1. PILE DRIVING BY WAVE MECHANICS
George Goble
Consulting Engineer

2. 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 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 DYNAMIIC RESISTANCE
WE WANT TO UNDERSTAND THE EFFECT OF AN IMPACT ON THE PILE IN ORDER TO DEAL WITH PROBLEMS LIKE THE ABOVE

3. Based on the assumption of linear elastic material
WAVE PROPAGATION
Based on the assumption of linear elastic material
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.
A stress wave propagates unchanged in magnitude at a constant speed, c, in a uniform cross section pile.

4. WAVE MECHANICS The Hammer Impact Generates a Stress Wave
The Wave Transmits the Driving Force

5. BASIC EXPRESSION GOVERNING ONE DIMENSIONAL WAVE PROPAGATION
∂2u/∂t2 = c2 ∂2u/∂x2

6. WAVE TRAVEL SPEED
E – Modulus of Elasticity
ρ - Mass Density

7. WAVE TRAVEL IN A PILE

8. FORCE A FUNCTION OF X F
at time t
at time t + Δt
x + ct X

9. FORCE A FUNCTION OF t F t

10. FORCE-VELOCITY PROPORTIONALITY
ε = (1/c) v
σ = (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

11. STRESS IMPEDANCE For Steel So 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

12. 4. A stress wave is reflected from the free end of a rod with the opposite sign. Compression reflects tension. E v c

13. 5. A stress wave reflects from a fixed end with the same sign
5. A stress wave reflects from a fixed end with the same sign. Compression reflects compression.
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.

14. 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

15. 7. If a rigid mass impacts a pile the stress is proportional to the velocity. The stress decays exponentially. 1

16. ENERGY CALCULATION
ΔΨ =FΔδ
Δδ = vΔt
Ψ = Fvdt

17. The Energy Passing a Point in a Pile During the Passage of a Stress Wave Is:
Ψ = Fvdt

18. 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

19. R L1 L R 2
Force R 2 EA c v R 2 F
Force EA c v

20. F+R 2
F - R 2
Force EA c v R EA c
Force, v R EA c
Force, v t

21. Soil Resistance Effects on Force and Velocity

22. Force and Velocity Measurements for Various Soil Conditions.

23. Energy transfer in easy driving conditions

24. Energy transfer in hard driving conditions

25. Effects of diesel hammer pre-ignition on energy transfer

26. Effects of diesel hammer pre-ignition on energy transfer cont.

27. Force and Velocity Measurements Illustrating Progressive Concrete Pile Damage

34. ANY QUESTIONS ?