Post on 23-Apr-2018
transcript
Outline
• This multimedia presentation consist of 3 parts:▫ Development of the MEDPG Database▫ MEPDG Sensitivity Studies▫ Local Calibration of MEPDG
2
NMDOT Design Method
AASHTO 1972 for Pavement Design with Probabilistic Approach
AASHTO 1993 for Check
▫ Based on AASHTO Road Tests in the 1960’s▫ Not Able to Predict Pavement Performance▫ Traffic Load Spectra, Climate are not Considered▫ Different Superpave mixes, Binders are not considered▫ Structural Number is considered only▫ Typically Conservative
4
Mechanistic Empirical Pavement Design Guide (MEPDG) – Design Basics
Mechanistic Empirical
Transfer FunctionsAnalytic
Mech.Pavement Analysis Model
σxσyσzτxyδzδθ
INPUT
Traffic
Climate
Materials
OUTPUTLongitudinal Cracking
Roughness IRI
Alligator CrackingTransverse Cracking
Rutting
5
Benefits of MEPDG
Effects of Differences in Climatic Conditions are Considered
Better Modeling of Pavement Materials
Incorporation of the Effects of Vehicles, tire pressures, etc.
Development of Better Pavement Diagnostic Techniques
Consideration of Seasonal and Aging Effects on Materials
6
AASHTO 1993 vs. MEPDG
Parameter AASHTO 1993 MEPDGTraffic ESAL (Equivalent Single Axle
Load), Truck Equivalent FactorAxle Load Spectra, Vehicle Class Distribution, Traffic Growth Factor, Truck speed
Materials Layer Coefficient, Resilient Modulus
Dynamic Modulus (E*),Resilient Modulus (Mr), Complex Modulus (G*)
Climate Seasonal Adjustments, Drainage Coefficients
Thermal properties, Wind Speed, Air Temperature, Depth to Water Table
Performance Design Life Rut, IRI, Different Type of Cracking
Outputs Structural Number or Pavement Thickness
Distress Over Time
7
Example of MEPDG Traffic Input
0
10
20
30
40
50
Cla
ss 4
Cla
ss 5
Cla
ss 6
Cla
ss 7
Cla
ss 8
Cla
ss 9
Cla
ss 1
0
Cla
ss 1
1
Cla
ss 1
2
Cla
ss 1
3
AA
DTT
Dis
tribu
tion
By
Veh
icle
Cla
ss (%
)
I 25I 40US 550 (NM 44)
Vehicle Class Distribution
Year Month Hour Axle Type
Load group0-2 2-4 ….. x-y
Single
Tandem
Tridem
Quad
Table: Axle Load Spectra
Axle SpacingTire Pressure
Wheel Base
General Traffic Inputs• Gear/Axle Configuration• Axle/Tire Spacing• Tire Pressure• Traffic Wander
8
Example of MEPDG Climatic Input
Create Virtual Weather Station byAveraging Surrounding Sites
Identify Weather Station
Choose from 800 sites
Insert Depth for Water Table
9
PG 5
8-28
PG 6
4-28
PG 7
0-22
PG 7
6-22
PG 8
2-22
AC
-20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Rutting Depth (in)
AC RutTotal Rut
PG 5
8-28
PG 6
4-28
PG 7
0-22
PG 7
6-22
PG 8
2-22 AC
-20
100
104
108
112
116
120
Terminal IRI
(in/mile)
PG 5
8-28
PG 6
4-28
PG 7
0-22
PG 7
6-22
PG 8
2-22
AC
-20
0
0.5
1
1.5
2
2.5
3
3.5
4
Long. Cracking
(ft/mi)
PG 5
8-28
PG 6
4-28
PG 7
0-22
PG 7
6-22
PG 8
2-22
AC
-20
0
0.1
0.2
0.3
0.4
Alligator Cracking
(%)
Variable Performance Grade
Influence of PG Grade on I-25 Using MEPDG
**AC-20 is Used for Existing Design
10
Local Calibration of MEPDG
Why Need Local Calibration MEPDG was Developed Using Pavement Data from LTPP Sections of all over USA
Among them NM has Only Two Test Sections (I10 & I25 District 1)
Maximum Benefits from MEPDG - LOCAL CALIBRATION
What is Local Calibration Minimizing the Difference Between the MEPDG Predicted Output Values and the
Field Observed Distresses of New Mexico’s Flexible Pavements
How to Do Local Calibration Adjusting the Distress Model Coefficients in MEPDG
Testing Localized Materials
Perform test section evaluations of stress/strain
11
Example Calibration of MEPDG’s Rut Model
Whereεp = Plastic Strainεr = Resilient StrainT = Layer TemperatureN = Number of Load Repetitionhac = Thickness of AC Layerkz = Function of Total Asphalt Layers Thicknessand Depth to Computational Point.
For National Calibration, Value of Coefficients: k1 = -3.35412, k2 = 1.5606, k3 = 0.4791
33221101rkrkk
rzr
p NTk βββεε
=
depth21z 0.328196depth)C(C k ××+=
27.428 h 1.7331 h 0.0172 C ac2ac2 +××=
17.342- h2.4868 h0.1039- C ac2ac1 ×+×=
The Regression Parameters: βr1, βr2, βr3 are the Local Calibration Coefficients, which will beDetermined to Represent New Mexico Conditions in the Proposed Study
12
Data Required for Calibration
Inputs: Test Statewide AC for E* Fatigue Endurance Limit, Creep Unbound, Subgrade Mr ICM for Seasonal Climate Effects Axle Load Spectra
Developing InputDatabase –Future Need
MEPDG
Mechanistic Model
MEPDG
Empirical Model
Pavement Performance: Rutting Fatigue Cracking Roughness – IRI Thermal/Environmental Cracking
Output
Inputs
13
Database Development
Database Development
Local Calibration Coefficients
NMDOT
NMDOT Mechanistic Empirical Pavement Design Guide Database
(MEPDG)
DatabaseServer
Phase 1
Database Project Phase
Phase 2
depth21z 0.328196depth)C(C k ××+=
Alli
gato
r Cra
ckin
g (%
)AC Layer Thickness (in)
Calibration
Sensitivity Analysis
14
Source of MEPDG Oracle Server Setup and Extraction of Data MEPDG Data Population of Data – Example and Analysis Database Security and Maintenance
Outline
16
• Local Calibration• Pavement Design• Geographic Information System(GIS) Oriented• Validation of data• Future Database Maintenance• Manage Data more Efficiently• Integrate with analysis• Visualize data• Avoid errors
Benefits of Database to MEPDG
18
Created following proxy Databases to extract data from DMP Files
Oracle Server Setup - Extraction of Data from NMDOT Databases
30 Databases
7 Databases (MEPDG Related)
Extracted Data and Populated
into Local ServerNMDOT
D6PB ( Database Username :- HMMS) DSS (Database Username :-dbuser) FA (Database Username :- EMSDBA) HOSM (Database Username :- SITE_MGR) PONP (Database Username :- PONTIS) TPLC (Database Username :- PLES) TIMS (Database Username :- TIMS)
19
Traffic Data
• Populated TRAFFIC_COUNT table with data using pythonscript
• Analyzed the Data from TRAFFIC_COUNT table andconverted the data into MEPDG format and stored it inTRAFFIC_NMDOT_GIS Table
• Calculated parameters like General growth rate, Compoundgrowth rate, General growth factor, etc stored inTRAFFIC_GENERAL_GROWTH_RATE table
Population of Data Example
24
Axle Load Spectra for Single Axle
0
6
12
18
24
30
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
No
of A
xles
Weight(lb)
00.00 Hrs
01.00 Hrs
02.00 Hrs
03.00 Hrs
04.00 Hrs
05.00 Hrs
06.00 Hrs
27
Axle Load Spectra for Tandem Axles
0
5
10
15
20
25
30
35
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
No
of A
xles
Weight(lb)
00.00 Hrs01.00 Hrs02.00 Hrs03.00 Hrs04.00 Hrs05.00 Hrs06.00 Hrs
28
• Data Acquisition & Processing
▫ 5900 individual candidate station locations extracted fromNOAA(National Oceanic and Atmospheric Administration) stationlists for NM, AZ, UT, CO, OK, and TX
30
Climate Normal Data
• Candidate stations used to retrieve available data
31
Climate Normal Data
State Number of Full Climate Normal Files
Number of Partial Climate Normal Files
Number of Error Files
Total Number of
Stations Attempted
New Mexico 123 19 567 709
Arizona 148 27 375 550
Utah 159 23 395 577
Colorado 162 33 489 684
Oklahoma 117 82 403 602
Texas 215 134 651 1000
924 318 2880 4122
• Retrieved data include climate normal (i.e. average) dailyvalues based upon period from 1971-2000
▫ Average daily maximum temperature (deg. F)▫ Average daily minimum temperature (deg. F)▫ Average daily mean temperature (deg. F)▫ Average daily precipitation (100ths of inch)▫ Cooling- and Heating-days
32
Climate Normal Data
• Database User▫ Not giving full privileges to dbuser to make changes in data tables
• Column Level VPD(Virtual Private Database)▫ Limiting user to access particular columns and other sensitive
information cannot be accessed
• Column-Masking▫ Columns contain sensitive information are returned as NULL values
Database Security and Maintenance
USER PASSWORD DESIGNATION
A NULL Research Assistant
B NULL Research Assistant
C NULL Research Assistant
34
Modules of the MEPDG
• Dynamic (Complex) Modulus (E*)
AC
• Resilient Modulus (Mr)
Unbound Layers
Materials
35
Dynamic (Complex) Modulus |*| E
Dynamic modulus key MEPDG Input E* related to temperature and time rate of loading E* comparable with FWD back calculated modulus
36
Sensitivity
• The study of how the change in outputs of a model can be apportion to thechange in inputs of the model
LowMedium
HighInput OutputMODEL
???
• To understand the impacts and relationships of the hundreds of inputvariables contained in the MEPDG
Example: Effect of aggregate gradation on roughness
• To identify critical points/ most significant risk factorsExample: Which variables are appropriate to prevent cracks
• For a fine-tuned calibration, it is important to analyze the sensitivity ofinput variables
• More appropriate design
• To have an idea about interacting inputs
40
Sensitivity and MEPDG
• Common trend of Sensitivity Analysis is local or changing one factor at a time• Drawbacks:
▫ MEPDG is heavily dependent on a large number of inputs▫ Interaction among inputs are not considered
Goal of this Study Identify , Rank and Quantify the effect of sensitive inputs considering
interaction with others
41
Objective of the Study
• Collect Long Term Pavement Performance (LTPP) and NMDOTmaterials, traffic and climate data, which represent local practice ofNM
• Perform one-to-one sensitivity analysis using New Mexicopavement sections
• Identify and rank a set of MEPDG inputs, sensitive to particulardistress criterion using advanced statistical approaches (such as:linear and nonlinear regression, nonparametric regression)
• Quantify the sensitivity of the inputs considering interactions
42
Data Collection
• Source▫ Data for New Mexico from LTPP Database▫ MEPDG Database
• Collected Data type▫ Traffic Data▫ Materials Data▫ Climatic Data
43
Preliminary Sensitivity Analysis
• 14 LTPP sections in New Mexico (12 sections of interstate highway I-25, one section of I-40 and one section of US 550)
• Preparation of sensitivity test matrix with collected data from LTPP database
• 1100 MEPDG simulations using test matrix
• Effects of variables on pavement distresses are identified from the simulation results using line plots, bar plots
44
Test Matrix for Preliminary Sensitivity Analysis
No Variable Range Value
1 Air Void (%) 2 to 10
2 Binder Content 8 to 15
3 Fine Content 2 to 12
4 AC thickness 3 to 10
5 Depth to GWT 2 to 25
6 Operational Speed 15 to 90
7 AADTT 800 to 2000
8 Base Thickness 4 to 18
9 Base Resilient Modulus 15000 to 45000
10 Performance GradePG 58-28, PG 64-28, PG 70-22,
PG 76-22, PG 82-22, AC 20
45
Preliminary Sensitivity Analysis: AC RutA
C R
ut (i
nch)
The input is not showingsame rate of sensitivityfor all test sections0
0.2
0.4
0.6
0.8
1
0 3 6 9 12
Variable Air Void (%)
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7
Performance Grade
46
Preliminary Sensitivity Analysis:Longitudinal Cracking
Long
itudi
nal C
rack
ing
(ft/m
ile) None of the sensitivity
curves exhibit similarpatterns for all testsections
0
400
800
1200
1600
2000
0 3 6 9 12
Variable Air Void (%)
0
100
200
300
400
2 4 6 8 10 12
AC thickness (in)
47
Preliminary Sensitivity Analysis:Alligator Cracking
Alli
gato
r Cra
ckin
g (%
)
Sensitive toonly one testsection
Sensitive to only few test sections
0
5
10
15
20
25
0 3 6 9 12
Variable Air Void (%)
0
5
10
15
20
25
3 5 7 9
Binder Content (%)
48
Findings on Preliminary Sensitivity Analysis No Variable Total
RutAC Rut
Terminal IRI
Longitudinal Cracking
Alligator Cracking
1 Air Void (%) S S S S S
2 Binder Content S S LS S S
3 Fineness Content S S LS S LS
4 AC thickness S S S S S
5 Depth to GWT LS LS LS LS LS
6 Operational Speed S S LS LS LS
7 AADTT S S S S S
8 Base Thickness LS LS LS S S
9 Base Resilient Modulus LS LS LS S S
10 Performance Grade S S LS LS S
S = Sensitive, LS = Low Sensitive
Comprehensive analysis of each variableand its interaction with other inputs need tobe fully investigated
49
Advanced Sensitivity Analysis
X1 X2 X3
Input Parameters Distribution
Y = y (x1, x2, x3…...)
Model
Output Distribution
Dy = Estimated variance
√Dy
<y>
Statistical
Methods
SensitivityDy
x2
x1
…x3
50
Flow Chart for SA
Development of Sensitivity Matrix
Defining Inputs and Outputs
Generation of Sample using
Latin Hypercube Sampling Method
Evaluate the Model
MEPDG Simulation
Developing Output
Distribution
Full Test Matrix
Using Statistical Approaches
Test of Correlation
Scatterplot Tests, Linear and Nonlinear Regression
Nonparametric Regression Procedure
Analysis of Results
Identification of Sensitive MEPDG
inputs
Ranking among sensitive inputs
Quantifying the sensitivity of
inputs considering interactionStatistical analyses in this study performed
with R statistical computing environment
51
Defining Inputs and Outputs
• 30 MEPDG input variables are selected of 3 fundamental types
▫ Traffic (X1 to X10)▫ Climate (X11, X12)▫ Materials (X13 to X30)
• 6 output variables from flexible pavement performances (Y1 to Y6)
• A flexible pavement structure is selected
Top AC LayerBottom AC Layer
Base Layer
Subgrade
52
Generation of Sample• Random LHS (Latin Hypercube Sampling) method is followed to generate sample for
an input variable x• x=xi,j where, i=number of sample or nLHS (750), j=data set (30)• During generation of sample, range of each x is divided in nLHS intervals of equal
probability.• Value for xi,j is randomly selected from each of the interval
0
1500
3000
4500
6000
0 150 300 450 600 750
AA
DT
T
No of Sample
Resultant Test Matrix (750 x 30)x =
x1,1 x1,2 x1,3 ………………… x1,30x2,1 x2,2 x2,3 …………………. x2,30………………………………………………….xi,1 ..................... xi,j ……… xi,30…………………………………………………...x750,1 x750,2 ……….………………. x750,30
53
750 MEPDG Outputs
Variable No Output Name Target Value Pass Fail
Y1 Terminal IRI 63 in/mile 728 22
Y2 Longitudinal Cracking 2000 ft/mile 570 180
Y3 Alligator Cracking 25% 703 47
Y4 Transverse Cracking 1000 ft/mile 749 1
Y5 Permanent Deformation (AC Only) 0.25 inch 199 551
Y6 Permanent Deformation (Total Pavement) 0.75 inch 450 300
• Target value set for Interstate/Highway• Pavement life is assumed 20 years
54
0
100
200
300
400
0 150 300 450 600 750
Term
inal
IRI
Distress PredictedDistress TargetInitial IRI
0
5000
10000
15000
0 150 300 450 600 750
Long
itudi
nal C
rack
ing
Distress Predicted Distress Target
0
50
100
150
0 150 300 450 600 750
Allig
ator
Cra
ckin
g
Distress Predicted
Distress Target
Output Distribution
Number of Simulation
55
Output Distribution
0
0.5
1
1.5
0 150 300 450 600 750
AC
Rut
Distress Predicted Distress Target
0
500
1000
1500
2000
0 150 300 450 600 750
Tran
sver
se C
rack
ing
Distress PredictedDistress Target
0
1
2
3
0 150 300 450 600 750
Tota
l Rut
Distress Predicted Distress Target
Number of Simulation
56
Correlation Test Result
Input Value Type Sign Input Value Type Sign Input Value Type Sign
X1 0.5500 L + X11 0.0800 N + X21 -0.0844 N -X2 0.0325 N + X12 -0.0903 N - X22 0.0784 N +X3 0.1379 S + X13 -0.1660 S - X23 0.0544 N +X4 0.4859 M + X14 0.0169 N + X24 0.0345 N +X5 -0.1172 S - X15 -0.0104 N - X25 -0.0944 N -X6 0.0455 N + X16 -0.0615 N - X26 -0.1346 S -X7 -0.0426 N - X17 0.1185 S + X27 -0.2207 S -X8 0.1555 S + X18 -0.3253 M - X28 0.0210 N +X9 -0.0261 N - X19 -0.0579 N - X29 0.0079 N +
X10 0.1873 S + X20 0.1109 S + X30 -0.1421 S -
Output Y6 (Total Rut)
N= None, S=Small, M=Medium, L=Large, (+)=Positive, (-)=NegativeN=(0.0 to 0.09)/(-0.09 to 0.0), S=(0.1 to 0.3)/(-0.3 to -0.1), M=(0.3 to 0.5)/(-0.5 to -0.03), L=(0.5 to 1.0)/(-1.0.5 to-0.5)
57
Correlation Test Result (Cont.)
0
1
2
3
0 1500 3000 4500 6000
0
1
2
3
0 25 50 75 1000
1
2
3
2 4 6 8
Output Y6 (Total Rut)
Percent of Trucks in Design Lane (%) (X4)
Initial two-way AADTT (X1)
Asphalt Layer Thickness (bottom Layer) (X18)
Tota
l Rut
(inc
h)
58
Scatterplots
• Common Means (CMN)• Common Locations (CL)• Statistical Independence (SI)• Linear Regression (REG)• Quadratic Regression (QREG)• Rank Correlation Coefficient (RCC)• Squared Rank Differences (SRD)• Combining Statistical (SRD/RCC)
Test Methods
59
Input Ranking
Test CMN Results CL Results SI Results REG Results
Rank Input p-value Input p-value Input p-value Input p-value
1 X18 0.0000 X1 0.0000 X1 0.0000 X18 0.0000
2 X1 0.0000 X4 0.0000 X4 0.0000 X1 0.0000
3 X4 0.0000 X18 0.0000 X18 0.0000 X4 0.0000
4 X13 0.0000 X26 0.0000 X26 0.0000 X13 0.0000
5 X26 0.0001 X27 0.0000 X13 0.0003 X27 0.0000
6 X27 0.0001 X13 0.0002 X10 0.0005 X26 0.0000
7 X25 0.0003 X10 0.0005 X27 0.0033 X25 0.0000
8 X22 0.0031 X3 0.0020 X8 0.0089 X22 0.0001
9 X3 0.0056 X5 0.0031 X17 0.0400 X3 0.0009
10 X8 0.0234 X8 0.0032 X5 0.0400 X10 0.0037
11 X10 0.0368 X30 0.0166 X29 0.0495 X8 0.0040
12 X9 0.0479 X17 0.0203
13 X30 0.0292
14 X5 0.0492
Output Y1=Terminal IRI
Level of Significance = 0.05
60
Input Ranking (Cont.)
Test QREG Results RCC Results SRD Results SRD/RCC Results
Rank Input p-value Input p-value Input p-value Input p-value
1 X1 0.0000 X1 0.0000 X4 0.0000 X1 0.0000
2 X4 0.0000 X4 0.0000 X1 0.0000 X4 0.0000
3 X18 0.0000 X18 0.0000 X18 0.0001 X18 0.0000
4 X13 0.0000 X26 0.0000 X26 0.0000
5 X26 0.0000 X27 0.0000 X27 0.0000
6 X27 0.0000 X13 0.0000 X13 0.0000
7 X25 0.0001 X10 0.0000 X10 0.0000
8 X22 0.0003 X8 0.0003 X5 0.0008
9 X3 0.0033 X3 0.0009 X8 0.0010
10 X5 0.0039 X5 0.0013 X3 0.0045
11 X8 0.0076 X30 0.0033 X30 0.0048
12 X10 0.0114 X17 0.0083 X17 0.0226
13 X30 0.0182 X22 0.0120 X25 0.0320
14 X9 0.0272 X12 0.0126 X12 0.0399
15 X25 0.0232 X11 0.0444
16 X11 0.0242
Output Y1=Terminal IRI
Leve
l of S
igni
fican
ce =
0.0
5
61
Identified Sensitive Inputs
Name of Test CMN CL SI REG QREG RCC SRD SRD/RCC
Terminal IRI
X18X1X4X13
X1X4X18X26
X1X4X18X26
X18X1X4X13
X1X4X18X13
X1X4X18X26X27
X1X4
X1X4X18X26X27
LongitudinalCracking
X18X4X1X24X25
X18X1X4X27X24X25X13
X18X4X1X27
X18X4X1X25X17
X18X4X1X25X17
X18X4X1X27X25X13X17
X18 X18X1X4X27X25X13X17
AlligatorCracking
X18X1X4X22X13
X18X4X1X22X13
X18X1X4
X18X1X4X22X13X25
X18X1X4X22X13X25
X18X4X1X22X13
X18X4
X1X4X18X22X13
62
Identified Sensitive Inputs (Cont.)
Name of Test CMN CL SI REG QREG RCC SRD SRD/RCC
TransverseCracking
N/A N/A X14X19X21X16X2
N/A N/A N/A N/A N/A
AC Rut
X1X4X10X18X8
X1X4X10X18
X1X4X10
X1X4X10X18X8
X1X4X10X18X8
X1X4X10X18X8
X1X4
X1X4X10X18X8
Total Rut
X1X4X18X27
X1X4X18X27
X1X4X18X26
X1X4X18X27X10X13
X1X4X18X27X10
X1X4X18X27X10
X1X4
X1X4X18X27X10
63
Most Important Inputs
Output 1 2 3 4Terminal IRI Bottom AC layer
ThicknessAADTT Percent of trucks
in design laneType of subgradeMaterial
Longitudinal Cracking Bottom AC layer Thickness
Percent of trucks in design lane
AADTT Modulus of Subgrade Layer
Alligator Cracking Bottom AC layer Thickness
AADTT Percent of trucks in design lane
Percent air void of bottom AC layer
Transverse CrackingGradation of Top AC layer
Gradation of Bottom AC layer
PG grade of bottom ac layer
PG grade of top ac layer
AC Rut AADTT Percent of trucks in design lane
Tire pressure Bottom AC layer Thickness
Total Rut AADTT Percent of trucks in design lane
Bottom AC layer Thickness
Modulus of subgrade
64
Linear Regression
Input Name R2 Increment R2 (%)
SRC PCC2 95% PCC2 CI p-Value
X18AC Layer Thickness (2nd AC Layer)
0.311 31 -0.547 0.424 (0.382, 0.487) 0.000
X4Percent of Trucks in Design Lane (%)
0.383 7 0.251 0.134 (0.097, 0.188) 0.000
X1 AADTT 0.440 6 0.239 0.124 (0.081, 0.171) 0.000
X24 Base Material Type 0.484 4 0.197 0.087 (0.055, 0.134) 0.000
X17 Air Void (%) (Top AC Layer) 0.518 3 0.178 0.072 (0.042, 0.112) 0.000
X25 Base Modulus 0.543 3 -0.154 0.055 (0.026, 0.089) 0.000
X13 AC Layer Thickness (Top Layer) 0.562 2 -0.139 0.046 (0.023, 0.085) 0.000
X27 Subgrade Modulus 0.576 1 0.124 0.036 (0.013, 0.068) 0.000
X15Effective binder content (%) (Top AC Layer)
0.586 1 -0.094 0.021 (0.004, 0.046) 0.021
X23 Base Thickness 0.594 1 -0.088 0.019 (0.000, 0.041) 0.027
X3Percent of Trucks in Design Direction (%)
0.597 0 0.057 0.008 (0.000, 0.029) 0.195
Output Y2 (Longitudinal Cracking)
SRC = Standardized Regression CoefficientPCC = Partial Correlation Coefficient
65
Rank Regression
Input Name R2 IncR2
(%)SRC PCC2 95% PCC2 CI p-Value
X18 AC Layer Thickness (2nd AC Layer) 0.485 49 -0.680 0.727 (0.680, 0.770) 0.000
X1 AADTT 0.555 7 0.249 0.262 (0.200, 0.321) 0.000
X4 Percent of Trucks in Design Lane (%) 0.615 6 0.236 0.241 (0.175, 0.312) 0.000
X27 Subgrade Modulus 0.676 6 0.253 0.269 (0.214, 0.327) 0.000
X24 Base Material Type 0.712 4 0.196 0.174 (0.121, 0.234) 0.000
X13 AC Layer Thickness (Top Layer) 0.746 3 -0.175 0.150 (0.104, 0.210) 0.000
X17 Percent Air Void (Top AC Layer) 0.777 3 0.175 0.150 (0.101, 0.202) 0.000
X25 Base Modulus 0.805 3 -0.159 0.126 (0.087, 0.178) 0.000
X26 Subgrade Material Type 0.812 1 0.077 0.032 (0.012, 0.060) 0.000
X15 Effective binder content (%) (Top AC layer) 0.816 0 -0.063 0.022 (0.005, 0.051) 0.006
X8 Traffic Growth Factor 0.821 1 0.073 0.029 (0.008, 0.063) 0.006
X23 Base Thickness 0.824 0 -0.062 0.021 (0.003, 0.048) 0.015
X16 Superpave Binder Grade (Top AC Layer) 0.825 0 0.030 0.005 (0.000, 0.021) 0.143
X19 Aggregate Gradation (2nd AC Layer) 0.825 0 0.006 0.000 (0.000, 0.007) 0.162
X11 Depth of Water Table 0.826 0 0.032 0.006 (0.000, 0.022) 0.247
Output Y2 (Longitudinal Cracking)
SRC = Standardized Regression Coefficient, PCC = Partial Correlation Coefficient
66
Summary of Regression Analysis
Model Name Linear Regression Rank Regression
R2 ≥10% 6-9% 3-5% ≤2% R2 ≥10% 6-9% 3-5% ≤2%
Y1 Terminal IRI
0.61 X18, X1
X4, X13
X26, X27, X30, X22, X10, X25, X8
0.85 X1, X4, X18
X26, X27, X10, X30
X13, X8, X3,
X29, X5,
X22, X12, X24
Y2 Longitudinal Cracking
0.61 X18 X4, X1
X24, X17, X25
X13, X27, X15, X23
0.84 X18 X1, X4, X27
X24, X13, X17, X25
X26, X8
Y3 Alligator Cracking
0.51 X18 X1 X4, X22, X13
X25, X24, X12, X27, X3
0.88 X18, X4, X1
X22, X13
X20, X24, X8,
X25, X27, X3
67
Summary of Regression Analysis
Model Name Linear Regression Rank Regression
R2 ≥10% 6-9% 3-5% ≤2% R2 ≥10% 6-9% 3-5% ≤2%
Y4 Transverse Cracking
0.01 X24 0.07 X16, X12, X24
Y5 Permanent Deformation (AC Only)
0.86 X1, X4
X10 X8, X18
X12, X13, X6, X16, X3,
X30, X5
0.88 X1, X4
X10 X18, X8
X12, X13, X5, X16, X3,
X30, X6
Y6 Permanent Deformation (Total Pavement)
0.85 X1, X4, X18
X27, X10, X30
X8, X13, X26, X12, X3, X5
0.86 X1, X4
X18 X10, X27, X30, X8
X26, X13, X12, X3, X5
68
Combined Ranking of Inputs• Terminal IRI:
1. Bottom AC layer Thickness2. AADTT3. Percent of trucks in Design Lane4. Type of Subgrade Material5. Top AC layer Thickness
• Longitudinal Cracking1. Bottom AC layer Thickness2. AADTT3. Percent of trucks in Design Lane4. Modulus of Base Layer5. Percent Air void of Top AC Layer
• Alligator Cracking1. Bottom AC layer Thickness2. Percent of trucks in Design Lane3. AADTT4. Percent Air void of Bottom AC Layer5. Top AC layer Thickness
69
Combined Ranking of Inputs• Transverse Cracking
1. PG grade of Top AC layer2. Type of Base Material3. Aggregate gradation of Top AC layer4. Aggregate gradation of Bottom AC layer5. PG grade of Bottom AC layer
• AC Rut1. AADTT2. Percent of trucks in Design Lane3. Tire Pressure4. Bottom AC layer Thickness 5. Traffic Growth Factor
• Total Rut1. AADTT2. Percent of trucks in Design Lane3. Bottom AC layer Thickness4. Modulus of Subgrade5. Tire Pressure
70
Nonparametric Regression Procedure• Nonparametric Regression Procedures are used to estimate the necessary
sensitivity index for each input
▫ Quadratic Response Surface Regression (QREG)▫ Multivariate Adaptive Regression Splines (MARS)▫ Gradient Boosting Machine (GBM)
• Single Variance Index (S) and Total variance Index (T) are calculated using theseprocedures
Fraction of Uncertainty due to
xj aloneS
SInteractions of
xj with other variables
T
71
QREG Results
Input Name S.hat T.hat Interactions 95% T CI p-value
X18 AC Layer Thickness (2nd AC Layer)
0.380 0.600 0.220 (0.576, 0.671) 0.000
X1 AADTT 0.148 0.187 0.039 (0.156, 0.248) 0.000
X22 Air Void (%) (AC 2nd Layer)
0.091 0.121 0.030 (0.093, 0.174) 0.000
X4 Percent of Trucks in Design Lane (%)
0.103 0.115 0.012 (0.067, 0.150) 0.000
X13 AC Layer Thickness (Top Layer)
0.088 0.088 0.000 (0.045, 0.126) 0.000
X24 Base Material Type 0.037 0.050 0.013 (0.012, 0.095) 0.004
X25 Base Modulus 0.052 0.052 0.000 (0.006, 0.082) 0.015
Y3 (Alligator Cracking)
S = Single Variance IndexT = Total Variance Index
72
MARS Result
Input Name S.hat T.hat Interactions 95% T CI p-value
X4 Percent of Trucks in Design Lane (%)
0.049 0.874 0.825 (0.026, 1.000) 0.000
X7 AADTT Distribution by Vehicle Class 11 (%)
0.354 0.406 0.052 (0.194, 0.812) 0.013
Y4 (Transverse Cracking)
S = Single Variance IndexT = Total Variance Index
73
GBM Result
Input Name S.hat T.hat Interactions 95% T CI p-value
X1 AADTT 0.424 0.485 0.061 (0.405, 0.501) 0.000
X4 Percent of Trucks in Design Lane (%)
0.362 0.400 0.038 (0.340, 0.433) 0.000
X10 Tire Pressure 0.109 0.116 0.007 (0.099, 0.165) 0.000
X18 AC Layer Thickness (2nd AC Layer)
0.036 0.036 0.000 (0.019, 0.068) 0.000
X8 Traffic Growth Factor
0.020 0.021 0.001 (0.003, 0.042) 0.012
X13 AC Layer Thickness (Top Layer)
0.027 0.027 0.000 (0.001, 0.031) 0.022
Y5 (Permanent Deformation (AC Only))
S = Single Variance IndexT = Total Variance Index
74
Summary Result
ModelTotal Effects Main Effects Interaction Effects
QREG MARS GBM QREG MARS GBM QREG MARS GBM
R2 0.95 0.94 0.93 0.95 0.94 0.93 0.95 0.94 0.93
≥10% X1
X4
X18
X1
X4
X18
X1
X4
X18
X1
X4
X18
X1
X4
X18
X1
X4
X18
N/A N/A N/A
6-9% X27
X10
X10
X30
X27
X10
X30 N/A N/A N/A
3-5% X30
X8
X13
X21
X27
X8
X13
X26
X10
X27
X13
X30 X10
X27
X8
X13
X26
X10
X13
X1 X1 X1
Output Y6 (Total Rut)
75
Consistency of Results
QREG (R2=0.95)
MARS(R2=0.94)
GBM(R2=0.93)
Output Y6 (Total Rut)
X1 X4
X18
X27
X30
X10
0
10
20
30
40
50
X1
X4
X18
X10
X27
X30
0
10
20
30
40
50
X1
X4
X18
X10
X27
X30
0
10
20
30
40
50
Varia
nce
Inde
x76
Consistency of Results (Cont.)
▫ Total variance index obtained in 3 cases are close to each other
▫ Range of 95% CI are almost similar in all cases
QREGMARS
GBM
0
10
20
30
40
50
QREG MARS GBM
0
5
10
15
20
X10 (Tire Pressure)
X4 (Percent of Trucks in Design Lane)
X18 (Bottom AC Layer Thickness)
Tota
l Var
ianc
e In
dex,
T (%
)
Output Y6 (Total Rut)
QREG
MARS
GBM
0
3
6
9
12
77
Remarks• High Sensitive Inputs:
▫ Terminal IRI: Bottom AC layer Thickness, AADTT and percent of trucks in designlane
▫ Longitudinal Cracking: Bottom AC layer Thickness, AADTT and Percent of trucksin Design Lane
▫ Alligator Cracking: Bottom AC layer Thickness, AADTT and Percent Air void ofBottom AC Layer
▫ Transverse cracking: AADTT and Percent of Vehicle class 11
▫ AC Rut: AADTT, Percent of trucks in Design Lane and Tire Pressure
▫ Total Rut: AADTT, Percent of trucks in Design Lane and Bottom AC layerThickness
78
Remarks (Cont.)
• Low Sensitive Inputs:▫ Percent of trucks in design direction▫ Traffic growth factor▫ Base thickness▫ Operational speed▫ GWT depth▫ Design lane width
79
Remarks (Cont.)
• Traffic input variables, such as Annual Average Daily Truck Traffic(AADTT) and Percent of Trucks in Design Lane are obtained to bethe most critical parameter
• For New Mexico, AC mix properties and AC thickness are veryimportant for roughness, longitudinal crack and fatigue crack. Baseproperties (modulus and thickness) have significant impact on longand fatigue crack
• Most interactive input is Bottom AC layer thickness
80
DATA FOR LOCAL CALIBRATIO
Local Calibration Performed using both
- LTPP pavement sections (11 data) - PMS data (13 data)
82
Calibration ≡ Find a set of calibration coefficients that minimizes the residual error
Validation is the process necessary to confirm that the new models work for cases different to those used in
calibration
Calibration and Validation
Target: Minimize the Sum of Squared Errors (SSE)( )2 −= istresspredictedDstressmeasuredDiSSE
Split-sample approach: 80% of pavement sections are used for calibration and 20% for validation (randomly chosen)
83
MEPDG Inputs and Outputs
TrafficClimate
MaterialsMEPDG
RuttingCracking
Roughness
INPUTS OUTPUTS
• 13 sections from NMDOT databases• 11 sections from LTPP database
84
Calibration Data
SHRP
IdRoad MP
Type of
Experiment
Constructio
n Date *
1002
1003
1005
1022
1112
2006
2007
2118
6033
6035
6401
US-70
US-70
I-25
US-550
US-62
US-550
US-550
I-40
I-25
I-40
I-40
310.1
320.9
263.8
125.1
81.3
89.5
106.2
346.2
159.3
96.7
107.7
GPS-6A
GPS-1
GPS-1
GPS-1
GPS-1
GPS-2
GPS-6A
GPS-2
GPS-6A
GPS-6A
GPS-6A
May, 1985
May, 1983
Sep, 1983
Sep, 1986
May, 1984
Jun, 1982
Jun, 1981
Dec, 1979
May, 1981
May, 1985
May, 1984
GPS-1,2 = AC on GBGPS-6A = AC overlay on AC
Section
#Road Milepoint
Type of
Section
Construction
Date *
NMDOT 2
NMDOT 4
NMDOT 5
NMDOT 6
NMDOT 10
NMDOT 12
NMDOT 15
NMDOT 19
NMDOT 20
NMDOT 21
NMDOT 23
NMDOT 25
NMDOT 27
I-10
I-40
I-40
I-40
I-25
US-54
US-62
US-64
US-64
US-70
US-82
US-84
US-180
148.0
183.0
187.0
243.0
252.0
82.0
35.0
97.0
205.0
254.0
135.0
183.0
114.0
Rehab.
New
New
Rehab.
New
New
New
Rehab.
New
New
New
Rehab.
New
07/1984
06/1999
06/1999
06/1986
07/1982
06/1977
05/1992
10/1983
10/1971
10/1986
09/1994
07/1985
09/1994* Date of last major improvement in the case of rehabilitated sections
13 NMDOT sections 11 LTPP sections
85
MEPDG model for prediction of total rutting:
(Rut in AC)
(Rut in GB)
(Rut in SG)
hAC, hGB, hSG = Thickness of layer (in)T = Pavement temperature (F)N = Number of load repetitionsεr = Resilient strainεv = Average vertical strainε0, β, ρ = Material properties
kZ = Factor that depends on hAC and depth of point where strain is being determinedk1 = -3.35412, k2 = 1.5606, k3 = 0.4791kGB = 2.03, kSG = 1.35βr1, βr2, βr3, βGB, βSG = Calibration coefficients
Permanent Deformation Model
332211
1
10 rkrkkzrACr
layers
i
ip
i NTkhhRut ββεβε ⋅⋅
=
⋅⋅⋅⋅⋅⋅=⋅= βρ
εεεβ
−
⋅⋅⋅⋅⋅+ N
rGBvGBGB ekh 0
βρ
εεεβ
−
⋅⋅⋅⋅⋅+ N
rSGvSGSG ekh 0
86
Only total rutting can be calibrated. Calibration of βr1, βr2, βr3, βGB, and βSG separately for each layer would require cutting trenches to measure the rut depth in
every layer
The application of nonlinear numerical optimization was considered but the problem would become too difficult because MEPDG uses a complex iterative process
For every ∆t, incremental distresses due to N and T at that particular time are cumulated and materials strength
changes due to temperature and moisture, then next step starts
Calibration of the Rutting Model
89
Calibration Matrix
βr2 and βr3 are nonlinear calibration coefficients (exponents to T and N).Thus, more sensitive thanβr1, βGB, and βSG.
• 1st run: By varying βr2and βr3, SSE is reduced from 4.7713 to 3.7917.• 2nd Run: By varying βr1, βGB, and βSG, SSE is reduced to 3.6415.
Set # βr2 βr3 SSE MRE
1 0,8 0,8 4,5047 0,02412 0,8 0,9 4,3604 0,02373 0,8 1 4,1495 0,02314 0,8 1,1 4,0597 0,02295 0,8 1,2 5,3874 0,02646 0,9 0,8 4,3367 0,02377 0,9 0,9 4,1106 0,02308 0,9 1 3,9686 0,02269 0,9 1,1 5,0355 0,025510 0,9 1,2 13,3237 0,041511 1 0,8 4,0628 0,022912 1 0,9 3,8808 0,022413 1 1 4,7713 0,024814 1 1,1 12,0744 0,039515 1 1,2 47,5539 0,078416 1,1 0,8 3,7917 0,022117 1,1 0,9 5,8508 0,027518 1,1 1 11,2647 0,038119 1,1 1,1 44,7627 0,076020 1,1 1,2 145,9079 0,137321 1,2 0,8 4,4497 0,024022 1,2 0,9 10,8591 0,037423 1,2 1 43,2231 0,074724 1,2 1,1 144,0629 0,136425 1,2 1,2 371,8553 0,219126 1,1 0,75 3,8665 0,022327 1,05 0,75 4,0342 0,022828 1,05 0,8 3,9040 0,022529 1,05 0,85 3,8364 0,0223
90
Coefficients β1 = 1.1, β2 = 1.1, β3 = 0.8, βGB = 0.8, and βSG = 1.2 reduces the SSE from 4.7713 to 3.6415.
After calibration, data is less scattered and closer to the line
Results
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pred
icte
d To
tal R
uttin
g (in
)
Measured Total Rutting (in)
LTPP Sections
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Pr
edic
ted
Tota
l Rut
ting
(in)
Measured Total Rutting (in)
LTPP SectionsNMDOT SectionsLinear (Line of Equality)
Uncalibrated Calibrated
91
Sections 2006, 6033, NMDOT 15, NMDOT 21, and NMDOT 25 are kept aside for validation. The new model improves the MEPDG prediction, the SSE
decreases from 0.3064 to 0.1142
Rutting Model Validation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25
Tota
l Rut
ting
(in)
Design Life (years)
Measured
Uncalibrated
Calibrated
NMDOT 25
92
Fatigue Cracking ModelMEPDG model for prediction of fatigue cracking:
Miner’s Law:
D = Fatigue damage at bottom or top of AC layerT = Number of periodsni = Number of load repetitions during TiNi = Number of load repetitions to fatigue crackingεt = Tensile strain at bottom or top of AC layerE = Stiffness of AC (psi)Vb = Effective asphalt content (%)Va = Percent of air voids (%)
k1 = 0.007566, k2 = 3.9492, k3 = 1.281βf1, βf2, βf3 = Calibration coefficientsFCbottom = Alligator cracking (% area)FCtop = Longitudinal cracking (ft/mile)C’1, C’2 = Factors based on hACC1, C2, C3 = Calibration coefficients
=
=T
i i
i
NnD
1
3322 1100432.0 11
ff kk
tff EkCN
ββ
εβ
⋅⋅
⋅
⋅⋅⋅⋅=
MC 10=
−
+= 69.084.4
ba
b
VVVM
+= ⋅⋅⋅+⋅ )100(log''
3102211160
1DCCCCbottom e
CFC
+⋅= ⋅⋅− )100(log
310211
56.10 DCCtop eCFC
93
Bottom Up Cracking:Calibration Matrix
Calibration coefficients βf1, βf2, and βf3 are not calibrated
because the number of load repetitions necessary to initiate
fatigue damage is unknown
By varying C1 and C2, the SSE is reduced from 4861.47 to 3537.84The coefficient C3 is fixed at the default value 6000
Set # C1 C2 C3 SSE MRE
1 0.25 0.25 6000 15082.72 1.622 0.25 0.625 6000 18217.61 1.783 0.25 1 6000 27329.87 2.184 0.25 1.5 6000 39688.19 2.625 0.25 2 6000 48542.23 2.906 0.625 0.25 6000 3537.84 0.787 0.625 0.625 6000 4184.23 0.858 0.625 1 6000 5729.43 1.009 0.625 1.5 6000 12219.83 1.4510 0.625 2 6000 23157.53 2.0011 1 0.25 6000 4876.49 0.9212 1 0.625 6000 4918.98 0.9213 1 1 6000 4861.47 0.9214 1 1.5 6000 4977.75 0.9315 1 2 6000 7220.50 1.1216 1.5 0.25 6000 5219.85 0.9517 1.5 0.625 6000 5223.26 0.9518 1.5 1 6000 5211.96 0.9519 1.5 1.5 6000 5163.09 0.9520 1.5 2 6000 5044.81 0.9321 2 0.25 6000 5251.35 0.9522 2 0.625 6000 5251.13 0.9523 2 1 6000 5249.79 0.9524 2 1.5 6000 5245.37 0.9525 2 2 6000 5231 29 0 95
96
Coefficients C1 = 0.625, C2 = 0.25 and C3 = 6000 reduce the SSE from 4861.47 to 3537.84. Data points get closer to line of equality
Results: Bottom Up Cracking
0
5
10
15
20
25
0 5 10 15 20 25
Pred
icte
d A
lliga
tor C
rack
ing
(%)
Measured Alligator Cracking (%)
LTPP Sections
NMDOT Sections
0
5
10
15
20
25
0 5 10 15 20 25Pr
edic
ted
Alli
gato
r Cra
ckin
g (%
)Measured Alligator Cracking (%)
LTPP Sections
NMDOT Sections
Uncalibrated Calibrated
97
Alligator Cracking Validation
Sections 1002, 1022, NMDOT 19, NMDOT 20, and NMDOT 27 are kept aside for validation. The new model improves the MEPDG prediction, the SSE decreases from 183.60 to 76.16
0
2
4
6
8
10
12
0 5 10 15
Alli
gato
r Cra
ckin
g (%
)
Design Life (years)
Measured
Uncalibrated
CalibratedNMDOT 27
98
Fatigue Cracking ModelMEPDG model for prediction of fatigue cracking:
Miner’s Law:
D = Fatigue damage at bottom or top of AC layerT = Number of periodsni = Number of load repetitions during TiNi = Number of load repetitions to fatigue crackingεt = Tensile strain at bottom or top of AC layerE = Stiffness of AC (psi)Vb = Effective asphalt content (%)Va = Percent of air voids (%)
k1 = 0.007566, k2 = 3.9492, k3 = 1.281βf1, βf2, βf3 = Calibration coefficientsFCbottom = Alligator cracking (% area)FCtop = Longitudinal cracking (ft/mile)C’1, C’2 = Factors based on hACC1, C2, C3 = Calibration coefficients
=
=T
i i
i
NnD
1
3322 1100432.0 11
ff kk
tff EkCN
ββ
εβ
⋅⋅
⋅
⋅⋅⋅⋅=
MC 10=
−
+= 69.084.4
ba
b
VVVM
+= ⋅⋅⋅+⋅ )100(log''
3102211160
1DCCCCbottom e
CFC
+⋅= ⋅⋅− )100(log
310211
56.10 DCCtop eCFC
99
Top Down Cracking:Calibration Matrix
By varying C1 and C2, the SSE is reduced from 603,101,012.34 to 58,406,192.29
The coefficient C3 is fixed at the default value 1000
Set # C1 C2 C3 SSE MRE
1 1 0.3 1000 645,006,970.17 285.362 1 1 1000 1,660,586,371.17 457.873 1 2.25 1000 3,306,382,014.97 646.084 1 3.5 1000 4,131,306,348.15 722.195 1 5 1000 4,704,069,017.36 770.636 3 0.3 1000 58,406,192.29 85.877 3 1 1000 164,870,343.26 144.278 3 2.25 1000 1,369,715,531.19 415.849 3 3.5 1000 2,569,406,002.47 569.5410 3 5 1000 3,365,469,711.99 651.8311 5 0.3 1000 94,519,508.65 109.2412 5 1 1000 82,731,955.85 102.2013 5 2.25 1000 385,880,672.89 220.7214 5 3.5 1000 1,370,064,827.49 415.8915 5 5 1000 2,462,362,046.06 557.5516 7 0.3 1000 104,188,084.77 114.6917 7 1 1000 101,542,737.84 113.2218 7 2.25 1000 112,599,922.33 119.2319 7 3.5 1000 603,101,012.34 275.9320 7 5 1000 1,545,935,462.19 441.7821 10 0.3 1000 1,545,935,462.19 115.5422 10 1 1000 105,597,022.35 115.4623 10 2.25 1000 103,391,480.45 114.2524 10 3.5 1000 147,298,191.72 136.3725 10 5 1000 646,631,817.72 285.72
100
Coefficients C1 = 3, C2 = 0.3 and C3 = 1000 reduce the SSE from 603,101,012.34 to 58,406,192.29. Data points get close to the line of equality and much better agreement is obtained
Results
0
1000
2000
3000
4000
5000
6000
0 1000 2000 3000 4000 5000 6000
Pred
icte
d Lo
ngitu
dina
l Cra
ckin
g (f
t/mi)
Measured Longitudinal Cracking (ft/mi)
LTPP Sections
NMDOT Sections
0
1000
2000
3000
4000
5000
6000
0 1000 2000 3000 4000 5000 6000Pr
edic
ted
Long
itudi
nal C
rack
ing
(ft/m
i)Measured Longitudinal Cracking (ft/mi)
LTPP Sections
NMDOT Sections
Uncalibrated Calibrated
101
Longitudinal Cracking Validation
Sections 1003, 6035, NMDOT 2, NMDOT 12, and NMDOT 23 are kept aside for validation. The new model improves the MEPDG prediction, the
SSE decreases from 407,098,600 to 802,600
0
2000
4000
6000
8000
10000
12000
0 5 10 15 20 25
Long
itudi
nal C
rack
ing
(ft/m
i)
Design Life (years)
Measured
Uncalibrated
Calibrated
NMDOT 2
102
IRI ModelMEPDG model for International Roughness Index
(IRI):
IRI = IRI at any given time (m/km)IRI0 = Initial IRI (m/km)SF = Site factoreage/20 - 1 = Age term (age is expressed in years)COVRD = Coefficient of variation of rut depths (%)(TCL)T = Total length of transverse cracks (m/km)(FC)T = Fatigue cracking in wheelpath (% lane area)(BC)T = Area of block cracking, (% of the lane area)(LCSNWP)MH = Sealed longitudinal cracks (m/km)RSD = Standard deviation of monthly rainfall (mm)P0.075 = Fraction passing the 0.075 mm sieve (%)
PI = Plasticity index of the soil (%)FI = Average annual freezing index (°C-days)P0.02 = Fraction passing the 0.02 mm sieve (%)Rm = Average annual rainfall (mm)IRIP = IRI at the reliab. level P (m/km)IRI = IRI at 50% reliability (m/km)STDIRI = Standard deviation of IRI at the level of mean IRI (m/km)ZP = Standard normal deviate
103
Calibration MatrixThe new calibration coefficients of the rutting and fatigue cracking models are used, and the MEPDG is run fordifferent values of the site factor
Set # Site Factor SSE MRE
1 default 265,638.14 4.962 0.001 308,583.03 5.343 0.015 268,903.98 4.994 0.1 919,555.57 9.225 1 101,768,736.60 97.006 0.01 278,288.97 5.07
The default value of 0.015 provides the lowest SSE which is 268,903 If the MEPDG is run using default distress models, the prediction is slightly better with a SSE of 265,638
104
The new rutting and fatigue cracking models and a Site Factor = 0.015 slightly increases the SSE from 265,638 to 268,903This model shows a good agreement
Results: IRI
0
50
100
150
200
250
300
0 50 100 150 200 250 300
Pred
icte
d IR
I (in
/mile
)
Measured IRI (in/mile)
LTPP Sections
NMDOT Sections
0
50
100
150
200
250
300
0 50 100 150 200 250 300Pr
edic
ted
IRI (
in/m
ile)
Measured IRI (in/mile)
LTPP Sections
NMDOT Sections
Uncalibrated
Calibrated
105
IRI Validation
Sections 1112, 2007, NMDOT 5, NMDOT 6, and NMDOT 10 are kept aside for validation. The MEPDG prediction barely varies with the new model, the SSE
slightly increases from 7,472.85 to 8,106
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25
IRI (
in/m
ile)
Design Life (years)
Measured
Uncalibrated
Calibrated
NMDOT 6
106
Summary of Local Calibration
• Rutting: βr1 = 1.1, βr2 = 1.1, βr3 = 0.8, βGB = 0.8, βSG = 1.2
• Alligator Cracking: C1 = 0.625, C2 = 0.25, C3 = 6000
• Longitudinal Cracking: C1 = 3, C2 = 0.3, C3 = 1000
• IRI: Site Factor = 0.015
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Implementation Note
• MEPDG database work needs to be continued
• The sets of calibration coefficients obtained for the MEPDG permanent deformation, fatigue cracking and IRI models can reduce the error in the prediction, and thus, be beneficial for pavement design.
• Improvement is still possible to achieve in the future
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