2Subgrade Strength/Stiffness California Bearing Ratio (CBR)Resistance Value (R-Value)Resilient Modulus (MR)Modulus of Subgrade Reaction (K)Each measure a different thing
3California Bearing Ratio (CBR) CBR: California Bearing Ratio Test.Developed by The California State Highways Department in 1930.Resistance of the material to uniaxial penetration.Measure of soil shear strength relative to standard crushed stone material.Field and laboratory test.
4California Bearing Ratio (CBR) Used in Pavement DesignPerformed on unbound layers:Subgrade layer,Subbase layerbase layer.
5California Bearing Ratio (CBR) Load a piston (area = 3 in2) at a constant rate (0.05 in/min)Record Load every 0.1 in penetrationTotal penetration not to exceed 0.5 in.Draw Load-Penetration Curve.
6CBR Test Equipment Soaking Samples for 4 days measure swelling and CBR PistonSurcharge WeightsAllow soaked samples to drain water for 15 min. then perform the CBR test. Min. surcharge weight = 10 lbSurcharge weights are added during testing and soaking to:Simulate the weight of pavement.Prevent heaving up around the piston.Soaking Samples for 4 daysmeasure swelling and CBRTypical Testing Machine
7CBR CalculationLoads and Stresses Corresponding to 0.1 and 0.2 inches Penetration for the Standard RocksPenetration0.1” (2.5 mm)0.2” (5.0 mm)Load of Standard Rocks (Ib)30004500Load of Standard Rocks (kN)13.2419.96Stress of Standard Rocks (KPa)689510342Stress of Standard Rocks (psi)10001500Calculate CBR at 0.1 in (25 mm) and 0.2 in (50 mm) deformation then use the Maximum value as the design CBR.
8CBR CurvesNeed correction because the piston is not exactly perpendicular with the soil sample.
10Influence of Moisture upon CBR CBR is evaluated at equilibrium moisture conditionUse relevant value of moisture content when assessing soils under laboratory conditions.
11Resistance Value (R-Value) Developed by California Division of Highways: 1940sMeasures frictional resistance of granular material to deformationUses the Hveem StabilometerTests material in a saturated condition (worst case scenario
13R-value Test (ASTM D2844) Pv Ph Pv = applied vertical pressure (typically 160 psi)Ph = transmitted horizontal pressureD2 = displacement of stabilometer fluid necessary to increase horizontal pressure from 5 to 100 psi.PvPh
14Typical R-Value Ranges General Soil TypeUSCS Soil TypeR-Value RangeClean gravelsGW30 – 80GPGravels with finesGMGCClean sandsSW10 – 50SPSands with finesSM20 – 60SCSilts and claysML5 – 20CLOL< 7MHCHOH
15Resilient Modulus (MR) Measures “stiffness” of the material under repeated load.Determines the load carrying capacity of the material.Used for HMA as well as unbound materialsUses a repeated load triaxial test.Used in most modern methods of pavement design.s1s3s3s2s1
17Typical Stress Strain Response During one Loading Cycle DwellUnloadingStrain vs. TimeeperStress vs. TimeLinearity: stress strain relationship, Viscosity: time dependency of strain under constant stress, Plastic or elastic: degree to which the material can rebound or recover strain after stress removal.
18Resilient Modulus er = DL/L load rest Time Load 21416loadrestTimeLoader = DL/LASU Advanced Pavement LaboratoryAnimation from University of Tokyo Geotechnical Engineering Lab
19Nonlinear Material Behavior: Coarse-Grained Soils Bulk stress: q = s1 + s2 + s3K1, K2 are material constantsK1 > 0K2 ≥ 0 (stress-stiffening)K2K1
20Nonlinear Material Behavior: Fine-Grained Soils Octahedral shear stress:K3, K4 are material constantsK3 > 0K4 ≤ 0 (stress-softening)log MRK3K4logtoct
21Combined Stress Dependence of MR (NCHRP 1-37A)Bulk (Confining) StressStiffening term (k2 > 0)Dominates for coarse granular soils (base, subbase)Shear (Deviatoric) StressSoftening Term (k3 < 0)Dominates for fine-grained soils (subgrade)
22Bulk Stress Stiffening Shear Stress Softening Effect of Stress on MRCoarse MaterialsFine MaterialsBulk Stress StiffeningShear Stress Softeningq = s1 + s2 + s3q = I = Bulk stress = First stress invarianttoct = Octahedral shear stress
23Effect of Moisture/Density on MR Moisture SofteningDensity Stiffening
24MR Model Including Moisture and Density S = degree of saturationd= dry unit weightkS, k= regression coefficientsa,b = constants (function of soil type)Pa = atmospheric pressure(NCHRP 1-37A)
25Correlations Conversions between CBR, R-value, MR Important points: No direct correlationEach test measures a fundamentally different propertyDeveloped correlations are only for limited data setsDirect correlation is like centigrade to farenheit, or liters to gallonsCBR = strength and resistance to penetrationR-value = frictional resistance to permanent deformationMR = stiffness or recoverable elastic movement
26Correlations (CBR MR) Origin: Heukelom and Klomp (1962)Limitation: Fine-grained non-expansive soils with soaked CBR 10Origin: NCHRP 1-37A – Mechanistic Design GuideLimitation: not statedUnits: CBR %MR, psi
27Correlations Origin: HDOT Limitation: Fine-grained non-expansive soils with soaked CBR 8Origin: 1993 AASHTO GuideLimitation: Fine-grained non-expansive soils with R 20
28Correlation Example MR R-Value MR vs. R-value for some Washington State soilsMRR-Value
29MR Correlations w/ Index Properties and Soil Classification (NCHRP 1-37A)
32Plate Loading TestMeasure supporting power of subgrades, subases, bases and a complete pavement.Field test.Data from the test are applicable for design of both flexible and rigid pavements.Results might need some corrections.
33Plate Loading Test Plate Loading Test Schematic Plate Loading Test ReactionReactionPressure GaugeHydraulic Jack12″ f Plate3 Deflection Dials18″ f Plate24″ f PlateReaction for Dial30″ f PlateTo minimize bending, series of plates are usedApply load through the hydraulic jack and the reaction beam (use heavy equipment), EX: loaderMeasure the deflection of the plates at at least three pointsDraw the load deflection relationshipTested LayerPlate Loading Test SchematicPlate Loading Test
34Effect of Plate Size p = n + m (P/A) p m n P/A p = Unit load (stress) n, m = Empirical values obtained by testP/A = Perimeter over areapTo determine m, n tests must be made on each soil using two different sizes of bearing plates using same deflectionmnP/A
35Modulus of Subgrade Reaction (k) Required for rigid pavement design.Stress , psi10 psiDK = modulus of subgrade reactionP = unit load on the plate (stress) (psi)D = deflection of the plate (in)For design use stress P = 10 psi (68.95 kN/m2)Deformation, in
36Corrections for K Correction due to saturation (worst case scenario). Correction due to bending of the plates.
37Correction Due to saturation Ks = modulus of subgrade reaction corrected for saturationKu = field modulus of subgrade reactionDu/Ds = ratio of the deflection in the unsaturated and saturated testsField ConditionSaturated ConditionStress10 psiDu10 psiStressDeformationRun laboratory consolidation or simple compression test on subgrade soil samples at both the field moisture content and dry density as well as saturated condition. Determine the ratio of the measured deflection in both tests corresponding to 10 psiDsDeformation
38Correction due to Bending of the Plates Some bending of the plates might occur When materials of high modulus are tested.Use chart for correction of k for plate bending.K (pci)Kcorrected (pci)
39Basic Plate Loading Test Types Deformation RateStressDeformationTimeStatic LoadStatic Load