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Frank Rausche, Garland Likins 2011, Pile Dynamics, Inc.

GRLWEAP ™ Fundamentals. Frank Rausche, Garland Likins 2011, Pile Dynamics, Inc. CONTENT. Background and Terminology Wave Equation Models Hammer Pile Soil The Program Flow Bearing graph Inspector’s Chart Driveability. Some important developments in Dynamic Pile Analysis.

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Frank Rausche, Garland Likins 2011, Pile Dynamics, Inc.

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  1. GRLWEAP™ Fundamentals Frank Rausche, Garland Likins 2011,Pile Dynamics, Inc.

  2. CONTENT • Background and Terminology • Wave Equation Models • Hammer • Pile • Soil • The Program Flow • Bearing graph • Inspector’s Chart • Driveability

  3. Some important developments in Dynamic Pile Analysis 1800s Closed Form Solutions & Energy Formulas 1950: Smith’s Wave Equation 1970: CAPWAP 1976: WEAP, TTI (mainframes) 1980s: GRLWEAP (PC’s) 1986: Hammer Performance Study 1996, 2006: FHWA Manual updates WEAP = Wave Equation Analysis of Piles

  4. WAVE EQUATION OBJECTIVES • Smith’s Basic Premise: • Replace Energy Formula • Use improved pile model (elastic pile) • Use improved soil model (elasto-plastic static with damping) • Allow for stress calculations • Later GRLWEAP improvements: • realistic Diesel hammer model (thermodynamics) • comparison with pile top measurements • development of more reliable soil constants • driveability and inspectors’ chart options • residual stress analysis option

  5. GRLWEAP Application • WHEN? • Before pile driving begins • After initial dynamic pile testing ( refined ) • WHY? • Equipment selection or qualification • Stress determination • Formulate driving criterion • Blow count calculation for desired capacity • Capacity determination from observed blow count

  6. Some WEAP Terminology • Hammer Ram plus hammer assembly • Hammer assembly All non-striking hammer components • Hammer efficiency Ratio of Ek just before impact to Ep • Driving system All components between hammer and pile top • Helmet weight Weight of driving system • Hammer cushion Protects hammer - between helmet and ram • Pile cushion Protects pile - between helmet and pile top • Cap Generally the striker plate + hammer cushion+helmet • Pile damping Damping of pile material • Soil damping Damping of soil in pile-soil interface • Quake Pile displacement when static resistance reaches ultimate

  7. Some WEAP Terminology • Bearing Graph Ult. Capacity and max. stress vs. blow count for a given penetration depth • Inspector’s Chart Calculates blow count and stresses for given ult. capacity at a given penetration depth as a function of stroke/energy • Driveability analysis Calculate blow count and stresses vs. depth based on static soils analysis • SRD Static Resistance to Driving • Soil set-up factor Ratio of long term to EOD resistance • Gain/loss factor Ratio of SRD to long term resistance • Variable set-up Setup occurring during a limited driving interruption

  8. THE WAVE EQUATION MODEL • The Wave Equation Analysis calculates the movements (velocities and displacements) of any point of a slender elastic rod at any time. • The calculation is based on rod • Length • Cross Sectional Area • Elastic Modulus • Mass density

  9. GRLWEAP Fundamentals • For a pile driving analysis, the “rod” is Hammer + Driving System + Pile • The rod is assumed to be elastic(?) and slender(?) • The soil is represented by resistance forces acting at the pile soil interface

  10. GRLWEAP - 3 Hammer Models

  11. External Combustion Hammer Modeling Cylinder and upper frame = assembly top mass Ram guides for assembly stiffness Drop height Ram: A, L for stiffness, mass Hammer base = assembly bottom mass

  12. External Combustion HammersRam Model Ram segments ~1m long Combined Ram-H.Cushion Helmet mass

  13. External Combustion HammersCombined Ram Assembly Model Ram segments Assembly segments Combined Ram-H.Cushion Helmet mass

  14. Diesel Hammer Combustion Pressure Model • Compressive Stroke, hC • Cylinder Area, ACH • Final Chamber Volume, VCH • Max. Pressure, pMAX Precompression-Combustion-Expansion- pressures from thermodynamics Ports hC

  15. DIESEL PRESSURE MODELLiquid Injection Hammers Pressure Port Closure Combustion Port Open Expansion Impact Compression pMAX Time

  16. Program Flow – Diesel HammersFixed pressure, variable stroke Setup hammer, pile, soil model Downward = rated stroke Downward = upward stroke Next Ru? Calculate pile and ram motion N Strokes match? N Find upward stroke Output

  17. Potential / Kinetic Energy WR WR h vi = Ö 2g h η EP = WR h (potential or rated energy) vi EK = ½ mR vi2 (kinetic energy) EK = ηEP (η - hammer efficiency) WP Max ET = ∫F(t) v(t) dt “Transferred Energy” EMX ETR = EMX/ ER = “transfer ratio”

  18. GRLWEAP hammer efficiencies • The hammer efficiency reduces the impact velocity of the ram; reduction factor is based on experience • Hammer efficiencies cover all losses which cannot be calculated • Diesel hammer energy loss due to precompression or cushioning can be calculated and, therefore, is not covered by hammer efficiency

  19. GRLWEAP diesel hammer efficiencies Open end diesel hammers: 0.80 (uncertainty of fall height, friction, alignment) Closed end diesel hammers: 0.80 (uncertainty of fall height, friction, power assist, alignment)

  20. Other ECH efficiency recommendations Single acting Air/Steam hammers: 0.67 (fall height, preadmission, friction, alignment) Double acting Air/Steam/Hydraulic: 0.50 (preadmission, reduced pressure, friction, alignment) Drop hammers winch released: 0.50 (uncertainty of fall height, friction, and winch losses) Free released drop hammers (rare): 0.67 (uncertainty of fall height friction)

  21. GRLWEAP hydraulic hammer efficiencies Hammers with internal monitor: 0.95 (uncertainty of hammer alignment) Hydraulic hammers (no monitor): 0.80 Power assisted hydraulic hammers: 0.80 (uncertainty of fall height, alignment, friction, power assist) If not measured, fall height must be assumed and can be quite variable – be cautious !

  22. VIBRATORY HAMMER MODEL

  23. VIBRATORY HAMMER MODEL Bias Mass with Line Force FL Connecting Pads m1 Oscillator with eccentric masses, me, radii, re and clamp m2 FV 2-mass system with vibratory force FV = me2 re sint FV = me [ω2resinωt - 2(t)]

  24. GRLWEAP Hammer data file

  25. Hammer: (Masses and Springs) Driving System: Cushions (Springs) Helmet (Mass) Hammer-Driving System-Pile-Soil Model Pile: Masses and Springs Soil: Elasto-Plastic Springs and Dashpots

  26. Driving System Modeling The Driving Systems Consists of • Helmet including inserts to align hammer and pile • Hammer Cushion to protect hammer • Pile Cushion to protect concrete piles

  27. GRLWEAP Driving System Help

  28. GRLWEAP Driving System Help

  29. GRLWEAP Pile Model To make realistic calculations possible • The pile is divided into N segments • of approximate length ∆L = 1 m (3.3 ft) • with mass m = ρ A ∆L • and stiffness k = E A / ∆L • there are N = L / ∆L pile segments • Divide time into intervals (typically 0.1 ms)

  30. Computational Time Increment, ∆t Time ∆t is a fraction (e.g. ½ ) of the critical time, which is ∆L/c ∆tcr ∆L ∆t L/c Length

  31. Driving system model (Concrete piles) Hammer Cushion: Spring plus Dashpot Helmet + Inserts Pile Cushion + Pile Top: Spring + Dashpot

  32. Non-linear springsSprings at material interfaces Hammer interface springs Cushions Helmet/Pile Splices with slacks

  33. Non-linear (cushion) springs • Parameters • Stiffness, k = EA/t • Coefficient of Restitution, COR • Round-out deformation,δr , or compressive slack • Tension slack, δs Compressive Force k /COR2 k Compressive Deformation δr δs

  34. Hammer cushion Pile cushion

  35. The Pile and Soil Model Mass density,  Modulus, E X-Area, A ∆L= L/N  1m Spring (static resistance) Dashpot (dynamic resist) Mass mi Stiffness ki

  36. Soil Resistance • Soil resistance slows pile movement and causes pile rebound • A very slowly moving pile only encounters static resistance • A rapidly moving pile also encounters dynamic resistance • The static resistance to driving may differ from the soil resistance under static loads • Pore pressure effects • Lateral movements • Plugging for open profiles • Etc.

  37. The Soil Model Segment i-1 Segment i Segment i+1 ki-1,Rui-1 Ji-1 ki,Rui RIGID SOIL SURROUNDING SOIL/PILE INTERFACE Ji ki+1,Rui+1 Ji+1

  38. Smith’s Soil Model Segment i ui vi Total Soil Resistance Rtotal = Rsi +Rdi Fixed

  39. Shaft Resistance and Quake Rsi -Rui Rui qi qi Recommended Shaft Quake ( qi ) 2.5 mm; 0.1 inches ui

  40. Recommended Toe Quakes, qt R Rut qt qt u Non-displacement piles Displacement piles 0.1” or 2.5 mm 0.04” or 1 mm on hard rock D/120: very dense/hard soils D/60: softer/loose soils D

  41. Smith’s Soil Damping Model (Shaft or Toe) Rd = RsJs v Pile Segment Smith damping factor, Js [s/m or s/ft] Fixed reference (soil around pile) Rd = RuJs v Smith-viscous damping factor Jsvi [s/m or s/ft] velocity v dashpot

  42. Alternative Soil ModelsCoyle-Gibson Results (1968) Clay Sand

  43. Recommended damping factorsafter Smith Shaft Clay: 0.65 s/m or 0.20 s/ft Sand: 0.16 s/m or 0.05 s/ft Silts: use an intermediate value Layered soils: use a weighted average Toe All soils: 0.50 s/m or 0.15 s/ft

  44. Numerical treatment:Force balance at a segment Force from upper spring, Fi Acceleration: ai=(Fi – Fi+1+Wi– Ri) / mi Velocity, vi, and Displacement, ui, from Integration Mass mi Resistance force, Ri (static plus damping) Weight, Wi Force from lower spring, Fi+1

  45. Wave Equation Analysis calculates displacement of all points of a pile as function of time. mi-1 Calculate displacements: uni = uoi + voit Calculate spring displacement: ci = uni - uni-1 Calculate spring forces: Fi = ki ci k = EA / ΔL uni-1 Fi, ci mi uni mi+1 uni+1

  46. Set or Blow Count Calculation from Extrapolated toe displacement R Maximum Set Calculated Ru Extrapolated Set Final Set Quake

  47. Blow Count Calculation • Once pile toe rebounds, max toe displacement is known, example: 0.3 inch or 7.5 mm • Final Set = Max Toe Displacement – Quake = 0.3 – 0.1 =0.2 inch = 7.5 - 2.5 = 5 mm • “Blow Count” is Inverse of “Final Set” BCT = 12 / 0.2 = 60 Bl / ft BCT = 1000 / 5 = 200 Bl / m

  48. Alternative Blow Count Calculationby RSA • Residual Stress Analysis is also called Multiple Blow Analysis • Analyzes several blows consecutively with initial stresses, displacements from static state at end of previous blow • Yields residual stresses in pile at end of blow; generally lower blow counts

  49. RESIDUAL STRESS OPTION BETWEEN HAMMER BLOWS, PILE AND SOIL STORE ENERGY Set for 2 Blows Convergence: Consecutive Blows have same pile compression/sets

  50. COMPUTATIONAL PROCEDURESmith’s Bearing Graph • Analyze for a range of capacities • In: Static resistance distribution assumed • Out: Pile static capacity vs. blow count • Out: Critical driving stresses vs. blow count • Out: Stroke for diesel hammers vs. blow count

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