Wave Equation Applications
description
Transcript of Wave Equation Applications
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Wave Equation Wave Equation ApplicationsApplications
2009 PDCA Professor Pile 2009 PDCA Professor Pile InstituteInstitute
Patrick HanniganGRL Engineers, Inc.
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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.
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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
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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
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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
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WHAT INFORMATION WHAT INFORMATION
DO WE NEED FORDO WE NEED FOR
GRLWEAP ANALYSIS ?GRLWEAP ANALYSIS ?
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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)
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REQUIRED INFORMATIONREQUIRED INFORMATION
• PilePile – Length,
– Cross Sectional Area
– Taper or Other Non-uniformities
– Specific Weight
– Splice Details
– Design Load
– Ultimate Capacity
– Pile Toe Protection
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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
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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
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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
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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
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GRLWEAP Example 2 Solution - SIGRLWEAP Example 2 Solution - SI
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GRLWEAP Example 3 ProblemGRLWEAP Example 3 Problem
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Example 3 Solution – Shallow DepthExample 3 Solution – Shallow Depth
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Example 3 Solution – Final DepthExample 3 Solution – Final Depth
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GRLWEAP Example 5 ProblemGRLWEAP Example 5 Problem
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Example 5 Solution – First PileExample 5 Solution – First Pile
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Example 5 Solution – Subsequent PilesExample 5 Solution – Subsequent Piles
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Example 5 Solution – H-pile AlternateExample 5 Solution – H-pile Alternate
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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
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GRLWEAP Example 6 Solution - SIGRLWEAP Example 6 Solution - SI
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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
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GRLWEAP Example 8 Solution - SIGRLWEAP Example 8 Solution - SI
6.3 mm 7.1 mm
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GRLWEAP Example 8 Solution - SIGRLWEAP Example 8 Solution - SI
7.9 mm 9.5 mm
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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