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 GRLWEAP (mainframes) (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 E k just before impact to E p

• • • • •

Driving system Helmet weight Hammer cushion Pile cushion Cap 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

• • • •

SRD Soil set-up factor Gain/loss factor Variable set-up 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

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 Ram H.Cushion

Helmet mass

External Combustion Hammers

Combined Ram Assembly Model

Ram segments Assembly segments Combined Ram H.Cushion

Helmet mass

Diesel Hammer Combustion Pressure Model

• • • •

Compressive Stroke, h

C

Cylinder Area, A

CH

Final Chamber Volume, V

CH

Max. Pressure, p

MAX

Precompression Combustion Expansion pressures from thermodynamics Ports h

C

DIESEL PRESSURE MODEL

Liquid Injection Hammers

Pressure Expansion Compression p MAX 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 N Strokes match?

Next Ru? N Output

Potential / Kinetic Energy

W R E P = W R h E K = ½ m R v i 2 E K = ηE P (potential or rated energy)

(kinetic energy)

( η - hammer efficiency) v i =



2g h η Max E T = ∫F(t) v(t) dt “Transferred Energy” EMX ETR = EMX/ E R = “transfer ratio” v i W R h W P

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: (uncertainty of fall height, friction, alignment) 0.80

Closed end diesel hammers: 0.80

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

Other ECH efficiency recommendations

Single acting Air/Steam hammers: (fall height, preadmission, friction, alignment) 0.67

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: (uncertainty of hammer alignment) 0.95

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

F L

Bias Mass with Line Force

m 1

Connecting Pads Oscillator with eccentric masses, m clamp e , radii, r e and

m 2 F V

2-mass system with vibratory force F V = m e



2 r e sin



t

GRLWEAP Hammer data file

Hammer-Driving System-Pile-Soil Model Hammer: (Masses and Springs) Driving System: Cushions (Springs) Helmet (Mass) Pile: Soil: Elasto-Plastic

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 there are k = E A / ∆L 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 ∆t cr ∆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

• • • •

Stiffness, k = EA/t Coefficient of Restitution, COR Round-out deformation, δ r , or compressive slack Tension slack, δ s

Compressive Force k k / COR

2 δ s δ r

Compressive Deformation

Hammer cushion Pile cushion

Material Aluminum Micarta Conbest Modulus (ksi) 350 280 Hamortex 125 Material Plywood Oak (transverse) Oak (parallel) Modulus (ksi) 30 new 75 used 60 750 Nylon 175-200

The Pile and Soil Model

Mass density,  Modulus, E X-Area, A ∆L= L/N  1m Mass m i Stiffness k i

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

Segment i Segment i+1

k i-1 ,R ui-1 J i-1 k i ,R ui J i k i+1 ,R ui+1 J i+1

Smith’s Soil Model

Total Soil Resistance R

total

= R

si

+R

di

Segment i u i v i Fixed

Shaft Resistance and Quake R si -R ui q i R ui q i u i Recommended Shaft Quake ( q i ) 2.5 mm; 0.1 inches

Recommended Toe Quakes, q t Non-displacement piles Displacement piles 0.1” or 2.5 mm 0.04” or 1 mm on hard rock D/120: very dense/hard soils D/60: softer/loose soils q t R ut R q t u D

Smith’s Soil Damping Model (Shaft or Toe) Pile Segment velocity v Fixed reference (soil around pile) R d = R s J s v Smith damping factor, J s [s/m or s/ft] R d = R u J s v Smith-viscous damping factor J svi [s/m or s/ft] dashpot

Sand

Alternative Soil Models

Coyle-Gibson Results (1968) Clay

Recommended damping factors after Smith

Shaft 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 segment

Force from upper spring, F i Resistance force, R i (static plus damping)

Mass m i

Weight, W i Force from lower spring, F i+1 Acceleration: a i

=

( F i – F i+1 + W i – R i ) / m i

Velocity, v i , and Displacement, u i , from Integration

Wave Equation Analysis calculates displacement of all points of a pile as function of time.

Calculate displacements:

u ni = u oi + v oi



t

Calculate spring displacement:

c i = u ni - u ni-1 Calculate spring forces: F i = k i c i u ni-1 u ni k = EA / ΔL u ni+1

m i-1 m i m i+1

F i , c i

Set or Blow Count Calculation from Extrapolated toe displacement

R Maximum Set R u Calculated 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 Choose first Ru Distribute Ru Set Soil Constants Time Increment Static Analysis Ram velocity

• • •

Dynamic Analysis Pile stresses Energy transfer Pile velocities Calculate Blow Count Increase Ru Increase R u ?

N 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

Bad OK

Question for Driveability:

WHAT IS R

U

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 Silt – Clay Silt Sand – Clay Fine Sand Sand - Gravel 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 changes Set-up Time Ru Remolding energy 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 Next G/L First depth of analysis - soil model Pile length and model Increase Depth Increase G/L?

N Increase Depth?

N Output

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

Pile Driving and Equipment Data Form

R a m Anvil

Ham mer Type : Se ri al No .: Man ufa ctur er s Max imu m Ra te d E ne rg y: (i n 2 ) Ma te ri al # 2 ( fo r Co mp osi te Cu shi on ) ( in 2 )

Helmet (Drive Head)

No. o f S he ets: Tota l Thi ckne ss of P ile Cus hio n: (i n 2 ) Pil e Typ e: Wal l Th ickn ess: ( in 2 ) We ig ht/Ft:

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