wave equation pda
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Wave Equation Applications2009 PDCA Professor Pile InstitutePatrick HanniganGRL Engineers, Inc.
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Analysis TypesBearing 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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Analysis TypesInspectors ChartFor a constant capacity (e.g. the required ultimate capacity), plots stroke vs blow countVariable energy hammers onlySingle acting diesel (open end)Double acting diesel (closed end)Single and Double Acting Hydraulic hammersPrimarily used for field controlFor an observed hammer stroke, what is minimum blow count?
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Analysis TypesDriveabilityUser 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 depthAnalysis Interpretation: predicted blow counts and stresses allow determination of driveability through problematic dense layersApplication: frequently used in the offshore oil industry
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Summary of Wave Equation ApplicationsDevelop 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
DO WE NEED FOR
GRLWEAP ANALYSIS ?
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REQUIRED INFORMATION HammerModelStroke and Stroke ControlAny Modifications
Driving SystemHelmet Weight (including Striker Plate & Cushions)Hammer Cushion Material (E, A, t, er)Pile Cushion Material (E, A, t, er)
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REQUIRED INFORMATIONPile Length,Cross Sectional AreaTaper or Other Non-uniformitiesSpecific WeightSplice DetailsDesign LoadUltimate CapacityPile Toe Protection
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REQUIRED INFORMATION SoilBoring Locations with ElevationsSoil DescriptionsN-values or Other Strength Parameters vs DepthElevation of ExcavationElevation of Pile Cut-offElevation of Water TableScour Depth or Other Later Excavations
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Pile Driving and Equipment Data Form
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GRLWEAP Example 1 & 2 Problem Ru = 330 kips
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68 blows / 0.25 m195 MPa1480 kN2.6 mGRLWEAP Example 1 Solution - SI
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GRLWEAP Example 2 Solution - SI
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GRLWEAP Example 3 Problem
Depth
4
8
12
16
(m)
0
20
(ft)
0
10
20
30
40
50
60
Loose
Silty
Fine Sand
N = 8
Hammer:
JUNTTAN HHK 3
200 mm (7.9 inch) Monocast MC 901
Helmet: 9.6
kN
(2.16 kips)
Pile: Square
Prestressed
Concrete
356 mm (14 inch)
Toe Resistance, 52%:
933
kN
(210 kips)
Medium Dense
Silty
Fine Sand
N = 14
Dense Sand
and Gravel
N = 34
Penetration Depth for
Tension Evaluation
Pile Cushion: 114 mm (4.5 inch) Plywood
Shaft Resistance, 33%:
597
kN
(134 kips)
Shaft Resistance, 5%:
97
kN
(22 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
Loose
Silty
Fine Sand
N = 8
Hammer Cushion:
Pile Length 12 m (39 ft)
Ultimate Capacity: 1807 kN (406 kips)
Shaft Resistance, 10%:
180
kN
(40 kips)
Medium Dense
Silty
Fine Sand
N = 14
Dense Sand
and Gravel
N = 34
Penetration Depth for
Tension Evaluation
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Example 3 Solution Shallow Depth
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Example 3 Solution Final Depth
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GRLWEAP Example 5 Problem
0
10
20
30
40
50
60
Depth
4
8
12
16
(m)
0
20
(ft)
Loose Slit
(Subject to
Scour)
Hammer:
Conmaco
140: 56.9 kJ (42 ft
-
kips)
Hammer Cushion:
152 mm (6 inch) Blue Nylon
Helmet: 18.09
kN
(4.1 kips)
Displacement Pile: Square Prestressed Concrete
356 mm (14 inch) x 14 m (46 ft) long
Driving Resistance: 2870
kN
(645 kips)
Minimum Penetration Requirement
Pile Cushion: 254 mm (10 inch) Plywood
24
70
Extremely Dense
Sand and Gravel
N = 110
Dense Sand
and Gravel
N = 33
Bedrock
Sheeting for Cofferdam
Non
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Displacement Pile: H
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Pile
HP 360x152 (14x102) x 16 m (52.5 ft) long
Driving Resistance: 2405kN (540 kips)
Ultimate Capacity: 1780
kN
(400 kips)
after Scour
0
10
20
30
40
50
60
4
8
12
16
(m)
0
20
(ft)
5 m
4 m
11.5 m
24
70
Non
-
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Example 5 Solution First Pile
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Example 5 Solution Subsequent Piles
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Example 5 Solution H-pile Alternate
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048121620Pile: 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 SandHammer: ICE 42-S: 56.9 kJ (42 ft-kips) or Vulcan 014: 56.9 kJ (42 ft-kips)Hammer Cushion: VariesHelmet: Varies0106050403020Depth(m) (ft)Very Dense Silty Fine SandGRLWEAP Example 6 Problem
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GRLWEAP Example 6 Solution - SI
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GRLWEAP Example 8 Problem
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) long
Ultimate Capacity; 1470
kN
(330 kips)
Toe Resistance, 53%:
779
kN
(175 kips)
Medium Sand
N = 10,
= 30
Shaft Resistance, 2%: 28
kN
(7 kips)
Medium Clay
C
u
= 36
kPa
(0.8
ksi
)
Dense Sand
N = 35,
= 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
60
Toe Resistance, 53%:
779
kN
(175 kips)
Medium Sand
N = 10,
= 30
Shaft Resistance, 2%: 28
kN
(7 kips)
Medium Clay
C
u
= 36
kPa
(0.8
ksi
)
Dense Sand
N = 35,
= 37.5
Shaft Resistance, 8%: 112
kN
(26 kips)
Shaft Resistance, 37%: 551
kN
(122 kips)
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GRLWEAP Example 8 Solution - SI 6.3 mm 7.1 mm
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GRLWEAP Example 8 Solution - SI 7.9 mm 9.5 mm
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GRLWEAP Example 8 Solution 7.9 mm 9.5 mmCriteria 0.90 FY = 279 MPa or 40.5 ksi, Blow count of 25 98 bl/.25 m or 30 - 120 bl/ft
Summary of Compression Stress and Blow Count Results Wall ThicknessCompressive StressBlow CountMminchMPaksiBlows/0.25 mBlows/ft6.30.25024435.41601957.10.28121330.91301587.90.31219728.61151409.50.37518326.5100120
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