1. Analyze the ki data for Materials A and B to identify trends between dry, optimum and wet conditions 2. Develop MR prediction models for each material as a function of moisture content using the ki data 3. Validate the models against additional test data to confirm their accuracy in predicting MR values

1. Improving MR Test Procedures
for Unbound Materials
TPF-5(177) Kick-Off Meeting
September 14, 2009
Dragos Andrei, Ph.D., P.E.
Associate Professor of Civil Engineering
California State Polytechnic University, Pomona

2. Presentation Outline
Projects NCHRP 1-28, 1-28A, 1-37A
Real life MR problem (SH130)
Variability: sources and measures
Conclusions and recommendations

3. NCHRP 1-28
Purpose: develop MR test procedures for
unbound materials and HMA
Team: R.D. Barksdale and J. Alba
Cost: ?
Test Program:
Influence of scalp and replace
Axial deformation measurement: external, internal
top-bottom, internal middle-half
Effect of compaction
And more
1997

4. NCHRP 1-28 Key Findings and
Recommendations
Use closed-loop, fully automated test
equipment
Implement a well-planned equipment
calibration program including the use of
synthetic specimens for verification
Axial deformation measurements should
be made internally - on the specimen
No more than two replicate tests needed
to assess variability
And more …

5. NCHRP 1-28A
Purpose: Finalize NCHRP 1-28 work on
development of a harmonized resilient
modulus test method
Team: M.W. Witczak, J. Uzan, C.W.
Schwartz (UMD)
Cost: $100,000
Test program: 30 MR tests were performed
on 6 materials from different sources:
FHWA-ALF, MnRoad, USACE-CRREL.
1999

6. NCHRP 1-28A Key Findings
Models including both θ and τoct were
clearly superior to the classical k1-k2
models
Log-log models were more accurate than
the corresponding semi-log models
The higher the number of ki parameters –
the better the goodness of fit (e.g. k1-k7)

7. Model Selection for MEPDG
Goodness of fit
Computational stability
Implementable in the general framework of
the ME-PDG
k2 k3
 θ   τ oct 
M R = k1 ⋅ pa ⋅   ⋅ 
p   p + 1

 a  a 

8. 1-28A “Smart” Stress
Sequences
Avoid premature failure during MR test:
τ 4
Failure line
Lines of (c=0, φ)
constant σ3
3 3
(Classic,
NCHRP 1-28)
2 Lines of
2 constant σ1/σ3
1 (Harmonized)
NCHRP 1-28A
1
σ

9. MR - Moisture Effects for
NCHRP 1-37A (MEPDG)
Purpose: Quantify the effect of changes in
moisture and density on MR and develop
predictive model
Team: M.W. Witczak, W.N. Houston (ASU)
Cost: ? (NCHRP 1-37A, ADOT)
Work Plan:
Phase I – Literature Review
Phase II – Laboratory Testing
2000

10. Phase I - Literature Review
MR reduces with increased moisture; the
reduction in modulus is greater for fine
grained materials
Regardless of the model used, a linear
relationship is observed when plotting:
log(MR) versus moisture

11. M R - M oisture M odel for Coarse-Grained M aterials
2.5
2
1.5
MR/MRopt
1
Literature Data
0.5
Predicted
0
-70 -60 -50 -40 -30 -20 -10 0 10 20 30
(S - S opt)%

12. M R - M oisture M odel for Fine-Grained M aterials
2.5
2.0
1.5
MR/MRopt
1.0
Literature Data
0.5
Predicted
0.0
-70 -60 -50 -40 -30 -20 -10 0 10 20 30
(S - S opt)%

13. MR – Moisture Model
b−a
a+
( (
1+ EXP β + k m ⋅ S − Sopt ))
M R = 10 ⋅ M Ropt
MOISTURE
ADJUSTMENT MR = FU*MRopt
FACTOR (FU)
MR = Resilient Modulus at S
MRopt = Resilient modulus at Sopt
a, b, km = Regression parameters
β = lne(-b/a) from condition of (0,1) intercept

14. Combined Effects of Moisture
and Stress in ME-PDG
b−a k2 k3
a+
( (
1+ EXP β + k m ⋅ S − Sopt ))  θ   τ oct 
M R = 10  p   p + 1
⋅ k1 ⋅ pa ⋅   ⋅  
 a  a 
MOISTURE STRESS
ADJUSTMENT DEPENDENT
FACTOR (FU) MR MODEL
This form was implemented in the ME-PDG
for “unfrozen” unbound materials
Calibration/validation of the model with
laboratory test data was desired

15. Phase II – Laboratory Testing
Arizona DOT Materials
4 base materials
4 subgrade soils
Each material tested at:
3 moisture contents (optimum, soaked and dried)
2 compactive efforts (standard and modified)
2 replicates (minimum)
Total: 96 tests performed using the
NCHRP 1-28A test protocol
2002

16. Key Findings
Density strongly affects the MR-S
relationship and should be added as a
predictor to the model based on S
When gravimetric moisture content (w)
was used instead, the effect of density
was greatly minimized
MR – Moisture models including stress
dependency (like the one in the ME-PDG)
were successfully used to fit the measured
lab test data

17. Goodness of Fit – Phoenix
Valley Subgrade
PVSG (A-2-4, SC) - MR(w-w opt , θ, τoct) Model
2
n =142, Se/Sy =0.15, R = 0.98
1,000,000
100,000
10,000
MR Predicted
Line of Equality
1,000
1,000 10,000 100,000 1,000,000
Measured Resilient Modulus (psi)

18. MR – moisture density effects
Phoenix Valley Subgrade (Theta = 20 psi, Tau = 3psi)
1,000,000
Standard
M odified
Predicted
100,000
10,000
wopt weq
1,000
0 2 4 6 8 10 12 14 16 18
Unbound Materials Characterization Seminar Seasonal 18
M oisture Content (% )

19. Goodness of Fit – Gray
Mountain Base GMAB2 (A-1-a, GW) - MR(w-w opt , θ, τoct) Model
2
n = 254, R = 0.90, Se/Sy = 0.32
1,000,000
100,000
10,000
MR Predicted
Line of Equality
1,000
1,000 10,000 100,000 1,000,000
Measured Resilient Modulus (psi)

20. ADOT Database of MR Model
Parameters
Material ID AASHTO USCS a b kw β k1 k2 k3 w opt std
%
Phoenix Valley Subgrade A-2-4 SC 0.24 41.88 67.255 0.974 467 0.358 -0.686 11.3
Yuma Area Subgrade A-1-a GP 1.00 94.01 82.757 8.714 1,468 0.838 -0.888 11.0
Flagstaff Area Subgrade A-2-6 SC 0.31 10.93 74.489 0.722 634 0.187 -0.855 19.0
Sun City Subgrade A-2-6 SC 0.13 19.22 53.166 0.360 747 0.224 -0.104 11.3
Grey Mountain Base A-1-a GW 0.00 2096.40 2.559 -0.539 1,423 0.758 -0.288 6.7
Salt River Base A-1-a SP 0.59 2096.41 22.401 2.666 1,170 0.919 -0.572 6.9
Globe Area Base A-1-a SP-SM 0.68 2096.44 35.787 2.981 1,032 0.830 -0.307 6.7
Precott Area Base A-1-a SP-SM 1.00 2096.45 144.223 8.711 1,092 0.784 -0.236 6.3
ADOT A-1-a AB2 Base Materials A-1-a SP-SM 0.60 2096.65 24.221 2.721 1,075 0.841 -0.305 6.7
ADOT A-2 Subgrade Materials A-2 SC 0.22 21.79 58.965 0.699 - - - -

21. Real Life MR Problem (SH130)
Unbound Materials Characterization Seminar
2004
21

22. Data
A new highway is being built
Subgrade material samples are taken
every 500 ft along the alignment
Three samples of similar soil type are
mixed together into one bulk sample
Bulk samples are tested in the lab for MR

23. Data (Cont’d)
2 materials types are identified: A and B
There are 18 bulk samples available for material
type A (500ft*3*18 = 5 miles)
There are 26 bulk samples available for material
type B (500ft*3*26 = 7.4 miles)
MR tests have been performed at several
moisture contents: optimum, optimum +3%,
optimum –3%;
ki values have been generated for each MR test

24. Data (Cont’d)
ki summary for material A
ki values
M aterial A Dry O pt W et
k0 kd kp k0 kd kp k0 kd kp
Bulk 1 34,945 -0.269416 0.041374 25,927 -0.424631 0.138661
Bulk 2 26,059 -0.358200 0.184400 20,050 -0.642000 0.221400
Bulk 3 32,310 -0.463600 0.215000
Bulk 4 39,246 -0.452120 0.222780 30,015 -0.553579 0.216564 22,066 -0.769445 0.282913
Bulk 5 24,119 -0.475278 0.249000 14,107 -0.687327 0.315109 8,461 -0.842200 0.426167
Bulk 6 36,126 -0.456090 0.154673 27,844 -0.727020 0.201938 21,122 -0.925180 0.207083
Bulk 7 42,680 -0.570230 0.160843 38,141 -0.778380 0.162280 31,534 -0.763180 0.210047
Bulk 8 19,661 -1.019400 0.253963 19,715 -1.072970 0.318132
Bulk 9 38,494 -0.696370 0.253942 33,400 -0.765790 0.229967
Bulk 10 20,213 -0.429262 0.133289 16,554 -0.889688 0.051060
Bulk 11 17,053 -0.391572 0.091538
Bulk 12 22,182 -0.597050 0.209439
Bulk 13 44,749 -0.440120 0.151803 33,003 -0.486720 0.100738 20,476 -0.828890 0.289046
Bulk 14 44,025 -0.444500 0.193159 35,647 -0.531140 0.148053 18,814 -0.789060 0.309538
Bulk 15 25,406 -0.532200 0.138999
Bulk 16 29,930 -0.661800 0.138978 49,448 -0.611131 0.109068 29,930 -0.661800 0.138978
Bulk 17 76,309 -0.661042 0.197695 80,426 -0.668775 0.024432 43,192 -0.824336 0.107594
Bulk 18 21,844
Unbound Materials Characterization Seminar
-0.566054 0.319420 13,508 -0.547370 0.394921 11,212 -0.596271 0.377779

25. Data (Cont’d)
ki summary for material B
ki values
M aterialB Dry O pt W et
k0 kd kp k0 kd kp k0 kd kp
Bulk 1 23,365 -0.348650 0.004737 20,368 -0.320091 0.073256
Bulk 2 16,217 -0.258300 0.112100
Bulk 3 30,631 -0.364700 0.220470
Bulk 4 24,762 -0.516916 0.141701
Bulk 5 22,528 -0.629430 0.183921 23,968 -0.711080 0.140339
Bulk 6 36,602 -0.477410 0.206208 28,487 -0.462120 0.128810 36,043 -0.884910 0.182773
Bulk 7 27,111 -0.414694 0.181205 19,836 -0.443360 0.183849 23,618 -0.501437 0.142133
Bulk 8 19,666 -0.597631 0.166676 20,570 -0.426370 0.127696 18,922 -0.499500 0.163446
Bulk 9 27,696 -0.549000 0.199591 28,934 -0.538650 0.156857
Bulk 10 24,063 -0.469080 0.270056 25,089 -0.420700 0.092194 22,614 -0.588240 0.165751
Bulk 11 43,466 -0.784977 0.092654
Bulk 12 19,722 -0.412176 0.084508
Bulk 13 17,208 -0.349799 0.021935 19,500 -0.461701 0.032617
Bulk 14 37,116 -0.367548 0.058294 19,200 -0.268777 0.043610
Bulk 15 21,791 -0.478329 0.000844
Bulk 16 16,217 -0.258268 0.112075 20,748 -0.316450 0.108480
Bulk 17 18,788 -0.280171 0.020924 36,440 -0.557328 0.064253
Bulk 18 16,702 -0.237235 0.101201 20,522 -0.157984 0.010217
Bulk 19 16,603 -0.220614 0.007347
Bulk 20 19,712 -0.210542 0.054659
Bulk 21 17,178 -0.386660 0.073877 15,272 -0.458540 0.094120
Bulk 22 32,566 -0.652312 0.069370 24,603 -0.510339 0.091400
Bulk 23 39,158 -0.388730 0.014278 29,345 -0.320550 0.203700
Bulk 24 46,102 -0.578312 0.118676 32,503 -0.614743 0.086852 29,304 -0.868461 0.186478
Bulk 25 65,680 -0.501018 Unbound Materials Characterization
0.236424 39,559 -0.454563 0.119634 Seminar
37,225 -0.538610 0.108260
Bulk 26 30,425 -0.531227 0.153134 35,397 -0.706704 0.168594 22,578 -0.577760 0.118513

26. Problem
Calculate the Effective MR (AASHTO)

27. Solution
M onth MR Dam age
Factor (df)
=1.18*10^8*M R^-2.32
Jan
Feb
What is Mreff M ar
Apr
M ay
Jun
Jul
Aug
Sep
O ct
Nov
Dec
MReff = Sum(dfi*MRi)/Sum(dfi)
We need MRi

28. Solution
MRi are a function of moisture and stress
For simplification, assume:
6 months @ optimum – 3% (DRY)
4 months @ optimum (OPT)
3 months @ optimum + 3% (WET)
Three different states of stress are needed
corresponding to Dry, Opt and Wet conditions
For each of the three cases, go through the
iterative procedure to find out the state of
stress corresponding to the average MR value

29. (1) Choose locations
within layers
(6) (2) Assume MR0
•IF: the two values values
compared are not close
enough; continue by
changing the assumed
value until the assumed
Linear Elastic (3) Calculate stresses
at the locations of
and calculated values
meet the convergence
Analysis interest
criteria
•ELSE: STOP and use
Iterative Process
the estimated state of
stress to predict the MR (4) Calculate MRcalc as
value in the subgrade a function of stresses
and ki
(5) Compare MRcalc from
Step (4) with MR0 from
Step (2)

30. Solution
Calculate MReff using the average MRdry,
MRopt, MRwet values:
MReff = 12,458 psi
Design Requirement MReff > 7,000 psi
Are we meeting the design requirement?
Plot the data:

31. M aterial A
Sd S3
40,000 Dry 5.4 2.2
Opt 4.9 2.0
W et 4.2 1.8
30,000
DRY
OPT
20,000 W ET
Dry Average
Opt Average
10,000 W et Average
0
10 13 16 19 22 25
M oisture Content (% )

32. MReff Quiz
What is the probability that:
(a) MReff > 12,485 psi ?
(b) MReff > 7,000 psi ?

33. Answer
What is the probability that:
(a) MReff > 12,485 psi ? 50%
(b) MReff > 7,000 psi ? > 50%, all we know
Is that satisfactory?

34. Solution
MR
Probability of Failure
Mrave, SMr
Mrdesign
Probability of Failure

35. Solution
MR High Variability
MR Variability
Low Variability
Mrave, SMr
Mrdesign

36. M aterial A
Sd S3
40,000 Dry 5.4 2.2
Opt 4.9 2.0
W et 4.2 1.8
30,000
DRY
OPT
20,000 W ET
Dry Average
Opt Average
10,000 W et Average
0
10 13 16 19 22 25
M oisture Content (% )

37. M aterial A
0.00014
0.00012
0.0001
0.00008 DRY
OPT
0.00006
W ET
0.00004
0.00002
0
0 10,000 20,000 30,000 40,000
Resilient M odulus

38. Solution
Calculate for each case (Dry, Opt, Wet) a
MR value corresponding to 85% reliability
(15% probability of failure):
M odified M R Design (psi) 12,800 7,600 5,000
z -1.02534 -1.03046 -1.04696
Probability that M R is greater than M R design 85% 85% 85%
uf 0.03 0.12 0.31 Effective M odulus
M R*uf 447 890 1,546 7,200
M onths 6 4 2 0.11
Average M C 12.9 15.7 18.8

39. M aterial A
Sd S3
40,000 Dry 5.4 2.2
Opt 4.9 2.0
W et 4.2 1.8
30,000
DRY
OPT
20,000 W ET
Dry Average
Opt Average
W et Average
10,000
85% Reliability
0
10 13 16 19 22 25
M oisture Content (% )

40. Sources of Variability
Within lab: Between labs:
Material Operator
State of stress Compaction
Moisture Moisture/Density
Density conditioning
Test method
Data reduction
Regression model
and definition of the
error

41. SH130 Limited MR Variability
Study
2 labs
3 materials tested wet, optimum, dry
4 models

42. Within Lab
Lab A: Average CV = 5%, max CV = 9%
Lab B: Average CV = 12%, max CV = 23%

43. Findings
Lab B had some issues with data at low
stress levels (low strain levels)
The differences between labs were
significant, especially for the wet and dry
conditions
The measured CV is a function of the
predictive model used

44. Measures of variability
Coefficient of variation of:
MR in arithmetic space – most used
MR in logarithmic space?
Resilient strain in arithmetic space?
Layer thickness?
The higher the modulus, the less
important variability is for design

45. Conclusions
“True” variability in soil and aggregate
properties is real and expected.
Probabilistic methods can be used to
handle this variability when working on
real design problems.

46. Conclusions (Continued)
“Artificial” variability can be minimized by:
Test system calibration and verification with
synthetic test specimens
Comparing “apples to apples” i.e. taking into
account that MR is a function of: stress, moisture
and density
Following the same procedures for: Specimen
preparation, Test method, Data reduction,
Regression analysis and predictive model

47. Thank you
For more info:
dandrei@csupomona.edu