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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 1800s 1950: 1970: 1976: 1980s: 1986: 1996, 2006: Closed Form Solutions & Energy Formulas Smith’s Wave Equation CAPWAP WEAP, TTI (mainframes) GRLWEAP (PC’s) Hammer Performance Study FHWA Manual updates WEAP = Wave Equation Analysis of Piles 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 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 Some WEAP Terminology • Hammer • Hammer assembly • Hammer efficiency Ram plus hammer assembly All non-striking hammer components Ratio of Ek just before impact to Ep • • • • • All components between hammer and pile top Weight of driving system Protects hammer - between helmet and ram Protects pile - between helmet and pile top Generally the striker plate + hammer cushion+helmet Driving system Helmet weight Hammer cushion Pile cushion Cap • Pile damping • Soil damping • Quake Damping of pile material Damping of soil in pile-soil interface Pile displacement when static resistance reaches ultimate 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 • • • • Static Resistance to Driving Ratio of long term to EOD resistance Ratio of SRD to long term resistance Setup occurring during a limited driving interruption SRD Soil set-up factor Gain/loss factor Variable set-up 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. 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 GRLWEAP - 3 Hammer Models 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 External Combustion Hammers Ram Model Ram segments ~1m long Combined RamH.Cushion Helmet mass External Combustion Hammers Combined Ram Assembly Model Ram segments Assembly segments Combined RamH.Cushion Helmet mass Diesel Hammer Combustion Pressure Model • • • • Compressive Stroke, hC Cylinder Area, ACH Final Chamber Volume, VCH Max. Pressure, pMAX PrecompressionCombustionExpansionpressures from thermodynamics Ports hC DIESEL PRESSURE MODEL Liquid Injection Hammers Open Expansion Port Pressure Compression pMAX Time Program Flow – Diesel Hammers Fixed pressure, variable stroke Setup hammer, pile, soil model Downward = rated stroke Calculate pile and ram motion Find upward stroke Downward = upward stroke Next Ru? N Strokes match? N Output Potential / Kinetic Energy EP = WR h (potential or rated energy) EK = ½ mR vi2 (kinetic energy) EK = ηEP (η - hammer efficiency) WR vi W R vi = 2g h η Max ET = ∫F(t) v(t) dt “Transferred Energy” EMX ETR = EMX/ ER = “transfer ratio” WP h 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 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) 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): (uncertainty of fall height friction) 0.67 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 ! VIBRATORY HAMMER MODEL VIBRATORY HAMMER MODEL FL Bias Mass with Line Force m1 Connecting Pads Oscillator with eccentric masses, me, radii, re and clamp m2 2-mass system with vibratory force FV = me 2 re sint FV GRLWEAP Hammer data file Hammer-Driving System-Pile-Soil Model Hammer: (Masses and Springs) Pile: Driving System: Cushions (Springs) Helmet (Mass) Soil: 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 GRLWEAP Driving System Help GRLWEAP Driving System Help 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) Computational Time Increment, ∆t ∆t is a fraction (e.g. ½ ) of the critical time, which is ∆L/c Time ∆tcr ∆L ∆t L/c Length Driving system model (Concrete piles) Hammer Cushion: Spring plus Dashpot Helmet + Inserts Pile Cushion + Pile Top: Spring + Dashpot Non-linear springs Springs at material interfaces Hammer interface springs Cushions Helmet/Pile Splices with slacks Non-linear (cushion) springs • Parameters Compressive Force • Stiffness, k = EA/t • Coefficient of Restitution, COR • Round-out deformation,δr , or compressive slack • Tension slack, δs δs k δr k /COR2 Compressive Deformation Hammer cushion Pile cushion Material Modulus (ksi) Material Modulus (ksi) Aluminum Micarta 350 Plywood 30 new 75 used Conbest 280 Oak 60 (transverse) Hamortex 125 Nylon 175-200 Oak (parallel) 750 The Pile and Soil Model Mass density, Modulus, E X-Area, A Mass mi Stiffness ki ∆L= L/N 1m Spring (static resistance) Dashpot (dynamic resist) 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. The Soil Model Segment i-1 RIGID SOIL SURROUNDING SOIL/PILE INTERFACE ki-1,Rui-1 Ji-1 ki,Rui Segment Ji i ki+1,Rui+1 Segment i+1 Ji+1 Smith’s Soil Model Total Soil Resistance Rtotal = Rsi +Rdi Segment i ui vi Fixed Shaft Resistance and Quake Rsi -Rui Rui qi qi Recommended Shaft Quake ( qi ) ui 2.5 mm; 0.1 inches Recommended Toe Quakes, qt Non-displacement piles Displacement piles 0.1” or 2.5 mm D/120: very dense/hard soils 0.04” or 1 mm on hard rock qt D/60: softer/loose soils qt D u Rut R Smith’s Soil Damping Model (Shaft or Toe) Rd = RsJs v Pile Segment Fixed reference (soil around pile) velocity v dashpot Smith damping factor, Js [s/m or s/ft] Rd = RuJs v Smith-viscous damping factor Jsvi [s/m or s/ft] Alternative Soil Models Coyle-Gibson Results (1968) Sand Clay Recommended damping factors after Smith Shaft Clay: Sand: Silts: Layered soils: 0.65 s/m or 0.20 s/ft 0.16 s/m or 0.05 s/ft use an intermediate value use a weighted average Toe All soils: 0.50 s/m or 0.15 s/ft Numerical treatment: Force balance at a segment Force from upper spring, Fi Resistance force, Ri Mass mi (static plus damping) Weight, Wi Force from lower spring, Fi+1 Acceleration: ai = (Fi – Fi+1 + Wi – Ri) / mi Velocity, vi, and Displacement, ui, from Integration Wave Equation Analysis calculates displacement of all points of a pile as function of time. Calculate displacements: uni = uoi + voi t mi-1 uni-1 Fi, ci Calculate spring displacement: ci = uni - uni-1 Calculate spring forces: mi uni Fi = ki ci mi+1 k = EA / ΔL uni+1 Set or Blow Count Calculation from Extrapolated toe displacement R Maximum Set Calculated Ru Extrapolated Set Final Set Quake 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 Alternative Blow Count Calculation by 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 RESIDUAL STRESS OPTION BETWEEN HAMMER BLOWS, PILE AND SOIL STORE ENERGY Set for 2 Blows Convergence: Consecutive Blows have same pile compression/sets COMPUTATIONAL PROCEDURE Smith’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 Bearing Graph: Required Blow Count For required capacity Find minimum blow count Bearing Graph: Capacity Determination Find indicated capacity For observed blow count Program Flow – Bearing Graph Input Model hammer & driving system Model Pile Distribute Ru Set Soil Constants Time Increment Increase Ru Static Analysis Ram velocity Dynamic Analysis • Pile stresses • Energy transfer • Pile velocities Increase R u? N Choose first Ru Calculate Blow Count Output PURPOSE OF ANALYSIS • Preliminary Equipment Selection – Hammer OK for Pile, Capacity – Includes stress check • Driving Criterion – Blow Count for Capacity and Stroke OUTPUT REVIEW • Blow Counts Satisfactory? • Stresses Less Than Allowable? • Economical Hammer, Pile? If not, consider reanalyzing with different hammer system, pile size. INSPECTOR’S CHART Constant capacity – analyze with variable energy or stroke OK Bad Question for Driveability: WHAT IS RU DURING DRIVING? • We call it Static Resistance to Driving (SRD), because we lose shaft resistance during driving. • Will we regain resistance by Soil Set-up primarily along shaft (may be 10 x in clay) • Driveability requires analyze with full loss of set-up (or with partial loss of set-up for a short driving interruption) Set-up factors Soil Type Setup Factor Clay 2 Silt – Clay 1 Silt 1.5 Sand – Clay 1.2 Fine Sand 1 Sand - Gravel 1 Thendean, G., Rausche, F., Svinkin, M., Likins, G. E., September, 1996. Wave Equation Correlation Studies. Proceedings of the Fifth International Conference on the Application of Stress-wave Theory to Piles 1996: Orlando, FL; 144-162. For Driveability: Static capacity changes Set-up Time Remolding energy Ru Ru/SF Ru/SF Time Driving Waiting Time Re-Drive • Set-up factor, SF • Capacity increases (Set-up) after driving stops • Capacity decreases (Remolds) during redrive Program Flow – Driveability Input Calculate Ru for first gain/loss Model hammer & driving system Analysis First depth of analysis - soil model Pile length and model Increase Depth Next G/L Increase G/L? N Increase Depth? Output N COMPUTATIONAL PROCEDURE Driveability Analysis • Analysis as the pile is penetrated – Input capacity with depth (static analysis) • Generates a driving record – Predicts blow count with depth – Stresses, (diesel stroke), with depth Static Soil Analysis Approximate for Bearing Graph: – Percent Shaft Resistance – Resistance Distribution Detailed for Driveability – Shaft Resistance vs Depth – End Bearing vs Depth – Set-up Factor Driveability PURPOSE OF ANALYSIS • Preliminary Equipment Selection – Hammer OK for Pile, Capacity • Driving Criterion – Blow Count for Capacity and stroke • Driveability – Acceptable Blow Count throughout – Acceptable Stresses throughout Co ntract No .: P ro ject: S tru cture Na me an d/o r No .: P ile Drivin g Co ntracto r o r Su bco n tracto r: Co un ty: (Piles d riv en b y) R a m Pile Driving and Equipment Data Form Hammer Man ufa cturer: Mo d el No .: Ham mer Type : Se rial No .: Man ufa cturers Max imu m Ra te d E ne rg y: Stro ke a t Max imu m Ra te d E ne rg y: Ran ge in O p era tin g E ne rg y: to Ran ge in O p era tin g S tro ke: to Ram W eigh t: (kip s) Mod ific atio ns: (ft-lbs) (ft) (ft-lbs) (ft) Anvil Striker Plate Weigh t: Thickne ss: (kips) Diam ete r: (in) (in ) Mate rial # 1 Hammer Cushion Ma te rial # 2 (fo r Co mp osite Cu shion ) Nam e: Na me : Area : (in2 ) A re a: Thickne ss/Plate : (in) Th ickn ess /P la te: No. o f P la tes: No . of Plate s: Tota l Thickne ss of Ha mm er Cu sh ion : Helmet (Drive Head) Weigh t: Pile Cushion (kips) Mate rial: Area : (in2 ) No. o f S he ets: Tota l Thickne ss of P ile Cus hio n: Th ickn ess /S h ee t: (in ) Pile Typ e: Wall Th ickn ess: Cro ss Se ctio na l Area : (in ) Tap er: (in 2) We ig ht/Ft: Orde re d Le n gth : Design Lo ad : Ultim ate P ile Ca pa city: (ft) (kip s) (kip s) Pile Descrip tion of S plice: Driv ing Sh oe /Clo su re P la te De scriptio n: Su bm itted By: Telep ho ne No.: (in 2) (in) Date : Fax No .: (in) Required Input Data • Hammer – Model – Energy level (stroke) • Driving system – Hammer cushion material (E, A), thickness – Helmet weight (of entire assembly) – Pile cushion material (E, A), thickness (for concrete piles only) Required Input Data • Soil (from Borings with elevations) – Type of soils – N-values vs depth or other strength parameters – Elevation of water table Data Entry •Resistance distribution •Simple •From soil input wizard •For driveability •Soil properties vs depth: •Shaft unit resistance – requires calculation •End bearing - requires calculation •Quakes and damping •Set-up factor •Analysis depths Available Help - Indirect GRLWEAP Help – Direct: F3 Area calculator from any area input field. Final Recommendation • Perform sensitivity studies on parameters • Plot upper and lower bound results • Note: low hammer efficiency not always conservative • Read the helps and disclaimers •On screen or after printing them • Compare results with dynamic testing Summary • There are 3 distinctly different hammer models – External Combustion Hammer models – Diesel hammer and pressure models – Vibratory hammer model • There are 3 components in driving system model – Hammer Cushion – Helmet and Inserts – Pile Cushion (concrete piles only) • Model Parameters can be found in GRLWEAP Help Section or Hammer data file. SUMMARY continued • The wave equation analysis works with “Static Resistance to Driving” (SRD) plus a Damping or Dynamic Resistance • Important analysis options include: – Bearing Graph – Inspector’s Chart – Driveability Graph • The whole package is geared towards standard analyses; some research options exist Summary: W.E. APPLICATIONS • Design stage – Preliminary hammer selection – Selection of pile section for driveability – Selection of material strength for driving • Construction stage – Hammer system approval – Contractors use to select equipment – One means of estimating blow count – Inspector’s chart for variable hammer stroke Summary: Purpose of analysis Develop driving criterion Final Set (Blow count) for a required capacity Final Set as a function of energy/stroke Check driveability Final Set (Blow Count) vs. depth Stresses vs. depth Optimal equipment To Minimize Driving Time