Fundamentals of Dynamic Driven Pile Analysis
© 2013, Pile Dynamics, Inc. - Frank Rausche, Ph.D., P.E.
1 GRLWEAP Fundamentals CONTENT • Introduction • Why, when and where wave equation • Wave Equation Models: Hammer, Pile, Soil • An Example • Summary
2 GRLWEAP Fundamentals GRLWEAP Application • WHEN? – Before pile driving begins, based on estimates – After initial pile tests using test results (refined WE) • WHY? – Formulate driving criterion (for required capacity) – Equipment (hammer and driving system) selection – Pile size/impedance selection – Stress and blow count calculation (driveability) – Capacity determination
3 GRLWEAP Fundamentals GRLWEAP Application: During Design
Get Factored Loads
Qft = Σ(fi Qi) Do Borings Perform required initial tests Decide Pile Type Ru Verification No and Resistance Satisfactory? Factor, φ No
Dynamic Required R = n Analysis:Driveable (1/φ) Q Establish Driving Criterion ft Pile? Do Static Analysis Drive Production Piles to Find Pile Length Blow Count Test as many as required
4 GRLWEAP Fundamentals Wave Equation Application: Capacity Determination by Bearing Graph GRL Engineers, Inc. 08-Aug-2012 GRLWEAP Example GRLWEAP Version 2010
20 20 DELMAG D 30-32 Ram Weight 29.37 kN 16 16 Efficiency 0.800 Pressure 9645 (99%) kPa Helmet Weight 17.79 kN 12 12 Hammer Cushion 19259 kN/mm Pile Cushion 1009 kN/mm COR of P.C. 0.500 8 8
Skin Quake 2.500 mm TensionStress (MPa)
CompressiveStress (MPa) Toe Quake 10.160 mm 4 4 Skin Damping 0.650 sec/m Toe Damping 0.500 sec/m Pile Length 20.50 m 0 0 Pile Penetration 14.01 m Pile Top Area 3716.12 cm2 4000 5 Skin Friction Pile Model Distribution 3200 4
2400 3 Stroke(m)
1600 2 UltimateCapacity (kN)
800 1
0 0 0 60 120 180 240 300 360 Res. Shaft = 71 % Blow Count (blows/.30m) (Proportional)
5 GRLWEAP Fundamentals GRLWEAP Application: Driveability Check
Blow Count < Acceptable
Stresses < Acceptable
6 GRLWEAP Fundamentals Dynamic Formulas
1893 Wellington (Engineering News) Now: Modified Gates
Energy Dissipated in Soil = Energy Provided by Hammer
(RUC)(Pile Set) = (Hammer Efficiency) (Wr h)
7 GRLWEAP Fundamentals ENR and Gates for D 19-42
Er = 42 kip-ft = 57 kN-m
4000
3500
3000
2500
2000
1500 Capacity in kN Capacityin 1000
500
0 0 25 50 75 100 125 150 175 200 Blows/0.25 m
Gates - w/ calculated Stroke ENR - Ru = Rd x 2
8 GRLWEAP Fundamentals Shortcomings of Formulas
• Rigid pile model • Poor hammer representation • Inherently inaccurate for both capacity and blow count predictions • No stress results • Unknown hammer energy • Relies on EOD Blow Counts
9 GRLWEAP Fundamentals The 1-D Wave Equation ρ(δ2u/ δt2) = E (δ2u/ δx2) E … elastic modulus f ρ … mass density
with c2 = E/ ρ ... Wave Speed Solution: u = f(x-ct) + g(x+ct)
g x x … length coordinate t ... time u … displacement
10 GRLWEAP Fundamentals THE WAVE EQUATION MODEL
• The Wave Equation Analysis calculates the displacement of any point of a slender elastic rod at any time using a difference method. • The calculation is based on rod – Length – Cross Sectional Area – Elastic Modulus – Mass density
11 GRLWEAP Fundamentals
GRLWEAP Fundamentals Hammer • For a pile driving analysis, the D.S. “slender, elastic rod” consists of Hammer+Driving System+Pile
• The soil is represented by resistance forces acting on the pile and Pile representing the forces in the pile-soil interface
12 GRLWEAP Fundamentals The Pile Model To solve the wave equation numerically:
• The hammer-pile system is divided into ∆L segments (masses and springs) – of length ∆L typically: ∆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
13 GRLWEAP Fundamentals We can model 3 hammer-pile systems
14 GRLWEAP Fundamentals 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
15 GRLWEAP Fundamentals External Combustion Hammers Ram Model
Ram segments ~1m long
Combined Ram- H.Cushion Helmet mass
16 GRLWEAP Fundamentals External Combustion Hammers Combined Ram Assembly Model
Ram segments
Assembly segments
Combined Ram- H.Cushion Helmet mass 17 GRLWEAP Fundamentals External Combustion Hammer Analysis Procedure • Static equilibrium analysis • Dynamic analysis starts when ram is within 1 ms of impact. • All ram segments then have velocity 1/2 VRAM = (2 g h η) – 0.001 g
g is the gravitational acceleration h is the equivalent hammer stroke and η is the hammer efficiency h = Hammer potential energy/ Ram weight
18 GRLWEAP Fundamentals External Combustion Hammer Analysis Procedure
• Dynamic analysis ends when
– Pile toe has rebounded to 80% of max dtoe – Pile has penetrated more than 4 inches
– Pile toe has rebounded to 98% of max dtoe and energy in pile is essentially dissipated
19 GRLWEAP Fundamentals
Diesel Hammers
Open Ended Open Closed Ended Closed
20 GRLWEAP Fundamentals Diesel Hammer Components
Piston = Ram
Cylinder
Fuel Port (closed by piston) pump Compressive stroke Combustion chamber
Impact block Hammer Cushion; Helmet
21 GRLWEAP Fundamentals Diesel Hammer Model
Ram segments ~1m long
Ram bottom/impact block Impact Block mass Hammer Cushion Helmet mass
22 GRLWEAP Fundamentals Diesel Hammer Combustion Pressure Model
• Compressive Stroke, hC
• Cylinder Area, ACH
• Final Chamber Volume, VCH
• Max. Pressure, pMAX Ports Precompression- h Combustion- C Expansion- Pressure
23 GRLWEAP Fundamentals DIESEL PRESSURE MODEL Liquid Injection Hammers
Liquid Injection Timing Parameters: Pressure Combustion Delay, ∆t
Combustion Duration, tD
Expansion:
1.25 Port p=pMAX(VCH/V) Open tD ∆t Compression:
1.35 p=patm(Vin/V) pMAX Time
24 GRLWEAP Fundamentals Energy, Efficiency and Measurements Potential (Rated) Kinetic Transferred
25 GRLWEAP Fundamentals WR Measured Transferred Energy
Max ET = ∫F(t) v(t) dt h (EMX, ENTHRU) WR
ηT = ENTHRU/ ER (transfer ratio or efficiency) Measure
ER = WR h Force, F(t) Manufacturer’s Rating Velocity, v(t)
26 GRLWEAP Fundamentals Measured Transfer Ratios for Diesels Steel Piles Concrete Piles
27 GRLWEAP Fundamentals SA Air Hammers – SA Hydraulic Hammers on Steel Piles
28 GRLWEAP Fundamentals GRLWEAP
Impact Hammer Efficiencies , ηh Diesel hammers: 0.80 Traditional air/steam hammers: 0.67 Hydraulic hammers: 0.80 Hammers with energy monitoring: 0.95
These efficiencies account for energy losses that we cannot calculate or otherwise assess!
29 GRLWEAP Fundamentals Vibratory Hammers
30 GRLWEAP Fundamentals Vibratory Hammer Model
• Line Force FL
• Bias Mass and m1
• Oscillator mass, m2
• Eccentric masses, me, m2 FV radii, re • Clamp Vibratory Force: 2 FV = me [ω resin ω t - a2(t)]
31 GRLWEAP Fundamentals Driving System Models
The Driving Systems Consists of 1. Helmet including inserts to align hammer and pile 2. Optionally: Hammer Cushion to protect hammer 3. For Concrete Piles: Softwood Cushion
32 GRLWEAP Fundamentals Driving System Model Example of a diesel hammer on a concrete pile
Hammer Cushion: Spring plus Dashpot Helmet + Inserts Pile Cushion + Pile Top: Spring + Dashpot
Pile Top Mass
33 GRLWEAP Fundamentals The Soil Model After Smith
Outer Soil: Interface Soil: Rigid Elasto-Plastic Springs and Viscous Dashpots
34 GRLWEAP Fundamentals 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 differs from the soil resistance under static loads
35 GRLWEAP Fundamentals Smith’s Soil Model Total Soil Resistance
Rtotal = Rsi +Rdi
R function of u Segment si i function of v i Rdi i
Fixed Displacemt ui Velocity vi
37 GRLWEAP Fundamentals Static Shaft Resistance Pile Segment Model Parameters R , q ui i Elastic spring with max. Static Resistance compression q (quake) Rigid plastic slider Rui with Resistance Rui
ksi = Rui /qi Fixed reference
quake, qi Pile Displacement 38 GRLWEAP Fundamentals Shaft Resistance and Quake Static Resistance
-Rui Rui qi
Recommended
qi Shaft Quakes: 2.5 mm or 0.1 inches Pile Displacement
39 GRLWEAP Fundamentals The Static Toe Resistance and Quake Static Toe Resistance
Rui qi For impact hammers
For vibratory hammers qi
Toe Displacement
40 GRLWEAP Fundamentals Recommended Toe Quakes, qt Static Toe Res. Non-displacement Displacement piles R piles qt ut 0.1” or 2.5 mm D/120: very dense/hard soils 0.04” or 1 mm on hard rock D/60: softer/loose soils qt
Toe Displacement
D
41 GRLWEAP Fundamentals Smith’s Soil Damping Model (Shaft or Toe)
Rd = RsJs v Fixed Pile Smith damping factor, reference J [s/m or s/ft] Segment (soil around s pile) Rd = RuJsv v Smith-viscous damping
factor Jsv [s/m or s/ft] velocity v For RSA and Vibratory Ananlysis
dashpot
42 GRLWEAP Fundamentals Recommended Smith damping factors
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 for bearing graph Toe All soils: 0.50 s/m or 0.15 s/ft
43 GRLWEAP Fundamentals Resistance Distribution
1. Simplest I. Percentage Shaft resistance (from static soils analysis) II. Triangular or Rectangular or Trapezoidal Only reasonable for a simple
Bearing Graph where little is Penetration known about soil. End Bearing = Total Capacity x (100% - Percent Shaft Resistance)
44 GRLWEAP Fundamentals Resistance Distribution
2. Still Simple: ST Analysis based on some knowledge of Soil Types
Reasonable for a simple Bearing Graph; for Driveability possible, but more accurate analysis should be done. Penetration
End Bearing = From Soil Type, Pile Bottom Area
45 GRLWEAP Fundamentals Resistance Distribution 3. More Involved: I. SA Input: SPT Blow Count, Friction
Angle or Unconfined Compressive Strength II. API (offshore wave version) Input: Friction Angle or Undrained Shear Strength
III. CPT Penetration Input: Cone Record including Tip Resistance and Sleeve Friction vs Depth.
All are good for a Bearing Graph May be OK for Driveability Analysis Local experience may provide better values
46 GRLWEAP Fundamentals Numerical Treatment • Predict displacements:
uni = uoi + voi ∆t uni-1 Mass i-1 R • Calculate spring compression: i-1
ci = uni - uni-1 Fi, ci
• Calculate spring forces: uni Mass i Ri
Fi = ki ci
• Calculate resistance forces: uni+1 Mass i+1 Ri+1 Ri = Rsi + Rdi
47 GRLWEAP Fundamentals Force balance at a segment
Force from upper spring, Fi
Resistance force, Ri Mass i Weight, Wi
Force from lower spring, Fi+1
Acceleration: ai = (Fi + Wi – Ri – Fi+1) / mi
Velocity, vi, and Displacement, ui, from Integration
48 GRLWEAP Fundamentals Set or Blow Count Calculation (a) Simplified: extrapolated toe displacement Static soil Resistance
Max. Displacement
Calculated
Extrapolated Ru
Pile Displacement
Final Set Quake
49 GRLWEAP Fundamentals (b) 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
50 GRLWEAP Fundamentals Blow Count Calculation (b) Residual Stress Analysis (RSA)
Set for 2 Blows
Convergence: Consecutive Blows have same pile compression/sets
51 GRLWEAP Fundamentals RSA: When and How • RSA is the preferable method of analysis for long slender piles (e.g., steel piles with Lp/D > 100 or Monotube/Taper Tube piles) • RSA calculates somewhat higher blow counts than standard analysis (non- conservative) • RSA calculates somewhat higher stresses than standard analysis (conservative)
52 GRLWEAP Fundamentals Program Flow – Bearing Graph
Input Distribute Ru Increase Ru Set Soil Constants
Model hammer, Static Equilibrium
driving system Ram velocity
and pile Dynamic analysis Y Increase
Ru? • Pile stresses • Energy transfer Choose first Ru • Pile velocities N
Calculate Blow Count Output
53 GRLWEAP Fundamentals Bearing Graph: Variable Capacity, One depth SI-Units; Clay and Sand Example; D19-42; HP 12x53;
54 GRLWEAP Fundamentals The Inspectors’ Chart: One Capacity and One Depth – Stroke Variable GRL Engineers, Inc. 21-Aug-2011 Demo 3-Inspector's Chart - D16-32 GRLWEAP Version 2010
250 250 DELMAG D 16-32 Capacity 1600.0 kN Ram Weight 15.66 kN 200 200 Efficiency 0.800 Pressure 9825 (99%) kPa Helmet Weight 8.45 kN 150 150 Hammer Cushion 10535 kN/mm COR of H.C. 0.800 Skin Quake 2.500 mm Toe Quake 2.500 mm 100 100 TensionStress (MPa) Skin Damping 0.259 sec/m
CompressiveStress (MPa) Toe Damping 0.500 sec/m Pile Length 18.28 m 50 50 Pile Penetration 16.76 m Pile Top Area 140.64 cm2
Skin Friction 0 0 Pile Model Distribution
3.50
3.10
2.70 Stroke(m)
2.30
1.90
1.50 40 80 120 160 200 240 280 Res. Shaft = 30 % Blow Count (blows/.25m) (Proportional)
55 GRLWEAP Fundamentals Formulas and Wave Equation D19-42; HP 12x53; Clay and Sand
4000
3500
3000
2500
2000
1500 Capacity in Capacity kN 1000
500
0 0 25 50 75 100 125 150 175 200 Blow s/0.25 m
Gates ENR GRLWEAP-Clay GRLWEAP-Sand
56 GRLWEAP Fundamentals Driveability Analysis
Basically: • Perform a static soil analysis – do it as accurately as possible • Perform wave equation analyses for
different depths with Ru from static soil analysis
• Plot calculated Ru, blow count, maximum stresses vs. depth
57 GRLWEAP Fundamentals Driveability Analysis
• Analyze a series of Bearing Graphs for different depths for SRD and/or LTSR • Put the results in sequence so that we get predicted blow count and stresses vs pile toe penetration • Note that, in many or most cases, shaft resistance is lower during driving (soil setup) and end bearing is about the same as long term • In the few cases of relaxation, the toe resistance is actually higher during driving than long term
58 GRLWEAP Fundamentals Program Flow – Driveability
Input Calculate Ru for first gain/loss Model Hammer & Next G/L Driving System Analysis
Choose first Depth to analyze Increase Y G/L?
Pile Length and N
Model Y Increase Output Depth? Increase Depth N
59 GRLWEAP Fundamentals Driveability Result
60 GRLWEAP Fundamentals Remarks About SRD
• WHAT IS RU DURING DRIVING? We call it SRD, because we lose static shaft resistance during driving. • In general, we will regain static resistance by Soil Setup - primarily along shaft (maybe up to 10x in clay) • During analysis we may want to analyze with full loss of setup or with partial loss of setup or with no loss of setup at all.
61 GRLWEAP Fundamentals For Driveability with variable setup time
• Setup time Setup Time Defines after how Ru much waiting time setup is gained Ru/SF
Time Ru Limit • Limit Distance Distance Defines after how Ru/SF much driving distance soil setup is lost Pile Penetration
62 GRLWEAP Fundamentals Summary • The wave equation helps for equipment selection, setting preliminary driving criteria and capacity determination, if testing is not feasible. • For capacity determination without measurements the factor of safety has to be greater than when doing measurements (GIGO).
63 GRLWEAP Fundamentals Summary • The wave equation analysis simulates what happens in the pile due to a hammer impact. • It calculates a relationship between capacity and blow count, or blow count vs. depth. • The analysis model represents hammer (3 types), driving system (cushions, helmet), pile (concrete, steel, timber) and soil (at the pile-soil interface) • GRLWEAP provides a variety of input help features (hammer and driving system data, static formulas among others).
64 GRLWEAP Fundamentals Summary
• Good hammer performance is essential for both good productivity and a meaningful construction control by blow count. • Wave Equation analysis results are only as good as the accuracy of the hammer efficiency and soil resistance input.
65 GRLWEAP Fundamentals Thank you for your attention For further information see: www.pile.com
QUESTIONS?
66 GRLWEAP Fundamentals