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Material Strength
Subgrade Strength/Stiffness
• California Bearing Ratio (CBR)
• Resistance Value (R-Value)
• Resilient Modulus (MR)
• Modulus of Subgrade Reaction (K)
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.
California Bearing Ratio (CBR)
• Used in Pavement Design
• Performed on unbound layers:



Subgrade layer,
Subbase layer
base layer.
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.
CBR Test Equipment
Piston
Surcharge
Weights
•Surcharge weights are added
during testing and soaking to:
• Simulate the weight of
pavement.
Typical Testing Machine
•Prevent heaving up
around the piston.
Soaking Samples for 4 days
measure swelling and CBR
CBR Calculation
Load or Stress of Soil


CBR  100 

 Load or Stress of Standard Rocks 
Loads and Stresses Corresponding to 0.1 and 0.2 inches
Penetration for the Standard Rocks
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
Penetration
Calculate CBR at 0.1 in (25 mm) and 0.2 in (50 mm) deformation
then use the Maximum value as the design CBR.
CBR Curves
800
700
Load (Ib)
600
500
400
300
Wrong Curve
Standard Curve
Need correction
200
100
0
0
0.1
0.2
0.3
0.4
Penetration (in)
0.5
0.6
CBR Curve Correction
700
600
Load (Ib)
500
400
300
200
100
0
0
0.1
0.0
0.2
0.1
0.3
0.4
0.2 Penetration (in)
0.5
0.6
Influence of Moisture upon CBR
700
600
CBR
500
400
300
200
100
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Moisture Content
Use relevant value of moisture content when assessing soils
under laboratory conditions.
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
Resistance Value (R-Value)
Stabilometer
R-value Test (ASTM D2844)
100
R  100 
2.5 Pv
( )(  1)  1
D2 Ph
Pv
Pv = applied
vertical pressure
(typically 160 psi)
Ph = transmitted
horizontal pressure
Ph
D2 = displacement
of stabilometer
fluid necessary to
increase horizontal
pressure from 5 to
100 psi.
Typical R-Value Ranges
General Soil Type
Clean gravels
Gravels with fines
Clean sands
Sands with fines
Silts and clays
USCS Soil Type
GW
GP
GM
GC
SW
SP
SM
SC
R-Value Range
30 – 80
30 – 80
10 – 50
20 – 60
ML
5 – 20
CL
5 – 20
OL
<7
MH
5 – 20
CH
5 – 20
OH
<7
Resilient Modulus (MR)
• Measures “stiffness” of the material under repeated load.
1   3
Deviator stress
MR 

Recoverable strain
r
1
3
3
• Determines the load carrying capacity of the material.
• Used for HMA as well as unbound materials
2
• Uses a repeated load triaxial test.
• Used in most modern methods of pavement design.
1
Triaxial Test Equipment
Loading Piston
External LVDT
Frame
Cell Pressure Inlet
Load Cell
Chamber
Top Platen
Soil Specimen
LVDT
LVDT Clamp
Inside Rods
Bottom Platen
Typical Stress Strain Response During one
Loading Cycle
30.0
Loading
Dwell
20.0
Unloading
15.0
10.0
Strain vs. Time
5.0
0.016
0.0
0.0
0.5
1.0
1.5
0.012
Time (se c)
Stress vs. Time
Strain (in/in)
Stre ss (psi)
25.0
r
0.008
p
0.004
0.000
0.0
0.5
1.0
Time (se c)
1.5
Resilient Modulus
Load
2
14
load
16
2
rest
14
16
Time
r = DL/L
ASU Advanced Pavement Laboratory
Animation from University of Tokyo Geotechnical Engineering Lab
Nonlinear Material Behavior:
Coarse-Grained Soils
MR  K1q
K2
log MR
K2
• Bulk stress: q = 1 + 2 + 3
• K1, K2 are material constants


K1 > 0
K2 ≥ 0 (stress-stiffening)
K1
log q
Nonlinear Material Behavior:
Fine-Grained Soils
MR  K 3 oct
K4
log MR
• Octahedral shear stress:
K3
• K3, K4 are material constants


K3 > 0
K4 ≤ 0 (stress-softening)
K4
log oct
Combined Stress Dependence of MR
q
M R  k1 pa 
 Pa




k2
  oct




1
 P

 a

k3
(NCHRP 1-37A)
Bulk (Confining) Stress
Shear (Deviatoric) Stress
• Stiffening term (k2 > 0)
• Softening Term (k3 < 0)
• Dominates for coarse granular
• Dominates for fine-grained
soils (base, subbase)
soils (subgrade)
Effect of Stress on MR
Coarse Materials
Fine Materials
log MR
log MR
log q
log oct
Bulk Stress  Stiffening
Shear Stress  Softening
q = 1 + 2 + 3
q = I = Bulk stress = First
stress invariant
oct = Octahedral shear stress
Effect of Moisture/Density on MR
log MR
log MR
S
Moisture  Softening
dry
Density  Stiffening
Correlations
• 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
Correlations (CBR  MR)
M R  1500CBR 
Origin: Heukelom and Klomp (1962)
Limitation: Fine-grained non-expansive soils with soaked CBR  10
M R  2555CBR 
0.64
Origin: NCHRP 1-37A – Mechanistic Design Guide
Limitation: not stated
Units: CBR  %
MR,  psi
Correlations
1500CBR   1155
R  Value 
555
Origin: HDOT
Limitation: Fine-grained non-expansive soils with soaked CBR  8
M R  1000  555R Value 
Origin: 1993 AASHTO Guide
Limitation: Fine-grained non-expansive soils with R  20
Correlation Example
MR vs. R-value for some Washington State soils
MR
R-Value
Subgrade Soil
Category
M r (ksi)
Poor
1.5
2
3
R- Value
4
1
CBR (%)
1
2
3
Medium
2
4
5
5
3
6
8
4
10
Good
15
10
5
Excellent
15
10
15
20
20
30
40
40
20
30
40
60
60 80 100
60
A-1-b
A-1-a
A-2-4
A-2-5
A-2-6
A-2-7
A-3
A-4
A-5
AASHTO Soil
Classification
50
A-6
A-7-5
A-7-6
80 100
MR Correlations
w/ Index
Properties and
Soil Classification
CH
MH
CL
ML
SW
Unified Soil
Classification
SP
SW - SC
SW - SM
SP - SC
SP - SM
SC
SM
GW
GP
GW - GC
GW - GM
GP - GC
GP - GM
GC
GM
(NCHRP 1-37A)
Plate 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.
Plate Loading Test
Reaction
Reaction
Hydraulic
Jack
12″ f Plate
18″ f Plate
24″ f Plate
30″ f Plate
Pressure
Gauge
3 Deflection
Dials
Reaction
for Dial
Tested Layer
Plate Loading Test Schematic
Plate Loading Test
Effect of Plate Size
p = n + m (P/A)
p = Unit load (stress)
n, m = Empirical values obtained by test
P/A = Perimeter over area
p
m
n
P/A
•Required for rigid pavement design.
P
K
Δ
K = modulus of subgrade reaction
Stress , psi
Modulus of Subgrade Reaction (k)
10 psi
P = unit load on the plate (stress) (psi)
D = deflection of the plate (in)
D
Deformation, in
• For design use stress P = 10 psi (68.95 kN/m2)
Corrections for K
• Correction due to saturation (worst case
scenario).
• Correction due to bending of the plates.
Correction Due to saturation
Du
Ks 
Ku
Ds
Ks = modulus of subgrade reaction corrected for saturation
Ku = field modulus of subgrade reaction
Du/Ds = ratio of the deflection in the unsaturated and saturated tests
10 psi
Du
Deformation
Saturated
Condition
Stress
Stress
Field
Condition
10 psi
Ds
Deformation
Correction 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)
Stress
Deformation
Rate
Basic Plate Loading Test Types
Deformation
Time
Static Load
Stress
Stress
Basic Plate Loading Test Types
Deformation
Accumulated Plastic Elastic
Deformation
Rebound
Deformation
Repeated Load
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