layer, if present at a depth of less than 10 ft, is already represented in the k-value obtained.
Seasonally Adjusted Subgrade k-Value: psi/in
If required, use the nomograph below to adjust the above subgrade k-value for fill and/or
rigid layer and enter the adjusted value here:
psi/in
Size image for better resolution.
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Traffic Worksheet
Performance Period: 20 years
Two-Way Daily Traffic (ADT): 64
Number of Lanes in Design Direction: 1
Percent of All Trucks in Design Lane: 100%
Percent Trucks in Design Direction: 100%
1 100.0% 4.0% 16.257 0.0% 11.25
2
3
4
5
6
78
9
10
11
12
13
um of % ADT: 100.0 Calculated ESALs: 11.25 million
(Should be 100)
Vehicle
Class
Percent of ADT
(Total = 100%)
Annual %
Growth
Average Initial
Truck Factor
(ESALs/truck)
Annual %
Growth in
Truck Factor
Accumulated
ESALs
(millions)
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Saved Data
Page 44
Select row to be exported and click the "Export" button.
ID Agency: Street Address: City: State:roject Number: Description:Clear
Example ERES 505 W. University Ave. ChampaignIL 1-20-98LCB Lean Concrete Base, 5-i
INCO INCO SOROAKO 35391Ramp Access Road
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Saved Data
Page 45
Location: nitial Serviceability, P1:erminal Serviceability, P2:
Champaign, IL 4.5 2.5 700
Soroako 4.5 2.5 725
28-day Mean Modulus of Rupture, (S'c)':
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Saved Data
Page 46
0.15
4500000 0.15 25000
6300000 0.15 1000000
Elastic Modulus of Slab, Ec: Poisson's Ratio for Concrete,: lastic Modulus of Base, Eb:
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Saved Data
Page 47
lab-Base Friction Factor, f:eliability Level (R):
6 1.4 90 0.34
19.68 1.4 90 0.3
esign Thickness of Base, Hb: verall Standard Deviation, S
0
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Saved Data
Page 48
ean Annual Wind Speed, WIND ean Annual Air Temperature, TEMPean Annual Precipitation, PRECIP
10.2 49.2 33.3
45 86 25.4
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Saved Data
Page 49
Subgrade k-Value ESALs dge Support Factor:Pavement TypeJoint Spacing:Dowel
1JPCP
16521.88065817 1JPCP 15 1.5
200 11.760973 0.94JRCP 26.247
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Saved Data
Page 50
Faulting Check Sheet (doweled)
ase/Slab Friction RestriantTRANGESlab ThicknessBase TypeFI CESAL AGECdDays90
0.8 6511.2398181822 050021.88065817 20 1 20
0.8 17.2197178071 0 11.760973
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Saved Data
Page 51
Faulting Check Sheet (non doweled) Corner Break Check Sheetill/Rigid Adjustment
Slab ThicknessBase TypeFI CESAL AGECdGradientTensile Stress top Adjusted k-Value Season1
11.2398181822 050021.88065817 201.1 1 120 175Fall
17.2197178071 0 11.760973
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Saved Data
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k-Value Sheet
Months1k1Season2Months2k2Season3Months3k3Season4Months4k4Season5Months5k5Season6
2150Winter 3300Spring 380Summer 4120
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Saved Data
Page 53
Months6Seasons6erformance Period:wo-Way Daily Traffic (ADT):umber of lanes in Design Direction
20 8000 2
20 64 1
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Saved Data
Page 54
ercent of All Trucks in Design Laneercent Trucks in Design DirectionADT1GADT1 TF1 GTF1ADT2GADT2
0.95 0.5 0.65 0.050.004 0.03 0.25 0.06
1 1 1 0.0416.26 0
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Traffic Sheet
TF2GTF2ADT3GADT3TF3GTF3ADT4GADT4TF4GTF4ADT5GADT5TF5GTF5ADT6GADT6TF6
0.39 0.02 0.1 0.081.62 0.05
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Saved Data
Page 56
GTF6ADT7GADT7TF7GTF7ADT8GADT8TF8GTF8ADT9GADT9TF9GTF9ADT10GADT10TF10
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Saved Data
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GTF10ADT11GADT11TF11GTF11ADT12GADT12TF12GTF12ADT13GADT13TF13GTF13
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FI&DAYS90
Page 58
SHRP_id State_id State County
13 1 'la%ama 'L456 3 7873
79 1 'la%ama CLE0R6E :7 72837
;123 1 'la%ama C
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FI&DAYS90
Page 59
127= Caliornia 0TTE = ;783;
:;7; Caliornia C'L'ER'S 1 1822
2=9 Caliornia EL 600
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2 9 Colorado P0EL< ;:: 118=9
1;: 9 Colorado R5< L'6C< 1219 118;:
313 9 Colorado 4EL 9 1;89
;9 3 Connecticut >'RT.'RT.ER6'6< 2 7;89:;7: 12 .lorida >5LLS5LLS
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=13 1= @eorgia >'LL 7=8::
=1 1= @eorgia >'R'LSa!aii '05 21832
17 1 5da*o ''S 32= 138;2
727 1 5da*o '66'5LT
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7729 19 5ndiana L' P'LL 9: =38:=
;;2 19 5ndiana P =79 ;7892
;3 13 5o!a CE'R 111 =:89
= 13 5o!a CL56T'LL :9: =18;
2 2 ?an$a$ RE6< ;=3 23813
3=: 2 ?an$a$ S>'46EE 739 =7822
13 2 ?an$a$ ST'..
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Page 63
297 2; aryland .REER5C? 21: =98;
2;1 2; aryland >'R.T 191 2:872
;== 2: inne$ota '?56@T'LL 1;9 78;
=9= 29 i$$i$$ippi 'RS>'LL 17 782;
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79= 29 i$$i$$ippi 'RS>'LL 1:; 78:7
=92 29 i$$i$$ippi 'RLES 7;2 =:839
7;: 23 i$$ouri ST LEBE66E 97= 1:8
;13 =1 6e%ra$+a '?'LL 37 27829
=29 =1 6e%ra$+a L'6C'STER :99 =18;
: =1 6e%ra$+a P>ELPS :;1 22837
=== =1 6e%ra$+a P5ERCE 997 2;8:;1= =2 6evada CL'R? 7 7819
=1= =2 6evada EL?< 2 7837
: =2 6evada EL?< 77 8;9
22: =2 6evada EL?< 9 987
=1 =2 6evada EL?< 1: 1182:
12 =2 6evada 56ER'L 2 =89;
121 =2 6evada 4'S>
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11 == 6e! >amp$*i ERR5'C? 12: =38:;
;;2 =; 6e! Jer$ey 0RL56@T'T>' 1= ;9832
=9 =: 6ort* CarolinaCLEEL'6 72 ;7819
1;7 =: 6ort* CarolinaC' 3: ;7899191: =: 6ort* Carolina. 9 ;;87=
192 =: 6ort* Carolina@R'65LLE 97 ;=83
2913 =: 6ort* Carolina@05L. 11 ;;8;=
792: =: 6ort* CarolinaR' 1 ;78:9
1=72 =: 6ort* CarolinaST'6LB 9 ;987
792 =: 6ort* CarolinaS0RRB 1:1 ;78291 =: 6ort* Carolina4'?E : ;7811
72 =9 6ort* a+ota C'SS 2==3 283
21 =9 6ort* a+ota @R'6 .
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3 =3
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17 ;2 Penn$ylvania 60ERL'6 3 ;=81
119 ;2 Penn$ylvania S' 171 2=8:;
=7= ; Sout* a+ota PE6656@TER.
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1;: ;9 Tea$ C'RS'ERS 12 71833
1113 ;9 Tea$ C>ER
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113 ;9 Tea$ R0S? 7; ;:8;2
=9:7 ;9 Tea$ S>ER'6 =9 13822
19: ;9 Tea$ S5T> 7 ;782
729: ;9 Tea$ T'RR'6T : =;82
7=1: ;9 Tea$ T'RR'6T 9 =;837
72:; ;9 Tea$ T'RR'6T 9 ==893
729; ;9 Tea$ T'RR'6T 9 =981729= ;9 Tea$ T'RR'6T 9 =:839
7=1 ;9 Tea$ T'RR'6T 3= =2839
1: ;9 Tea$ TERRB 1;7 198:7
1 ;9 Tea$ TR'5S ;: 2:8::
=7:3 ;9 Tea$ '6 A'6T 9 ;=8;
=773 ;9 Tea$ 4'L?ER 2: ;789;
7==; ;9 Tea$ 4>EELER 2; 228=
=793 ;9 Tea$ 45L'R@ER 1 27831
7=1 ;9 Tea$ 45SE 9 =:82
119 ;9 Tea$ 45TTE6E6 17:1 =38:
1; 7 ermont @R'6 5SLE 1197 =87:
221 71 irginia C'RRES'PE'?E C5TB :3 ;872
1;1: 71 irginia .'005ER 29 ;;82:
12 71 irginia .LE6R5C< 129 ;=8
73 71 irginia >E6R5C< 1= ;28;2
79 71 irginia 6
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191 7= 4a$*ington CL'R? : 9;81
12 7= 4a$*ington C
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#A$S%&
79
=3
;:
;1
79
=3
71
;2
7
;3
7
7
1:7
1:=
1:=
1:
93
:3
=:
3
3=
111
111
1
=:
=
:
;
7
7
;
77
7:
7:
79
2
79
:1
7
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7:
:=
1
1:
1:11=
37
3
22
==
2
9:
17
1
11
3;173
1;3
79
2
:
1
:
:
:
=
2211
3
=2
23
:;
3
27
=
23
:9
:9
;7
==
==
1:
;1
7
3
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7
;
2:
3
9
1
;2=
2
27
1
17
:1
;:
;1
77
7=
=
9233
17
:
3:
7
7
9;
:2
9:
2
11;11;
11;
7
77
72
:
:1
:2
=;
:=
727
7;
:2
3
1:
3;
2:
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2
=9
9
;9
1
=;
;:33
9:
:3
;:
71
;
7
1
1
;1
23
27
17
13
;7
1;
1:
;9
;
2
=2
==
17
=2
1
1
1;
13
19
17
=1
1:
1:29
12
17
11
3
1=
3
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1
12
1;
==
=;
=9
2=12
=;
17
1;
1=
12
=
2
17
11
11
1=7
77
71
1
;
29
=:
;1
2
=;
;
==29
;
3
1;
12
29
=7
:1
9=
=
=
22
1
1
2
=
2;
22
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=1
=7
7
1
7
77
2
9
3
3
;
;
;
1:
12
1212
12
11
:
;
1
1
1
1
1;
:1=
1
9
3
3
1
;3
7:
7:
=9
=
7;79
7;
73
79
7:
;3
;3
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;2
=
7=
77
7
:;
::
;=
=:
=9
=9
;2
27
27
27
27
7279
9
=:
;
=
=
=;
2=
2;
:
29
292;
=7
29
=
2=
2;
72
=1
=;
=:
73
23123
;
;7
;7
1;
;
=
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:
13
19
19
1
17
;:2
=
1:
:7
:7
=
7
21
79
1
;7
2
7
==
=
=:
;:
=2
=
23=
;=
23
9
11
;1
=9
2=
;;
22:
1;
9
3
1;
11
12
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9
11
11
12
7
2
73:1
91
=
32
3
3
:
:=
:1
72
;
9
3
3
1;
;=
3
1
1
1
1=
29
222=
1:
12
9
9
;
12
1
1=
1
1
1217
=
1
11
1;
17
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3
1
1
7
;;
77;3
77
;3
:;
2=
7;
=1
1;
7=
2:
21
2=1
:
=
21
9
2;
13
29
13
;=
;2
21;2
;2
1;
=3
2:
29
21
=3
1:
97
97
12;31
17
32
1
33
11=
73
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7
77
:7
:;
:
12
1119
32
3;
2
122
39
3;
37
99
17
:7
11
3
1=
79
97
:
:2
::
;
:1
11:
:997
11
11=
1=
32
97
97
:3
9:
11
:=
77=
7
93
72
3
:2
:1
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3
71
:7
93
3=
9:
933
97
:9
12
:2
93
:;
11
91
3
71
==;
1;
1
7:
;;
:7
;=
=
;=
29
1
11
;
21
21
2
=
=7
=3
29
;9
7=
9
==
27
=7
=;
23
9
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1
=2
=
2
;
==
217
1;
2
11
=1
2=
=
3
2
12
1;
1;
12
12
1
9
=
:
:
9
12
1===
22
2=
=;
19
;
22
1
1
27