Investigating the Relationship Between Resilient · PDF fileInvestigating the Relationship...
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Investigating the Relationship Between the Resilient
Modulus and Gmax
Peter DavichGeomechanics
University of Minnesota
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The Resilient Modulus (Mr)
A dynamic measure of a material’s elastic (Young’s) modulus.
Relates stress and strain in the material.Commonly measured by taking the slope of an elastic portion of the stress/strain curveUsed for many design purposes
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LTPP Protocol 46
Distributed by the Federal Highway Administration
Designed to calculate Mrfor pavement base and subgrade materials.
Involves a lengthy triaxial test.
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LTPP Protocol 46 Procedure
Prepare the specimen
0.1 second axial haversine load
0.9 seconds of material recovery
Calculate Mr by dividing axial stress by axial strain and repeat
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Axial Deformation Versus Time
Time
Def
orm
atio
n
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LTPP Protocol 46 Values
Seating load15 psi (103 kPa) confining pressure15 psi (103 kPa) maximum axial stress500-1000 load applications
Actual test5 confining pressures: 3,5,10,15,20 psi3 max axial stress values per pressure100 load applications per stress – only the last 5 are considered in the final calculation
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Gmax
The apparent value of the elastic shear modulus for very small strains
Can be calculated by taking the slope at the end of a very small unloading and reloading curve on the stress/strain diagramOften assumed to be equivalent to Mr
Actual relationship not well defined
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Bender ElementsA reliable method
for calculating Gmax
Relatively simple testInsert piezoelectric strips into the top and bottom of a material specimenInduce the vibration of one stripRecord the wavespeed of the resultant shear wave
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Bender Elements
~5 mm
- Record Cs, then use this equation:
2max scG ρ=
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Parametric Study
Report recently written to see what parameters may impact testing
Several parameters will have important effects on the results
Soil densityMoisture contentStrain level induced by the elementsOther bender element/testing issues
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Soil Density (ρ)
Appears in the GMAX equation: GMAX = ρcs
2
Should have a known value and be held constant during testing
Most sands are effectively incompressible within the range being tested (0-20 psi)
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Moisture Content
Used to be difficult to test with bender elements
Nazarian and Yuan (2001) constructed moisture-modulus curves
Largest moduli did not occur at Proctor optimum water content: often several percentage points below
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Example Moisture-Modulus Curve
0
100
200
300
400
5 5.5 6 6.5 7 7.5
Moisture Content (percent)
Mea
sure
d M
odul
us (M
Pa)
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Strain Level
The shear modulus (G) varies with the amount of strain applied during measurement
Three distinct strain levels: ‘very small’, ‘small’, and ‘large’
Bender elements test only within the ‘very small’ zone, therefore, they record GMAX
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Strain Level
Stre
ss GMAXGMAX
“Ver
y Sm
all”
stra
in
“Lar
ge” s
train
“Sm
all”
stra
in
0.00
1% Strain
0.01
%
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Strain Level
Strain (Logarithmic Scale)
Shea
r Mod
ulus
(G)
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Other Issues
Aging (Volumetric Creep) Phenomenon
Identification of the shearwave arrival time (nearfield effect)
Compression waves move more quicklyAnalytical solution proposed by Sanches-Salinero et al.Do not use square pulses (one frequency only)
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Future Work
Build a bender element into the top cap and base pedestal of a triaxial cell
Measure Mr and Gmax simultaneously for a variety of samples
Construct a useful relationship between them
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Any Questions?