Florida Department of Transport APT and Instrumentation Workshop

Florida Department of
Transport
APT and Instrumentation
Workshop
Subgrade Deformation:
The development of mechanisticempirical design transfer functions
from HVS data
H L Theyse
Transportek CSIR
Structure of presentation
„ Background
Subgrade definition
„ Site selection
„
„ Analysis
process
„ Elastic response
„ Plastic response
„ Design models
Background and
analysis process
Subgrade Deformation:
The development of mechanisticempirical design transfer functions
from HVS data
Subgrade definition
Wearing course
Base layer
Subbase layer
Upper selected
subgrade
Lower selected
subgrade
In situ subgrade
Pavement structural layers
•High shear stresses
•Large strains
Pavement foundation or
subgrade:
•Low shear stresses
•Small strains
HVS tests used in study
Louis Trichardt
Bultfontein
Rooiwal
Cullinan
Bapsfontein
Amanzimtoti
Richmond
Umkomaas
East London
Port Elizabeth
Analysis process
HVS tests:
Multi Depth Deflectometer data
Elastic response:
•Direct calculation (εv δs)
•Back-calculation (εv σv)
Plastic response:
•Non-linear regression model
Subgrade behaviour:
•Resilient modulus
•Characteristics of permanent deformation
•Permanent deformation design model
HVS testing:
MDD installation
„ MDD
modules at
layer interfaces
„ Anchor at 2,5 to 3 m
Pavement
structure
MDD
installation
MDDmodule
Reference point
anchored at
2,5 to 3 m
Elastic response
Subgrade Deformation:
The development of mechanisticempirical design transfer functions
from HVS data
Elastic response:
Depth deflection bowls
„
„
256 data points on
each bowl
Peak deflections
DEFLECTION (mm)
0
Depth (mm)
60 mm
-0.1
200 mm
-0.2
375 mm
-0.3
550 mm
800 mm
-0.4
-0.5
Direction of wheel movement
DISTANCE
Elastic response:
Depth deflection profile
„
Direct calculation
„
„
„
Average vertical strain
between MDD modules
Elastic subgrade
deflection
Back-calculation
„
„
At least 2 modules in
subgrade
Vertical stress and strain
at top of subgrade
0
DEFLECTION (mm)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
200
400
HVS load
repetitions
10
74559
176540
600
378922
462878
800
589502
1000
DEPTH (mm)
MDD depth deflection data:
Deflection history
500RF
MDD 4
Deflection (micron)
2000
1500
1000
500
0
0.0E+00
1.0E+06
2.0E+06
3.0E+06
Load Repetitions
0
213
396
100 kN
625
1000
MDD depth deflection data:
Deflection profile
500RF
MDD 4
Deflection (micron)
0
500
1000
0
Depth (mm)
200
400
600
800
1000
100 kN
1500
2000
202575
647499
224501
706985
252495
759745
299731
824952
360090
894991
405258
943566
456768
993404
467202
1058019
480464
1119882
498752
1168178
509327
1207827
554991
Analysis process:
Average layer elastic strain
500RF
Elastic strain (mocrostrain)
MDD 4
2000
1500
1000
500
0
0E+00
1E+06
2E+06
3E+06
Load Repetitions
0 - 213
213 - 396
396 - 625
100 kN
625 - 1000
Analysis process:
Direct vs. back-calculation
Subgrade deflection from
MLLE (micron)
Vertical subgrade deflection comparison
MLLE vs LVDT
1500
1000
500
0
0
500
1000
1500
Subgrade deflection from LVDTs (micron)
Vertical strain from MLLE (microstrain)
Analysis process:
Direct vs. back-calculation
4000
3000
2000
1000
0
0
1000
2000
3000
Vertical strain from LVDTs (microstrain)
4000
Plastic response
Subgrade Deformation:
The development of mechanisticempirical design transfer functions
from HVS data
Analysis process:
Permanent MDD displacement
Initial bedding-in
„ Eventual linear rate of
displacement
„ Non-linear regression
model
PD = mN + a(1 – e-bN)
a = bedding-in
m = linear displacement
rate
„
Permanent MDD Displacement (mm)
Depth (mm)
3
80mm
2.5
240mm
2
440mm
1.5
660mm
1
900mm
0.5
0
0
1
2
3
HVS Wheel-load Repetitions
Millions
4
Analysis process:
Permanent MDD displacement
Permanent MDD displacement
a
a(1 – e-bN)
m
a
1
mN
Number of load repetitions, N
Analysis process:
Permanent MDD displacement
PD (mm)
R2 = 0,989
SEE = 0,014
0,700
0,600
0,500
0,400
0,300
0,200
Model
Data
0,100
0,000
0
1000000 2000000 3000000 4000000
HVS load repetitions
Plastic response:
Bedding-in “a”
Permanent deformation bedding-in vs critical parameter
Bedding-in "a" (mm)
10
8
6
4
2
0
0
200
400
600
800
1000
1200
Subgrade elastic deflection (micron)
40 kN
60 kN
70 kN
100 kN
1400
Plastic response:
Linear deformation rate “m”
PD rate "m" (mm/repetition)
Linear permanent deformation rate vs critical parameter
1.0E-05
7.5E-06
5.0E-06
2.5E-06
0.0E+00
0
200
400
600
800
1000
1200
Subgrade elastic deflection (micron)
40 kN
60 kN
70 kN
100 kN
1400
Plastic response:
Critical parameter, εv
Permanent deformation (mm
Subgrade permanent deformation at 200 000 load repetitions
20
15
40 kN
60 kN
70 kN
100 kN
10
5
0
0
500
1000
1500
2000
2500
Vertical strain from LVDT (microstrain)
3000
Plastic response:
Critical parameter, σv
Permanent deformation (mm
Subgrade permanent deformation at 200 000 load repetitions
20
15
40 kN
60 kN
70 kN
100 kN
10
5
0
0.0
50.0
100.0
Vertical stress (kPa)
150.0
200.0
Plastic response:
Critical parameter, δs
Permanent deformation (mm
Subgrade permanent deformation at 200 000 load repetitions
20
15
40 kN
60 kN
70 kN
100 kN
10
5
0
0
400
800
Subgrade elastic deflection (micron)
1200
Design models
Subgrade Deformation:
The development of mechanisticempirical design transfer functions
from HVS data
Subgrade design transfer
functions (S-N curves)
„
„
„
„
„
S-N data
S - Stress parameter
N - Number of repetitions to reach a certain,
predetermined level of subgrade deformation
N solved from regression function for each MDD
module from top of subgrade downwards
Regression of S-N data on a log-linear scale
Plastic response:
S(vertical strain)-N data
S-N data
7 mm plastic deformation
Bearing capacity
(repetitions)
1.0E+09
1.0E+08
40 kN
60 kN
70 kN
100 kN
1.0E+07
1.0E+06
1.0E+05
0
500
1000
1500
2000
Vertical strain (microstrain)
2500
3000
Plastic response:
S(vertical stress)-N data
S-N data
7 mm plastic deformation
Bearing capacity
(repetitions)
1.0E+09
1.0E+08
40 kN
60 kN
70 kN
100 kN
1.0E+07
1.0E+06
1.0E+05
0.0
50.0
100.0
150.0
Vertical stress (kPa)
200.0
Plastic response:
S(subgrade deflection)-N data
S-N data
7 mm plastic deformation
Bearing capacity
(repetitions)
1.0E+09
1.0E+08
40 kN
60 kN
70 kN
100 kN
1.0E+07
1.0E+06
1.0E+05
0
500
1000
Subgrade elastic deflection (micron)
1500
Plastic response:
S-N subgrade deformation model
5 mm subgrade deformation
R2 = 0,672
SEE = 0,379
1,E+09
1,E+08
Cycles
1,E+07
1,E+06
1,E+05
1,E+04
1,E+03
0
200
400
600
800
1000
1200
Subgrade elastic deflection (micron)
Model
G6
G7
G8
G10
1400
Plastic response:
S-N subgrade design models
Subgrade Design Curves
1,E+09
Cycles
1,E+08
3 mm
1,E+07
5 mm
7 mm
1,E+06
13 mm
1,E+05
1,E+04
0
200
400
600
800
1000
Subgrade Elastic Deflection (micron)
1200
Plastic deformation model:
Conclusions
„
„
„
„
„
Model based on measured parameters
Models only valid for low shear stress zone in
pavement
Simplified model of subgrade response under
normal road traffic loads
„ Good enough for design purpose
Subgrade elastic deflection yields the best S-N
correlation
Model not calibrated for field variables
„
„
„
Density
Degree of saturation
Further refinements are possible
Model refinement
Subgrade Deformation:
The development of mechanisticempirical design transfer functions
from HVS data
Issues to address
„
Calibration of a continuous model
„
„
„
Recursive/incremental distress analysis
Pavement systems approach to rutting
Resilient modulus models for the pavement
subgrade
„
„
Current work based on measured parameters
Subgrade elastic deflection will have to be
calculated in the design case
Continuous model
„ Applied
to HVS data from Richmond
Field Station, CA (CALAPT program)
„ Each set of readings contains
„
Number of repetitions (N)
Subgrade elastic deflection (δs)
„ Total subgrade plastic deformation (PD)
„
„
Data triplets – N, δs, PD
Approach to calibration
Pavement
MDD
structure installation
0
DEFLECTION (mm)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
HVS load
repetitions
200
10
74559
400
‹ δs @ N
176540
MDDmodule
600
378922
462878
800
589502
1000
DEPTH (mm)
Permanent MDD Displacement (mm)
3
Depth (mm)
80mm
2.5
240mm
2
440mm
1.5
660mm
1
Reference point
anchored at
2,5 to 3 m
900mm
0.5
0
0
1
2
3
HVS Wheel-load Repetitions
Millions
4
‹ PD @ N
Models fitted
„ PD
„ PD
α
β
s
=AN δ
bN
c
s
= (mN+a)(1-e ) δ
6
5
anent deform
Subgrade perm
4
3
2
2.5e+6
2.0e+6
tio
ns
1
0
1.2
1.0e+6
1.0
Subg
rade
0.8
0.6
elast
ic
defle
5.0e+5
0.4
ction
0.2
(mm)
0.0
0.0
pe
ti
1.5e+6
Re
ation (mm)
Continuous subgrade distress
models
Continuous subgrade distress
models
m)
Deformation (m
6
0
1
2
3
4
5
6
N vs SED vs PD
5
anent
Subgrade Perm
4
3
2
2.0e+6
1
1.2
1.0
0.8
Subg
rade
Elast 0.6
ic De 0.4
0.2
flectio
n (mm
)
5.0e+5
0.0
Re
pe
1.0e+6
0
titi
o
ns
1.5e+6
Deflection calculation in the
design case
„ Use
MDD deflection data with
Top-cap MDD module
„ Two modules in subgrade
„
„ Do
MDD back-calculation
„ Combine data for similar materials
„ Investigate non-linearity if possible
HVS-section Nr: 332A2
Region:
Instrumentation detail
Pavement structure
0
2
4
100
200
6
8
10
12
MDD
MDD
50
50
MDD
MDD
200
200
MDD
MDD
375
375
14
Type
16
500
MDD
550
MDD
MDD
MDD
800
800
550
600
700
800
900
1000
MDD anchor
at 3 m depth
MDD anchor
at 3 m depth
Depth (mm)
Load sequence detail:
Repetitions
Related reports:
Test information
No report available
From
To
Wheel load
Tyre pressure
0
604 735
40 kN
520 kPa
No
604 735
1 245 733
60 kN
690 kPa
No
Water added
Material properties
(UCS, CBR, MDD, OMC,etc)
Field
Density
(kg/cub m)
MC
(%)
TRH14
class
0 - 50
Asphalt
New and old asphalt surfacing layers
50 - 250
Crushed
Stone
mDD = 2233, OMC = 5,5
CBR = 91 @ 98 %
GM = 2,25
99,5% mDD
3,1
G2
250 - 370
Natural
gravel
subbase
mDD = 1908, OMC = 10,3
CBR = 48 @ 95 %
GM = 2,06
87,4% mDD
12,9
G5
370 +
In-situ
subgrade
Stony limestone and sand
mDD = 1926 OMC = 12,1
CBR = 27 @ 93 %
GM = 1,65
95,8% mDD
11,2
G6
300
400
Year of test: 1988
Pavement material information
Layer
Test section point
0
Road Nr: N2/11
Port Elizabeth, Eastern Cape
Upper subgrade Mr
Frequency
Upper Subgrade
45
40
35
30
25
20
15
10
5
0
100%
80%
60%
40%
20%
0%
0
20
40
60
80
100 120 140 160 180 200 More
Bin
Frequency
Cumulative %
Lower subgrade Mr
Lower Subgrade
100%
Frequency
20
80%
15
60%
10
40%
5
20%
0
0%
0
50
100 150 200 250 300 350 400 450 500 More
Bin
Frequency
Cumulative %
Deep in-situ subgrade Mr
Deep in situ Subgrade
35
100%
Frequency
30
80%
25
20
60%
15
40%
10
20%
5
0
0%
0
50
100 150 200 250 300 350 400 450 500 More
Bin
Frequency
Cumulative %
To summarize
„
Best correlation was found between subgrade
permanent deformation and subgrade elastic
deflection
„
„
Subgrade elastic deflection selected as the critical
parameter for subgrade design model
Model does not explain a lot of the variation
in data
„
„
„
Effect of moisture content and density excluded
Data not available
Given the amount of deformation contributed by
the subgrade – no further refinement
To summarize (continued)
„ Working
on
Back-calculations
„ Non-linear model calibration
„ Calibration of continuous distress model for
South African data
„