2009 TRB Workshop
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The document summarizes a resilient modulus model developed for unbound pavement layers that accounts for the effects of moisture, stress state, and freezing/thawing. Key aspects include: - A "universal" resilient modulus model relates MR to confining pressure, deviator stress, and moisture. - MR decreases nonlinearly with increased moisture content according to sigmoid curves developed for coarse-grained and fine-grained materials. - Freezing/thawing is modeled using adjustment factors based on material type and season to account for very high or reduced modulus. - The model is implemented in the Mechanistic-Empirical Pavement Design Guide to predict seasonal variations in MR at the node and layer
2009 TRB Workshop
- 1. Resilient Modulus Model 2009 TRB Annual Meeting Workshop Environmental Effects in the ME-PDG January 11, 2009 Dragos Andrei, Ph.D., P.E.
- 2. Stress Dependent MR Model A harmonized resilient modulus test method was developed at the University of Maryland, under NCHRP project 1-28A 30 MR tests were performed on 6 materials from different sources: FHWA-ALF, MnRoad, USACE-CRREL. Data was analyzed with 14 models including the classical “k1-k2”models, the “Universal” model and the “SHRP- Superpave” MR model 1999
- 3. “Universal” MR Model Applicable to both coarse-grained and fine-grained materials Includes both the volumetric and shear components of stress Normalization by pa makes ki parameters dimensionless k2 k3 ⎛ θ ⎞ ⎛ τ oct ⎞ M R = k1 ⋅ pa ⋅ ⎜ ⎟ ⋅ ⎜ ⎜p ⎟ ⎜ p ⎟ ⎟ ⎝ a⎠ ⎝ a ⎠
- 4. Variations of the “Universal” Model Use semi-log instead of log-log form Replace θ with (θ – 3k6) or σ3 Replace τoct/pa with (τoct/pa + 1) or (σcyc/pa+1) Replace τoct/pa with (τoct/pa + k7), where k7>1 k2 k3 ⎛ θ − 3k6 ⎞ ⎛ τ oct ⎞ M R = k1 ⋅ pa ⋅ ⎜ ⎜ p ⎟ ⎜ p ⎟ ⋅⎜ + k7 ⎟ ⎟ ⎝ a ⎠ ⎝ a ⎠
- 5. Key Findings of the 1-28A Study 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 Models using θ and τoct were generally more accurate than those using σ3 and σcyc The higher the number of ki parameters – the better the goodness of fit
- 6. Model Selection for Implementation in ME-PDG 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 ⎠
- 7. MR - Moisture Effects Literature review performed at Arizona State University in an effort to quantify the effect of changes in moisture and density on MR Data retrieved from published papers: Li and Selig, Drumm et al, Jin et al, Jones and Witczak, Rada and Witczak, Santha, CRREL, Muhanna et al. 2000
- 8. Key Findings of ASU Study 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 Some researchers used S while others preferred w The compactive energy (standard or modified) was not always specified
- 9. Analysis Use approach from Li and Selig paper to normalize MR, w and S with respect to values at optimum and to plot change in MR versus change in moisture Use the literature models to create MR- moisture data points Divide materials into: Coarse-Grained and Fine-Grained Use sigmoid model form to fit the “data”
- 10. 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)%
- 11. 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)%
- 12. 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
- 13. a, b, km Values for ME-PDG Coarse-Grained: a = -0.3123 b = 0.3 (maximum MR/MRopt ratio of 2) km = 6.8157 Fine-Grained: a = -0.5934 b = 0.4 (maximum MR/MRopt ratio of 2.5) km = 6.1324
- 14. MRopt Estimates in the ME-PDG Several options available: USCS Classification AASHTO Classification CBR R-Value AASHTO Structural Layer Coefficient Gradation and Atterberg Limits
- 15. 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 ⋅ k1 ⋅ pa ⋅ ⎜ ⎟ ⋅ ⎜ ⎜ p ⎟ ⎜ p + 1⎟⎟ ⎝ 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
- 16. Moisture Variation in Unbound Pavement Layers Compaction – optimum moisture content FU With time – equilibrium moisture content Seasonal – variations around equilibrium Freezing – soil becomes very stiff ? Thawing – temporary softening below equilibrium stiffness
- 17. Freeze-Thaw Effects: Freezing From Literature: MR = 2,500,000 psi for non-plastic materials MR = 1,000,000 psi for plastic materials Model Form: MR = FF*MRopt FF = Adjustment factor for frozen materials 2001
- 18. Freeze-Thaw Effects: Thawing Modulus Reduction Factor 0.40 … 0.85 as a function of plasticity index and % fines (wPI) Recovery Period 90 … 150 days as a function of wPI Model Form: MR = FR*MRopt FR = Adjustment factor for thawing (recovering) materials
- 19. Example M innesota 100 FROZEN 10 Fenv OPTIMUM TR 1 EQUILIBRIUM EQUILIBRIUM RECOVERY 0.1 08/23/96 12/01/96 03/11/97 06/19/97 09/27/97 Tim e
- 20. From NODE to LAYER … Tim e (days) Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 SPRING 1 AC ANALOGY 2 3 FF FF FF FF FF FF FF FF FR FR FR FR FR FR BASE 4 FF FF FF FF FF FF FF FF FR FR FR FR FR FR 5 FF FF FF FF FF FF FF FR FR FR FR FR FR FR 6 FF FF FF FF FF FF FF FR FR FR FR FR FR FR 7 FF FF FF FF FF FF FF FR FR FR FR FR FR FR 8 FF FF FF FF FF FF FF FR FR FR FR FR FR FR 9 FF FF FF FF FF FF FF FR FR FR FR FR FR FR SUBBASE 10 FF FF FF FF FF FF FF FR FR FR FR FR FR FR 11 FF FF FF FF FF FF FR FR FR FR FR FR FR FR 12 FF FF FR FR FR FR FR FR FR FR FR FR FR FR 13 FF FR FR FR FR FR FR FR FR FR FR FR FR FR 14 FR FR FR FR FR FR FR FR FR FR FR FU FU FU 15 FR FR FR FR FR FR FR FR FR FR FU FU FU FU 16 FR FR FR FR FR FR FR FR FU FU FU FU FU FU 17 FR FR FR FR FR FU FU FU FU FU FU FU FU FU SUBGRADE 18 FR FR FU FU FU FU FU FU FU FU FU FU FU FU 19 FU FU FU FU FU FU FU FU FU FU FU FU FU FU 20 FU FU FU FU FU FU FU FU FU FU FU FU FU FU 21 FU FU FU FU FU FU FU FU FU FU FU FU FU FU LEGEND: 22 FU FU FU FU FU FU FU FU FU FU FU FU FU FU FROZEN 23 FU FU FU FU FU FU FU FU FU FU FU FU FU FU RECOVERING 24 FU FU FU FU FU FU FU FU FU FU FU FU FU FU UNFROZEN
- 21. Fenv = Layer Adjustment Factor Principle: Find Fenv corresponding to an equivalent (composite) modulus that produces the same average displacement over the total thickness of the layer/sublayer for the considered analysis period (1 month or 2 weeks). t total ⋅ htotal Fenv = ⎛ n ⎛ hnode t total ⎞⎞ ∑ ⎜ node =1 ⎜ F ⎜ ∑ ⎜ ⎟⎟ ⎟⎟ t =1 ⎝ ⎝ node ,time ⎠⎠ hnode = Length between mid-point nodes htotal = Total height of the considered layer/sublayer ttotal = The desired time period (either a two-week period or a month period) Fnode,t = Adjustment factor at a given node and time increment which could be FF , FR , or FU
- 22. Fenv Calculation Example Tim e (days) Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3 50 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 BASE 4 50 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 F env = 1.45 5 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.7 6 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.7 7 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.7 8 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.7 9 75 75 75 75 75 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 SUBBASE 10 75 75 75 75 75 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 F env = 0.92 11 75 75 75 75 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 12 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 13 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 LEGEND: 14 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1 1 1 FRO ZEN 15 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1 1 1 1 RECOVERING 16 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1 1 1 1 1 1 UNFRO ZEN MR (layer, analysis period) = Fenv*MRopt All calculations done in EICM !
- 23. ADOT MR-Moisture Lab Study 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
- 24. 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 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
- 25. Effect of Density (Compactive Energy) Phoenix Valley Subgrade (A-2-4, SC), Hot Conditions 1,000,000 Resilient Modulus (psi) 100,000 Standard Measured Standard Sigmoid 10,000 Modified Measured Modified Sigmoid 1,000 0.0 20.0 40.0 60.0 80.0 100.0 Degree of Saturation (%)
- 26. Using Moisture Content Phoenix Valley Subgrade (A-2-4, SC), Hot Conditions 1,000,000 Standard Modified Predicted Resilient Modulus (psi) 100,000 10,000 1,000 0 2 4 6 8 10 12 14 16 18 Moisture Content (%)
- 27. 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)
- 28. 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)
- 29. Fu for ADOT Base Materials Grey Mountain Base (A-1-a, GW) 100 10 MR/MRopt 1 0.1 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 wi - wopt (%)
- 30. Fu for ADOT A-2/SC Subgrade Soils All A-2 Subgrades, M R - Moisture Model 2 n = 36, R = 0.96, Se/Sy = 0.20 100 PVSG (A-2-4), PI=9.9, p200=21.6 FCSG (A-2-6), PI=17.2, p200=31.5 SCSG (A-2-4), PI=12.1, p200=25 Predicted 10 1 0.1 -12 -10 -8 -6 -4 -2 0 2 4 6 wi - wopt (%)
- 31. 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 - - - -
- 32. Final Remarks Moisture, density and state of stress all affect MR and should be included in a M-E predictive methodology Changes in moisture will trigger significant changes in MR, especially for fine-grained materials Coarse-grained materials are especially affected by changes in the state of stress
- 33. Final Remarks (Cont’d) The MR-Moisture material models implemented in the ME-PDG were verified through a limited laboratory testing study performed at ASU Agencies could engage in similar studies to develop a database of material properties for typical unbound pavement materials used on highway construction projects.