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Material StrengthMaterial Strength
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Subgrade Strength/StiffnessSubgrade Strength/Stiffness
• California Bearing Ratio (CBR)
• Resistance Value (R-Value)
• Resilient Modulus (MR)
• Modulus of Subgrade Reaction (K)
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California Bearing Ratio (CBR)California 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.
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California Bearing Ratio (CBR)California Bearing Ratio (CBR)
• Used in Pavement Design
• Performed on unbound layers: Subgrade layer, Subbase layer base layer.
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California Bearing Ratio (CBR)California Bearing Ratio (CBR)
• Load a piston (area = 3 in2) at a constant rate (0.05 in/min)
• Record Load every 0.1 in penetration
• Total penetration not to exceed 0.5 in.
• Draw Load-Penetration Curve.
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CBR Test EquipmentCBR Test Equipment
Soaking Samples for 4 daysmeasure swelling and CBRTypical Testing Machine
Surcharge Weights
•Surcharge weights are added during testing and soaking to:
• Simulate the weight of pavement.
•Prevent heaving up around the piston.
Piston
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CBR CalculationCBR Calculation
Rocks Standard of Stressor Load
Soil of Stressor Load100CBR
Calculate CBR at 0.1 in (25 mm) and 0.2 in (50 mm) deformation then use the Maximum value as the design CBR.
Penetration 0.1” (2.5 mm) 0.2” (5.0 mm)
Load of Standard Rocks (Ib) 3000 4500
Load of Standard Rocks (kN) 13.24 19.96
Stress of Standard Rocks (KPa) 6895 10342
Stress of Standard Rocks (psi) 1000 1500
Loads and Stresses Corresponding to 0.1 and 0.2 inches Penetration for the Standard Rocks
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CBR CurvesCBR Curves
0
100
200
300
400
500
600
700
800
0 0.1 0.2 0.3 0.4 0.5 0.6
Penetration (in)
Lo
ad
(Ib
)
Wrong Curve
Standard Curve
Need correction
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CBR Curve CorrectionCBR Curve Correction
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4 0.5 0.6
Penetration (in)
Lo
ad
(Ib
)
0.0 0.1 0.2
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Influence of Moisture upon CBRInfluence of Moisture upon CBR
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4 0.5 0.6
Moisture Content
CB
R
Use relevant value of moisture content when assessing soils
under laboratory conditions.
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Resistance Value (R-Value)Resistance Value (R-Value)
• Developed by California Division of Highways: 1940s
• Measures frictional resistance of granular material to deformation
• Uses the Hveem Stabilometer
• Tests material in a saturated condition (worst case scenario
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Resistance Value (R-Value)Resistance Value (R-Value)
Stabilometer
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Ph
Pv
R-value Test (ASTM D2844)R-value Test (ASTM D2844)
1)1)(5.2
(
100100
2
h
v
PP
D
RPv = applied vertical pressure (typically 160 psi)
Ph = transmitted horizontal pressure
D2 = displacement of stabilometer fluid necessary to increase horizontal pressure from 5 to 100 psi.
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Typical R-Value RangesTypical R-Value Ranges
General Soil Type USCS Soil Type R-Value Range
Clean gravelsGW
30 – 80GP
Gravels with finesGM
30 – 80GC
Clean sandsSW
10 – 50SP
Sands with finesSM
20 – 60SC
Silts and clays
ML 5 – 20
CL 5 – 20
OL < 7
MH 5 – 20
CH 5 – 20
OH < 7
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Resilient Modulus (MResilient Modulus (MRR))
• Measures “stiffness” of the material under repeated load.
• Determines the load carrying capacity of the material.
• Used for HMA as well as unbound materials
• Uses a repeated load triaxial test.
• Used in most modern methods of pavement design.
r
RM
31
strain eRecoverabl
stressDeviator
1
3
2
3
1
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Triaxial Test EquipmentTriaxial Test Equipment
Inside Rods
Load Cell
ChamberSoil Specimen
Bottom Platen
Top Platen
Frame
External LVDTLoading Piston
Cell Pressure Inlet
LVDT Clamp LVDT
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Typical Stress Strain Response During one Typical Stress Strain Response During one Loading CycleLoading Cycle
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.0 0.5 1.0 1.5
Time (sec)
Str
ess
(psi
)
0.000
0.004
0.008
0.012
0.016
0.0 0.5 1.0 1.5
Time (sec)
Str
ain
(in
/in
)Stress vs. Time
Strain vs. Time
p
r
DwellLoading
Unloading
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Resilient ModulusResilient Modulus
Animation from University of Tokyo Geotechnical Engineering Lab
2 14 16 2 14 16
load rest Time
Load
r = L/L
ASU Advanced Pavement Laboratory
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Nonlinear Material Behavior:Nonlinear Material Behavior:Coarse-Grained SoilsCoarse-Grained Soils
• Bulk stress: = 1 + 2 + 3
• K1, K2 are material constants K1 > 0
K2 ≥ 0 (stress-stiffening)
log MR
log
log MR
log oct
K1
K2
21
KR KM
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Nonlinear Material Behavior:Nonlinear Material Behavior:Fine-Grained SoilsFine-Grained Soils
• Octahedral shear stress:
• K3, K4 are material constants K3 > 0
K4 ≤ 0 (stress-softening)
K3K4
log MR
log oct
43
KoctR KM
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Combined Stress Dependence of MCombined Stress Dependence of MRR
(NCHRP 1-37A)
Bulk (Confining) Stress
• Stiffening term (k2 > 0)
• Dominates for coarse granular soils (base, subbase)
Shear (Deviatoric) Stress
• Softening Term (k3 < 0)
• Dominates for fine-grained soils (subgrade)
32
11
k
a
octk
aaR PP
pkM
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Effect of Stress on MEffect of Stress on MRR
log MR
log
log MR
log oct
Bulk StressBulk Stress Stiffening Stiffening Shear StressShear Stress Softening Softening
= 1 + 2 + 3
oct = Octahedral shear stress = I = Bulk stress = First stress invariant
Coarse Materials Fine Materials
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Effect of Moisture/Density on MEffect of Moisture/Density on MRR
log MR
S dry
log MR
MoistureMoisture Softening Softening DensityDensity Stiffening Stiffening
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CorrelationsCorrelations
• Conversions between CBR, R-value, MR
• Important points: No direct correlation Each test measures a fundamentally different property Developed correlations are only for limited data sets
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Correlations (CBR Correlations (CBR M MRR))
CBRM R 1500Origin: Heukelom and Klomp (1962)Limitation: Fine-grained non-expansive soils with soaked CBR 10
64.02555 CBRM R Origin: NCHRP 1-37A – Mechanistic Design GuideLimitation: not stated
Units: CBR %
MR, psi
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CorrelationsCorrelations
555
11551500ValueR
CBR
Origin: HDOTLimitation: Fine-grained non-expansive soils with soaked CBR 8
Value R5551000 RM
Origin: 1993 AASHTO GuideLimitation: Fine-grained non-expansive soils with R 20
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Correlation ExampleCorrelation Example
MR vs. R-value for some Washington State soils
MR
R-Value
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50 6040302015108654321.5
1 2 3 4 5 10 15 20 40 60 80 100
1008060403020151054321
Poor Medium Good ExcellentSubgrade Soil Category
Unified SoilClassification
AASHTO SoilClassification
Mr (ksi)
CBR (%)
R- Value
A-1-b
A-2-7A-3
A-4A-5
A-6
A-7-6
CHMH
CLML
SW
GMGC
GP - GMGP - GC
GW - GM
GW - GCGP
GW
SMSC
SP - SM
SP - SC
SW - SM
SW - SCSP
A-1-a
A-7-5
A-2-5A-2-4
A-2-6
50 6040302015108654321.5
1 2 3 4 5 10 15 20 40 60 80 100
1008060403020151054321
Poor Medium Good ExcellentSubgrade Soil Category
Unified SoilClassification
AASHTO SoilClassification
Mr (ksi)
CBR (%)
R- Value
A-1-b
A-2-7A-3
A-4A-5
A-6
A-7-6
CHMH
CLML
SW
GMGC
GP - GMGP - GC
GW - GM
GW - GCGP
GW
SMSC
SP - SM
SP - SC
SW - SM
SW - SCSP
A-1-a
A-7-5
A-2-5A-2-4
A-2-6
MMR R CorrelationsCorrelations
w/ Index w/ Index Properties andProperties and
Soil ClassificationSoil Classification
(NCHRP 1-37A)
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Plate Loading TestPlate Loading Test
• Measure 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.
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Plate Loading TestPlate Loading Test
Plate Loading TestPlate Loading Test Schematic
Reaction
Pressure Gauge
3 Deflection Dials
Reaction for Dial
Hydraulic Jack
30″ Plate
24″ Plate18″ Plate
Tested Layer
12″ Plate
Reaction
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Effect of Plate SizeEffect of Plate Size
p = n + m (P/A)
p = Unit load (stress)
n, m = Empirical values obtained by test
P/A = Perimeter over area
n
m
P/A
p
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Modulus of Subgrade Reaction (k)Modulus of Subgrade Reaction (k)
K = modulus of subgrade reaction
P = unit load on the plate (stress) (psi)
= deflection of the plate (in)
• For design use stress P = 10 psi (68.95 kN/m2)
Δ
PK
•Required for rigid pavement design.
Str
ess
, psi
10 psi
Deformation, in
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Corrections for KCorrections for K
• Correction due to saturation (worst case scenario).
• Correction due to bending of the plates.
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Correction Due to saturationCorrection Due to saturation
us
us KK
Ks = modulus of subgrade reaction corrected for saturation
Ku = field modulus of subgrade reaction
u/s = ratio of the deflection in the unsaturated and saturated tests
Deformation
Str
ess 10 psi
u s
10 psiS
tres
s
Deformation
Saturated Condition
Field Condition
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Correction due to Bending of the PlatesCorrection 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)
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Basic Plate Loading Test TypesBasic Plate Loading Test Types
Deformation
Str
ess
Time
Def
orm
atio
n
Rat
e
Static Load
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Basic Plate Loading Test Types Basic Plate Loading Test Types
DeformationS
tres
s
Deformation
Str
ess
Accumulated Plastic Deformation
Elastic Rebound
Repeated Load
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