PILE DRIVING BY WAVE MECHANICS

1. PILE DRIVINGBYWAVE 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. WAVEPROPAGATION 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 • 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. 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 v Force, R EA c t v Force,

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 ?