PILE DRIVING BY WAVE MECHANICS

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PILE DRIVINGBYWAVE 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
• ? - Mass Density

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WAVE TRAVEL IN A PILE
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FORCE A FUNCTION OF X
F
at time t
at time t ?t
X
x ct
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FORCE A FUNCTION OF t
F
t
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FORCE-VELOCITY PROPORTIONALITY e (1/c) v s
(E/c) v F (EA/c) v SO IF THE PARTICLE VELOCITY
IS KNOWN THEN STRESS AND FORCE CAN BE
CALCULATED OR THE REVERSE SO, FOR GRAPHIC
REPRESENTATION THE F v PROPORTIONALITY CAN BE
USED COMPRESSION AND DOWN VELOCITY
POSITIVE TENSION 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 (?2gh)1/2 11.2 ft/sec
• ? is the efficiency
• s (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
v
c
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5. A stress wave reflects from a fixed end with
the same sign. Compression reflects compression.

1. 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
?? F?d ?d v?t ? ?Fvdt
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1. The Energy Passing a Point in a Pile During the
   Passage of a Stress Wave Is

? ?Fvdt
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The Energy Passing a Point in a Pile During the
Passage of a Stress Wave Is
? ?Fvdt If F EA/c (v) Then ? c/EA ?F2 dt
Assumes No Reflections Half Kinetic Half
Strain
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R
L1
L
R 2
Force
R 2
EA c
v
R 2
F
Force
EA c
v
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FR 2
F - R 2
Force
EA c
v
R
EA c
v
Force,
R
EA c
t
v
Force,
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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