GRLWEAP: Fundamentals, Models, Results
Frank Rausche 2011, Pile Dynamics, Inc.
Backg Ba ckgrou round nd – Pa Part rt 1 • • • • • • •
Histor Hist ory y and and Obje Object ctiv ives es Driven Driv en Pile Pile Desig Design, n, Energ Energy y Concep Concepts ts Wave Wav e Equa Equatio tion n Pile Pile Mod Model el Hamm Ha mmer er Mo Mod del els s Wave Wav e Equa Equatio tion n Soil Soil Mod Model el Wave Wa ve Equ Equat atio ion n Nume Numeric rics s Pro rog gra ram m Flo Flow w– • Beari rin ng Gra Graph ph • In Insp spec ecto tor’ r’s s Cha Chart rt
Dynamic Pile Analysis Developments 1800s 1850s 1950: 1960s 1976: 1980s: 1986: 1996, 2006:
Closed Form Solutions First Energy Formula Smith’s Wave Equation Dynamic Testing and CAPWAP WEAP,, TTI WEAP GRLWEAP Hammer Performance Study FHWA Manual updates
WAVE EQUATION OBJECTIVES • Sm Smit ith’ h’s s Basi Basic c Prem Premis ise: e: – Replace Energy Energy Formula Formula – Use improved improved pile model model (elastic (elastic pile) and and soil model model (elasto-plastic static resistance with damping) – Allow for realistic stress stress calculation calculations s
• Additi Additional onal GRLWEA GRLWEAP P developm development ents s expand expand the basic capabilities
Inspectors’ Graph analysis option Driveability Driveab ility analysis option Diesel hammer analysis Residual stress analysis Static geotechnical analyses Special offshore analysis options
GRLWEAP Analysis Options • Bearing Graph for capacity from observed blow count – Hammer performance performance fixed – One depth depth – Assumed c capacity apacity values values (10) (10)
• Inspectors’ Chart for required blow count – Hammer performance performance variable – One depth depth – One capacity capacity
• Driveab Driveability ility Analy Analysis sis for anticipated blow counts – Hammer performance performance fixed – Assumed depth values values (100) – Several capacity capacity v values alues for each depth depth (5)
GRLWEAP Objectives • WH WHEN EN SH SHOU OULD LD WE DO TH THE E ANA ANALY LYSI SIS? S? – Before pile pile driving driving begins – After initial initial pile tests tests have been done done (refined) (refined)
• FO FOR R WHA WHAT T PUR PURPO POSE SE? ? – Formulat Formulate e driving criterion: criterion: • Sa Safe fe st stre ress sses es • Requi Required red blow blow count for for sufficien sufficientt capacity capacity
– Adequa Adequate te equipment equipment (e.g., hammer) hammer) selection selection – Pile stress stress determination determination – Blow count count calculation calculation for required required capacity capacity – Capaci Capacity ty from observed observed blow blow count
Basic design approach for driven piles 1. Obt btai ain n Design Load (Qd) from structural design 2. De Deci cide de on on Safety Concept (FS) 3. De Deci cide de on on Pile Type based on suitability and availability 4. Perform Perform Static Static Pile Pile Analysis, Analysis, determine determine Ultimate Capacity (Ru) for assumed Pile Length. Length. 5. Fi Find nd Pile Pile Length Length so so that Ru > FS Qd
Basic design approach continued 6.
Compute Blow Count for Ru - ch chec eck k Driveability by GRLWEAP
7. Either Either perfor perform m an init initial ial Test Program, testing piles dynamically, sometimes statically 8. Es Esta tabl blis ish h Installation Criterion (min. penetration, required blow count) 9. In Inst stal alll Production Piles to criterion 10.For all production piles, final pile length is determined at installation time Reference: Hannigan, P.J., G.G. Goble, G.E. Likins, and F. Rausche. Design and Construction of Driven Pile Foundations Foundations - Volumes 1 and 2 . Publication Numbers FHWA-NHI-05-042 and 043. Washington, D.C.: U.S. Department of Transportation Federal Highway Administration, 2006.
Factor of Safety Ru ≤ (FS) Qd • Ru
Ultimate Capacity (Nominal or Characteristic Resistance)
• FS
Global Factor of Safety (1.5 < F.S. < 10) (for LRFD: FS =Combined Load/Resistance Factor)
• Qd
Design Load (Safe Load, Working Load, Sum of Unfactored Loads)
GRLWEAP works exclusively with R u
Static Analysis Methods Q
Ru = Rs + Rt
Ru = f s As + qt At
f s, As …Unit/Shaft Resistance, Area qt, At … Unit/End Bearing, Area Rs
Rt
The α -Method For example: Total Stress method for cohesive soils
•
Rs = f s As
with
f s = α cU
α is an empirical adhesion factor cU is the undrained shear strength
•
Rt = 9 cU
After Tomlinson, 1979
The β-Method primarily for cohesionless soils
•
Rs = f s As with f s = β po
β = ko tan(δ)
po is the effective overburden pressure ko is some earth pressure coefficient
•
Rt = Nt po At Nt is a bearing capacity factor
after Fellenius, 1991
... with certain limits
Static Analysis Methods
GRLWEAP’s Static Analysis Methods
Q
Icon Input ST SA CPT API
Rs
Basic Analysis
Soil Type Effective Stress, Total Stress SPT N-value Effective Stress R at cone tip and sleeve Schmertmann Effective Stress, Total Stress φ, Su
• GRLWEAP’s static analysis methods may be used for dynamic analysis preparation (resistance distribution, estimate of capacity for driveability). • For design, be sure to use a method based on local experience.
Rt
Use of Static Analysis Methods • Should always be done for finding reasonable pile type and length • For driven piles static analysis is only a starting point, since pile length is determined in the field (exceptions are piles driven to depth, for example, because of high soil setup) • For LRFD when finding pile length by static analysis method use resistance factor for selected capacity verification method
Energy Considerations If we take PDA measurements….
…we can calculate the Transferred Energy
W R
Max ET = ∫F(t) v(t) dt (ENTHRU)
h W R
ηT = ENTHRU/ ER
(transfer ratio or efficiency)
Measure Force, F(t) Velocity, v(t)
ER = WR h Manufacturer’s Rating
DIESEL HAMMERS ON STEEL PILES
DIESEL HAMMERS ON CONC./TIMBER PILES
N = 732; MEDIAN = 36.8%
N = 394; MEDIAN = 24.9%
100%
100%
90%
90%
80%
80%
70%
70%
E 60% L I T N 50% E C R E 40% P
E 60% L I T N 50% E C R 40% E P
30%
30%
20%
20%
10%
10% 0%
0% 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
0%
100%
10%
20%
ENERGY TRANSFER RATIO [EMX / E-RATED]
30%
40%
50%
60%
70%
80%
90%
ENERGY TRANSFER RATIO [EMX / E-RATED]
50%
50%
45% 40%
MEAN = 26.1% STANDARD DEVIATION = 7.9%
45%
MEAN = 36.8% STANDARD DEVIATION = 9.5%
40%
35%
35%
Y 30% C N E 25% U Q E R 20% F
Y 30% C N E 25% U Q E R 20% F
15%
15%
10%
10%
5%
5%
0%
0% 0 -5 %
1 0- 15 %
2 0- 25 %
3 0- 35 %
4 0- 45 %
5 0- 55 %
6 0- 65 %
7 0- 75 %
8 0- 85 %
ENERGY TRANSFER RATIO [EMX / E-RATED]
9 0- 95 %
0 -5 %
1 0- 15 %
2 0- 25 %
3 0- 35 %
4 0- 45 %
5 0- 55 %
6 0- 65 %
7 0- 75 %
ENERGY TRANSFER RATIO [EMX / E-RATED]
8 0- 85 %
9 0- 95 %
100%
For all impact hammers GRLWEAP needs impact velocity EP = WR h EP = WR h η
(potential, ideal)
EK = ½ mR vi2 mR = WR / g EP = EK
(kinetic energy)
v i =
(η = Hammer efficiency )
W R
v i W R
2g hη
W P
Energy (Dynamic) Formulas Energy Dissipated in Soil = Energy Provided by Hammer Ru (s + sl) = ηWr h sl … “lost” set (empirical or measured), η … efficiency of hammer/driving
system
h
Bearing Graphs from 2 Energy Formulas Hammer D 19-42; E r = 59 kJ 4000 4000 [900] 3500
Ru = ηEr /(s + sl) η = 1/3; sl = 2.5mm
R u -3000 kN [kips] N k 2500 n i y t 2000 i c 2000 a p [450] a 1500 C
Ru = 1.6 Ep ½ log(10Blows/25mm) – 120 kN
1000 500
0
0 00
25
50 5
75
10 100 125 Blows/25mm Blows/0.25 m
Ga te s - w / ca lc ul ate d Str ok e
150 15
175
E NR - R u = Rd x 2
THE WAVE EQUATION MODEL • The Wave Equation Analysis calculates the displacement 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
20 200
GRLWEAP Fundamentals • For a pile driving analysis, the “rod” is Hammer+Driving System+Pile
r e m m a H
D.S.
• The rod is assumed to be elastic(?) and slender(?) e l i P
• The soil is represented by resistance forces acting at the pile soil interface
GRLWEAP Pile Model To solve the wave equation numerically: • The pile is divided into N segments – of approximate length ∆L typically: ∆L = 1 m (3.3 ft) – with mass m = ρ A ∆L
∆L
– and stiffness k = E A / ∆L – there are
N = L / ∆L pile segments
• The analysis time is divided into intervals typically:
∆t = 0.1 ms
GRLWEAP 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
GRLWEAP 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 Hammer Model • Ram modeled like rod • Stroke is an input (Energy/Ram Weight) • Impact Velocity Calculated from Stroke with Hammer Efficiency Reduction: v i = (2 g h η ) ½ • Assembly also modeled because it may impact during pile rebound • Note approximation in data file: Assembly mass = Total hammer mass – Ram 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
External Combustion Hammer Procedure
• Static equilibrium analysis • Dynamic analysis starts when ram is within 1 ms of impact. • All ram segments then have velocity V RAM = (2 g h η )1/2 – 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
External Combustion Hammer Procedure
• Dynamic analysis ends when – Pile toe has rebounded to 80% of max d toe – Pile has penetrated more than 4 inches – Pile toe has rebounded to 98% of max d toe and energy in pile is essentially dissipated
DIESEL HAMMERS Open Ended
Closed Ended
Diesel hammer components Piston = Ram
Cylinder Port (closed by piston) Compressive stroke Combustion chamber Impact block Hammer Cushion; Helmet
DIESEL Hammer MODEL • Ram, Impact Block modeled like rods • Compression, Expansion Pressures from Gas Law • Combustion Pressure from rated energy – measurements; different for Atomized and Liquid Fuel injection • Ram velocity reduced by efficiency just before impact
Diesel Hammer Ram Model
Ram segments ~1m long
Ram bottom/impact block Impact Block mass Hammer Cushion Helmet mass
Diesel Hammer Combustion Pressure Model • Compressive Stroke, hC • Cylinder Area, ACH • Final Chamber Volume, V CH • Max. Pressure, pMAX PrecompressionCombustionExpansionPressure
Ports hC
DIESEL PRESSURE MODEL Liquid Injection Hammers
Pressure
Combustion Delay, ∆ t Combustion Duration, t D
Expansion: ∆t
t D
p=pMAX (V CH /V)1.25
t r o P
s n e p O
Compression: p=patm(V in /V)1.35
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
GRLWEAP hammer efficiencies (E k /E P ) •The hammer efficiency reduces the impact velocity of the ram; it 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
Modern Hydraulic Hammer Efficiencies Hammers with internal monitor:
0.95
uncertainty of hammer alignment
Hydraulic drop hammers:
0.80
uncertainty of fall height, alignment, friction
Power assisted hydraulic hammers:
0.80
uncertainty of fall height, alignment, friction, power assist
Air/Steam/Traditional Hydraulic Hammer 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 Hammer Efficiency Recommendations • Drop hammers brake released:
0.50
covers uncertainty of fall height and winch losses
• Drop hammers free released: covers uncertainty of fall height
0.67
VIBRATORY HAMMER MODEL
VIBRATORY HAMMER MODEL • Line Force
F L
• Bias Mass and
m1
• Oscillator mass, m 2 • Eccentric masses, me, radii, r e
m2 F V
• Clamp
Vibratory Force: FV = me [ω2r esin ω t - a2(t)]
GRLWEAP Hammer data file
Driving System Modeling Driving Systems Consists of 1.
Helmet including inserts to align hammer and pile
2. Hammer Cushion to protect hammer 3. Pile Cushion to protect concrete piles
Driving system model (Concrete piles)
Hammer Cushion: Spring plus Dashpot Helmet + Inserts Pile Cushion + Pile Top: Spring + Dashpot
Non-linear springs for cushions and slacks Compressive Force
Parameters 1.
Stiffness, k = EA/t
2.
Coefficient of Restitution, COR
3.
Round-out deformation, δ r , or compressive slack
4.
k
k / COR 2
Tension slack, δ s
δ s
δ r
Compressive Deformation
Non-linear springs Springs at material interfaces
Hammer interface springs Cushions Helmet/Pile Splices with slacks
The Pile and Soil Model Mass density, Modulus, E X-Area, A
Mass, mi Stiffness, ki
∆L= L/N 1m (default)
Soil Model Spring (static resistance) Dashpot (dynamic resistance)
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
Soil Model Parameters ki-1,Rui-1 Segment i-1 RIGID SOIL
e c a f r e t n I l i o S e l i P
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
Fixed
u i v i
Static Shaft Resistance Model Parameters R ui , q i
R si R ui
Elastic spring with max. compression q (quake)
k si = R ui /q i 1
u i quake, q i
Rigid plastic slider with Resistance R ui
Fixed reference
Shaft Resistance and Quake R si -R ui
R ui
q i
q i Recommended Shaft Quake: 2.5 mm; 0.1 inches
u i
Recommended Toe Quakes, q t 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
q t
D/60: softer/loose soils
q t
D
u
R ut R
Smith’s Soil Damping Model (Shaft or Toe) R d = R sJ s v Pile Segment
Fixed reference (soil around pile)
Smith damping factor, J s [s/m or s/ft]
R d = R u J sv v Smith-viscous damping factor J sv [s/m or s/ft]
velocity v
For RSA and Vibratory Ananlysis
dashpot
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
GRLWEAP Help for Dynamic Soil Resistance Parameters
How to Distribute the Static Soil Resistance Along Pile and at Toe Resistance Along 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 known about soil .
End Bearing = Total Capacity x (100% - Percent Shaft Resistance)
n o i t a r t e n e P
How to Distribute the Static Soil Resistance Along Pile and at toe 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.
n o i t a r t e n e P
End Bearing = From Soil Type, Pile Bottom Area
How to Distribute the Static Soil Resistance Along Pile and at toe 3. More Involved: I.
SA
Input: SPT Blow Count, Friction Angle or Undrained Shear Strength
II. API Input: Friction Angle or
Undrained Shear Strength
III. CPT
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
n o i t a r t e n e P
Numerical Treatment • Predict displacements: uni = uoi + voi ∆ t
mi-1
• Calculate spring compression:
Ri-1
uni-1
Fi, ci
ci = uni - uni-1
• Calculate spring forces: Fi = ki ci
mi
Ri
mi+1
Ri+1
uni
• Calculate resistance forces: Ri = Rsi + Rdi uni+1
Force balance at a segment Force from upper spring, F i
Resistance force, Ri
Mass mi Weight, Wi
Force from lower spring, F i+1
Acceleration: ai = (Fi + Wi – Ri – Fi+1) / mi Velocity, vi, and Displacement, ui, from Integration
Set or Blow Count Calculation (a) Simplified: extrapolated toe displacement
R
Maximum Set
Calculated
R u
Extrapolated
Set Final Set
Quake
(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
Blow Count Calculation (b) Residual Stress Analysis (RSA)
Set for 2 Blows Convergence: Consecutive Blows have same pile compression/sets
Program Flow – Bearing Graph Input
Distribute Ru Set Soil Constants
Model hammer, driving system and pile
Static Equilibrium Ram velocity Dynamic analysis
Choose first Ru
• Pile stresses • Energy transfer • Pile velocities
Calculate Blow Count
Increase Ru
Increase R u ?
N Output
Y
Bearing Graph: Variable Capacity, One depth SI-Units; Clay and Sand Example; D19-42; HP 12x53;
The Inspectors’ Chart: One Capacity and One Depth – Stroke Variable GRL Engineers, Inc. Demo 3-Inspector's Chart - D16-32
21-Aug-2011 GRLWEAP Version 2010
250
250
) a 200 P M ( s s e r t S 150 e v i s s e r p m 100 o C
200
150
100
50
50
0
0
DELMAG D 16-32
) a P M ( s s e r t S n o i s n e T
Capacity Ram Weight Efficiency Pres sure Helm et Weight H am m er C us hi on COR of H.C. Skin Quake Toe Quake Skin Dam ping Toe Dam ping Pile Length Pile Penetration Pile Top Area
Pile Model
1600.0 kN 15.66 kN 0.800 9825 (99%) kPa 8.45 kN 1 05 35 k N/m m 0.800 2.500 2.500 0.259 0.500
mm mm s ec/m s ec/m
18.28 m 16.76 m 140.64 cm2 Skin Friction Distribution
3.50
3.10
) m ( e 2.70 k o r t S 2.30
1.90
1.50 40
80
120
160
200
Blow Count (blows/.25m)
240
280
Res. Shaft = 30 % (Proportional)
Formulas and Wave Equation D19-42; HP 12x53; Clay and Sand 4000 3500 3000 N k 2500 n i y t 2000 i c a p a 1500 C
1000 500 0 0
25
50
75
100
125
150
175
Blow s/0.25 m
Gates
ENR
GRLWEAP-Clay
GRLWEAP-Sand
SUMMARY • GRLWEAP simulates the what happens when a hammer strikes a pile • GRLWEAP is based on Smith’s model with important extensions such as: – Realistic hammer models (ECH, OED, CED, VIB) – Non-linear spring models for interfaces and slacks – Alternative soil models – Residual stress analysis
200
SUMMARY, continued • GRLWEAP , to simplify input offers four static pile analysis methods – Soil type based (ST) – N-value and qu based (SA) – φ and Su based (API) – Cone Penetrometer based (CPT)
Summary, continued • GRLWEAP models 3 distinctly different hammer models – External Combustion Hammer models – Diesel hammer and pressure models – Vibratory hammer model
• GRLWEAP works with 3 components in the driving system model – Hammer Cushion – Helmet and Inserts – Pile Cushion
Summary, continued • Basic Analysis options are the – Bearing Graph which relates 10 bearing capacity values and stresses to blow count and – Inspector’s Chart which relates required blow count to a hammer’s energy level (or stroke) for one capacity value.
End of GRLWEAP Fundamentals
Questions?
Bearing Graph Workshop examples
• Bearing Graph; CE Pipe driven by diesel hammer • Bearing Graph and Inspector’s Chart for inclined/battered concrete pile • Steel follower on concrete pile
Diesel hammer bearing graph Hammer: Find appropriate OE Diesel Find Associated Driving System Pile: 12-3/4x3/8”; 325x10 mm Closed Ended Pipe Length L = 50’ (15 m) LP
L
Soil: Sand Desired working load 50 tons Safety Concept: Wave Equation Only Expected Penetration LP = 45’ (14 m)
Continue: Concrete pile bearing graph and Inspector’s Chart Hammer: Find appropriate ECH Both Hammer and Driving System Pile: PPSC - 24x24”; 610x610 mm; L = 80’ (24 m) Soil: 10’ (3 m) Medium Clay 20’ (6 m) Stiff Silt 30’ (9 m) Soft Clay 30’ (9 m) Dense Sand Water table: 15’ (4.5 m) below grade Desired working load 150 tons Safety Concept: Dynamic Testing Expected penetration 75’ (22.5 m)
Steel Follower on Concrete Pile Hammer: Up to 10 ton Hydraulic Helmet/Hammer Cushion: see Tables
Water depth
Penetration
Follower: LF = 42.5’ - 12,800 mm LF 18x2”-42’ - 450x50-12,650 mm pipe 18x18x6” - 500x500x150 mm plate Pile Cushion: LC 8” - 200 mm used plywood LC LT Pile: PPC 20x20” LP = 50’ L p 500x500 mm LP = 15 m Water Depth: 40’ - 12 m Soil Information: See CPT data Expected pile penetration: LP = 43’ (13 m) Required working load: Q D = 180 k (900 kN)
