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 Inspectors Chart Driveability

Some important developments in Dynamic Pile Analysis1800s 1950: 1970: 1976: 1980s: 1986: 1996, 2006: Closed Form Solutions & Energy Formulas Smiths Wave Equation CAPWAP WEAP, TTI (mainframes) GRLWEAP (PCs) Hammer Performance Study FHWA Manual updates

WEAP = Wave Equation Analysis of Piles

WAVE EQUATION OBJECTIVES Smiths 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 Driving system Helmet weight Hammer cushion Pile cushion Cap 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

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 Calculates blow count and stresses for given ult. capacity at a given penetration depth as a function of stroke/energy 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

Inspectors Chart

Driveability analysis

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 massRam guides for assembly stiffness Drop height

Ram: A, L for stiffness, massHammer base = assembly bottom mass

External Combustion HammersRam Model

Ram segments ~1m long

Combined RamH.Cushion Helmet mass

External Combustion HammersCombined 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 MODELLiquid Injection Hammers

Pressure

Compression

pMAX

Port

Expansion

Time

Open

Program Flow Diesel Hammers Fixed pressure, variable strokeSetup hammer, pile, soil model

Downward = rated stroke

Calculate pile and ram motion

Downward = upward stroke

Next Ru?

NStrokes match?

NOutput

Find upward stroke

Potential / Kinetic EnergyEP = WR h(potential or rated energy)

WR

EK = mR vi2EK = EP

(kinetic energy)( - hammer efficiency)

vi W R

h

vi = 2g h Max ET = F(t) v(t) dt Transferred Energy EMX ETR = EMX/ ER = transfer ratioWP

GRLWEAP hammer efficienciesThe 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 efficienciesOpen end diesel hammers:(uncertainty of fall height, friction, alignment)

0.80 0.80

Closed end diesel hammers:

(uncertainty of fall height, friction, power assist, alignment)

Other ECH efficiency recommendationsSingle acting Air/Steam hammers:(fall height, preadmission, friction, alignment)

0.67 0.50

Double acting Air/Steam/Hydraulic:

(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 efficienciesHammers with internal monitor:(uncertainty of hammer alignment)

0.950.80 0.80

Hydraulic hammers (no monitor): Power assisted hydraulic hammers:

(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 MODELFL

Bias Mass with Line ForceConnecting Pads

m1

Oscillator with eccentric masses, me, radii, re and clamp

m2

FV

2-mass system with vibratory force

FV = me 2 re sint

GRLWEAP Hammer data file

Hammer-Driving System-Pile-Soil ModelHammer: (Masses and Springs)

Driving System: Cushions (Springs) Helmet (Mass)

Pile:

Soil:

Driving System ModelingThe 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 ModelTo make realistic calculations possible The pile is divided into N segments of approximate length L = 1 m (3.3 ft) with mass m = 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, tt is a fraction (e.g. ) of the critical time, which is L/c Time

tcr L t L/cLength

Driving system model (Concrete piles)

Hammer Cushion: Spring plus Dashpot

Helmet + InsertsPile Cushion + Pile Top: Spring + Dashpot

Non-linear springsSprings at material interfaces

Hammer interface springs

CushionsHelmet/Pile Splices with slacks

Non-linear (cushion) springs Parameters Stiffness, k = EA/t Coefficient of Restitution, COR Round-out deformation,r , or compressive slack Tension slack, s

Compressive Force

k

k /COR2

s

r

Compressive Deformation

Hammer cushionMaterial Modulus (ksi)

Pile cushionMaterial Plywood Oak(transverse)

Modulus (ksi) 30 new 75 used 60 750

Aluminum Micarta Conbest Hamortex Nylon

350 280 125 175-200

Oak (parallel)

The Pile and Soil ModelMass density, Modulus, E X-Area, A L= L/N 1m

Mass mi Stiffness ki

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 ModelSegment

ki-1,Rui-1 Ji-1 ki,Rui

i-1

RIGID SOIL SURROUNDING SOIL/PILE INTERFACE

Segment i

Ji

ki+1,Rui+1Segment i+1

Ji+1

Smiths Soil ModelTotal Soil Resistance Rtotal = Rsi +Rdi

Segment iFixed

ui vi

Shaft Resistance and QuakeRsi-Ruiqi

Rui

qi Recommended Shaft Quake ( qi )

ui

2.5 mm; 0.1 inches

Recommended Toe Quakes, qtNon-displacement piles 0.1 or 2.5 mm 0.04 or 1 mm on hard rock Displacement piles

D/120: very dense/hard soils D/60: softer/loose soils

qt

Rut R

qt

D

u

Smiths Soil Damping Model (Shaft or Toe) Rd = RsJs v Pile SegmentFixed reference (soil around pile)Smith damping factor, Js [s/m or s/ft]

Rd = RuJs vSmith-viscous damping factor Jsvi [s/m or s/ft]

velocity v dashpot

Alternative Soil ModelsCoyle-Gibson Results (1968)Sand Clay

Recommended damping factors after SmithShaft Clay: Sand: Silts: Layered soils: Toe All 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

0.50 s/m or 0.15 s/ft

Numerical treatment: Force balance at a segmentForce from upper spring, Fi

Resistance force, Ri(static plus damping)

Mass mi

Weight, Wi

Force from lower spring, Fi+1

Acceleration: ai = (Fi Fi+1 + Wi Ri) / miVelocity, 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 Calculate spring displacement: ci = uni - uni-1 Calculate spring forces:uni uni-1

mi-1Fi, ci mi

Fi = ki cimi+1

k = EA / L

uni+1

Set or Blow Count Calculation from Extrapolated toe displacement

R

Maximum Set

Ru

Calculated

Extrapolated

SetFinal 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 OPTIONBETWEEN HAMMER BLOWS, PILE AND SOIL STORE ENERGY

Set for 2 BlowsConvergence: Consecutive Blows have same pile compression/sets

COMPUTATIONAL PROCEDURE

Smiths 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 GraphInput Distribute Ru Set Soil Constants Time Increment Static Analysis Ram velocity Dynamic Analysis Pile stresses Energy transfer Pile velocities Increase R u? Increase Ru

Model hammer & driving system

Model Pile

NOutput

Choose first Ru Calculate Blow Count

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.

INSPECTORS CHARTConstant 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 factorsSoil Type Clay Silt Clay Silt Sand Clay Fine Sand Sand - Gravel Setup Factor 2 1 1.5 1.2 1 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 changesSet-up TimeRu

Remolding energy

Ru/SF

Ru/SFTime Driving Waiting Time Re-Drive

Set-up factor, SF Capacity increases (Set-up) after driving stops Capacity decreases (Remolds) during redrive

Program Flow DriveabilityInput 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?

NIncrease 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 AnalysisApproximate 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: Co un ty:

S tru cture Na me an d/o r No .: P ile Drivin g Co ntracto r o r Su bco n tracto r: (Piles d riv en b y)

R a m

Hammer

Pile Driving and Equipment Data Form

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)

AnvilStriker Plate Weigh t: Thickne ss: Mate rial # 1 (kips) Diam ete r: (in ) (in)

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 :

(in 2) (in)

Helmet (Drive Head) Weigh t:

(kips)

Pile Cushion

Mate rial: Area : (in2 ) No. o f S he ets: Tota l Thickne ss of P ile Cus hio n: Pile Typ e: Wall Th ickn ess: Cro ss Se ctio na l Area :

Th ickn ess /S h ee t: (in )

(in)

(in ) Tap er: (in 2) We ig ht/Ft: (ft) (kip s) (kip s)

Pile Orde re d Le n gth : Design Lo ad : Ultim ate P ile Ca pa city: 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.: Date : Fax No .:

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 EntryResistance distributionSimple From soil input wizard

For driveabilitySoil 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 disclaimersOn 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 Inspectors 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 Inspectors chart for variable hammer stroke

Summary: Purpose of analysisDevelop 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