Download - PILE DRIVING BY WAVE MECHANICS
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PILE DRIVINGBY
WAVE MECHANICS
George Goble
GOBLE PILE TEST
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A STUPID QUESTION
• WHAT MAKES A PILE PENETRATE?• A FORCE
– IF WE PUSH SLOWLY BUT HARD ENOUGH IT WLL MOVE DOWN AGAINST THE SOIL RESISTANCE
• THE MAGNITUDE OF THE PUSH WILL BE THE PILE CAPACITY (BUT HOW DO WE DEFINE CAPACITY)
– BUT WHAT IF WE USE A VERY BRIEF PUSH THAT WILL PENETRATE THE PILE? PERHAPS AN IMPACT
• THAT FORCE WILL BE LARGER THAN THE CAPACITY?
• THERE IS A DYNAMIC RESISTANCE
• WE WANT TO UNDERSTAND THE EFFECT OF AN IMPACT ON THE PILE IN ORDER TO DEAL WITH PROBLEMS LIKE THE ABOVE
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WAVE PROPAGATION
Based on the assumption of linear elastic material
1. If a force is suddenly applied to the end of a pile a wave (disturbance) is generated that travels along the pile. When the wave passes a point on the pile the point displaces with some velocity and acceleration. A force is present in the pile. The disturbance can be expressed as a wave of any of these quantities.
2. A stress wave propagates unchanged in magnitude at a constant speed, c, in a uniform cross section pile.
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SOME WAVE SPEEDS
• Steel – 16,800 feet/sec.– Almost 12,000 miles/hour
• Concrete – 11,000 to 14,000 feet/sec– Both Modulus and Density Vary so Wave
Speed Varies
• Wave Speed Is a Material Property
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WAVE MECHANICS
• The Hammer Impact Generates a Stress Wave
• The Wave Transmits the Driving Force
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BASIC EXPRESSION GOVERNING ONE DIMENSIONAL WAVE PROPAGATION
∂2u/∂t2 = c2 ∂2u/∂x2
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WAVE TRAVEL SPEED
• E – Modulus of Elasticity
• ρ - Mass Density
Ec
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WAVE TRAVEL IN A PILE
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FORCE A FUNCTION OF X
X
F
at time t at time t + Δt
x + ct
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FORCE A FUNCTION OF t
t
F
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FORCE-VELOCITY PROPORTIONALITY
ε = (1/c) vσ = (E/c) v
F = (EA/c) v
SO IF THE PARTICLE VELOCITY IS KNOWNTHEN STRESS AND FORCE CAN BE CALCULATED
OR THE REVERSE
SO, FOR GRAPHIC REPRESENTATION THE F – v PROPORTIONALITY CAN BE USED
COMPRESSION AND DOWN VELOCITY POSITIVETENSION AND UP VELOCITY NEGATIVE
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STRESS IMPEDANCE
• For Steel– E/c = 30,000/16,800– E/c = 1.80 ksi/ft/sec
• So– If an Air Hammer Falls 3.0 feet with an
Efficiency of 65%• vi = (η2gh)1/2 = 11.2 ft/sec
– η is the efficiency
• σ = (E/c) v = (1.8)(11.2) = 20 ksi
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4. A stress wave is reflected from the free end of a rod with the opposite sign. Compression reflects tension.
E
cv
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5. A stress wave reflects from a fixed end with the same sign. Compression reflects compression.
6. An increase in cross section will reflect a wave of the same sign. A decrease in cross section will reflect a wave of the opposite sign.
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REFLECTIONS FROM PILE SECTION CHANGES
• Section Increases Reflect Compression and Up Velocity
• Section Decreases Reflect Tension and Down Velocity
• The Larger the Section Change the Larger the Reflection
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7. If a rigid mass impacts a pile the stress is proportional to the velocity. The stress decays exponentially.
1
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ENERGY CALCULATION
ΔΨ =FΔδ
Δδ = vΔt
Ψ =
FvdtRod
F
F
DISPLACEMENT
F
OR
CE
(F
)
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8. The Energy Passing a Point in a Pile During the Passage of a Stress Wave Is:
Ψ = Fvdt
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The Energy Passing a Point in a Pile During the Passage of a Stress Wave Is:
Ψ = Fvdt
If F = EA/c (v)
Then Ψ = c/EA F2 dt
Assumes No Reflections
Half Kinetic – Half Strain
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L1
L
R2
R2
R2
Force
EA c
v
Force
R
F
EA c
v
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F - R 2
Force
F+R 2
EA c
v
R
t
REA c
vForce,
EA c
vForce,
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Soil Resistance Effects on Force and Velocity
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Force and Velocity Measurements for Various Soil Conditions.
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Energy transfer in easy driving conditions
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Energy transfer in hard driving conditions
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Effects of diesel hammer pre-ignition on energy transfer
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Effects of diesel hammer pre-ignition on energy transfer cont.
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Force and Velocity Measurements Illustrating Progressive Concrete Pile Damage