Measuring strain and acceleration at one point Strain transducer Accelerometer PDA testing data acquisition

PDA Measurements and Quantities Outline Measurement equipment installation of sensors immediate results Case Method equations Integrity Stresses Bearing capacity Summary

Measuring strain and acceleration at one point Strain transducer Accelerometer PDA testing data acquisition

Measurements on land Sensors pick up strain and acceleration Measurements on cylinder piles

Measurements on a follower, nearshore Measurements offshore

The Objective: Measuring Pile top force and velocity by the Pile Driving i Analyzer PDA testing data acquisition Need Minimum 2 strain measurements per pil to compensate for bending Place symmetrically about neutral axis Need 4 to assess 2 axis bending

AMX, SX1, SX2 a 1 (t), a 2 (t), one acc. on each side a 1 (t) a 2 (t), one on each side AMX = max ½ (a 1 +a 2 ) SX1 SX2 1 (t), 2 (t), one strain on each side Average Force and Velocity F 1 (t) = ε 1 (t) A E F 2 (t) = ε 2 (t) A E FMX = max ½ (F 1 +F 2 ) VMX = max ½ (v 1 + v 2 ) v 1 (t) = a 1 (t) dt v 2 (t) = a 2 (t) dt

Pile top force and velocity from PDA F(t) = ½ [F 1 (t) + F 2 (t)] v(t) = ½ [v 1 (t) + v 2 (t)] Z FMX = max F(t) We are measuring the total t force and the total t velocity We plot both together using Z to scale velocity What is wave up and what is wave down? Transferred Energy EMX E R = W R h Manufacturer s Rating Max E T = F(t) v(t) dt (ENTHRU, EMX) e T = ENTHRU/ E R (transfer efficiency) W R W R h Measure Force, F(t) Velocity, v(t)

Transferred Energy as a means of judging hammer performance Wave-Up and Wave-Down:WD1, WU2 t 1 t 2 W d1 d1 = F d at time t 1 W u2 = F u at time t 2

PDA Pile Stress Monitoring Assure dynamic stresses during driving remain below acceptable limits Average comp. stresses at sensor location Bending stresses at sensor location Tensile stresses somewhere in pile Compressive stresses at pile bottom FMX, CSX Force (Stress) Maximum at gage location FMX = av EA ; CSX = av E Strain transducer FMX: Ensure that sufficient force is applied to mobilize resistance CSX: Ensure safe pile top stress compare with stress limits

CSI Maximum compressive stress at an individual transducer: CSI = i E Strain transducer CSI To determine effect of bending on stresses at gage location

Pile force at any location below sensors The force at any section along the pile length can be determined from the superposition of the forces in the upward traveling and downward traveling waves F = F u + F d First, let's look at reflecting waves Wave Travel - Free Pile Time 0 L/c 2L/c Pile compresses: top moves down 1x Pile compresses: top moves down 2x Pile stretches: toe moves down 2x

Pile force at any location The force at x equals the sum of the upward wave at the pile top a time x/c later and the downward wave at the pile top x/c earlier: F [x,(2l-x )/c] = F u [0,2L/c] + F d [0,(2L-2x)/c] t = 0 t 3 =(2L-2x)/c (2L-x)/c 2L/c x/c x/c x Tension Stress Calculation Wave-Up F u F d Min. Compr.- down Max. Compr.- down Max. Tension - up

Tension Stress Calculation Wave-Up toe top t 3 Point of max tension Tension Stress Distribution Max. Tension Wave Up CTX, TSX Maximum Computed Tensio ension force (stress) throughout record considering downward tension wave. CTX = Max CTN TSX = CTX / A W d, max-tension tension + W u, u, min-comp. -T +C

Tension Stress Calculation Wave-Down 2L/c Max. Tension Wave Down Min. Comp. Wave Up Limitations of Force Calculation Superposition of waves for stress calculation only reasonably accurate, if: Pile is uniform and elastic Pile has no cracks Waves do not change significantly between top (measurement point) and location of calculated stress value

Pile Damage: BTA, LTD Pile damage causes a tension reflection before 2L/c The time at which the tension reflection arrives at the gage location indicates the depth to the damage: LTD = t damage / 2c LTD The extent of the damage is quantified with the damage factor BTA ( ) Reflection at an Impedance Change t = 0 L/c 2x/c 2L/c Z 1 F d,1 F u1 x A B F d2 Z 2 F A = F B : F u,1 + F d,1 = F d,2 v A =v B : v u,1 + v d,1 = v d,2 2 nd equation: (Z 2 /Z 1 )(Z 1 v u,1 + Z 1 v d,1 ) = Z 2 v d,2 with = Z 2 /Z 1 : (- F u,1 + F d,1 ) = F d,2 = F u,1 + F d,1 = (F u,1 + F d,1 ) / (- F u,1 + F d,1 )

Damage Example F d,1 d,1 = ½(F t1 +Zv t1 t1 ) t 1 F u,1 t 3 u,1 = ½(F t3 -Zv Zv t3 ) Limitations of Beta Calculation Applicable only to uniform piles Detection of more than one major damage yields questionable results Assessment of cracks or cracked splice condition does not conform with basic -derivation Gradual or very short impedance changes do not conform with -derivation Due to measurement inaccuracies (e.g. bending) false PDA damage diagnostics are possible

PDA Capacity Monitoring THE 1965 (Phase 1) equation was based on a rigid body model: R u =F(t o ) - m p a(t o ) Time t o is time of zero velocity no damping t o The Case Method Equation Later, in 1968, we derived the Case Method Equation, based on an elastic pile, considering wave propagation in the pile and an ideally plastic soil resistance. The following is a simplified derivation.

Resistance Waves L/c L x F d,1 -Fd,1 ½R i R B R i -½R i ½R i R B Upward traveling wave at time 2L/c: F u,2 = -F d,1 + ½R i + ½R i + R B or RTL = F u,2 + F d,1 The Case Method Equation RTL = F u,2 + F d,1 or: RTL = ½(F 1 + Zv 1 + F 2 -Zv 2 ) F 1 and v 1 are pile top force and velocity at time 1 F 2 and v 2 are pile top force and velocity at time 2 Time 2 is 2L/c after Time 1: t 2 = t 1 + 2L/c RTL is the total t pile resistance: Dynamic + static; shaft resistance + end bearing RTL is mobilized during time 2L/c following time t 1

RTL = ½ (F 1 + F 2 ) + ½ Mc/L(v 1 v 2 ) 5,450 kn 5.75 m/s 5,550 kn 0.1 m/s t 1 t2 Pile is 305 mm square, prestressed concrete A = 0.094 m 2 ; E = 40,000,000 kpa; c = 4,000 m/s; Z = 940 kn/m/s RTL = ½ (5,450 +5,550) + ½ (5.75 0.1) 940 RTL = 5,500 + 2,660 = 8,160 kn RTL = F d,1 + F u,2 F = 5450 kn F =2,820 kn, F = 50 kn F = 2,730 kn RTL = 5,450 + 2,730 = 8,180 kn

Fixed Pile, Stresses + Resistance/Force at Bottom, CFB For pure end bearing pile: RTL = Force at bottom = F d,1 + F u,2 In General: Computed Force at Pile Bottom: CFB = R toe = RTL R shaft (R shaft we shall discuss later) Computed Stress at Pile Bottom CSB = CFB / A

Case Damping Factor To calculate static resistance dynamic resistance is subtracted from total resistance. For calculating dynamic (damping) resistance, a viscous damping parameter, J v, is introduced R d = J v v [kn kn/m/s][m/s] Non-dimensionalization leads to the Case Damping Factor, J c : J c = J v / Z Thus, R d = J c Z v We use toe velocity; it includes resistance effects! t = 0 Toe Velocity L/c x/c 2L/c L x F d,1 -Fd,1 ½R i R B R i -½R i ½R i R B Toe velocity: due to impact wave = 2F d,1 /Z due to resistance = -( ½R i + ½R i + R B )/Z or v toe = (2F d,1 RTL)/Z

Case Method Static Resistance Total Resistance = Static + Dynamic Resistance R static = RTL - R d R static static = F u,2 + F d,1 -J c (2 F d,1 F d1 F u,2 ) R static static = (1 J c )F d,1 + (1 + J c )F u,2 or static = ½ (1-J c )[F 1 + Zv 1 ] + ½ (1+J c )[F 2 -Zv 2 ] R static R static = (1 J c ) F d,1 + (1 + J c ) F u,2 F = 5450 kn F =2,820 kn F = 50 kn F = 2,730 kn RTL = 5,450 + 2,730 = 8,180 kn For example with J c =.3 R static = (1 -.3) 5,450 + (1 +.3) 2,730 = 7,350 kn

When to choose t 1? When PDA s where slow, t 1 was selected at the time of the first velocity peak RSP RSP is sensitive to choice of damping factor because of high velocity. t 1 t 2 = 2L/c + t 1 RXi... Calculates R static at all times after the first velocity peak Selects the maximum R static for J C = i 2L/c t 1 t 2

Choose damping so that RS curve becomes flat What Case Damping Factor to choose? Almost always, we choose damping factor based on correlation with CAPWAP or static load test. J typically varies between 0.4 for clean sands and 1.0 for clays.

Pile with shaft resistance: Equilibrium ½ R compressive upward wave R - ½R tensile downward wave Pile top force and velocity of pile with shaft resistance

... and its wave up and down ½R R Ri - Wave up

PDA approximate Shaft Resistance The valley of uncertainty: Extrapolate Wave up! yields SFT; deduct damping to get SFR An Example: PDA Capacity Results End of Driving

PDA Capacity Results Restrike; Blow No. 1 Restrike Blow No. 2

Restrike, blow No. 4 What about the toe reflection?

Case Method Unloading Correction: RSU Where pile top rebounds before wave reaches toe Lost friction? RSU, RUI Case Method Capacity Correction t-vzero t-vzero Lost friction RSU(J=0) = RTL(time 0) + ½ Lost Friction Reduce RSU(J=0) using damping approach

Essential PDA Input AR, LE, EM, WS (SP, WC) JC Calibrations Records A1, A2, F1, F2 Quantities Sampling Frequency (5,000; 10,000;...) Capacity Considerations Concluded Measurements of pile top force and velocity give information about magnitude and location of resistance Resistance varies over time during the impact event; requires proper choice of Case Method Damping is highest at beginning of impact and then diminishes over time during event Damping must consider soil type All simplified methods must be backed up by CAPWAP or static load test

Why do we need Case Method? To calculate capacity for all blows not CAPWAP analyzed (capacity vs.depth) BUT: Case Method Capacity always needs a CAPWAP or static load test correlation to select proper method/damping Summary PDA measurements together with stress wave considerations yield information on dynamic stresses and pile integrity. Incident and reflection waves can be superimposed to yield information on extreme stresses in pile Because of the wave propagation it is possible to determine location of resistance or impedance changes