2. GRL Dynamic Pile testing with the Pile Driving Analyzer® © 1998 Goble Rausche Likins and Associates and Dr. Julian Seidel

3. GRL SummarySummary History of Dynamic Pile TestingHistory of Dynamic Pile Testing Measuring stress wavesMeasuring stress waves Fundamentals of Wave MechanicsFundamentals of Wave Mechanics The Case Method (Pile Driving Analyzer)The Case Method (Pile Driving Analyzer) –Capacity –Stresses –Integrity –Hammer performance

4. GRL 18th Century:Closed Form Solutions Late 19th Century:Engineering News Formula 1920’s: First Strain Measurements 1950:Smith’s Wave Equation Program 1964:Case Project began under Dr. G.G. Goble 1968:Pile Driving Analyzer ® (PDA) 1970:CAPWAP ® 1972:Pile Dynamics, Inc. founded 1976: WEAP program 1977:Saximeter 1982:Hammer Performance Analyzer 1986: Hammer Performance Study 1989:Pile Integrity Testing (PIT) 1996: FHWA Manual 1998:Pile Installation Recorders (PIR) 1999:Remote PDA History of Dynamic Pile Testing/Analysis

5. GRL 1-D Wave Theory Hammer causes a downward travelling stress-wave to enter the pileHammer causes a downward travelling stress-wave to enter the pile Soil resistance causes stress-wave reflectionsSoil resistance causes stress-wave reflections Stress in pile can be represented by 1-dimensional Wave TheoryStress in pile can be represented by 1-dimensional Wave Theory These stress-waves can be measured and identified with measurement of force and velocity near the pile topThese stress-waves can be measured and identified with measurement of force and velocity near the pile top

6. GRL W2W2W2W2 m2m2m2m2 m2m2m2m2 W1W1W1W1 m1m1m1m1 m1m1m1m1 v1v1v1v1 v1v1v1v1 v1v1v1v1 v1v1v1v1 Newtonian Collision Analogy Hammer is a concentrated mass “Rigid body” motion assumption is reasonable Hammer is a concentrated mass “Rigid body” motion assumption is reasonable Pile is a longitudinally-distributed mass “Rigid body” motion assumption is not reasonable Motion is dominated by stress-wave effects Pile is a longitudinally-distributed mass “Rigid body” motion assumption is not reasonable Motion is dominated by stress-wave effects

7. GRL Impact on elastic rod F dL time = dt Compressed Zone Cross-sectional area, A Elastic modulus, E Mass density,  Cross-sectional area, A Elastic modulus, E Mass density,  Stress,  = F/A Wavespeed, c = dL/dt Stress,  = F/A Wavespeed, c = dL/dt

8. GRL Particle Velocity FdLF F dx dx = F dL EA EA dx = F dL EA EA v = dx = F dL = F c dt EA dt E A dt EA dt E A v = dx = F dL = F c dt EA dt E A dt EA dt E A Particle Speed Wave Speed

9. GRL v = F c EA EA v = F c EA EAdL Cross-sectional area, A Mass density,  Cross-sectional area, A Mass density,  Wavespeed a = dv = d Fc dt dt EA dt dt EA a = dv = d Fc dt dt EA dt dt EA F = ma = dL A  a = dL A  a F = ma = dL A  a = dL A  a F = dL A  F c dt E A dt E A F = dL A  F c dt E A dt E A c 11 c 2 = E c 2 = E    US  US  SI  SI

10. GRL Wavespeed Example (SI units) Determine the wavespeed for a concrete pile with the following properties: E = 40,000 MPa  = 24.5 kN/m 3 Answer:Determine the wavespeed for a concrete pile with the following properties: E = 40,000 MPa  = 24.5 kN/m 3 Answer: c 2 = 40,000 x 1000 x 9.81 / 24.5c 2 = 40,000 x 1000 x 9.81 / 24.5 c 2 = 1.602x10 7 m 2 /s 2c 2 = 1.602x10 7 m 2 /s 2 c = 4002 m/s ~ 4000 m/s.c = 4002 m/s ~ 4000 m/s. 

11. GRL Force, velocity, stress and strain v = d x = F dL = Fc dt EA dt EA dt EA dt EA v = d x = F dL = Fc dt EA dt EA dt EA dt EA Particle Speed Wave Speed F = EAv c c Pile Impedance F = EAv c = Zv = Zv F = EAv c = Zv = Zv F =  = v E A c F =  = v E A c  =  = v E c  =  = v E c  US  US  SI  SI

12. GRL F,v, ,  Example (SI units) A steel H-pile of 12,000 mm 2 x-secn area reaches a peak velocity of 6.2 m/s during impact. What are the peak strain, stress and force in the pile-top? (For steel, E = 210,000 MPa, c = 5120 m/s).A steel H-pile of 12,000 mm 2 x-secn area reaches a peak velocity of 6.2 m/s during impact. What are the peak strain, stress and force in the pile-top? (For steel, E = 210,000 MPa, c = 5120 m/s). Answer:Answer:  = v/c = 6.21/5120 = 1.213x10 -3  = v/c = 6.21/5120 = 1.213x10 -3  = .E = 1.213x10 -3 x 210,000 = 255 MPa  = .E = 1.213x10 -3 x 210,000 = 255 MPa F = .A = 255 x 12,000x10 -6 = 3.06 MN F = .A = 255 x 12,000x10 -6 = 3.06 MN 

13. GRL Force and Velocity Measurements W 2W Strain transducer Accelerometer

14. GRL Measuring stress waves Strain transducer Accelerometer

15. GRL Strain Transducer C C Resistance strain gages connected in Wheatstone bridge configuration CT TC T T TC CT F =  A =  EA

16. GRL AccelerometersAccelerometersPiezo-electricAccelerometerPiezo-electricAccelerometer mass spring quartzcrystal Piezo-resistiveAccelerometerPiezo-resistiveAccelerometer v =  a.dt mass strain gage cantilever

17. GRL Sign Conventions Force: Compression -positive (+)Compression -positive (+) Tension -negative (-)Tension -negative (-) Velocity: Downward -positive (+)Downward -positive (+) Upward-negative (-)Upward-negative (-)

18. GRL Infinite Pile Compressivestress-wave Wavespeed, c F(x,t) Compression = +ve v(x,t) Motion down pile = + F = EAv c = Zv = Zv F = EAv c = Zv = Zv Cross-sectional area, A Elastic modulus, E Cross-sectional area, A Elastic modulus, E x = constant

19. GRL Time domain - infinite pile ExponentialDecay F = EAv c c

20. GRL Finite pile with free end + Free End : F = 0 +F-F - incident force wave reflected in opp. sense

21. GRL Direction of Motion Downward Travelling (incident) Waves TOPTOE Force + Velocity + V Force - Velocity - F= Zv T C V

22. GRL Direction of Motion Upward Travelling (reflected) Waves TOPTOEV Velocity - Force + V Velocity + Force - F=-ZvF=-ZvC T

23. GRL Finite pile with free end F+, v+ + F-, v+ + +v+v incident wave pushes pile down reflected tension wave pulls pile down Free End : v doubled x = constant

24. GRL Time Domain - free pile Characteristic tension response - velocity increases relative to force response time = 2L/c  US  US  SI  SIZv F

25. GRL Free end example (SI) A 25m long 300mm segmental precast concrete pile is installed through deep organic sediments. Pile resistance is negligible. The pile modulus is 38,000 MPa. What is the maximum tension stress in the pile for a peak pile-top velocity of 1.15 m/s? What action do you recommend?A 25m long 300mm segmental precast concrete pile is installed through deep organic sediments. Pile resistance is negligible. The pile modulus is 38,000 MPa. What is the maximum tension stress in the pile for a peak pile-top velocity of 1.15 m/s? What action do you recommend? AnswerAnswer c =  E/  = 38,000x9.81x10 3 /24.5 = 3900 m/sc =  E/  = 38,000x9.81x10 3 /24.5 = 3900 m/s  = v/c = 1.15/3900 = 2.95x10 -4  = v/c = 1.15/3900 = 2.95x10 -4  = .E = 11.2 MPa. (Tension = Compression)  = .E = 11.2 MPa. (Tension = Compression) Reduce the drop heightReduce the drop height 

26. GRL Finite pile on rigid base + -+v-v incident wave pushes pile down reflected wave pushes pile up GRANITE Fixed End : v = 0

27. GRL Finite pile on rigid base v+, F+ +C v-, F+ +C+F+F incident wave pushes pile down reflected wave pushes pile up GRANITE x = constant Fixed End : F doubled

28. GRL Time domain - pile on rigid base Characteristic compression response - force increases relative to velocity response time = 2L/c  US  US  SI  SIF Zv

29. GRL Fixed end example (SI) A 10m long 300mmx6mm wall Grade 250 steel pipe pile is installed through soft clay on to fresh basalt rock. What is the maximum section stress at the pile toe if the maximum pile-top velocity is 3.22 m/s? What is likely to result?A 10m long 300mmx6mm wall Grade 250 steel pipe pile is installed through soft clay on to fresh basalt rock. What is the maximum section stress at the pile toe if the maximum pile-top velocity is 3.22 m/s? What is likely to result? AnswerAnswer c =  E/  = 210,000x9.81x10 3 /78.5 = 5120 m/sc =  E/  = 210,000x9.81x10 3 /78.5 = 5120 m/s  = v/c = 3.22/5120 = 6.29x10 -4  = v/c = 3.22/5120 = 6.29x10 -4  = 2 .E = 264 MPa. (double compression in)  = 2 .E = 264 MPa. (double compression in) Buckling of the pile toe (esp local)Buckling of the pile toe (esp local) 

30. GRL Separation of Waves F  =Zv  Downward Waves F  =-Zv  Upward Waves F = F  + F  v = v  + v  F  = ½ (F+Zv) Downward Waves F  = ½ (F-Zv) Upward Waves  US  US  SI  SI E=mc 2 E=mc 2

31. GRL Waves - Proof 1 F  = Zv  2 F  = -Zv  3 F = F  +F  4 v = v  +v  5  Zv = Zv  +Zv  6  Zv = F  - F  7  +  : F + Zv = 2F  …or F  = ½(F + Zv) 8  -  : F - Zv = 2F  …or F  = ½(F - Zv) 

32. GRL Waves example (SI) At impact a 300mmx6mm wall Grade 250 steel pipe pile achieves a peak velocity of 5.34 m/s, 10m above ground level. At time 2L/c later, the force and velocity are measured at 1620 kN and -2.67 m/s. What are the upward and downward waves at impact and 2L/c later? AnswerAt impact a 300mmx6mm wall Grade 250 steel pipe pile achieves a peak velocity of 5.34 m/s, 10m above ground level. At time 2L/c later, the force and velocity are measured at 1620 kN and -2.67 m/s. What are the upward and downward waves at impact and 2L/c later? Answer EA/c = 210,000x5542x10 -3 /5120= 227 kNs/mEA/c = 210,000x5542x10 -3 /5120= 227 kNs/m At impact F d = 227x5.34 = 1214 kN; F u = 0 kNAt impact F d = 227x5.34 = 1214 kN; F u = 0 kN At 2L/c F d = ½(1620+227x-2.67) = 507 kNAt 2L/c F d = ½(1620+227x-2.67) = 507 kN At 2L/c F u = ½(1620-227x-2.67) = 1113 kNAt 2L/c F u = ½(1620-227x-2.67) = 1113 kN 

33. GRL Waves - pile on rigid base F Zv F,Zv F  = ½(F + Zv) F  = ½(F - Zv)

34. GRL Time of reflection xR Total travel distance = 2x Wavespeed = c Reflection from resistance at x arrives at pile-top at time arrives at pile-top at time Reflection from resistance at x arrives at pile-top at time arrives at pile-top at time 2x/c  US  US  SI  SI

35. GRL Timing example (SI) Measurments on an existing preast concrete pile of unknown length indicate a modulus of 35,000 MPa. The dynamic records show a compressive response commencing 4.3ms after impact, and a tension response at 11.7ms. What is the depth to soil resistance, and estimate the pile length. AnswerMeasurments on an existing preast concrete pile of unknown length indicate a modulus of 35,000 MPa. The dynamic records show a compressive response commencing 4.3ms after impact, and a tension response at 11.7ms. What is the depth to soil resistance, and estimate the pile length. Answer c =  E/  = 35,000x9.81x10 3 /24.5 = 3740 m/sc =  E/  = 35,000x9.81x10 3 /24.5 = 3740 m/s Length to resistance = ½(3.74x4.3) = 8.0mLength to resistance = ½(3.74x4.3) = 8.0m Pile length = ½(3.74x11.7) = 21.9mPile length = ½(3.74x11.7) = 21.9m 

36. GRL Typical pile response toe response time = 2L/c start of toe response response from shaft only response from pile base timing and amount of separation is a function of location and extent of soil resistance

37. GRL Typical pile response toe response time = 2L/c F  = ½ (F+Zv) exponential decay FFFF returning compressive reflections lift pile-top force…....and slow the pile-top down relative to the “no resistance” pile

38. GRL Typical pile response F  = ½ (F-Zv) toe response time = 2L/c F=½RF=½RF=½RF=½R F=½RF=½RF=½RF=½R upward travelling wave before 2L/c is related to the cumulative shaft resistance R shaft  2F  @ 2L/c

39. GRL Typical pile response Q. Why may it be preferable to view data as F , F  ? Downward wave - isolates input from driving system Upward wave - isolates response from pile/soil  US  US  SI  SI

40. GRL Shaft resistance (SI) 2340kN; 3.34 m/s 1420kN -1.32m/s Problem: Make an approximate estimate of the pile shaft resistance. Problem: Make an approximate estimate of the pile shaft resistance. Answer:Answer: Z = 2340/3.34 = 700 kNs/mZ = 2340/3.34 = 700 kNs/m R shaft @ 2 x F é @ 2L/cR shaft @ 2 x F é @ 2L/c R shaft @ 2x ½(1420-700x-1.32) = 2344 kNR shaft @ 2x ½(1420-700x-1.32) = 2344 kN 

41. GRL Conclusion Pile driving events can be evaluated using 1-D Wave Mechanics principlesPile driving events can be evaluated using 1-D Wave Mechanics principles Stress-waves cause changes in force and particle velocityStress-waves cause changes in force and particle velocity Force and velocity are related by the pile impedanceForce and velocity are related by the pile impedance Waves travelling both up and down a pile can be separated by F and V measurementWaves travelling both up and down a pile can be separated by F and V measurement Soil resistance causes reflections which can be interpreted to determine extent and location of resistanceSoil resistance causes reflections which can be interpreted to determine extent and location of resistance

42. GRL Case-Goble Capacity A pile is struck at time t 1. The impact force generates a wave F(down,t 1 ) F( ,t 1 ) L The impact wave returns to the pile top at time The impact wave returns to the pile top at time t 2 = t 1 + 2L/c together with all resistance waves F( ,t 2 )

43. GRL The Case Method Equation At time t 2 = t 1 + 2L/c the upward traveling waves arriving at the pile top include the reflection of the initial impact wave plus the sum of all resistances: Or, rearranging we solve for the resistance: R = (F 2 -v 2 Z)/2 + (F 1 +v 1 Z)/2 where R is the total pile resistance, mobilized at a time L/c after t 1. F( ,t 2 ) = - F( ,t 1 ) + R 

44. GRL The Case Method Equation R = 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 R is the total pile resistance present at the time of the test, and mobilized by the hammer impact.

45. GRL Static Resistance example - US units 2L/c = 10ms Zv 2 F2F2F2F2 Zv 1 F1F1F1F1

46. GRL Case-Goble Static Resistance R static = R - R dynamic Total Resistance = Static + Dynamic  US  US  SI  SI J c = ? J c = ? Need to estimate R dynamic (Estimate it from pile velocity)

47. GRL Case Damping Factor To calculate static from total resistance, a viscous damping parameter, J v, is introducedTo calculate static from total resistance, a viscous damping parameter, J v, is introduced R d = J v v Non-dimensionalization leads to the Case Damping Factor, J c :Non-dimensionalization leads to the Case Damping Factor, J c : J c = J v  Z  R d = J c Z v J c = ? J c = ?

48. GRL Case-Goble Static Resistance R static = R - R dynamic R s = (1-J c )[F 1 + Zv 1 ]/2 + (1+J c )[F 2 - Zv 2 ]/2 Total Resistance = Static + Dynamic  US  US  SI  SI J c = ? J c = ?

49. GRL Case Damping Factor Values for RMX 00.20.40.60.81.0 Gravel0.30.4 Sand 0.40.5 Clay 0.71.0 Silt 0.50.7 Reducing Grain Size Reducing Increasing Damping factor Increasing 

50. GRL Restrike testing - fine grained soils log time capacity 1 day 10 days 100 days 1000 days Technically desirable E Economically desirable Restrike testing generally under- taken 1 to 10 days after installation

51. GRL Mobilized Resistance Displacement, x Resistance, R Displacement for full mobilization Mobilized Resistance Ultimate Resistance Maximum test displacement

52. GRL Resistance: Rules for good correlation Need to Mobilize CapacityNeed to Mobilize Capacity (sufficient set per blow) Account for time dependent strength changes Account for time dependent strength changes Setup - Capacity increase Relaxation - Capacity decrease Therefore, restrike test pile after sufficient wait using a sufficiently large impact weight

53. GRL Capacity Results Capacity Results GRLWEAPGRLWEAP by numerical analysis of assumed pile/hammer/soil prior to installationby numerical analysis of assumed pile/hammer/soil prior to installation Case MethodCase Method measured by PDA during installationmeasured by PDA during installation CAPWAPCAPWAP by numerical analysis of measured PDA data after installationby numerical analysis of measured PDA data after installation

54. GRL The Pile Driving Analyzer calculates...

55. GRL … PDA Results … PDA Results Case Method Bearing CapacityCase Method Bearing Capacity Pile StressesPile Stresses Compressive at TopCompressive at Top Bending at TopBending at Top Tension Below TopTension Below Top Compressive at BottomCompressive at Bottom Pile Integrity (Beta)Pile Integrity (Beta) Transferred EnergyTransferred Energy

56. GRL PDA RESULTS vs GRLWEAP CAPACITYCAPACITY –PDA: from force and velocity records –GRLWEAP: from analysis and blow count TOP STRESSESTOP STRESSES –PDA:directly measured –GRLWEAP: from analysis and blow count Note:Note: Max. Compressive Stress does NOT always occur at Pile Top Max. Compressive Stress does NOT always occur at Pile Top