PILE DRIVING BY WAVE MECHANICS George Goble GOBLE PILE TEST 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 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. 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 WAVE MECHANICS • The Hammer Impact Generates a Stress Wave • The Wave Transmits the Driving Force BASIC EXPRESSION GOVERNING ONE DIMENSIONAL WAVE PROPAGATION ∂2u/∂t2 = c2 ∂2u/∂x2 WAVE TRAVEL SPEED E c • E – Modulus of Elasticity • ρ - Mass Density WAVE TRAVEL IN A PILE FORCE A FUNCTION OF X F at time t at time t + Δt x + ct X FORCE A FUNCTION OF t F t 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 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 4. A stress wave is reflected from the free end of a rod with the opposite sign. Compression reflects tension. E c v 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. 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 7. If a rigid mass impacts a pile the stress is proportional to the velocity. The stress decays exponentially. 1 ΔΨ =FΔδ F Δδ = vΔt Ψ = Fvdt FORCE (F) ENERGY CALCULATION F Rod DISPLACEMENT 8. The Energy Passing a Point in a Pile During the Passage of a Stress Wave Is: Ψ = Fvdt 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 R L1 L Force EA v c Force F EA c v R 2 R 2 R 2 F+R 2 F-R 2 Force EA v c R Force, EA v c R Force, EA v c t Soil Resistance Effects on Force and Velocity Force and Velocity Measurements for Various Soil Conditions. Energy transfer in easy driving conditions Energy transfer in hard driving conditions Effects of diesel hammer pre-ignition on energy transfer Effects of diesel hammer pre-ignition on energy transfer cont. Force and Velocity Measurements Illustrating Progressive Concrete Pile Damage