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 da

measure swelling and CB

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
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

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

CBR Curve Correction

0.0

0.1

0.2

Influence of Moisture upon CBR

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

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
Determines the load carrying capacity of the material.
Used for HMA as well as unbound materials

1
3

Uses a repeated load triaxial test.

Used in most modern methods of pavement design.

Triaxial Test Equipment

Loading Piston

Cell Pressure Inlet

External LVDT

Frame

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 (sec)

Stress vs. Time

Strain (in/in)

Stress (psi)

25.0

0.008

0.004

0.000
0.0

0.5

1.0
Time (se c)

1.5

Resilient Modulus
Load

14

16

load rest

14

16

Time

r = L/L

ASU Advanced Pavement Laboratory

Animation from University of Tokyo Geotechnical Engineering Lab

Nonlinear Material Behavior:

Coarse-Grained Soils

MR K1

K2

log MR
K2

Bulk stress: = 1 + 2 + 3
K1, K2 are material constants

K1 > 0

K2 0 (stress-stiffening)

K1

log

Nonlinear Material Behavior:

Fine-Grained Soils

MR K 3 oct

K4

Octahedral shear stress:

K3, K4 are material constants

K3 > 0

K4 0 (stress-softening)

log MR
K3

K4

log oct

Combined Stress Dependence of MR

M R k1 p a
Pa

k2

oct

1
P

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

log oct

Bulk Stress Stiffening

Shear Stress Softening

= 1 + 2 + 3
= I = Bulk stress = First
stress invariant

oct = Octahedral shear stress

Effect of Moisture/Density on MR
log MR

log MR

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

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

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
Subgrade Soil
Category
Category
Mr (ksi)
Mr (ksi)

Poor
Poor
1.5
1.5

CBR (%)
CBR (%)

R- Value
R- Value

Medium
Good
Medium
Good
4

4 5
4 5

10
10

AASHTO Soil
AASHTO Soil
Classification
Classification

A-7-6
A-7-6
CH
CH

Unified Soil
Unified Soil
Classification
Classification

A-7-5
A-7-5

MH
MH

Excellent
Excellent

15
20
15
20

10
10

30
30

10 15 20
10 15 20

15
15

40 50 60
40 50 60

40
60 80 100
40
60 80 100

30
30

40
60
80 100
40
60
80 100
A-1-b A-1-a
A-1-b A-1-a
A-2-4
A-2-4
A-2-5
A-2-5
A-2-6
A-2-6
A-2-7
A-2-7 A-3
A-3
A-4
A-4
A-5
A-6 A-5
A-6
20
20

MR Correlations
w/ Index
Properties and
Soil Classification

CL
CL
ML
ML

SW
SW
SP
SP
SW - SC
SWSW
- SC
- SM
SW - SM

SP - SC
SP - SC

SP - SM
SP - SM

SC
SC

SM
SM
GP
GW - GCGP
GW - GC

GW
GW

GW - GM
GW - GM

GP - GC
GP - GC
GP - GM
GP - GM
GC
GC
GM
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 Plate
18 Plate
24 Plate
30 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

n
P/A

Required for rigid pavement design.

P
K

K = modulus of subgrade reaction

Stress , psi

Modulus of Subgrade Reaction (k)

10 psi

P = unit load on the plate (stress) (psi)

= deflection of the plate (in)

For design use stress P = 10 psi (68.95 kN/m2)

Deformation, in

Corrections for K
Correction due to saturation (worst case
scenario).

Correction due to bending of the plates.

Correction Due to saturation

u
Ks
Ku
s
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

10 psi

Deformation

Saturated
Condition

Stress

Stress

Field
Condition

10 psi

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

To do a good job you need to

study Hard, dont you?!