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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)
Analysis Results: Capacity, stress, stroke
(OED) vs. Blow count
Analysis Application: Hammer approvals,
capacity assessments, hammer sizing.
Inspector’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 Types
Driveability
User 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 Types
Summary of
Wave Equation Applications
Develop Driving Criterion
Blow Count for a Required Ultimate Capacity
Blow Count for Capacity as a Function of Energy / Stroke
Check Driveability
Blow Count vs. Penetration Depth
Driving Stresses vs Penetration Depth
Determine Optimal Driving Equipment
Driving Time
Refined Matching Analysis
Adjust Input Parameters to Fit Dynamic Measurements
WHAT INFORMATION
DO WE NEED FOR
GRLWEAP ANALYSIS ?
REQUIRED INFORMATION
• Hammer
– Model
– Stroke and Stroke Control
– Any Modifications
• Driving System
– Helmet Weight (including Striker Plate & Cushions)
– Hammer Cushion Material (E, A, t, er)
– Pile Cushion Material (E, A, t, er)
REQUIRED INFORMATION
• Pile
– Length,
– Cross Sectional Area
– Taper or Other Non-uniformities
– Specific Weight
– Splice Details
– Design Load
– Ultimate Capacity
– Pile Toe Protection
REQUIRED INFORMATION
• Soil
– 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 Driving
and
Equipment
Data Form
Contract No.: Structure Name and/or No.:
Project:
Pile Driving Contractor or Subcontractor:
County:
(Piles driven by)
Manufacturer: Model No.:
Ham mer Type: Serial No.:
Manufacturers Maximum Rated Energy: (ft-lbs)
Hammer Stroke at Maximum Rated Energy: (ft)
Range in Operating Energy: to (ft-lbs)
Range in Operating Stroke: to (ft)
Ram W eight: (kips)
Modifications:
Striker Weight: (kips) Diam eter: (in)
Plate Thickness: (in)
Material #1 Material #2
(for Composite Cushion)
Nam e: Name:
Hammer Area: (in2
) Area: (in2
)
Cushion Thickness/Plate: (in) Thickness/Plate: (in)
No. of Plates: No. of Plates:
Total Thickness of Hamm er Cushion:
Helmet
(Drive Head) Weight: (kips)
Pile Material:
Cushion Area: (in2
) Thickness/Sheet: (in)
No. of Sheets:
Total Thickness of Pile Cushion: (in)
Pile Type:
Wall Thickness: (in) Taper:
Cross Sectional Area: (in2
) Weight/Ft:
Pile
Ordered Length: (ft)
Design Load: (kips)
Ultim ate Pile Capacity: (kips)
Description of Splice:
Driving Shoe/Closure Plate Description:
Subm itted By: Date:
Telephone No.: Fax No.:
Telephone No.: Fax No.:
Contract No.: Structure Name and/or No.:
Project:
Pile Driving Contractor or Subcontractor:
County:
(Piles driven by)
Manufacturer: Model No.:
Ham mer Type: Serial No.:
Manufacturers Maximum Rated Energy: (ft-lbs)
Hammer Stroke at Maximum Rated Energy: (ft)
Range in Operating Energy: to (ft-lbs)
Range in Operating Stroke: to (ft)
Ram W eight: (kips)
Modifications:
Striker Weight: (kips) Diam eter: (in)
Plate Thickness: (in)
Material #1 Material #2
(for Composite Cushion)
Nam e: Name:
Hammer Area: (in2
) Area: (in2
)
Cushion Thickness/Plate: (in) Thickness/Plate: (in)
No. of Plates: No. of Plates:
Total Thickness of Hamm er Cushion:
Helmet
(Drive Head) Weight: (kips)
Pile Material:
Cushion Area: (in2
) Thickness/Sheet: (in)
No. of Sheets:
Total Thickness of Pile Cushion: (in)
Pile Type:
Wall Thickness: (in) Taper:
Cross Sectional Area: (in2
) Weight/Ft:
Pile
Ordered Length: (ft)
Design Load: (kips)
Ultim ate Pile Capacity: (kips)
Description of Splice:
Driving Shoe/Closure Plate Description:
Subm itted By: Date:
Telephone No.: Fax No.:
Telephone No.: Fax No.:
R
a
m
Anvil
Depth
4
8
12
16
(m)
0
20
(ft)
0
10
20
30
40
50
60
Medium
Sand
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 Pipe
OD 356 mm (14 inch)
Wall 8 mm (0.314 inch)
Shaft Resistance, 84%:
Triangular Distribution
1240 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
Medium
Sand
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 Pipe
OD 356 mm (14 inch)
Wall 8 mm (0.314 inch)
Shaft Resistance, 84%:
Triangular Distribution
1240 kN (280 kips)
Toe Resistance, 16%:
240 kN (54 kips)
GRLWEAP Example 1 & 2 Problem
Ru = 330 kips
68 blows / 0.25 m
27-Aug-2003
GRL Engineers, Inc.
GRLWEAP (TM) Version 2003
FHWA - GRLWEAP EXAMPLE #1
27-Aug-2003
GRL Engineers, Inc.
GRLWEAP (TM) Version 2003
FHWA - GRLWEAP EXAMPLE #1
C
o
m
p
r
e
s
s
i
v
e
S
t
r
e
s
s
(
M
P
a
)
0
50
100
150
200
250
T
e
n
s
i
o
n
S
t
r
e
s
s
(
M
P
a
)
0
50
100
150
200
250
Blow Count (blows/.25m)
U
l
t
i
m
a
t
e
C
a
p
a
c
i
t
y
(
k
N
)
0.0 25.0 50.0 75.0 100.0 125.0 150.0
0
400
800
1200
1600
2000
Blow Count (blows/.25m)
S
t
r
o
k
e
(
m
e
t
e
r
)
0.0 25.0 50.0 75.0 100.0 125.0 150.0
0.00
1.00
2.00
3.00
4.00
5.00
DELMAG D 12-42
Efficiency 0.800
Helmet 7.60 kN
Hammer Cushion 10535 kN/mm
Skin Quake 2.500 mm
Toe Quake 3.000 mm
Skin Damping 0.160 sec/m
Toe Damping 0.500 sec/m
Pile Length m
Pile Penetration m
Pile Top Area cm2
20.00
19.00
86.51
Pile Model
Skin Friction
Distribution
Res. Shaft = 84 %
(Proportional)
195 MPa
1480 kN
2.6 m
GRLWEAP Example 1 Solution - SI
31-Jan-2005
GRL Engineers, Inc.
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #2
31-Jan-2005
GRL Engineers, Inc.
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #2
Compressive
Stress
(MPa)
0
50
100
150
200
250
Tension
Stress
(MPa)
0
50
100
150
200
250
Blow Count (blows/.25m)
Stroke
(m)
33 54 74 95 115 136 156
1.50
2.00
2.50
3.00
3.50
4.00
DELMAG D 12-42
Capacity 1480.0 kN
Efficiency 0.800
Helmet 7.60 kN
Hammer Cushion 10699 kN/mm
Skin Quake 2.540 mm
Toe Quake 5.931 mm
Skin Damping 0.164 sec/m
Toe Damping 0.490 sec/m
Pile Length
Pile Penetration
Pile Top Area
20.00
19.00
87.46
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 84 %
(Proportional)
GRLWEAP Example 2 Solution - SI
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)
Medium Dense
Silty Fine Sand
N’ = 14
Dense Sand
and Gravel
N’ = 34
Penetration Depth for
Tension Evaluation
Shaft Resistance, 10%:
180 kN (40 kips)
GRLWEAP Example 3 Problem
31-Jan-2005
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #3, 114mm @ 3.5m
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #3, 209mm @ 3.5m
31-Jan-2005
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #3, 114mm @ 3.5m
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #3, 209mm @ 3.5m
Compressive
Stress
(MPa)
0
4
8
12
16
20
Tension
Stress
(MPa)
0
4
8
12
16
20
Blow Count (blows/.25m)
Ultimate
Capacity
(kN)
0 40 80 120 160 200 240
0
500
1000
1500
2000
2500
JUNT TAN HHK 3 JUNT TAN HHK 3
Stroke 1.00 1.00 m
Efficiency 0.800 0.800
Helmet 9.60 9.60 kN
Hammer Cushion 1989 1989 kN/mm
Pile Cushion 229 125 kN/mm
Skin Quake 2.500 mm 2.500 mm
Toe Quake 5.994 mm 5.994 mm
Skin Damping 0.161 sec/m 0.161 sec/m
Toe Damping 0.500 sec/m 0.500 sec/m
Pile Length
Pile Penetration
Pile Top Area
12.00
3.50
1267.35
Pile Model
Skin Friction
Distribution
Res. Shaft = 48 %
(Proportional)
12.00
3.50
1267.35
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 48 %
(Proportional)
Example 3 Solution – Shallow Depth
31-Jan-2005
GRL Engineers, Inc.
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP E
XAMPLE #3, 209mm @ 11.5m
31-Jan-2005
GRL Engineers, Inc.
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP E
XAMPLE #3, 209mm @ 11.5m
Compressive
Stress
(MPa)
0
4
8
12
16
20
Tension
Stress
(MPa)
0
4
8
12
16
20
Blow Count (blows/.25m)
Ultimate
Capacity
(kN)
0 25 50 75 100 125 150
0
500
1000
1500
2000
2500
JUNT TAN HHK 3
Stroke 1.00 m
Efficiency 0.800
Helmet 9.60 kN
Hammer Cushion 1989 kN/mm
Pile Cushion 376 kN/mm
Skin Quake 2.500 mm
Toe Quake 6.000 mm
Skin Damping 0.160 sec/m
Toe Damping 0.500 sec/m
Pile Length
Pile Penetration
Pile Top Area
12.00
11.50
1267.35
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 48 %
(Proportional)
Example 3 Solution – Final Depth
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-Displacement Pile: H-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)
24
70
Non-
5 m
4 m
11.5 m
GRLWEAP Example 5 Problem
GRL Engineers, Inc. 2005 Jan 17
FHWA - GRLWEAP EXAMPLE #5 - First Pile Gain/Loss 1 at Shaft and Toe 1.000 / 1.000 GRLWEAP(TM) Version 2005
D
e
p
t
h
(
m
)
0 20 40 60 80
2
4
5
7
9
11
13
14
16
18
Blow Count (blows/.25m)
D
e
p
t
h
(
m
)
0 1000 2000 3000 4000
2
4
5
7
9
11
13
14
16
18
Ult. Capacity (kN)
0 10 20 30 40
2
4
5
7
9
11
13
14
16
18
Tension (MPa)
0 10 20 30 40
2
4
5
7
9
11
13
14
16
18
Comp. Stress (MPa)
0.0 0.5 1.0 1.5 2.0
2
4
5
7
9
11
13
14
16
18
Stroke (m)
0.0 10.0 20.0 30.0 40.0
2
4
5
7
9
11
13
14
16
18
ENTHRU (kJ)
Example 5 Solution – First Pile
GRL Engineers, Inc. 2005 Jan 17
FHWA - GRLWEAP EXAMPLE #5 - Later Piles Gain/Loss 1 at Shaft and Toe 1.330 / 1.330 GRLWEAP(TM) Version 2005
D
e
p
t
h
(
m
)
0 50 100 150 200
2
4
5
7
9
11
13
14
16
18
Blow Count (blows/.25m)
D
e
p
t
h
(
m
)
0 1000 2000 3000 4000
2
4
5
7
9
11
13
14
16
18
Ult. Capacity (kN)
0 10 20 30 40
2
4
5
7
9
11
13
14
16
18
Tension (MPa)
0 10 20 30 40
2
4
5
7
9
11
13
14
16
18
Comp. Stress (MPa)
0.0 0.5 1.0 1.5 2.0
2
4
5
7
9
11
13
14
16
18
Stroke (m)
0.0 10.0 20.0 30.0 40.0
2
4
5
7
9
11
13
14
16
18
ENTHRU (kJ)
Example 5 Solution – Subsequent Piles
GRL Engineers, Inc. 2005 Jan 17
FHWA - GRLWEAP EXAMPLE #5 - H-Pile Gain/Loss 1 at Shaft and Toe 1.000 / 1.000 GRLWEAP(TM) Version 2005
D
e
p
t
h
(
m
)
0 100 200 300 400
2
4
5
7
9
11
13
14
16
18
Blow Count (blows/.25m)
D
e
p
t
h
(
m
)
0 4000 8000 12000 16000
2
4
5
7
9
11
13
14
16
18
Ult. Capacity (kN)
0 100 200 300 400
2
4
5
7
9
11
13
14
16
18
Tension (MPa)
0 100 200 300 400
2
4
5
7
9
11
13
14
16
18
Comp. Stress (MPa)
0.0 0.5 1.0 1.5 2.0
2
4
5
7
9
11
13
14
16
18
Stroke (m)
0.0 10.0 20.0 30.0 40.0
2
4
5
7
9
11
13
14
16
18
ENTHRU (kJ)
Example 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: Varies
0
10
60
50
40
30
20
Depth
(m) (ft)
Very Dense
Silty Fine Sand
GRLWEAP Example 6 Problem
31-Jan-2005
GRL Engineers, Inc.
FHWA-GRLWEAP EXAMPLE #6 - Lt Ram, 10mm
GRLWEAP (TM) Version 2005
FHWA-GRLWEAP EXAMPLE #6 - Hy Ram, 10mm
31-Jan-2005
GRL Engineers, Inc.
FHWA-GRLWEAP EXAMPLE #6 - Lt Ram, 10mm
GRLWEAP (TM) Version 2005
FHWA-GRLWEAP EXAMPLE #6 - Hy Ram, 10mm
Compressive
Stress
(MPa)
0
80
160
240
320
400
Tension
Stress
(MPa)
0
80
160
240
320
400
Blow Count (blows/.25m)
Ultimate
Capacity
(kN)
0 50 100 150 200 250 300
0
500
1000
1500
2000
2500
Blow Count (blows/.25m)
Stroke
(m)
0 50 100 150 200 250 300
0
2
4
6
8
10
ICE 42-S VULCAN VUL 014
Efficiency 0.800 0.670
Helmet 9.12 7.45 kN
Hammer Cushion 6075 1417 kN/mm
Skin Quake 2.500 mm 2.500 mm
Toe Quake 10.000 mm 10.000 mm
Skin Damping 0.150 sec/m 0.150 sec/m
Toe Damping 0.500 sec/m 0.500 sec/m
Pile Length
Pile Penetration
Pile Top Area
20.00
16.00
103.41
Pile Model
Skin Friction
Distribution
Res. Shaft = 30 %
(Proportional)
20.00
16.00
103.41
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 30 %
(Proportional)
GRLWEAP 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) long
Ultimate Capacity; 1470 kN (330 kips)
Toe Resistance, 53%:
779 kN (175 kips)
Medium Sand
N’ = 10, Φ = 30° Shaft Resistance, 2%: 28 kN (7 kips)
Medium Clay
Cu = 36 kPa (0.8 ksi)
Dense Sand
N’ = 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
60
Toe Resistance, 53%:
779 kN (175 kips)
Medium Sand
N’ = 10, Φ = 30° Shaft Resistance, 2%: 28 kN (7 kips)
Medium Clay
Cu = 36 kPa (0.8 ksi)
Dense Sand
N’ = 35, Φ = 37.5°
Shaft Resistance, 8%: 112 kN (26 kips)
Shaft Resistance, 37%: 551 kN (122 kips)
GRLWEAP Example 8 Problem
31-Jan-2005
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #8 - 6.3 mm Wall
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #8 - 7.1 mm Wall
31-Jan-2005
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #8 - 6.3 mm Wall
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #8 - 7.1 mm Wall
Compressive
Stress
(MPa)
0
75
150
225
300
375
Tension
Stress
(MPa)
0
75
150
225
300
375
Blow Count (blows/.25m)
Ultimate
Capacity
(kN)
0 50 100 150 200 250 300
0
400
800
1200
1600
2000
Blow Count (blows/.25m)
Stroke
(m)
0 50 100 150 200 250 300
0
1
2
3
4
5
BERMINGH B2005 BERMINGH B2005
Efficiency 0.800 0.800
Helmet 7.12 7.12 kN
Hammer Cushion245185 245185 kN/mm
Skin Quake 2.500 mm 2.500 mm
Toe Quake 2.500 mm 2.500 mm
Skin Damping 0.150 sec/m 0.150 sec/m
Toe Damping 0.500 sec/m 0.500 sec/m
Pile Length
Pile Penetration
Pile Top Area
15.00
14.00
62.88
Pile Model
Skin Friction
Distribution
Res. Shaft = 47 %
(Proportional)
15.00
14.00
70.69
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 47 %
(Proportional)
GRLWEAP Example 8 Solution - SI
 6.3 mm  7.1 mm
31-Jan-2005
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #8 - 7.9 mm Wall
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #8 - 9.5 mm Wall
31-Jan-2005
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #8 - 7.9 mm Wall
GRLWEAP (TM) Version 2005
FHWA - GRLWEAP EXAMPLE #8 - 9.5 mm Wall
Compressive
Stress
(MPa)
0
50
100
150
200
250
Tension
Stress
(MPa)
0
50
100
150
200
250
Blow Count (blows/.25m)
Ultimate
Capacity
(kN)
0 50 100 150 200 250 300
0
400
800
1200
1600
2000
Blow Count (blows/.25m)
Stroke
(m)
0 50 100 150 200 250 300
0
1
2
3
4
5
BERMINGH B2005 BERMINGH B2005
Efficiency 0.800 0.800
Helmet 7.12 7.12 kN
Hammer Cushion245185 245185 kN/mm
Skin Quake 2.500 mm 2.500 mm
Toe Quake 2.500 mm 2.500 mm
Skin Damping 0.150 sec/m 0.150 sec/m
Toe Damping 0.500 sec/m 0.500 sec/m
Pile Length
Pile Penetration
Pile Top Area
15.00
14.00
78.45
Pile Model
Skin Friction
Distribution
Res. Shaft = 47 %
(Proportional)
15.00
14.00
93.86
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 47 %
(Proportional)
GRLWEAP Example 8 Solution - SI
 7.9 mm  9.5 mm
GRLWEAP 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

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Wave Equation Applications for Pile Foundation Analysis

  • 1. Wave Equation Applications 2009 PDCA Professor Pile Institute Patrick Hannigan GRL Engineers, Inc.
  • 2. Analysis Types Bearing 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.
  • 3. Inspector’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 Types
  • 4. Driveability User 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 Types
  • 5. Summary of Wave Equation Applications Develop Driving Criterion Blow Count for a Required Ultimate Capacity Blow Count for Capacity as a Function of Energy / Stroke Check Driveability Blow Count vs. Penetration Depth Driving Stresses vs Penetration Depth Determine Optimal Driving Equipment Driving Time Refined Matching Analysis Adjust Input Parameters to Fit Dynamic Measurements
  • 6. WHAT INFORMATION DO WE NEED FOR GRLWEAP ANALYSIS ?
  • 7. REQUIRED INFORMATION • Hammer – Model – Stroke and Stroke Control – Any Modifications • Driving System – Helmet Weight (including Striker Plate & Cushions) – Hammer Cushion Material (E, A, t, er) – Pile Cushion Material (E, A, t, er)
  • 8. REQUIRED INFORMATION • Pile – Length, – Cross Sectional Area – Taper or Other Non-uniformities – Specific Weight – Splice Details – Design Load – Ultimate Capacity – Pile Toe Protection
  • 9. REQUIRED INFORMATION • Soil – 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
  • 10. Pile Driving and Equipment Data Form Contract No.: Structure Name and/or No.: Project: Pile Driving Contractor or Subcontractor: County: (Piles driven by) Manufacturer: Model No.: Ham mer Type: Serial No.: Manufacturers Maximum Rated Energy: (ft-lbs) Hammer Stroke at Maximum Rated Energy: (ft) Range in Operating Energy: to (ft-lbs) Range in Operating Stroke: to (ft) Ram W eight: (kips) Modifications: Striker Weight: (kips) Diam eter: (in) Plate Thickness: (in) Material #1 Material #2 (for Composite Cushion) Nam e: Name: Hammer Area: (in2 ) Area: (in2 ) Cushion Thickness/Plate: (in) Thickness/Plate: (in) No. of Plates: No. of Plates: Total Thickness of Hamm er Cushion: Helmet (Drive Head) Weight: (kips) Pile Material: Cushion Area: (in2 ) Thickness/Sheet: (in) No. of Sheets: Total Thickness of Pile Cushion: (in) Pile Type: Wall Thickness: (in) Taper: Cross Sectional Area: (in2 ) Weight/Ft: Pile Ordered Length: (ft) Design Load: (kips) Ultim ate Pile Capacity: (kips) Description of Splice: Driving Shoe/Closure Plate Description: Subm itted By: Date: Telephone No.: Fax No.: Telephone No.: Fax No.: Contract No.: Structure Name and/or No.: Project: Pile Driving Contractor or Subcontractor: County: (Piles driven by) Manufacturer: Model No.: Ham mer Type: Serial No.: Manufacturers Maximum Rated Energy: (ft-lbs) Hammer Stroke at Maximum Rated Energy: (ft) Range in Operating Energy: to (ft-lbs) Range in Operating Stroke: to (ft) Ram W eight: (kips) Modifications: Striker Weight: (kips) Diam eter: (in) Plate Thickness: (in) Material #1 Material #2 (for Composite Cushion) Nam e: Name: Hammer Area: (in2 ) Area: (in2 ) Cushion Thickness/Plate: (in) Thickness/Plate: (in) No. of Plates: No. of Plates: Total Thickness of Hamm er Cushion: Helmet (Drive Head) Weight: (kips) Pile Material: Cushion Area: (in2 ) Thickness/Sheet: (in) No. of Sheets: Total Thickness of Pile Cushion: (in) Pile Type: Wall Thickness: (in) Taper: Cross Sectional Area: (in2 ) Weight/Ft: Pile Ordered Length: (ft) Design Load: (kips) Ultim ate Pile Capacity: (kips) Description of Splice: Driving Shoe/Closure Plate Description: Subm itted By: Date: Telephone No.: Fax No.: Telephone No.: Fax No.: R a m Anvil
  • 11. Depth 4 8 12 16 (m) 0 20 (ft) 0 10 20 30 40 50 60 Medium Sand 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 Pipe OD 356 mm (14 inch) Wall 8 mm (0.314 inch) Shaft Resistance, 84%: Triangular Distribution 1240 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 Medium Sand 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 Pipe OD 356 mm (14 inch) Wall 8 mm (0.314 inch) Shaft Resistance, 84%: Triangular Distribution 1240 kN (280 kips) Toe Resistance, 16%: 240 kN (54 kips) GRLWEAP Example 1 & 2 Problem Ru = 330 kips
  • 12. 68 blows / 0.25 m 27-Aug-2003 GRL Engineers, Inc. GRLWEAP (TM) Version 2003 FHWA - GRLWEAP EXAMPLE #1 27-Aug-2003 GRL Engineers, Inc. GRLWEAP (TM) Version 2003 FHWA - GRLWEAP EXAMPLE #1 C o m p r e s s i v e S t r e s s ( M P a ) 0 50 100 150 200 250 T e n s i o n S t r e s s ( M P a ) 0 50 100 150 200 250 Blow Count (blows/.25m) U l t i m a t e C a p a c i t y ( k N ) 0.0 25.0 50.0 75.0 100.0 125.0 150.0 0 400 800 1200 1600 2000 Blow Count (blows/.25m) S t r o k e ( m e t e r ) 0.0 25.0 50.0 75.0 100.0 125.0 150.0 0.00 1.00 2.00 3.00 4.00 5.00 DELMAG D 12-42 Efficiency 0.800 Helmet 7.60 kN Hammer Cushion 10535 kN/mm Skin Quake 2.500 mm Toe Quake 3.000 mm Skin Damping 0.160 sec/m Toe Damping 0.500 sec/m Pile Length m Pile Penetration m Pile Top Area cm2 20.00 19.00 86.51 Pile Model Skin Friction Distribution Res. Shaft = 84 % (Proportional) 195 MPa 1480 kN 2.6 m GRLWEAP Example 1 Solution - SI
  • 13. 31-Jan-2005 GRL Engineers, Inc. GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #2 31-Jan-2005 GRL Engineers, Inc. GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #2 Compressive Stress (MPa) 0 50 100 150 200 250 Tension Stress (MPa) 0 50 100 150 200 250 Blow Count (blows/.25m) Stroke (m) 33 54 74 95 115 136 156 1.50 2.00 2.50 3.00 3.50 4.00 DELMAG D 12-42 Capacity 1480.0 kN Efficiency 0.800 Helmet 7.60 kN Hammer Cushion 10699 kN/mm Skin Quake 2.540 mm Toe Quake 5.931 mm Skin Damping 0.164 sec/m Toe Damping 0.490 sec/m Pile Length Pile Penetration Pile Top Area 20.00 19.00 87.46 m m cm2 Pile Model Skin Friction Distribution Res. Shaft = 84 % (Proportional) GRLWEAP Example 2 Solution - SI
  • 14. 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) Medium Dense Silty Fine Sand N’ = 14 Dense Sand and Gravel N’ = 34 Penetration Depth for Tension Evaluation Shaft Resistance, 10%: 180 kN (40 kips) GRLWEAP Example 3 Problem
  • 15. 31-Jan-2005 GRL Engineers, Inc. FHWA - GRLWEAP EXAMPLE #3, 114mm @ 3.5m GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #3, 209mm @ 3.5m 31-Jan-2005 GRL Engineers, Inc. FHWA - GRLWEAP EXAMPLE #3, 114mm @ 3.5m GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #3, 209mm @ 3.5m Compressive Stress (MPa) 0 4 8 12 16 20 Tension Stress (MPa) 0 4 8 12 16 20 Blow Count (blows/.25m) Ultimate Capacity (kN) 0 40 80 120 160 200 240 0 500 1000 1500 2000 2500 JUNT TAN HHK 3 JUNT TAN HHK 3 Stroke 1.00 1.00 m Efficiency 0.800 0.800 Helmet 9.60 9.60 kN Hammer Cushion 1989 1989 kN/mm Pile Cushion 229 125 kN/mm Skin Quake 2.500 mm 2.500 mm Toe Quake 5.994 mm 5.994 mm Skin Damping 0.161 sec/m 0.161 sec/m Toe Damping 0.500 sec/m 0.500 sec/m Pile Length Pile Penetration Pile Top Area 12.00 3.50 1267.35 Pile Model Skin Friction Distribution Res. Shaft = 48 % (Proportional) 12.00 3.50 1267.35 m m cm2 Pile Model Skin Friction Distribution Res. Shaft = 48 % (Proportional) Example 3 Solution – Shallow Depth
  • 16. 31-Jan-2005 GRL Engineers, Inc. GRLWEAP (TM) Version 2005 FHWA - GRLWEAP E XAMPLE #3, 209mm @ 11.5m 31-Jan-2005 GRL Engineers, Inc. GRLWEAP (TM) Version 2005 FHWA - GRLWEAP E XAMPLE #3, 209mm @ 11.5m Compressive Stress (MPa) 0 4 8 12 16 20 Tension Stress (MPa) 0 4 8 12 16 20 Blow Count (blows/.25m) Ultimate Capacity (kN) 0 25 50 75 100 125 150 0 500 1000 1500 2000 2500 JUNT TAN HHK 3 Stroke 1.00 m Efficiency 0.800 Helmet 9.60 kN Hammer Cushion 1989 kN/mm Pile Cushion 376 kN/mm Skin Quake 2.500 mm Toe Quake 6.000 mm Skin Damping 0.160 sec/m Toe Damping 0.500 sec/m Pile Length Pile Penetration Pile Top Area 12.00 11.50 1267.35 m m cm2 Pile Model Skin Friction Distribution Res. Shaft = 48 % (Proportional) Example 3 Solution – Final Depth
  • 17. 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-Displacement Pile: H-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) 24 70 Non- 5 m 4 m 11.5 m GRLWEAP Example 5 Problem
  • 18. GRL Engineers, Inc. 2005 Jan 17 FHWA - GRLWEAP EXAMPLE #5 - First Pile Gain/Loss 1 at Shaft and Toe 1.000 / 1.000 GRLWEAP(TM) Version 2005 D e p t h ( m ) 0 20 40 60 80 2 4 5 7 9 11 13 14 16 18 Blow Count (blows/.25m) D e p t h ( m ) 0 1000 2000 3000 4000 2 4 5 7 9 11 13 14 16 18 Ult. Capacity (kN) 0 10 20 30 40 2 4 5 7 9 11 13 14 16 18 Tension (MPa) 0 10 20 30 40 2 4 5 7 9 11 13 14 16 18 Comp. Stress (MPa) 0.0 0.5 1.0 1.5 2.0 2 4 5 7 9 11 13 14 16 18 Stroke (m) 0.0 10.0 20.0 30.0 40.0 2 4 5 7 9 11 13 14 16 18 ENTHRU (kJ) Example 5 Solution – First Pile
  • 19. GRL Engineers, Inc. 2005 Jan 17 FHWA - GRLWEAP EXAMPLE #5 - Later Piles Gain/Loss 1 at Shaft and Toe 1.330 / 1.330 GRLWEAP(TM) Version 2005 D e p t h ( m ) 0 50 100 150 200 2 4 5 7 9 11 13 14 16 18 Blow Count (blows/.25m) D e p t h ( m ) 0 1000 2000 3000 4000 2 4 5 7 9 11 13 14 16 18 Ult. Capacity (kN) 0 10 20 30 40 2 4 5 7 9 11 13 14 16 18 Tension (MPa) 0 10 20 30 40 2 4 5 7 9 11 13 14 16 18 Comp. Stress (MPa) 0.0 0.5 1.0 1.5 2.0 2 4 5 7 9 11 13 14 16 18 Stroke (m) 0.0 10.0 20.0 30.0 40.0 2 4 5 7 9 11 13 14 16 18 ENTHRU (kJ) Example 5 Solution – Subsequent Piles
  • 20. GRL Engineers, Inc. 2005 Jan 17 FHWA - GRLWEAP EXAMPLE #5 - H-Pile Gain/Loss 1 at Shaft and Toe 1.000 / 1.000 GRLWEAP(TM) Version 2005 D e p t h ( m ) 0 100 200 300 400 2 4 5 7 9 11 13 14 16 18 Blow Count (blows/.25m) D e p t h ( m ) 0 4000 8000 12000 16000 2 4 5 7 9 11 13 14 16 18 Ult. Capacity (kN) 0 100 200 300 400 2 4 5 7 9 11 13 14 16 18 Tension (MPa) 0 100 200 300 400 2 4 5 7 9 11 13 14 16 18 Comp. Stress (MPa) 0.0 0.5 1.0 1.5 2.0 2 4 5 7 9 11 13 14 16 18 Stroke (m) 0.0 10.0 20.0 30.0 40.0 2 4 5 7 9 11 13 14 16 18 ENTHRU (kJ) Example 5 Solution – H-pile Alternate
  • 21. 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: Varies 0 10 60 50 40 30 20 Depth (m) (ft) Very Dense Silty Fine Sand GRLWEAP Example 6 Problem
  • 22. 31-Jan-2005 GRL Engineers, Inc. FHWA-GRLWEAP EXAMPLE #6 - Lt Ram, 10mm GRLWEAP (TM) Version 2005 FHWA-GRLWEAP EXAMPLE #6 - Hy Ram, 10mm 31-Jan-2005 GRL Engineers, Inc. FHWA-GRLWEAP EXAMPLE #6 - Lt Ram, 10mm GRLWEAP (TM) Version 2005 FHWA-GRLWEAP EXAMPLE #6 - Hy Ram, 10mm Compressive Stress (MPa) 0 80 160 240 320 400 Tension Stress (MPa) 0 80 160 240 320 400 Blow Count (blows/.25m) Ultimate Capacity (kN) 0 50 100 150 200 250 300 0 500 1000 1500 2000 2500 Blow Count (blows/.25m) Stroke (m) 0 50 100 150 200 250 300 0 2 4 6 8 10 ICE 42-S VULCAN VUL 014 Efficiency 0.800 0.670 Helmet 9.12 7.45 kN Hammer Cushion 6075 1417 kN/mm Skin Quake 2.500 mm 2.500 mm Toe Quake 10.000 mm 10.000 mm Skin Damping 0.150 sec/m 0.150 sec/m Toe Damping 0.500 sec/m 0.500 sec/m Pile Length Pile Penetration Pile Top Area 20.00 16.00 103.41 Pile Model Skin Friction Distribution Res. Shaft = 30 % (Proportional) 20.00 16.00 103.41 m m cm2 Pile Model Skin Friction Distribution Res. Shaft = 30 % (Proportional) GRLWEAP Example 6 Solution - SI
  • 23. 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, Φ = 30° Shaft Resistance, 2%: 28 kN (7 kips) Medium Clay Cu = 36 kPa (0.8 ksi) Dense Sand N’ = 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 60 Toe Resistance, 53%: 779 kN (175 kips) Medium Sand N’ = 10, Φ = 30° Shaft Resistance, 2%: 28 kN (7 kips) Medium Clay Cu = 36 kPa (0.8 ksi) Dense Sand N’ = 35, Φ = 37.5° Shaft Resistance, 8%: 112 kN (26 kips) Shaft Resistance, 37%: 551 kN (122 kips) GRLWEAP Example 8 Problem
  • 24. 31-Jan-2005 GRL Engineers, Inc. FHWA - GRLWEAP EXAMPLE #8 - 6.3 mm Wall GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #8 - 7.1 mm Wall 31-Jan-2005 GRL Engineers, Inc. FHWA - GRLWEAP EXAMPLE #8 - 6.3 mm Wall GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #8 - 7.1 mm Wall Compressive Stress (MPa) 0 75 150 225 300 375 Tension Stress (MPa) 0 75 150 225 300 375 Blow Count (blows/.25m) Ultimate Capacity (kN) 0 50 100 150 200 250 300 0 400 800 1200 1600 2000 Blow Count (blows/.25m) Stroke (m) 0 50 100 150 200 250 300 0 1 2 3 4 5 BERMINGH B2005 BERMINGH B2005 Efficiency 0.800 0.800 Helmet 7.12 7.12 kN Hammer Cushion245185 245185 kN/mm Skin Quake 2.500 mm 2.500 mm Toe Quake 2.500 mm 2.500 mm Skin Damping 0.150 sec/m 0.150 sec/m Toe Damping 0.500 sec/m 0.500 sec/m Pile Length Pile Penetration Pile Top Area 15.00 14.00 62.88 Pile Model Skin Friction Distribution Res. Shaft = 47 % (Proportional) 15.00 14.00 70.69 m m cm2 Pile Model Skin Friction Distribution Res. Shaft = 47 % (Proportional) GRLWEAP Example 8 Solution - SI  6.3 mm  7.1 mm
  • 25. 31-Jan-2005 GRL Engineers, Inc. FHWA - GRLWEAP EXAMPLE #8 - 7.9 mm Wall GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #8 - 9.5 mm Wall 31-Jan-2005 GRL Engineers, Inc. FHWA - GRLWEAP EXAMPLE #8 - 7.9 mm Wall GRLWEAP (TM) Version 2005 FHWA - GRLWEAP EXAMPLE #8 - 9.5 mm Wall Compressive Stress (MPa) 0 50 100 150 200 250 Tension Stress (MPa) 0 50 100 150 200 250 Blow Count (blows/.25m) Ultimate Capacity (kN) 0 50 100 150 200 250 300 0 400 800 1200 1600 2000 Blow Count (blows/.25m) Stroke (m) 0 50 100 150 200 250 300 0 1 2 3 4 5 BERMINGH B2005 BERMINGH B2005 Efficiency 0.800 0.800 Helmet 7.12 7.12 kN Hammer Cushion245185 245185 kN/mm Skin Quake 2.500 mm 2.500 mm Toe Quake 2.500 mm 2.500 mm Skin Damping 0.150 sec/m 0.150 sec/m Toe Damping 0.500 sec/m 0.500 sec/m Pile Length Pile Penetration Pile Top Area 15.00 14.00 78.45 Pile Model Skin Friction Distribution Res. Shaft = 47 % (Proportional) 15.00 14.00 93.86 m m cm2 Pile Model Skin Friction Distribution Res. Shaft = 47 % (Proportional) GRLWEAP Example 8 Solution - SI  7.9 mm  9.5 mm
  • 26. GRLWEAP 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