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Wave Equation Applications. 2009 PDCA Professor Pile Institute. Patrick Hannigan GRL Engineers, Inc. Analysis Types. Bearing Graph - Proportional Resistance (most common) - Constant Shaft (i.e. pile driven to rock) - Constant Toe (i.e. friction pile) - PowerPoint PPT Presentation
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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