### Wave Equation Applications

```Wave Equation
Applications
2011 PDCA Professor Pile Institute
Patrick Hannigan
GRL Engineers, Inc.
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
– 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
C o ntr ac t N o .:
P ro je c t :
S t ru c t u r e N a m e a n d / o r N o .:
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 un ty :
( P i le s d riv e n b y )
R
a
m
Ham mer
M an ufa c tur er :
M o d el N o .:
H am m er T y pe :
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 :
S t ro k e a t M a x im u m R a te d E n e rg y :
R a n g e in O p e ra t in g E n e rg y :
R a n g e in O p e ra t in g S t ro k e :
R am W ei gh t:
M o d if ic a t io n s :
(f t -l b s )
(f t )
to
to
(f t -l b s )
(f t )
( k ip s )
Anvil
St riker
Plat e
W ei gh t:
T hi c k ne s s :
(k i p s )
M a t e ri a l # 1
Ham mer
Cu sh ion
D i a m e t e r:
N am e:
Ar ea :
T hi c k ne s s /Pl ate :
M a te ri a l # 2
( fo r C o m p o s i t e C u s h i o n )
Name:
(i n 2 )
A re a :
(i n )
T h ic k n e s s /P la t e :
N o . o f P la 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 :
( in 2)
(i n )
N o . of Pl ate s :
Hel met
W ei gh t:
(k i p s )
Pile
Cu sh ion
M a t e ri a l:
Ar ea :
(i n 2 )
T h ic k n e s s /S h e e t :
N o. o f S he ets :
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 :
C ro s s S e c t io n a l A r e a :
( in )
( in 2)
O r d e re d L e n g t h :
D es i gn Lo ad :
U lt im a t e P il e C a p a c it y :
( ft)
( k ip s )
( k ip s )
T ap er :
W e ig h t / F t :
Pile
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 :
T el ep ho ne N o.:
(i n )
(in )
D ate :
F ax N o .:
(i n )
Example Problems
FHWA Pile Manual – Chapter 16
#1 - General Bearing Graph
#2 – Constant Capacity / Variable Stroke
#3 – Tension and Compression Stress Control
#4 – Use of Soil Setup
#5 – Drivability Studies
#6 – Driving System Characteristics
#7 – Assessment of Pile Damage
#8 – Selection of Wall Thickness
#9 – Evaluation of Vibratory Driving
GRLWEAP Program – 23 Examples
GRLWEAP Standard Examples
•Example 1: Generation of a Bearing Graph for an Open End Diesel Hammer
•Example 2: Closed End Hammer, Non Uniform Pile, Equipment Check
•Example 3: Concrete Pile, ECH, Tension Stress Check
•Example 4: Diesel Hammer Input
•Example 5: Pile Segment and Damping Input
•Example 6: Comparison of Damping Parameters
•Example 7: Reduced Diesel Fuel and Quake Variation
•Example 8: Effects of Splice/Slack on Pile Stress
•Example 9: Residual Stress Analysis (RSA)
•Example 10: Pile Damping, Long Piles, Diesel Hammer Performance
•Example 11: Drivability Analysis (Blow Count vs. Depth)
•Example 12: Inspector's Chart or Constant Capacity Option
•Example 13: Composite Pile, Second Toe and Critical Stresses
•Example 14: Two Pile Analysis Considering Follower with Long Skirt
•Example 15: Mandrel Driven Pile
•Example 16: Drilled Shaft Test with No Helmet
•Example 17: Vibratory Hammer Analysis
•Example 18: Pile and Hammer Gravity Changes
•Example 19: Static Soil Analysis
•Example 20: Steel Follower on Concrete Pile
•Example 21: Using ST and Variable Pile Cushion Stiffness
•Example 22: Drivability Analysis for a large, non-uniform pipe pile – Offshore Wave 2010
•Example 23: CPT Based Static Analysis Input Example
GRLWEAP Example 1 & 2 Problem
H a m m e r:
D e lm a g D 1 2 -4 2 ; 4 6 kJ (3 4 ft-kip s)
D e p th
(m )
(ft)
0
0
4
10
20
H a m m e r C u sh io n :
5 0 m m (2 in ch ) A lu m in u m + C o n b e st
H e lm e t: 7 .6 k N (1 .7 kip s)
M e d iu m
Sand
N ’ = 20
P ile : C lo se d E n d P ip e
O D 3 5 6 m m (1 4 in ch )
W a ll 8 m m (0 .3 1 4 in ch)
8
30
12
16
40
S h a ft R e sista n ce , 8 4 % :
T ria n g u la r D istrib u tio n
1 2 4 0 k N (2 8 0 kip s)
50
60
20
T o e R e sista n ce , 1 6 % :
2 4 0 k N (5 4 kip s)
GRLWEAP Example 1 Solution
50
T e n s i o n S tr e s s ( k s i )
50
40
30
20
40
30
Helmet Weight
Hamm er Cushion
COR of H.C.
10
10
0
0
500
400
1.70 kips
60155 kips/in
0.800
0.100
0.234
0.050
0.150
Pile Length
Pile Penetration
Pile Top Area
66.00 ft
62.00 ft
13.41 in2
Pile Model
in
in
sec/ft
sec/ft
Skin Friction
Distribution
8
300
6
200
4
100
2
0
0
2.82 kips
0.800
1640 (100%)) psi
Skin Quake
Toe Quake
Skin Damping
Toe Damping
10
8.4 ft
2
GRLWEAP Ve
DELMAG D 12-42
Ram Weight
Efficiency
Pressure
20
S tr o k e ( ft)
330 kips
U l ti m a te C a p a c i ty ( k i p s )
27.9 ksi
C o m p r e s s i v e S tr e s s ( k s i )
GRL Engineers, Inc.
FHWA #1: Delmag D12-42, 14" x 0.312" CEP
50
85 blows / ft
100
150
Blow Count (bl/ft)
200
250
0
300
Res. Shaft = 84 %
(Proportional)
GRLWEAP Example 2 Solution
T e n s i o n S tr e s s ( k s i )
C o m p r e s s i v e S tr e s s ( k s i )
GRL Engineers, Inc.
FHWA #2: Delmag D12-42, 14" x 0.312" CEP
50
40
30
20
50
40
10
0
20
GRLWEAP Ve
DELMAG D 12-42
Capacity
Ram Weight
Efficiency
Pressure
330.0 kips
2.82 kips
0.800
1640 (100%)) psi
30
Helm et Weight
Ham m er Cushion
COR of H.C.
20
10
Skin Quake
Toe Quake
Skin Dam ping
Toe Dam ping
0.100
0.234
0.050
0.150
0
Pile Length
Pile Penetration
Pile Top Area
66.00 ft
62.00 ft
13.41 in2
11.00
Pile Model
1.70 kips
60155 kips/in
0.800
in
in
sec/ft
sec/ft
Skin Friction
Distribution
S tr o k e ( ft)
10.00
9.00
8.4 ft
8.00
7.00
85 blows / ft
6.00
40
60
80
100
Blow Count (bl/ft)
120
140
160
Res. Shaft = 84 %
(Proportional)
GRLWEAP Example 3 Problem
Penetration Depth for
Tension Evaluation
Depth
4
Pile Cushion: 114 mm (4.5 inch) Plywood
0
10
Loose Silty
Fine Sand
N’ = 8
20
30
16
40
20
Medium Dense
Silty Fine Sand
N’ = 14
Shaft Resistance, 33%:
597 kN (134 kips)
Shaft Resistance, 5%:
97 kN (22 kips)
50
60
Pile: Square Prestressed Concrete
Pile Length 12 m (39 ft)
356 mm (14 inch)
Ultimate Capacity: 1807 kN (406 kips)
Shaft Resistance, 10%:
180 kN (40 kips)
8
12
Hammer Cushion:
200 mm (7.9 inch) Monocast MC 901
Helmet: 9.6 kN (2.16 kips)
(m) (ft)
0
Hammer:
JUNTTAN HHK 3
Dense Sand
and Gravel
N’ = 34
Toe Resistance, 52%:
933 kN (210 kips)
Example 3 Solution – Shallow Depth
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #3, 114mm @ 3.5m
FHWA - GRLWEAP EXAMPLE #3, 209mm @ 3.5m
GRLWEAP (TM) Version 2005
20
Tension Stress (MPa)
Compressive Stress (MPa)
20
31-Jan-2005
16
12
8
16
12
8
4
4
0
0
JUNT T AN HHK 3
Stroke
Effi ci ency
Hel m et
Ham m er Cushi on
Pi l e Cushi on
Ski n
T oe
Ski n
T oe
Quake
Quake
Dam ping
Dam pi ng
JUNT T AN HHK 3
1.00
0.800
1.00 m
0.800
9.60
1989
229
2.500
5.994
0.161
0.500
Pi l e Length
12.00
Pi l e Penetration
3.50
Pi l e T op Area 1267.35
9.60 kN
1989 kN/mm
125 kN/mm
mm
mm
sec/m
sec/m
2.500
5.994
0.161
0.500
mm
mm
sec/m
sec/m
12.00 m
3.50 m
1267.35 cm 2
Ultimate Capacity (kN)
2500
Ski n Fri cti on
Ski n Fri cti on
Pi l e M odel Di stri buti on Pi l e M odel Di stri buti on
2000
1500
1000
500
0
0
40
80
120
160
200
Bl ow Count (bl ows/.25m )
240
Res. Shaft = 48 %
(Proportional )
Res. Shaft = 48 %
(Proportional )
Example 3 Solution – Final Depth
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #3, 209mm @ 11.5m
20
Tension Stress (MPa)
Compressive Stress (MPa)
20
16
12
8
31-Jan-2005
GRLWEAP (TM) Version 2005
JUNT T AN HHK 3
16
Stroke
Effi ci ency
12
Hel m et
Ham m er Cushi on
Pi l e Cushi on
8
4
4
0
0
Ski n
T oe
Ski n
T oe
Quake
Quake
Dam ping
Dam pi ng
Pi l e Length
Pi l e Penetration
Pi l e T op Area
1.00 m
0.800
9.60 kN
1989 kN/mm
376 kN/mm
2.500
6.000
0.160
0.500
mm
mm
sec/m
sec/m
12.00 m
11.50 m
1267.35 cm 2
2500
Ultimate Capacity (kN)
Pi l e M odel
Ski n Fri cti on
Di stri buti on
2000
1500
1000
500
0
0
25
50
75
100
125
Bl ow Count (bl ows/.25m )
150
Res. Shaft = 48 %
(Proportional )
GRLWEAP Example 4 Problem
Hammer: Vulcan 08: 35.3 kJ (26 ft-kips)
Hammer Cushion: 216 mm (8.5 inch) Hamortex
Helmet: 11.6 kN (2.6 kips)
Depth
(m)
0
Pile Cushion: 152 mm (6 inch) Plywood
(ft)
0
10
4
Stiff Clay
20
8
30
12
16
40
50
60
20
cu = 70 kPa
(1.5 ksf)
Setup Factor
= 1.33
Pile: Square Precast Concrete
Pile Length 16 m (52.5 ft)
Pile Penetration 15 m (49.2 ft)
305 mm (12 inch)
Ultimate Capacity 1340 kN (300 kips)
Shaft Resistance, 92%
Uniform Distribution
1233 kN (276 kips)
Toe Resistance, 8%
107 kN (24 kips)
Example 4 Solution
T e n s i o n S tr e s s ( k s i )
C o m p r e s s i v e S tr e s s ( k s i )
GRL Engineers, Inc.
FHWA - GRLWEAP EXAMPLE #4
5
4
3
2
5
3.25 ft
8.00 kips
0.670
Helm et Weight
Ham m er Cushion
Pile Cushion
COR of P.C.
2.60 kips
2176 kips/in
1800 kips/in
0.500
1
Skin Quake
Toe Quake
Skin Dam ping
Toe Dam ping
0.100
0.100
0.200
0.150
0
Pile Length
Pile Penetration
Pile Top Area
3
2
U l ti m a te C a p a c i ty ( k i p s )
0
VULCAN VUL 08
Stroke
Ram Weight
Efficiency
4
1
21-Ju
GRLWEAP Versio
in
in
sec/ft
sec/ft
52.50 ft
49.20 ft
144.00 in2
Skin Friction
Distribution
500
Pile Model
400
300
200
100
0
0
50
100
150
Blow Count (bl/ft)
200
250
300
Res. Shaft = 92 %
(Proportional)
81 blows / ft without anticipated soil set-up (300 kips)
42 blows / ft with anticipated soil set-up (225 kips)
GRLWEAP Example 6 Problem
Hammer:
ICE 42-S: 56.9 kJ (42 ft-kips)
or
Vulcan 014: 56.9 kJ (42 ft-kips)
Depth
(m)
0
Hammer Cushion: Varies
(ft)
Helmet: Varies
0
10
4
20
8
Loose
Silty Fine
Sand
30
12
16
20
Shaft Resistance, 30%
Triangular Distribution
540 kN (121 kips)
40
50
60
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)
Very Dense
Silty Fine Sand
Toe Resistance, 70%
1260 kN (284 kips)
GRLWEAP Example 6 Solution
U l ti m a te C a p a c i ty ( k i p s )
20-Jun-2011
GRLWEAP Version 2010
T e n s i o n S tr e s s ( k s i )
C o m p r e s s i v e S tr e s s ( k s i )
GRL Engineers, Inc.
GRLWEAP EXAMPLE #6 - ICE 42-S, 14"x.375"
GRLWEAP EXAMPLE #6 - VUL 014, 14"x.375"
50
40
30
20
50
Ram Weight
Efficiency
Pressure
30
Helm et Weight
Ham m er Cushion
COR of H.C.
10
10
0
0
14.00 kips
0.670
Variable psi
2.05
34825
0.920
Pile Length
Pile Penetration
Pile Top Area
66.00
52.50
16.05
Skin Friction
Distribution
1.67 kips
8112 kips/in
0.920
in
in
sec/ft
sec/ft
0.100
0.400
0.050
0.150
Pile Model
Skin Friction
Distribution
S tr o k e ( ft)
8.00
6.00
99 bl / ft
228 bl / ft
100
4.00
50
100
150
Blow Count (bl/ft)
200
250
2.00
300
Res. Shaft = 30 %
(Proportional)
in
in
sec/ft
sec/ft
66.00 ft
52.50 ft
16.05 in2
10.00
200
0
0
4.09
0.800
1081 (100%)
0.100
0.400
0.050
0.150
Pile Model
300
VULCAN VUL 014
Skin Quake
Toe Quake
Skin Dam ping
Toe Dam ping
12.00
400
42-S
40
20
500
ICE
Res. Shaft = 30 %
(Proportional)
Questions ? ? ?
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