2009 mr pooled fund study
DESCRIPTION
About variability in MR test resultsTRANSCRIPT
Improving MR Test Procedures for Unbound Materials
TPFTPF--5(177) Kick5(177) Kick--Off MeetingOff MeetingSeptember 14, 2009September 14, 2009
DragosDragos Andrei, Ph.D., P.E.Andrei, Ph.D., P.E.Associate Professor of Civil EngineeringAssociate Professor of Civil EngineeringCalifornia State Polytechnic University, PomonaCalifornia State Polytechnic University, Pomona
Presentation Outline
Projects NCHRP 1Projects NCHRP 1--28, 128, 1--28A, 128A, 1--37A37AReal life MR problem (SH130)Real life MR problem (SH130)Variability: sources and measuresVariability: sources and measuresConclusions and recommendationsConclusions and recommendations
1997
NCHRP 1-28Purpose: develop MR test procedures for Purpose: develop MR test procedures for unbound materials and HMAunbound materials and HMATeam: R.D. Barksdale and J. AlbaTeam: R.D. Barksdale and J. AlbaCost: ?Cost: ?Test Program:Test Program:
Influence of scalp and replaceInfluence of scalp and replaceAxial deformation measurement: external, internal Axial deformation measurement: external, internal toptop--bottom, internal middlebottom, internal middle--halfhalfEffect of compactionEffect of compactionAnd moreAnd more
NCHRP 1-28 Key Findings and Recommendations
Use closedUse closed--loop, fully automated test loop, fully automated test equipmentequipmentImplement a wellImplement a well--planned equipment planned equipment calibration program including the use of calibration program including the use of synthetic specimens for verificationsynthetic specimens for verificationAxial deformation measurements should Axial deformation measurements should be made internally be made internally -- on the specimenon the specimenNo more than two replicate tests needed No more than two replicate tests needed to assess variabilityto assess variabilityAnd more And more ……
1999
NCHRP 1-28APurpose: Finalize NCHRP 1Purpose: Finalize NCHRP 1--28 work on 28 work on development of a harmonized resilient development of a harmonized resilient modulus test methodmodulus test methodTeam: M.W. Team: M.W. WitczakWitczak, J. , J. UzanUzan, C.W. , C.W. Schwartz (UMD)Schwartz (UMD)Cost: $100,000Cost: $100,000Test program: 30 Test program: 30 MMRR tests were performed tests were performed on 6 materials from different sources: on 6 materials from different sources: FHWAFHWA--ALF, ALF, MnRoadMnRoad, USACE, USACE--CRREL.CRREL.
NCHRP 1-28A Key Findings Models including both Models including both θθ and and ττoctoct were were clearly superior to the classical clearly superior to the classical kk11--kk22modelsmodelsLogLog--log models were more accurate than log models were more accurate than the corresponding semithe corresponding semi--log modelslog modelsThe higher the number of The higher the number of kkii parameters parameters ––the better the goodness of fit (e.g. kthe better the goodness of fit (e.g. k11--kk77))
Model Selection for MEPDG
Goodness of fitGoodness of fitComputational stabilityComputational stabilityImplementable in the general framework of Implementable in the general framework of the MEthe ME--PDGPDG
32
11
k
a
oct
k
aaR pppkM
+⋅
⋅⋅=
τθ
1-28A “Smart” Stress Sequences
Avoid premature failure during MAvoid premature failure during MRR test:test:
Lines of constant σ3(Classic, NCHRP 1-28)
1
2
3
Failure line(c=0, φ)
σ
τ
1
2
3
4
Lines of constant σ1/σ3(Harmonized) NCHRP 1-28A
2000
MR - Moisture Effects for NCHRP 1-37A (MEPDG)
Purpose: Quantify the effect of changes in Purpose: Quantify the effect of changes in moisture and density on moisture and density on MMRR and develop and develop predictive modelpredictive modelTeam: M.W. Team: M.W. WitczakWitczak, W.N. Houston (ASU), W.N. Houston (ASU)Cost: ? (NCHRP 1Cost: ? (NCHRP 1--37A, ADOT)37A, ADOT)Work Plan:Work Plan:
Phase I Phase I –– Literature ReviewLiterature ReviewPhase II Phase II –– Laboratory TestingLaboratory Testing
Phase I - Literature ReviewMMRR reduces with increased moisture; the reduces with increased moisture; the reduction in modulus is greater for fine reduction in modulus is greater for fine grained materialsgrained materialsRegardless of the model used, a linear Regardless of the model used, a linear relationship is observed when plotting: relationship is observed when plotting: log(log(MMRR)) versus moistureversus moisture
MR - Moisture Model for Coarse-Grained Materials
0
0.5
1
1.5
2
2.5
-70 -60 -50 -40 -30 -20 -10 0 10 20 30(S - Sopt)%
MR/M
Rop
t
Literature Data
Predicted
MR - Moisture Model for Fine-Grained Materials
0.0
0.5
1.0
1.5
2.0
2.5
-70 -60 -50 -40 -30 -20 -10 0 10 20 30(S - Sopt)%
MR/M
Rop
t
Literature Data
Predicted
MR – Moisture Model
MMRR = Resilient Modulus at = Resilient Modulus at SSMMRoptRopt = Resilient modulus at = Resilient modulus at SSoptopt
a, b, ka, b, kmm = Regression parameters= Regression parametersββ = = lnlnee((--bb//aa) from condition of (0,1) intercept) from condition of (0,1) intercept
( )( )Ropt
SSkEXPaba
R MM optm ⋅= −⋅++−
+β110
MOISTURE ADJUSTMENT FACTOR (FU)
MR = FU*MRopt
( )( )32
110 11
k
a
oct
k
aa
SSkEXPaba
R pppkM optm
+⋅
⋅⋅⋅= −⋅++
−+ τθβ
Combined Effects of Moisture and Stress in ME-PDG
This form was implemented in the METhis form was implemented in the ME--PDG PDG for for ““unfrozenunfrozen”” unbound materialsunbound materialsCalibration/validation of the model with Calibration/validation of the model with laboratory test data was desiredlaboratory test data was desired
MOISTURE ADJUSTMENT FACTOR (FU)
STRESS DEPENDENTMR MODEL
Phase II – Laboratory Testing
Arizona DOT MaterialsArizona DOT Materials4 base materials4 base materials4 4 subgradesubgrade soilssoils
Each material tested at:Each material tested at:3 moisture contents (optimum, soaked and dried)3 moisture contents (optimum, soaked and dried)2 2 compactivecompactive efforts (standard and modified)efforts (standard and modified)2 replicates (minimum)2 replicates (minimum)
Total: 96 tests performed using the Total: 96 tests performed using the NCHRP 1NCHRP 1--28A test protocol28A test protocol
2002
Key FindingsDensity strongly affects the Density strongly affects the MMRR--SSrelationship and should be added as a relationship and should be added as a predictor to the model based on predictor to the model based on SSWhen gravimetric moisture content (When gravimetric moisture content (ww) ) was used instead, the effect of density was used instead, the effect of density was greatly minimizedwas greatly minimizedMR MR –– Moisture models including stress Moisture models including stress dependency (like the one in the MEdependency (like the one in the ME--PDG) PDG) were successfully used to fit the measured were successfully used to fit the measured lab test datalab test data
PVSG (A-2-4, SC) - MR(w-wopt , θ, τoct) Model
n =142, Se/Sy =0.15, R2 = 0.98
1,000
10,000
100,000
1,000,000
1,000 10,000 100,000 1,000,000
Measured Resilient Modulus (psi)
MR Predicted
Line of Equality
Goodness of Fit – Phoenix Valley Subgrade
Unbound Materials Characterization Seminar 18
MR – moisture density effectsPhoenix Valley Subgrade (Theta = 20 psi, Tau = 3psi)
1,000
10,000
100,000
1,000,000
0 2 4 6 8 10 12 14 16 18Moisture Content (%)
StandardModifiedPredicted
wopt weq
Seasonal
GMAB2 (A-1-a, GW) - MR(w-wopt , θ, τoct) Model
n = 254, R2 = 0.90, Se/Sy = 0.32
1,000
10,000
100,000
1,000,000
1,000 10,000 100,000 1,000,000
Measured Resilient Modulus (psi)
MR Predicted
Line of Equality
Goodness of Fit – Gray Mountain Base
ADOT Database of MR Model Parameters
Material ID AASHTO USCS a b k w β k 1 k 2 k 3 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 - - - -
Unbound Materials Characterization Seminar 21
Real Life MR Problem (SH130)
2004
Data
A new highway is being builtA new highway is being builtSubgradeSubgrade material samples are taken material samples are taken every 500 ft along the alignmentevery 500 ft along the alignmentThree samples of similar soil type are Three samples of similar soil type are mixed together into one bulk samplemixed together into one bulk sampleBulk samples are tested in the lab for MBulk samples are tested in the lab for MRR
Data (Cont’d)
2 materials types are identified: A and B2 materials types are identified: A and BThere are 18 bulk samples available for material There are 18 bulk samples available for material type A (500ft*3*18 = 5 miles)type A (500ft*3*18 = 5 miles)There are 26 bulk samples available for material There are 26 bulk samples available for material type B (500ft*3*26 = 7.4 miles)type B (500ft*3*26 = 7.4 miles)MMRR tests have been performed at several tests have been performed at several moisture contents: optimum, optimum +3%, moisture contents: optimum, optimum +3%, optimum optimum ––3%;3%;kkii values have been generated for each Mvalues have been generated for each MRR testtest
Unbound Materials Characterization Seminar
Data (Cont’d)
kkii summary for material Asummary for material A
k0 kd kp k0 kd kp k0 kd kpBulk 1 34,945 -0.269416 0.041374 25,927 -0.424631 0.138661Bulk 2 26,059 -0.358200 0.184400 20,050 -0.642000 0.221400Bulk 3 32,310 -0.463600 0.215000Bulk 4 39,246 -0.452120 0.222780 30,015 -0.553579 0.216564 22,066 -0.769445 0.282913Bulk 5 24,119 -0.475278 0.249000 14,107 -0.687327 0.315109 8,461 -0.842200 0.426167Bulk 6 36,126 -0.456090 0.154673 27,844 -0.727020 0.201938 21,122 -0.925180 0.207083Bulk 7 42,680 -0.570230 0.160843 38,141 -0.778380 0.162280 31,534 -0.763180 0.210047Bulk 8 19,661 -1.019400 0.253963 19,715 -1.072970 0.318132Bulk 9 38,494 -0.696370 0.253942 33,400 -0.765790 0.229967Bulk 10 20,213 -0.429262 0.133289 16,554 -0.889688 0.051060Bulk 11 17,053 -0.391572 0.091538Bulk 12 22,182 -0.597050 0.209439Bulk 13 44,749 -0.440120 0.151803 33,003 -0.486720 0.100738 20,476 -0.828890 0.289046Bulk 14 44,025 -0.444500 0.193159 35,647 -0.531140 0.148053 18,814 -0.789060 0.309538Bulk 15 25,406 -0.532200 0.138999Bulk 16 29,930 -0.661800 0.138978 49,448 -0.611131 0.109068 29,930 -0.661800 0.138978Bulk 17 76,309 -0.661042 0.197695 80,426 -0.668775 0.024432 43,192 -0.824336 0.107594Bulk 18 21,844 -0.566054 0.319420 13,508 -0.547370 0.394921 11,212 -0.596271 0.377779
Material Aki values
Dry Opt Wet
Unbound Materials Characterization Seminar
Data (Cont’d)kkii summary for material Bsummary for material B
k0 kd kp k0 kd kp k0 kd kpBulk 1 23,365 -0.348650 0.004737 20,368 -0.320091 0.073256Bulk 2 16,217 -0.258300 0.112100Bulk 3 30,631 -0.364700 0.220470Bulk 4 24,762 -0.516916 0.141701Bulk 5 22,528 -0.629430 0.183921 23,968 -0.711080 0.140339Bulk 6 36,602 -0.477410 0.206208 28,487 -0.462120 0.128810 36,043 -0.884910 0.182773Bulk 7 27,111 -0.414694 0.181205 19,836 -0.443360 0.183849 23,618 -0.501437 0.142133Bulk 8 19,666 -0.597631 0.166676 20,570 -0.426370 0.127696 18,922 -0.499500 0.163446Bulk 9 27,696 -0.549000 0.199591 28,934 -0.538650 0.156857Bulk 10 24,063 -0.469080 0.270056 25,089 -0.420700 0.092194 22,614 -0.588240 0.165751Bulk 11 43,466 -0.784977 0.092654Bulk 12 19,722 -0.412176 0.084508Bulk 13 17,208 -0.349799 0.021935 19,500 -0.461701 0.032617Bulk 14 37,116 -0.367548 0.058294 19,200 -0.268777 0.043610Bulk 15 21,791 -0.478329 0.000844Bulk 16 16,217 -0.258268 0.112075 20,748 -0.316450 0.108480Bulk 17 18,788 -0.280171 0.020924 36,440 -0.557328 0.064253Bulk 18 16,702 -0.237235 0.101201 20,522 -0.157984 0.010217Bulk 19 16,603 -0.220614 0.007347Bulk 20 19,712 -0.210542 0.054659Bulk 21 17,178 -0.386660 0.073877 15,272 -0.458540 0.094120Bulk 22 32,566 -0.652312 0.069370 24,603 -0.510339 0.091400Bulk 23 39,158 -0.388730 0.014278 29,345 -0.320550 0.203700Bulk 24 46,102 -0.578312 0.118676 32,503 -0.614743 0.086852 29,304 -0.868461 0.186478Bulk 25 65,680 -0.501018 0.236424 39,559 -0.454563 0.119634 37,225 -0.538610 0.108260Bulk 26 30,425 -0.531227 0.153134 35,397 -0.706704 0.168594 22,578 -0.577760 0.118513
MaterialBki values
Dry Opt Wet
Calculate the Effective MR (AASHTO)
Problem
Solution
What is What is MMreffreff
MMReffReff = = Sum(dfSum(dfii**MMRiRi)/Sum(df)/Sum(dfii))We need We need MMRiRi
Month MR Damage Factor (df)=1.18*10^8*MR^-2.32
JanFebMarAprMayJunJulAugSepOctNovDec
Solution
MMRiRi are a function of moisture and stressare a function of moisture and stressFor simplification, assume:For simplification, assume:
6 months @ optimum 6 months @ optimum –– 3% (DRY)3% (DRY)4 months @ optimum (OPT)4 months @ optimum (OPT)3 months @ optimum + 3% (WET)3 months @ optimum + 3% (WET)
Three different states of stress are needed Three different states of stress are needed corresponding to Dry, Opt and Wet conditionscorresponding to Dry, Opt and Wet conditionsFor each of the three cases, go through the For each of the three cases, go through the iterative procedure to find out the state of iterative procedure to find out the state of stress corresponding to the average Mstress corresponding to the average MRR valuevalue
(1) Choose locations within layers
(2) Assume MR0
values
(3) Calculate stressesat the locations of
interest
(4) Calculate MRcalc as
a function of stressesand ki(5) Compare MR
calc from Step (4) with MR
0 from Step (2)
(6)
•IF: the two values compared are not close
enough; continue by changing the assumed
value until the assumed and calculated values meet the convergence
criteria
•ELSE: STOP and use the estimated state of
stress to predict the MR value in the subgrade
Linear Elastic Analysis
Iterative ProcessIterative Process
Solution
Calculate Calculate MMReffReff using the average using the average MMRdryRdry, , MMRoptRopt, , MMRwetRwet values:values:MMReffReff = 12,458 psi= 12,458 psiDesign Requirement Design Requirement MMReffReff > 7,000 psi> 7,000 psiAre we meeting the design requirement?Are we meeting the design requirement?Plot the data:Plot the data:
Material A
0
10,000
20,000
30,000
40,000
10 13 16 19 22 25
Moisture Content (%)
DRYOPTWETDry AverageOpt AverageWet Average
Sd S3Dry 5.4 2.2Opt 4.9 2.0Wet 4.2 1.8
MReff Quiz
What is the probability that:What is the probability that:
(a) (a) MMReffReff > 12,485 psi ?> 12,485 psi ?
(b) (b) MMReffReff > 7,000 psi ?> 7,000 psi ?
What is the probability that:What is the probability that:
(a) (a) MMReffReff > 12,485 psi ? > 12,485 psi ?
(b) (b) MMReffReff > 7,000 psi ?> 7,000 psi ?
Answer
50%
> 50%, all we know
Is that satisfactory?
Solution
Probability of FailureProbability of Failure MR
Mrave, SMr
Mrdesign
Probability of Failure
Solution
MMRR VariabilityVariabilityLow Variability
MR
Mrave, SMr
Mrdesign
High Variability
Material A
0
10,000
20,000
30,000
40,000
10 13 16 19 22 25
Moisture Content (%)
DRYOPTWETDry AverageOpt AverageWet Average
Sd S3Dry 5.4 2.2Opt 4.9 2.0Wet 4.2 1.8
Material A
0
0.00002
0.00004
0.00006
0.00008
0.0001
0.00012
0.00014
0 10,000 20,000 30,000 40,000
Resilient Modulus
DRYOPTWET
Solution
Calculate for each case (Dry, Opt, Wet) a Calculate for each case (Dry, Opt, Wet) a MMRR value corresponding to 85% reliability value corresponding to 85% reliability (15% probability of failure): (15% probability of failure):
Modified MR Design (psi) 12,800 7,600 5,000z -1.02534 -1.03046 -1.04696
Probability that MR is greater than MR design 85% 85% 85%uf 0.03 0.12 0.31 Effective Modulus
MR*uf 447 890 1,546 7,200Months 6 4 2 0.11
Average MC 12.9 15.7 18.8
Material A
0
10,000
20,000
30,000
40,000
10 13 16 19 22 25
Moisture Content (%)
DRYOPTWETDry AverageOpt AverageWet Average85% Reliability
Sd S3Dry 5.4 2.2Opt 4.9 2.0Wet 4.2 1.8
Sources of VariabilityWithin lab:Within lab:
MaterialMaterialState of stressState of stressMoistureMoistureDensityDensity
Between labs:Between labs:OperatorOperatorCompactionCompactionMoisture/Density Moisture/Density conditioningconditioningTest methodTest methodData reductionData reductionRegression model Regression model and definition of the and definition of the errorerror
SH130 Limited MR Variability Study
2 labs2 labs3 materials tested wet, optimum, dry3 materials tested wet, optimum, dry4 models4 models
Within Lab
Lab A: Average CV = 5%, max CV = 9%Lab A: Average CV = 5%, max CV = 9%Lab B: Average CV = 12%, max CV = 23%Lab B: Average CV = 12%, max CV = 23%
Findings
Lab B had some issues with data at low Lab B had some issues with data at low stress levels (low strain levels)stress levels (low strain levels)The differences between labs were The differences between labs were significant, especially for the wet and dry significant, especially for the wet and dry conditionsconditionsThe measured CV is a function of the The measured CV is a function of the predictive model usedpredictive model used
Measures of variability
Coefficient of variation of:Coefficient of variation of:MR in arithmetic space MR in arithmetic space –– most usedmost usedMR in logarithmic space?MR in logarithmic space?Resilient strain in arithmetic space?Resilient strain in arithmetic space?Layer thickness?Layer thickness?
The higher the modulus, the less The higher the modulus, the less important variability is for designimportant variability is for design
Conclusions
““TrueTrue”” variability in soil and aggregate variability in soil and aggregate properties is real and expected. properties is real and expected. Probabilistic methods can be used to Probabilistic methods can be used to handle this variability when working on handle this variability when working on real design problems.real design problems.
Conclusions (Continued)
““ArtificialArtificial”” variability can be minimized by:variability can be minimized by:Test system calibration and verification with Test system calibration and verification with synthetic test specimenssynthetic test specimensComparing Comparing ““apples to applesapples to apples”” i.e. taking into i.e. taking into account that Maccount that MRR is a function of: stress, moisture is a function of: stress, moisture and densityand densityFollowing the same procedures for: Specimen Following the same procedures for: Specimen preparation, Test method, Data reduction, preparation, Test method, Data reduction, Regression analysis and predictive modelRegression analysis and predictive model
