wave equation applications

Wave Equation Wave Equation ApplicationsApplications

2009 PDCA Professor Pile 2009 PDCA Professor Pile InstituteInstitute

Patrick HanniganGRL Engineers, Inc.

Analysis TypesAnalysis TypesBearing GraphBearing Graph

- Proportional Resistance (most common)- Constant Shaft (i.e. pile driven to rock)- Constant Toe (i.e. friction pile)

Analysis Results: Capacity, stress, stroke (OED) vs. Blow count

Analysis Application: Hammer approvals, capacity assessments, hammer sizing.

Inspector’s ChartInspector’s Chart– For a constant capacity (e.g. the required

ultimate capacity), plots stroke vs blow count

– Variable energy hammers only• Single acting diesel (open end)

• Double acting diesel (closed end)

• Single and Double Acting Hydraulic hammers

– Primarily used for field control• For an observed hammer stroke, what is minimum

blow count?

Analysis TypesAnalysis Types

DriveabilityDriveabilityUser inputs detailed soil profile including expected soil

strength losses, splice depths, wait times, etc.

GRLWEAP calculates soil resistance and associated numerical results at user specified analysis depths.

Analysis Result: blow count, stresses, and transferred energy versus depth

Analysis Interpretation: predicted blow counts and stresses allow determination of driveability through problematic dense layers

Application: frequently used in the offshore oil industry

Analysis TypesAnalysis Types

Summary of Summary of Wave Equation Wave Equation ApplicationsApplications

Develop Driving CriterionBlow Count for a Required Ultimate Capacity Blow Count for Capacity as a Function of Energy / Stroke

Check DriveabilityBlow Count vs. Penetration DepthDriving Stresses vs Penetration Depth

Determine Optimal Driving EquipmentDriving Time

Refined Matching AnalysisAdjust Input Parameters to Fit Dynamic Measurements

WHAT INFORMATION WHAT INFORMATION

DO WE NEED FORDO WE NEED FOR

GRLWEAP ANALYSIS ?GRLWEAP ANALYSIS ?

REQUIRED INFORMATIONREQUIRED INFORMATION

• HammerHammer– Model

– Stroke and Stroke Control

– Any Modifications

• Driving SystemDriving System– Helmet Weight (including Striker Plate & Cushions)

– Hammer Cushion Material (E, A, t, er)

– Pile Cushion Material (E, A, t, er)

REQUIRED INFORMATIONREQUIRED INFORMATION

• PilePile – Length,

– Cross Sectional Area

– Taper or Other Non-uniformities

– Specific Weight

– Splice Details

– Design Load

– Ultimate Capacity

– Pile Toe Protection

REQUIRED INFORMATIONREQUIRED INFORMATION

• SoilSoil– Boring Locations with Elevations

– Soil Descriptions

– N-values or Other Strength Parameters vs Depth

– Elevation of Excavation

– Elevation of Pile Cut-off

– Elevation of Water Table

– Scour Depth or Other Later Excavations

Pile Pile Driving Driving

and and Equipment Equipment Data FormData Form

C o n t r a c t N o . : S t ru c t u r e N a m e a n d / o r N o .: P ro je c t :

P il e D r iv in g C o n t r a c t o r o r S u b c o n tr a c t o r: C o u n t y :

( P i le s d riv e n b y )

M a n u f a c t u r e r : M o d e l N o . : H a m m e r T y p e : S e ri a l N o . : M a n u f a c t u r e r s M a x im u m R a te d E n e rg y : ( f t - l b s )

Hammer S t ro k e a t M a x im u m R a te d E n e rg y : ( f t )R a n g e in O p e ra t in g E n e rg y : t o ( f t - l b s )R a n g e in O p e ra t in g S t ro k e : t o ( f t )R a m W e i g h t : ( k ip s )M o d if ic a t io n s :

Striker W e i g h t : ( k i p s ) D i a m e t e r: ( i n )Plate T h i c k n e s s : ( in )

M a t e r i a l # 1 M a te r i a l # 2( fo r C o m p o s i t e C u s h i o n )

N a m e : N a m e : Hammer A r e a : ( i n 2) A re a : ( in 2)Cushion T h i c k n e s s / P l a t e : ( i n ) T h ic k n e s s /P la t e : ( i n )

N o . o f P la t e s : N o . o f P l a t e s : T o t a l T h i c k n e s s o f H a m m e r C u s h io n :

Helmet(Drive Head) W e i g h t : ( k i p s )

Pile M a t e ri a l: Cushion A r e a : ( i n 2) T h ic k n e s s /S h e e t : ( i n )

N o . o f S h e e t s : T o t a l T h i c k n e s s o f P ile C u s h io n : ( in )

P il e T y p e : W a l l T h ic k n e s s : ( in ) T a p e r : C ro s s S e c t io n a l A r e a : ( in 2) W e ig h t / F t :

PileO r d e re d L e n g t h : ( f t )D e s i g n L o a d : ( k ip s )U lt im a t e P il e C a p a c it y : ( k ip s )

D e s c r ip t io n o f S p li c e :

D riv in g S h o e /C lo s u re P la t e D e s c ri p t io n :

S u b m it t e d B y : D a t e : T e l e p h o n e N o . : F a x N o . : T e l e p h o n e N o . : F a x N o . :

C o n t r a c t N o . : S t ru c t u r e N a m e a n d / o r N o .: P ro je c t :

P il e D r iv in g C o n t r a c t o r o r S u b c o n tr a c t o r: C o u n t y :

( P i le s d riv e n b y )

M a n u f a c t u r e r : M o d e l N o . : H a m m e r T y p e : S e ri a l N o . : M a n u f a c t u r e r s M a x im u m R a te d E n e rg y : ( f t - l b s )

Hammer S t ro k e a t M a x im u m R a te d E n e rg y : ( f t )R a n g e in O p e ra t in g E n e rg y : t o ( f t - l b s )R a n g e in O p e ra t in g S t ro k e : t o ( f t )R a m W e i g h t : ( k ip s )M o d if ic a t io n s :

Striker W e i g h t : ( k i p s ) D i a m e t e r: ( i n )Plate T h i c k n e s s : ( in )

M a t e r i a l # 1 M a te r i a l # 2( fo r C o m p o s i t e C u s h i o n )

N a m e : N a m e : Hammer A r e a : ( i n 2) A re a : ( in 2)Cushion T h i c k n e s s / P l a t e : ( i n ) T h ic k n e s s /P la t e : ( i n )

N o . o f P la t e s : N o . o f P l a t e s : T o t a l T h i c k n e s s o f H a m m e r C u s h io n :

Helmet(Drive Head) W e i g h t : ( k i p s )

Pile M a t e ri a l: Cushion A r e a : ( i n 2) T h ic k n e s s /S h e e t : ( i n )

N o . o f S h e e t s : T o t a l T h i c k n e s s o f P ile C u s h io n : ( in )

P il e T y p e : W a l l T h ic k n e s s : ( in ) T a p e r : C ro s s S e c t io n a l A r e a : ( in 2) W e ig h t / F t :

PileO r d e re d L e n g t h : ( f t )D e s i g n L o a d : ( k ip s )U lt im a t e P il e C a p a c it y : ( k ip s )

D e s c r ip t io n o f S p li c e :

D riv in g S h o e /C lo s u re P la t e D e s c ri p t io n :

S u b m it t e d B y : D a t e : T e l e p h o n e N o . : F a x N o . : T e l e p h o n e N o . : F a x N o . :

Ram

Anvil

Depth

4

8

12

16

(m)

0

20

(ft)

0

10

20

30

40

50

60

MediumSand

N’ = 20

Hammer:Delmag D 12-42; 46 kJ (34 ft-kips)

Hammer Cushion:50 mm (2 inch) Aluminum + Conbest

Helmet: 7.6 kN (1.7 kips)

Pile: Closed End PipeOD 356 mm (14 inch)Wall 8 mm (0.314 inch)

Shaft Resistance, 84%:Triangular Distribution1240 kN (280 kips)

Toe Resistance, 16%:240 kN (54 kips)

Depth

4

8

12

16

(m)

0

20

4

8

12

16

(m)

0

20

(ft)

0

10

20

30

40

50

60

(ft)

0

10

20

30

40

50

60

MediumSand

N’ = 20

Hammer:Delmag D 12-42; 46 kJ (34 ft-kips)

Hammer Cushion:50 mm (2 inch) Aluminum + Conbest

Helmet: 7.6 kN (1.7 kips)

Pile: Closed End PipeOD 356 mm (14 inch)Wall 8 mm (0.314 inch)

Shaft Resistance, 84%:Triangular Distribution1240 kN (280 kips)

Toe Resistance, 16%:240 kN (54 kips)

GRLWEAP Example 1 & 2 ProblemGRLWEAP Example 1 & 2 Problem

Ru = 330 kips

68 blows / 0.25 m

27-Aug-2003GRL Engineers, Inc. GRLWEAP (TM) Version 2003FHWA - GRLWEAP EXAMPLE #1

27-Aug-2003GRL Engineers, Inc. GRLWEAP (TM) Version 2003FHWA - GRLWEAP EXAMPLE #1

Co

mp

res

siv

e S

tre

ss

(M

Pa

)

0

50

100

150

200

250

Te

ns

ion

Str

es

s (

MP

a)

0

50

100

150

200

250

Blow Count (blows/.25m)

Ult

ima

te C

ap

ac

ity

(k

N)

0.0 25.0 50.0 75.0 100.0 125.0 150.00

400

800

1200

1600

2000

Blow Count (blows/.25m)

Str

ok

e (

me

ter)

0.0 25.0 50.0 75.0 100.0 125.0 150.00.00

1.00

2.00

3.00

4.00

5.00

DELMAG D 12-42

Efficiency 0.800

Helmet 7.60 kNHammer Cushion 10535 kN/mm

Skin Quake 2.500 mmToe Quake 3.000 mmSkin Damping 0.160 sec/mToe Damping 0.500 sec/m

Pile Length mPile Penetration mPile Top Area cm2

20.00 19.00 86.51

Pile ModelSkin FrictionDistribution

Res. Shaft = 84 %(Proportional)

195 MPa

1480 kN

2.6 m

GRLWEAP Example 1 Solution - SIGRLWEAP Example 1 Solution - SI

GRLWEAP Example 2 Solution - SIGRLWEAP Example 2 Solution - SI

GRLWEAP Example 3 ProblemGRLWEAP Example 3 Problem

Example 3 Solution – Shallow DepthExample 3 Solution – Shallow Depth

Example 3 Solution – Final DepthExample 3 Solution – Final Depth

GRLWEAP Example 5 ProblemGRLWEAP Example 5 Problem

Example 5 Solution – First PileExample 5 Solution – First Pile

Example 5 Solution – Subsequent PilesExample 5 Solution – Subsequent Piles

Example 5 Solution – H-pile AlternateExample 5 Solution – H-pile Alternate

0

4

8

12

16

20

Pile: Closed End Pipe Pile Length 20 m (66 ft) Pile Penetration 16 m (52.5 ft) 355 mm (14 inch) x 9.5 mm (3/8 inch) Ultimate Capacity 1800 kN (405 kips)

Shaft Resistance, 30% Triangular Distribution 540 kN (121 kips)

Toe Resistance, 70% 1260 kN (284 kips)

Loose Silty Fine

Sand

Hammer: ICE 42-S: 56.9 kJ (42 ft-kips) or Vulcan 014: 56.9 kJ (42 ft-kips)

Hammer Cushion: Varies

Helmet: Varies0

10

60

50

40

30

20

Depth

(m) (ft)

Very Dense Silty Fine Sand

GRLWEAP Example 6 ProblemGRLWEAP Example 6 Problem

GRLWEAP Example 6 Solution - SIGRLWEAP Example 6 Solution - SI

Depth

4

8

12

16

(m)

0

20

(ft)

0

10

20

30

40

50

60

Hammer: Berming B 2005; 32.7 kJ (24 ft-kips)

Hammer Cushion:152 mm (6 inch) Aluminum + Micarta

Helmet: 7.1 kN (1.6 kips)Pile: Closed End Pipe

324 mm (12.75 inch) x 15 m (50 ft) longUltimate Capacity; 1470 kN (330 kips)

Toe Resistance, 53%:779 kN (175 kips)

Medium SandN’ = 10, Φ = 30° Shaft Resistance, 2%: 28 kN (7 kips)

Medium ClayCu = 36 kPa (0.8 ksi)

Dense SandN’ = 35, Φ = 37.5°

Shaft Resistance, 8%: 112 kN (26 kips)

Shaft Resistance, 37%: 551 kN (122 kips)

Depth

4

8

12

16

(m)

0

20

4

8

12

16

(m)

0

20

(ft)

0

10

20

30

40

50

60

(ft)

0

10

20

30

40

50

60Toe Resistance, 53%:

779 kN (175 kips)

Medium SandN’ = 10, Φ = 30° Shaft Resistance, 2%: 28 kN (7 kips)

Medium ClayCu = 36 kPa (0.8 ksi)

Dense SandN’ = 35, Φ = 37.5°

Shaft Resistance, 8%: 112 kN (26 kips)

Shaft Resistance, 37%: 551 kN (122 kips)

GRLWEAP Example 8 ProblemGRLWEAP Example 8 Problem

GRLWEAP Example 8 Solution - SIGRLWEAP Example 8 Solution - SI

6.3 mm 7.1 mm

GRLWEAP Example 8 Solution - SIGRLWEAP Example 8 Solution - SI

7.9 mm 9.5 mm

GRLWEAP Example 8 SolutionGRLWEAP Example 8 Solution

7.9 mm 9.5 mm

Summary of Compression Stress and Blow Count Results

Wall Thickness Compressive Stress Blow Count

Mm inch MPa ksi Blows/0.25 m Blows/ft

6.3 0.250 244 35.4 160 195

7.1 0.281 213 30.9 130 158

7.9 0.312 197 28.6 115 140

9.5 0.375 183 26.5 100 120

Criteria 0.90 FY = 279 MPa or 40.5 ksi,

Blow count of 25 – 98 bl/.25 m or 30 - 120 bl/ft