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GRLWEAP™ FundamentalsFundamentalsGRLWEAP™ FundamentalsFundamentals
Frank RauscheFrank Rausche
2009,2009, GRL Engineers, Inc.GRL Engineers, Inc.
CONTENTCONTENTCONTENTCONTENT•• Background and TerminologyBackground and Terminology
•• Wave Equation Hammer ModelsWave Equation Hammer Models
•• Background and TerminologyBackground and Terminology
•• Wave Equation Hammer ModelsWave Equation Hammer Models
•• Wave Equation Pile ModelWave Equation Pile Model
•• Wave Equation Soil ModelWave Equation Soil Model
•• The Program FlowThe Program Flow–– Bearing graphBearing graph
D i bilitD i bilit
•• Wave Equation Pile ModelWave Equation Pile Model
•• Wave Equation Soil ModelWave Equation Soil Model
•• The Program FlowThe Program Flow–– Bearing graphBearing graph
D i bilitD i bilit–– DriveabilityDriveability
–– Inspector’s ChartInspector’s Chart
•• SummarySummary
–– DriveabilityDriveability
–– Inspector’s ChartInspector’s Chart
•• SummarySummary
1800s1800s Closed Form Solutions and Energy Closed Form Solutions and Energy FormulasFormulas
1800s1800s Closed Form Solutions and Energy Closed Form Solutions and Energy FormulasFormulas
Some important developments in Some important developments in Dynamic Pile AnalysisDynamic Pile Analysis
FormulasFormulas1950:1950: Smith’s Wave EquationSmith’s Wave Equation1976: 1976: WEAP, TTIWEAP, TTI1980s:1980s: GRLWEAPGRLWEAP1986:1986: Hammer Performance StudyHammer Performance Study1996, 2006:1996, 2006: FHWA Manual updatesFHWA Manual updates
FormulasFormulas1950:1950: Smith’s Wave EquationSmith’s Wave Equation1976: 1976: WEAP, TTIWEAP, TTI1980s:1980s: GRLWEAPGRLWEAP1986:1986: Hammer Performance StudyHammer Performance Study1996, 2006:1996, 2006: FHWA Manual updatesFHWA Manual updates
WAVE EQUATION OBJECTIVESWAVE EQUATION OBJECTIVESWAVE EQUATION OBJECTIVESWAVE EQUATION OBJECTIVES
•• Smith’s Basic Premise: Smith’s Basic Premise: –– Replace Energy FormulaReplace Energy Formula–– Use improved pile model (elastic pile) and soil model Use improved pile model (elastic pile) and soil model
((elastoelasto plastic with damping)plastic with damping)
•• Smith’s Basic Premise: Smith’s Basic Premise: –– Replace Energy FormulaReplace Energy Formula–– Use improved pile model (elastic pile) and soil model Use improved pile model (elastic pile) and soil model
((elastoelasto plastic with damping)plastic with damping)((elastoelasto--plastic with damping)plastic with damping)–– Allow for stress calculationsAllow for stress calculations
•• Later GRLWEAP improvements:Later GRLWEAP improvements:–– realistic Diesel hammer modelrealistic Diesel hammer model–– comparison with pile top measurementscomparison with pile top measurements
development of more reliable soil constantsdevelopment of more reliable soil constants
((elastoelasto--plastic with damping)plastic with damping)–– Allow for stress calculationsAllow for stress calculations
•• Later GRLWEAP improvements:Later GRLWEAP improvements:–– realistic Diesel hammer modelrealistic Diesel hammer model–– comparison with pile top measurementscomparison with pile top measurements
development of more reliable soil constantsdevelopment of more reliable soil constants–– development of more reliable soil constantsdevelopment of more reliable soil constants–– driveabilitydriveability and inspectors’ chart optionsand inspectors’ chart options–– residual stress analysis optionresidual stress analysis option
–– development of more reliable soil constantsdevelopment of more reliable soil constants–– driveabilitydriveability and inspectors’ chart optionsand inspectors’ chart options–– residual stress analysis optionresidual stress analysis option
GRLWEAP ApplicationGRLWEAP ApplicationGRLWEAP ApplicationGRLWEAP Application
•• WHEN?WHEN?–– Before pile driving beginsBefore pile driving begins
•• WHEN?WHEN?–– Before pile driving beginsBefore pile driving begins
–– or after initial pile tests have been done (refined)or after initial pile tests have been done (refined)
•• WHY?WHY?–– Formulate driving criterionFormulate driving criterion
–– Equipment selectionEquipment selection
–– Stress determinationStress determination
–– or after initial pile tests have been done (refined)or after initial pile tests have been done (refined)
•• WHY?WHY?–– Formulate driving criterionFormulate driving criterion
–– Equipment selectionEquipment selection
–– Stress determinationStress determination
–– Blow count calculationBlow count calculation
–– Capacity determinationCapacity determination
–– Blow count calculationBlow count calculation
–– Capacity determinationCapacity determination
Some WEAP TerminologySome WEAP TerminologySome WEAP TerminologySome WEAP Terminology
•• Hammer Hammer Ram plus hammer assemblyRam plus hammer assembly
•• Hammer Assembly Hammer Assembly All nonAll non--striking hammer componentsstriking hammer components
•• Hammer efficiencyHammer efficiency Ratio ofRatio of EE just before impact tojust before impact to EE
•• Hammer Hammer Ram plus hammer assemblyRam plus hammer assembly
•• Hammer Assembly Hammer Assembly All nonAll non--striking hammer componentsstriking hammer components
•• Hammer efficiencyHammer efficiency Ratio ofRatio of EE just before impact tojust before impact to EE•• Hammer efficiencyHammer efficiency Ratio of Ratio of EEkk just before impact to just before impact to EEpp
•• Driving system Driving system All components between hammer and pile topAll components between hammer and pile top
•• Helmet weightHelmet weight WeightWeight of driving systemof driving system
•• Hammer cushionHammer cushion Protects hammer Protects hammer -- between helmet and rambetween helmet and ram
•• Pile cushionPile cushion Protects pile Protects pile -- between helmet and pile topbetween helmet and pile top
•• CapCap Generally the striker plate + hammerGenerally the striker plate + hammercushion+helmetcushion+helmet
•• Hammer efficiencyHammer efficiency Ratio of Ratio of EEkk just before impact to just before impact to EEpp
•• Driving system Driving system All components between hammer and pile topAll components between hammer and pile top
•• Helmet weightHelmet weight WeightWeight of driving systemof driving system
•• Hammer cushionHammer cushion Protects hammer Protects hammer -- between helmet and rambetween helmet and ram
•• Pile cushionPile cushion Protects pile Protects pile -- between helmet and pile topbetween helmet and pile top
•• CapCap Generally the striker plate + hammerGenerally the striker plate + hammercushion+helmetcushion+helmet
•• Pile dampingPile damping DampingDamping of pile materialof pile material
•• Soil dampingSoil damping DampingDamping of soil in pileof soil in pile--soil interfacesoil interface
•• QuakeQuake Pile displacement when static resistance Pile displacement when static resistance reaches ultimatereaches ultimate
•• Pile dampingPile damping DampingDamping of pile materialof pile material
•• Soil dampingSoil damping DampingDamping of soil in pileof soil in pile--soil interfacesoil interface
•• QuakeQuake Pile displacement when static resistance Pile displacement when static resistance reaches ultimatereaches ultimate
Some WEAP TerminologySome WEAP TerminologySome WEAP TerminologySome WEAP Terminology
•• Bearing Graph Bearing Graph Ult. Capacity and max. stress vs. blow countUlt. Capacity and max. stress vs. blow count
•• DriveabilityDriveability analysisanalysis Calculate blow count and stresses vs. depth Calculate blow count and stresses vs. depth based on static soils analysisbased on static soils analysis
•• Bearing Graph Bearing Graph Ult. Capacity and max. stress vs. blow countUlt. Capacity and max. stress vs. blow count
•• DriveabilityDriveability analysisanalysis Calculate blow count and stresses vs. depth Calculate blow count and stresses vs. depth based on static soils analysisbased on static soils analysisbased on static soils analysisbased on static soils analysis
•• Inspector’s ChartInspector’s Chart Calculates blow count, stresses for given Calculates blow count, stresses for given ult. capacity as a function of stroke/energy ult. capacity as a function of stroke/energy
•• Soil setup factorSoil setup factor Ratio of long term to EOD resistance Ratio of long term to EOD resistance
•• Gain/loss factorGain/loss factor Ratio of SRD to long term resistanceRatio of SRD to long term resistance
•• SRDSRD Static resistance to drivingStatic resistance to driving
•• Variable setupVariable setup SetupSetup occurring during a limited driving occurring during a limited driving
based on static soils analysisbased on static soils analysis
•• Inspector’s ChartInspector’s Chart Calculates blow count, stresses for given Calculates blow count, stresses for given ult. capacity as a function of stroke/energy ult. capacity as a function of stroke/energy
•• Soil setup factorSoil setup factor Ratio of long term to EOD resistance Ratio of long term to EOD resistance
•• Gain/loss factorGain/loss factor Ratio of SRD to long term resistanceRatio of SRD to long term resistance
•• SRDSRD Static resistance to drivingStatic resistance to driving
•• Variable setupVariable setup SetupSetup occurring during a limited driving occurring during a limited driving interruptioninterruptioninterruptioninterruption
THE WAVE EQUATION MODELTHE WAVE EQUATION MODELTHE WAVE EQUATION MODELTHE WAVE EQUATION MODEL
•• The Wave Equation Analysis calculates The Wave Equation Analysis calculates the displacement of any point of a slender the displacement of any point of a slender
•• The Wave Equation Analysis calculates The Wave Equation Analysis calculates the displacement of any point of a slender the displacement of any point of a slender elastic rod at any time.elastic rod at any time.
•• The calculation is based on rod The calculation is based on rod
–– LengthLength
–– Cross Sectional AreaCross Sectional Area
–– Elastic ModulusElastic Modulus
elastic rod at any time.elastic rod at any time.
•• The calculation is based on rod The calculation is based on rod
–– LengthLength
–– Cross Sectional AreaCross Sectional Area
–– Elastic ModulusElastic ModulusElastic ModulusElastic Modulus
–– Mass densityMass density
Elastic ModulusElastic Modulus
–– Mass densityMass density
GRLWEAP FundamentalsGRLWEAP FundamentalsGRLWEAP FundamentalsGRLWEAP Fundamentals
•• For a pile driving analysis, the “rod” isFor a pile driving analysis, the “rod” is•• For a pile driving analysis, the “rod” isFor a pile driving analysis, the “rod” isFor a pile driving analysis, the rod is For a pile driving analysis, the rod is Hammer+Driving System+PileHammer+Driving System+Pile
•• The rod is assumed to be elastic(?) and The rod is assumed to be elastic(?) and slender(?)slender(?)
For a pile driving analysis, the rod is For a pile driving analysis, the rod is Hammer+Driving System+PileHammer+Driving System+Pile
•• The rod is assumed to be elastic(?) and The rod is assumed to be elastic(?) and slender(?)slender(?)
•• The soil is represented by resistance The soil is represented by resistance forces acting at the pile soil interfaceforces acting at the pile soil interface
•• The soil is represented by resistance The soil is represented by resistance forces acting at the pile soil interfaceforces acting at the pile soil interface
GRLWEAP Hammer ModelsGRLWEAP Hammer ModelsGRLWEAP Hammer ModelsGRLWEAP Hammer Models
Potential / Kinetic EnergyPotential / Kinetic Energy WWRR
hh
EEPP = W= WRR hh (potential or rated energy)(potential or rated energy)
WWvvEEKK = ½= ½ mmRR vvii22 ((kinetic energykinetic energy)) hhWWRR
vvii
EEK K = = ηηEEPP ((ηη -- hammer efficiency)hammer efficiency)
vvii = = 2g h 2g h ηη
EEKK ½ ½ mmRR vvii ((kinetic energykinetic energy))
NNWWPP
Note:Note:EET T = = ηηT T EEPP ((ηηTT -- transfer efficiency)transfer efficiency)
Cylinder and upper frame =Cylinder and upper frame =
External Combustion Hammer ModelingExternal Combustion Hammer ModelingExternal Combustion Hammer ModelingExternal Combustion Hammer Modeling
Cylinder and upper frame Cylinder and upper frame assembly top massassembly top mass
Drop heightDrop height
Ram guides for assembly stiffnessRam guides for assembly stiffness
Ram: A, L for stiffness, massRam: A, L for stiffness, mass
Hammer base = Hammer base = assembly bottom mass assembly bottom mass
External Combustion HammersExternal Combustion HammersRam ModelRam Model
External Combustion HammersExternal Combustion HammersRam ModelRam Model
Ram segments Ram segments ~1m long~1m long
Ram segments Ram segments ~1m long~1m long
Combined RamCombined Ram--H.CushionH.Cushion
Helmet massHelmet mass
Combined RamCombined Ram--H.CushionH.Cushion
Helmet massHelmet mass
External Combustion HammersExternal Combustion HammersCombined Ram Assembly ModelCombined Ram Assembly Model
External Combustion HammersExternal Combustion HammersCombined Ram Assembly ModelCombined Ram Assembly Model
Ram segments Ram segments
Assembly segmentsAssembly segments
Ram segments Ram segments
Assembly segmentsAssembly segments
Combined RamCombined Ram--H.CushionH.Cushion
Helmet massHelmet mass
Combined RamCombined Ram--H.CushionH.Cushion
Helmet massHelmet mass
DIESEL HAMMERSDIESEL HAMMERSDIESEL HAMMERSDIESEL HAMMERS
Diesel hammer componentsDiesel hammer componentsDiesel hammer componentsDiesel hammer components
Piston = RamPiston = RamPiston = RamPiston = Ram
Port (closed by piston)Port (closed by piston)Port (closed by piston)Port (closed by piston)
Combustion chamberCombustion chamberCombustion chamberCombustion chamber
CylinderCylinderCylinderCylinder
Compressive strokeCompressive strokeCompressive strokeCompressive stroke
Impact blockImpact blockImpact blockImpact block
Hammer Cushion; HelmetHammer Cushion; HelmetHammer Cushion; HelmetHammer Cushion; Helmet
Diesel Hammer Ram ModelDiesel Hammer Ram ModelDiesel Hammer Ram ModelDiesel Hammer Ram Model
Ram segments ~1m longRam segments ~1m longRam segments ~1m longRam segments ~1m long
Impact Block massImpact Block massImpact Block massImpact Block mass
Ram bottom/impact blockRam bottom/impact blockRam bottom/impact blockRam bottom/impact block
Hammer CushionHammer Cushion
Helmet massHelmet mass
Hammer CushionHammer Cushion
Helmet massHelmet mass
Impact Block massImpact Block massImpact Block massImpact Block mass
Diesel Hammer Combustion Pressure ModelDiesel Hammer Combustion Pressure ModelDiesel Hammer Combustion Pressure ModelDiesel Hammer Combustion Pressure Model
•• Compressive Stroke, Compressive Stroke, hhCC•• Compressive Stroke, Compressive Stroke, hhCC
PrecompressionPrecompression--PrecompressionPrecompression--PortsPortsPortsPorts
•• Cylinder Area, Cylinder Area, AACHCH
•• Final Chamber Volume, Final Chamber Volume, VVCHCH
•• Max. Pressure, pMax. Pressure, pMAXMAX
•• Cylinder Area, Cylinder Area, AACHCH
•• Final Chamber Volume, Final Chamber Volume, VVCHCH
•• Max. Pressure, pMax. Pressure, pMAXMAX
CombustionCombustion--ExpansionExpansion--PressurePressure
CombustionCombustion--ExpansionExpansion--PressurePressure
PortsPortsPortsPorts
hhCChhCC
DIESEL PRESSURE MODELDIESEL PRESSURE MODELLiquid Injection HammersLiquid Injection Hammers
DIESEL PRESSURE MODELDIESEL PRESSURE MODELLiquid Injection HammersLiquid Injection Hammers
Liquid Injection Timing Parameters:Liquid Injection Timing Parameters:Liquid Injection Timing Parameters:Liquid Injection Timing Parameters:
PressurePressure Combustion Delay, Combustion Delay, ttCombustion Delay, Combustion Delay, tt
Por
t P
ort
Ope
nO
pen
Por
t P
ort
Ope
nO
pen
ttDD
Compression:Compression:Compression:Compression:
Expansion:Expansion:
p=pp=pMAXMAX(V(VCHCH/V)/V)1.251.25
Expansion:Expansion:
p=pp=pMAXMAX(V(VCHCH/V)/V)1.251.25
yyyy
Combustion Duration, tCombustion Duration, tDDCombustion Duration, tCombustion Duration, tDD
t t
TimeTimeTimeTime
ppMAXMAX
Compression:Compression:
p=pp=patmatm(V(Vinin/V)/V)1.351.35
Compression:Compression:
p=pp=patmatm(V(Vinin/V)/V)1.351.35
Program Flow Program Flow –– Diesel HammersDiesel HammersFixed pressure, variable strokeFixed pressure, variable stroke
Program Flow Program Flow –– Diesel HammersDiesel HammersFixed pressure, variable strokeFixed pressure, variable stroke
Setup hammer,Setup hammer,pile, soil model pile, soil model
Downward = Downward = upward strokeupward stroke
Downward = Downward = rated strokerated stroke
Calculate pile andCalculate pile andram motionram motion
Next Ru? Next Ru?
NN
Find upward Find upward stroke stroke
Output Output
Strokes Strokes match?match?
NN
NN
GRLWEAP hammer efficienciesGRLWEAP hammer efficienciesGRLWEAP hammer efficienciesGRLWEAP hammer efficiencies
••The hammer efficiency reduces the The hammer efficiency reduces the impact velocity of the ram; it is based on impact velocity of the ram; it is based on p y ;p y ;experienceexperience••Hammer efficiencies cover all losses Hammer efficiencies cover all losses which cannot be calculatedwhich cannot be calculated••Diesel hammer energy loss due to Diesel hammer energy loss due to
ii hi i bhi i bprecompressionprecompression or cushioning can be or cushioning can be calculated and, therefore, is not covered calculated and, therefore, is not covered by hammer efficiencyby hammer efficiency
GRLWEAP diesel hammer efficienciesGRLWEAP diesel hammer efficienciesGRLWEAP diesel hammer efficienciesGRLWEAP diesel hammer efficiencies
Open end diesel hammers:Open end diesel hammers: 0.800.80(uncertainty of fall height, friction, alignment)(uncertainty of fall height, friction, alignment)
Closed end diesel hammers:Closed end diesel hammers: 0.800.80(uncertainty of fall height, friction, power assist, (uncertainty of fall height, friction, power assist, alignment)alignment)
GRLWEAP hydraulic hammer GRLWEAP hydraulic hammer efficienciesefficiencies
GRLWEAP hydraulic hammer GRLWEAP hydraulic hammer efficienciesefficiencies
Hammers with internal monitor:Hammers with internal monitor: 0.950.95(uncertainty of hammer alignment)(uncertainty of hammer alignment)
Hydraulic drop hammers:Hydraulic drop hammers: 0.800.80Power assisted hydraulic hammers:Power assisted hydraulic hammers: 0.800.80(uncertainty of fall height, alignment, friction, power assist) (uncertainty of fall height, alignment, friction, power assist)
Other ECH efficiency recommendationsOther ECH efficiency recommendationsOther ECH efficiency recommendationsOther ECH efficiency recommendations
Single acting Air/Steam hammers:Single acting Air/Steam hammers: 0.670.67(fall height, preadmission, friction, alignment)(fall height, preadmission, friction, alignment)D bl ti Ai /St /H d liD bl ti Ai /St /H d li 0 500 50Double acting Air/Steam/Hydraulic:Double acting Air/Steam/Hydraulic: 0.500.50(preadmission, reduced pressure, friction, alignment)(preadmission, reduced pressure, friction, alignment)
Drop hammers winch released:Drop hammers winch released: 0.500.50(covers uncertainty of fall height and winch losses) (covers uncertainty of fall height and winch losses) Free released drop hammers:Free released drop hammers: 0.670.67(covers uncertainty of fall height) (covers uncertainty of fall height)
VIBRATORY VIBRATORY HAMMER MODELHAMMER MODEL
VIBRATORY VIBRATORY HAMMER MODELHAMMER MODEL
VIBRATORY HAMMER MODELVIBRATORY HAMMER MODELVIBRATORY HAMMER MODELVIBRATORY HAMMER MODEL
FFLLFFLL
mmmmBias Mass with Line ForceBias Mass with Line ForceBias Mass with Line ForceBias Mass with Line Force
FFVVFFVV
mm11mm11
mm22mm22
Bias Mass with Line ForceBias Mass with Line ForceBias Mass with Line ForceBias Mass with Line Force
Connecting Pads Connecting Pads Connecting Pads Connecting Pads
Oscillator with eccentric Oscillator with eccentric masses, mmasses, mee, radii, r, radii, ree and and clampclamp
Oscillator with eccentric Oscillator with eccentric masses, mmasses, mee, radii, r, radii, ree and and clampclamp
22--mass system with vibratory forcemass system with vibratory force
FFV V = m= mee [[22rreesinsint t --22(t)](t)]
22--mass system with vibratory forcemass system with vibratory force
FFV V = m= mee [[22rreesinsint t --22(t)](t)]
Driving System ModelingDriving System ModelingDriving System ModelingDriving System ModelingDriving Systems Consists ofDriving Systems Consists of
–– Helmet including inserts to align hammer and pileHelmet including inserts to align hammer and pile
–– Hammer Cushion to protect hammerHammer Cushion to protect hammer
Driving Systems Consists ofDriving Systems Consists of–– Helmet including inserts to align hammer and pileHelmet including inserts to align hammer and pile
–– Hammer Cushion to protect hammerHammer Cushion to protect hammerpp
–– Pile Cushion to protect concrete pilesPile Cushion to protect concrete piles
pp
–– Pile Cushion to protect concrete pilesPile Cushion to protect concrete piles
GRLWEAP Pile ModelGRLWEAP Pile ModelGRLWEAP Pile ModelGRLWEAP Pile Model
To make realistic calculations possibleTo make realistic calculations possible•• The pile is divided into N segmentsThe pile is divided into N segments
To make realistic calculations possibleTo make realistic calculations possible•• The pile is divided into N segmentsThe pile is divided into N segments
–– of approximate length of approximate length ∆L = ∆L = 1 m (3.3 ft)1 m (3.3 ft)
–– with mass with mass m = m = ρρ A ∆L A ∆L
–– and stiffnessand stiffness k = E A / ∆Lk = E A / ∆L
–– there are there are N = L / ∆L pile segmentsN = L / ∆L pile segments
–– of approximate length of approximate length ∆L = ∆L = 1 m (3.3 ft)1 m (3.3 ft)
–– with mass with mass m = m = ρρ A ∆L A ∆L
–– and stiffnessand stiffness k = E A / ∆Lk = E A / ∆L
–– there are there are N = L / ∆L pile segmentsN = L / ∆L pile segments
•• Divide time into intervals Divide time into intervals (typically 0.1 ms)(typically 0.1 ms)
•• Divide time into intervals Divide time into intervals (typically 0.1 ms)(typically 0.1 ms)
Computational Time Increment, Computational Time Increment, ∆∆ttComputational Time Increment, Computational Time Increment, ∆∆tt∆∆t is a fraction (e.g. ½ ) of the critical time, which is t is a fraction (e.g. ½ ) of the critical time, which is ∆∆L/cL/c∆∆t is a fraction (e.g. ½ ) of the critical time, which is t is a fraction (e.g. ½ ) of the critical time, which is ∆∆L/cL/c
TimeTime
∆ttcrcr
∆LL
L/cL/c
∆t
LengthLength
Time IncrementTime IncrementTime IncrementTime Increment
••Time Increment must be a fraction of the critical time Time Increment must be a fraction of the critical time increment forincrement for numerical stabilitynumerical stabilityincrement for increment for numerical stabilitynumerical stability
••Typically, the time increment is ½ of the critical valueTypically, the time increment is ½ of the critical value
••Soil resistance has to be considered when Soil resistance has to be considered when calculating the critical time incrementcalculating the critical time increment
••Hammer segments are often criticalHammer segments are often critical
Hammer:Hammer:
(Masses and (Masses and Springs)Springs)
Hammer:Hammer:
(Masses and (Masses and Springs)Springs)
Driving System: Cushions Driving System: Cushions (Springs)(Springs)Helmet (Mass)Helmet (Mass)
Driving System: Cushions Driving System: Cushions (Springs)(Springs)Helmet (Mass)Helmet (Mass)
HammerHammer--Driving SystemDriving System--PilePile--Soil ModelSoil Model
Pile:Pile:
Masses andMasses and
Pile:Pile:
Masses andMasses and
Soil:Soil:
ElastoElasto--PlasticPlastic
Soil:Soil:
ElastoElasto--PlasticPlastic
Springs)Springs)Springs)Springs) Helmet (Mass)Helmet (Mass)Helmet (Mass)Helmet (Mass)
Masses and Masses and SpringsSprings
Masses and Masses and SpringsSprings
ElastoElasto--Plastic Plastic Springs and Springs and
DashpotsDashpots
ElastoElasto--Plastic Plastic Springs and Springs and
DashpotsDashpots
Driving system Driving system model (Concrete model (Concrete
piles)piles)
Driving system Driving system model (Concrete model (Concrete
piles)piles)p )p )p )p )
Hammer Cushion: Spring Hammer Cushion: Spring plus Dashpotplus Dashpot
Hammer Cushion: Spring Hammer Cushion: Spring plus Dashpotplus Dashpot
Pile Cushion + Pile Top: Pile Cushion + Pile Top: Spring + DashpotSpring + Dashpot
Pile Cushion + Pile Top: Pile Cushion + Pile Top: Spring + DashpotSpring + Dashpot
Helmet + InsertsHelmet + InsertsHelmet + InsertsHelmet + Inserts
NonNon--linear springslinear springsSprings at material interfacesSprings at material interfaces
NonNon--linear springslinear springsSprings at material interfacesSprings at material interfaces
Hammer interface springsHammer interface springsHammer interface springsHammer interface springsHammer interface springsHammer interface springs
CushionsCushions
H l t/PilH l t/Pil
Hammer interface springsHammer interface springs
CushionsCushions
H l t/PilH l t/PilHelmet/PileHelmet/Pile
Splices with slacksSplices with slacks
Helmet/PileHelmet/Pile
Splices with slacksSplices with slacks
NonNon--linear (cushion) springslinear (cushion) springsNonNon--linear (cushion) springslinear (cushion) springs
•• ParametersParameters•• Stiffness, k = EA/tStiffness, k = EA/t
•• ParametersParameters•• Stiffness, k = EA/tStiffness, k = EA/t
Compressive Compressive ForceForceCompressive Compressive ForceForce
•• Coefficient of Restitution, Coefficient of Restitution, CORCOR
•• RoundRound--out out deformation,deformation,δδrr , or , or compressive slackcompressive slack
•• Tension slack, Tension slack, δδss
•• Coefficient of Restitution, Coefficient of Restitution, CORCOR
•• RoundRound--out out deformation,deformation,δδrr , or , or compressive slackcompressive slack
•• Tension slack, Tension slack, δδssk /k /CORCOR22k /k /CORCOR22kk
δδrrδδrrδδssδδssCompressive Compressive DeformationDeformation
Compressive Compressive DeformationDeformation
L= L/N L= L/N 1m1m
Mass density, Mass density, Modulus, EModulus, EXX Area AArea A
The Pile and Soil ModelThe Pile and Soil ModelThe Pile and Soil ModelThe Pile and Soil Model
XX--Area, AArea, A
Spring (static resistance)Spring (static resistance)Dashpot (dynamic resist)Dashpot (dynamic resist)
Mass mMass mi i Stiffness kStiffness kii
Soil ResistanceSoil ResistanceSoil ResistanceSoil Resistance
•• Soil resistance slows pile movement and Soil resistance slows pile movement and causes pile reboundcauses pile rebound
•• A very slowly moving pile only encountersA very slowly moving pile only encounters
•• Soil resistance slows pile movement and Soil resistance slows pile movement and causes pile reboundcauses pile rebound
•• A very slowly moving pile only encountersA very slowly moving pile only encounters•• A very slowly moving pile only encounters A very slowly moving pile only encounters static resistancestatic resistance
•• A rapidly moving pile also encounters dynamic A rapidly moving pile also encounters dynamic resistanceresistance
•• The static resistance to driving differs from the The static resistance to driving differs from the soil resistance under static loadssoil resistance under static loads
•• A very slowly moving pile only encounters A very slowly moving pile only encounters static resistancestatic resistance
•• A rapidly moving pile also encounters dynamic A rapidly moving pile also encounters dynamic resistanceresistance
•• The static resistance to driving differs from the The static resistance to driving differs from the soil resistance under static loadssoil resistance under static loads
The Soil ModelThe Soil ModelThe Soil ModelThe Soil Model
Segment Segment
ii--11
KKii--11,R,Ruiui--11KKii--11,R,Ruiui--11
JJii--11JJii--11ii--11
Segment Segment
ii
ii--11ii--11
kkii,R,Ruiuikkii,R,Ruiui
JJiiJJii
RIGID SOIL RIGID SOIL SURROUNDINGSURROUNDINGSOIL/PILE SOIL/PILE INTERFACEINTERFACE
RIGID SOIL RIGID SOIL SURROUNDINGSURROUNDINGSOIL/PILE SOIL/PILE INTERFACEINTERFACE
Segment Segment
i+1 i+1
kki+1i+1,R,Rui+1ui+1kki+1i+1,R,Rui+1ui+1
JJi+1i+1JJi+1i+1
Smith’s Soil ModelSmith’s Soil ModelSmith’s Soil ModelSmith’s Soil Model
Total Soil ResistanceTotal Soil ResistanceRRtotaltotal = R= Rsisi +R+Rdidi
Total Soil ResistanceTotal Soil ResistanceRRtotaltotal = R= Rsisi +R+Rdidi
SegmentSegment
ii
uuii
vvii
FixedFixed
Shaft Resistance and QuakeShaft Resistance and QuakeShaft Resistance and QuakeShaft Resistance and Quake
RR ii
RRsisi--RR ii
qqii
RRuiui
qqii
RRuiui
uuii
Recommended Shaft Quake:Recommended Shaft Quake:
2.5 mm; 0.1 inches2.5 mm; 0.1 inches
Recommended Toe Quakes, qRecommended Toe Quakes, qttRecommended Toe Quakes, qRecommended Toe Quakes, qtt
0.1” or 2.5 mm0.1” or 2.5 mm RRqq RRututD/120: very dense/hard D/120: very dense/hard
ilil
Displacement pilesDisplacement pilesNonNon--displacement displacement pilespiles
0.04” or 1 mm on 0.04” or 1 mm on hard rockhard rock
qqtt
RRqqttRRututsoilssoils
D/60: softer/loose soilsD/60: softer/loose soils
uuDD
Smith’s Soil Damping Model (Shaft or Toe)Smith’s Soil Damping Model (Shaft or Toe)Smith’s Soil Damping Model (Shaft or Toe)Smith’s Soil Damping Model (Shaft or Toe)
PilePile Smith damping factor,Smith damping factor,
RRdd = R= RssJJss vv
PilePileSegmentSegment
JJs s [s/m or s/ft][s/m or s/ft]Fixed Fixed reference reference (soil around (soil around pile)pile)
RRdd = R= RuuJJss vv
SmithSmith--viscous damping viscous damping factor Jfactor Jsvi svi [s/m or s/ft][s/m or s/ft]
velocity vvelocity v
dashpotdashpot
Alternative Soil ModelsCoyle-Gibson Results (1968)
Alternative Soil ModelsCoyle-Gibson Results (1968)
SandSand ClayClay
Recommended damping factorsRecommended damping factorsafter Smithafter Smith
Recommended damping factorsRecommended damping factorsafter Smithafter Smith
ShaftShaft
ClCl 0 65 /0 65 / 0 20 /ft0 20 /ft
ShaftShaft
ClCl 0 65 /0 65 / 0 20 /ft0 20 /ftClay:Clay: 0.65 s/m0.65 s/m or 0.20 s/ftor 0.20 s/ft
Sand:Sand: 0.16 s/m or 0.05 s/ft0.16 s/m or 0.05 s/ft
Silts:Silts: use an intermediate valueuse an intermediate value
Layered soils: Layered soils: use a weighted average use a weighted average
Clay:Clay: 0.65 s/m0.65 s/m or 0.20 s/ftor 0.20 s/ft
Sand:Sand: 0.16 s/m or 0.05 s/ft0.16 s/m or 0.05 s/ft
Silts:Silts: use an intermediate valueuse an intermediate value
Layered soils: Layered soils: use a weighted average use a weighted average
ToeToe
All soils:All soils: 0.50 s/m0.50 s/m or 0.15 s/ftor 0.15 s/ft
ToeToe
All soils:All soils: 0.50 s/m0.50 s/m or 0.15 s/ftor 0.15 s/ft
Numerical treatmentNumerical treatmentNumerical treatmentNumerical treatment
Force from upper spring, FForce from upper spring, Fii
Mass mMass mi i
Force from lower spring, FForce from lower spring, Fi+1i+1
Resistance force, RResistance force, RiiWeight, WWeight, Wii
Acceleration: aAcceleration: aii = (F= (Fi i + W+ Wi i –– RRii –– FFi+1i+1) / m) / mii
Velocity, vVelocity, vii, and Displacement, u, and Displacement, uii, from Integration, from Integration
Set or Blow Count Calculation from Set or Blow Count Calculation from Extrapolated toe displacementExtrapolated toe displacement
Set or Blow Count Calculation from Set or Blow Count Calculation from Extrapolated toe displacementExtrapolated toe displacement
RRRRM i S tM i S tM i S tM i S tMaximum SetMaximum SetMaximum SetMaximum Set
RRuuRRuu
CalculatedCalculatedCalculatedCalculated
SetSetSetSetFinal SetFinal SetFinal SetFinal Set QuakeQuakeQuakeQuake
ExtrapolatedExtrapolatedExtrapolatedExtrapolated
Alternative Blow Count CalculationAlternative Blow Count Calculationby RSAby RSA
Alternative Blow Count CalculationAlternative Blow Count Calculationby RSAby RSA
•• Residual Stress Analysis is also called Residual Stress Analysis is also called Multiple Blow AnalysisMultiple Blow Analysis
•• Residual Stress Analysis is also called Residual Stress Analysis is also called Multiple Blow AnalysisMultiple Blow AnalysisMultiple Blow AnalysisMultiple Blow Analysis
•• Analyzes several blows consecutively with Analyzes several blows consecutively with initial stresses, displacements from static initial stresses, displacements from static state at end of previous blowstate at end of previous blow
•• Yields residual stresses in pile at end ofYields residual stresses in pile at end of
Multiple Blow AnalysisMultiple Blow Analysis
•• Analyzes several blows consecutively with Analyzes several blows consecutively with initial stresses, displacements from static initial stresses, displacements from static state at end of previous blowstate at end of previous blow
•• Yields residual stresses in pile at end ofYields residual stresses in pile at end ofYields residual stresses in pile at end of Yields residual stresses in pile at end of blow; generally lower blow countsblow; generally lower blow countsYields residual stresses in pile at end of Yields residual stresses in pile at end of blow; generally lower blow countsblow; generally lower blow counts
RESIDUAL STRESS OPTIONRESIDUAL STRESS OPTIONRESIDUAL STRESS OPTIONRESIDUAL STRESS OPTIONBETWEEN HAMMER BLOWS PILE AND SOIL STORE ENERGYBETWEEN HAMMER BLOWS PILE AND SOIL STORE ENERGYBETWEEN HAMMER BLOWS PILE AND SOIL STORE ENERGYBETWEEN HAMMER BLOWS PILE AND SOIL STORE ENERGY
Set for 2 BlowsSet for 2 Blows
Convergence:Convergence:C ti BlC ti BlConsecutive Blows Consecutive Blows
have same have same pile compression/setspile compression/sets
HP 12x53; Clay/Sand Bearing Graph; D19HP 12x53; Clay/Sand Bearing Graph; D19--42 42 SISI--UnitsUnits
HP 12x53; Clay/Sand Bearing Graph; D19HP 12x53; Clay/Sand Bearing Graph; D19--42 42 SISI--UnitsUnits
Inspector’s Chart Inspector’s Chart Inspector’s Chart Inspector’s Chart
Question for Question for DriveabilityDriveability::WHAT IS RWHAT IS RUU DURING DRIVING? DURING DRIVING?
Question for Question for DriveabilityDriveability::WHAT IS RWHAT IS RUU DURING DRIVING? DURING DRIVING?
•• We call it Static Resistance to Driving (SRD), We call it Static Resistance to Driving (SRD), •• We call it Static Resistance to Driving (SRD), We call it Static Resistance to Driving (SRD),
because we lose shaft resistance during driving.because we lose shaft resistance during driving.
•• Will we regain resistance by Will we regain resistance by Soil SetupSoil Setup --
primarily along shaft (may be 10 x in clay)primarily along shaft (may be 10 x in clay)
•• DriveabilityDriveability requires analyze with full loss of requires analyze with full loss of
because we lose shaft resistance during driving.because we lose shaft resistance during driving.
•• Will we regain resistance by Will we regain resistance by Soil SetupSoil Setup --
primarily along shaft (may be 10 x in clay)primarily along shaft (may be 10 x in clay)
•• DriveabilityDriveability requires analyze with full loss of requires analyze with full loss of
setup (or with partial loss of setup for a short setup (or with partial loss of setup for a short
driving interruption)driving interruption)
setup (or with partial loss of setup for a short setup (or with partial loss of setup for a short
driving interruption)driving interruption)
Setup factorsSetup factorsSetup factorsSetup factors
Soil Type Setup Factor
Clay 2
Silt – Clay 1
Silt 1.5
Sand – Clay 1.2
Fine Sand 1
Sand - Gravel 1
For Driveability with variable setup timeFor Driveability with variable setup timeFor Driveability with variable setup timeFor Driveability with variable setup time
Setup TimeSetup Time•• Setup factor, SFSetup factor, SF
•• Setup timeSetup time
•• Setup factor, SFSetup factor, SF
•• Setup timeSetup time
RuRu
Time Time
Ru/SFRu/SF
Setup TimeSetup Time
RR
Remolding Remolding EnergyEnergy
Ru/SFRu/SF
RuRu
Energy Energy
•• Remolding Remolding
energyenergy
DriveabilityDriveability
SummarySummarySummarySummaryThere are 3 distinctly different hammer modelsThere are 3 distinctly different hammer models
–– External Combustion Hammer modelsExternal Combustion Hammer models
–– Diesel hammer and pressure modelsDiesel hammer and pressure models
There are 3 distinctly different hammer modelsThere are 3 distinctly different hammer models–– External Combustion Hammer modelsExternal Combustion Hammer models
–– Diesel hammer and pressure modelsDiesel hammer and pressure modelsDiesel hammer and pressure modelsDiesel hammer and pressure models
–– Vibratory hammer modelVibratory hammer model
•• There are 3 components in the driving system There are 3 components in the driving system modelmodel–– Hammer CushionHammer Cushion
–– Helmet and InsertsHelmet and Inserts
Diesel hammer and pressure modelsDiesel hammer and pressure models
–– Vibratory hammer modelVibratory hammer model
•• There are 3 components in the driving system There are 3 components in the driving system modelmodel–– Hammer CushionHammer Cushion
–– Helmet and InsertsHelmet and InsertsHelmet and InsertsHelmet and Inserts
–– Pile CushionPile Cushion
•• Model Parameters can be found in GRLWEAP Model Parameters can be found in GRLWEAP Help Section or Hammer data file.Help Section or Hammer data file.
Helmet and InsertsHelmet and Inserts
–– Pile CushionPile Cushion
•• Model Parameters can be found in GRLWEAP Model Parameters can be found in GRLWEAP Help Section or Hammer data file.Help Section or Hammer data file.
SUMMARY continuedSUMMARY continuedSUMMARY continuedSUMMARY continued
•• The wave equation analysis works with “Static The wave equation analysis works with “Static Resistance to Driving” (SRD) plus a Damping or Resistance to Driving” (SRD) plus a Damping or D i R i tD i R i t
•• The wave equation analysis works with “Static The wave equation analysis works with “Static Resistance to Driving” (SRD) plus a Damping or Resistance to Driving” (SRD) plus a Damping or D i R i tD i R i tDynamic Resistance Dynamic Resistance
•• Important analysis options include Important analysis options include DriveabilityDriveabilityand Inspector’s Chartand Inspector’s Chart
•• The whole package is geared towards standard The whole package is geared towards standard analyses; some research options existanalyses; some research options exist
Dynamic Resistance Dynamic Resistance
•• Important analysis options include Important analysis options include DriveabilityDriveabilityand Inspector’s Chartand Inspector’s Chart
•• The whole package is geared towards standard The whole package is geared towards standard analyses; some research options existanalyses; some research options existy ; py ; py ; py ; p