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GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com
QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 1 of 27
QUAKE/W – ProShake Comparison1 Introduction
ProShake is a commercially available software product for doing one-dimensional ground response analyses. It was developed and is being maintained under the guidance of Professor Steven L. Kramer at Washington State University at Pullman, Washington, who is also the author of the book, Geotechnical Earthquake Engineering.
ProShake is being marketed by EduPro Civil Systems, Inc, Sammamish, WA, USA. Their website is: http://www.proshake.com
ProShake is a useful tool for checking the performance of QUAKE/W, since it is an independently developed product, and since it is based on a completely different formulation than that used in QUAKE/W. Comparison of results from these two entirely different products is a good way of validating the QUAKE/W formulation and implementation.
This example gives the results of a comparison study for three different earthquake records.
2 Formulations
ProShake is based on a frequency domain formulation. It is basically a mode superposition method. This method uses a Fast Fourier Transform (FFT) to convert the input motion from a time domain into a Fourier series frequency domain. The response at any location in the frequency domain can be obtained by using the input motion together with a transfer function. After computing the response in the frequency domain, the method uses an inverse FFT to transform the solution back to a time domain.
QUAKE/W, on the other hand, is based on a finite element formulation with a direct integration scheme in the time domain. “Direct integration” means no transformation of the equations into the frequency domain is required. Stated another way, the motion equations are solved directly using a finite-difference time-stepping procedure.
3 Problem configuration and setup
ProShake comes with an example problem that replicates the example soil profile used in the original SHAKE user’s manual. SHAKE was a computer program developed at the University of California at Berkeley in the 1970’s. A later version was known as SHAKE91. Today, a version with a Windows interface is available as SHAKE2000 (www.shake2000.com). ProShake uses this profile to compare the results from ProShake with SHAKE91. By having been around for so long, this soil profile has become a standard of sorts for this type of verification.
The soil profile in SHAKE and ProShake must be defined as layers with constant properties. The layers allow for some variation in properties with depth.
The SHAKE profile consists of an upper 30-foot (9 m) layer of sand. Below the sand from a depth of 30 ft down to 70 feet (21 m) is a clay layer, and under the clay is sand down to 150 feet below the ground surface. The bedrock is at the 150-foot (45 m) level. For analysis, this profile is divided into 17 layers. The upper 10 feet (3m) is divided into two 5-foot (1.5m) layers. The remaining layers are all 10 feet (3 m) in thickness. In ProShake, the bedrock is considered as a layer (#17) and is deemed to extend down a great undefined distance.
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 2 of 27
The watertable is 10 feet below the ground surface (the watertable actually does not come into play, since all material properties are specified as constant for each layer; that is, they are not a function of the effective overburden stress).
The ProShake problem definition can be simulated in QUAKE/W with a column of elements, as shown in Figure 1. There are 16 regions with one element per region.
The base of the column is fixed. This has the effect of the earthquake motion being applied at the column base. Another way to look at this is that the bedrock is infinitely stiff and the full earthquake motion is felt at the base of the column.
The sides of the column are fixed in the vertical direction, which ensures that all the motion is in the horizontal direction only, an assumption inherent in the ProShake 1D formulation.
To make a comparison between ProShake and QUAKE/W, it is vitally important to uncheck all outcrop options in ProShake and to apply the earthquake motion at the top of the rock; that is, do not use the outcrop options in ProShake.
12
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Earthquake response of level ground
Dis
tanc
e - f
eet
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
Figure 1 The SHAKE soil profile defined in QUAKE/W
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 3 of 27
4 Material Properties
The material properties used for each of the layers are summarized in the following table:
Layer Number
Material Name
Thickness (m)
Unit Weight (kN/m3)
Gmax (MPa)
Vs (m/sec)
Poisson’s Ratio QUAKE/W
Modulus Curve
Damping Curve
1 Sand 1.52 19.64 185.87 304.8 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
2 Sand 1.52 19.64 150.56 274.32 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
3 Sand 3.05 19.64 150.56 274.32 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
4 Sand 3.05 19.64 167.75 289.56 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
5 Clay 3.05 19.64 185.87 304.8 0.45 Clay (Seed and Sun 1989)
Clay (Idriss 1990)
6 Clay 3.05 19.64 185.87 304.8 0.45 Clay (Seed and Sun 1989)
Clay (Idriss 1990)
7 Clay 3.05 19.64 224.9 335.28 0.45 Clay (Seed and Sun 1989)
Clay (Idriss 1990)
8 Clay 3.05 19.64 224.9 335.28 0.45 Clay (Seed and Sun 1989)
Clay (Idriss 1990)
9 Sand 3.05 20.42 326.69 396.24 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
10 Sand 3.05 20.42 326.69 396.24 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
11 Sand 3.05 20.42 378.88 426.72 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
12 Sand 3.05 20.42 378.88 426.72 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
13 Sand 3.05 20.42 434.94 457.2 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
14 Sand 3.05 20.42 434.94 457.2 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
15 Sand 3.05 20.42 494.86 487.68 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
16 Sand 3.05 20.42 626.31 548.64 0.45 Sand (Seed and Idriss 1970)
Sand (Idriss 1990)
17 Rock infinite 21.99 3333.49 1219.2 0.01
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 4 of 27
The G reduction functions and Damping Ratio functions for the sand and clay are shown in Figure 2 and Figure 3.
Sand (Seed and Idriss 1970)
G / G
max
Cyclic Shear Strain (%)
0.0
0.2
0.4
0.6
0.8
1.0
Sand (Idriss 1990)
Dam
ping
Ratio
Cyclic Shear Strain (%)
0.0
0.1
0.2
0.3
0.4
Figure 2 Property functions for the sand
clay (Seed and Sun 1989)
G / G
max
Cyclic Shear Strain (%)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Clay (Idriss 1990)Da
mpin
g Ra
tio
Cyclic Shear Strain (%)
0.0
0.1
0.2
0.3
0.4
Figure 3 Property functions for the clay
5 Input Motions
The comparisons are done here for three different earthquake time-history records. The prime motivation in selecting these records was to include records with difference frequency contents. The predominant frequencies of the selected motions vary from 1.2 Hz to 12 Hz.
The records are referred to here as:
The Treasure Island Earthquake
The El Centro Earthquake
The Saguenay Earthquake
The Treasure Island and El Centro Earthquakes were in California, USA. The Saguenay Earthquake was in Quebec, Canada.
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 5 of 27
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0time ( sec )
Acc
eler
atio
n ( g
)
Figure 4 The Treasure Island Earthquake
-0.40-0.30-0.20-0.100.000.100.200.300.40
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0time ( sec )
Acc
eler
atio
n ( g
)
Figure 5 The El Centro Earthquake
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0time ( sec )
Acc
eler
atio
n ( g
)
Figure 6 The Saguenay Earthquake
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 6 of 27
6 Comparison graphs
The data from both QUAKE/W and ProShake were taken into EXCEL to create graphs, so that the results from both pieces of software are on the same graph.
All the graphs are self-explanatory as to the variable that is being compared.
There are two types of graphs. One group shows the variation with time at the top of the column. The other group shows the peak values on a depth profile.
7 The Treasure Island Earthquake
The Loma Prieta Earthquake (M 6.9) occurred on October 17, 1989. The epicenter was near the Loma Prieta Peak in the Santa Cruz Mountains in California to the south-east of the San Francisco Bay area. The time-history record used here was obtained from a nearby recording station on the Treasure Island Military Base. The predominant period for this record is about 0.64 seconds.
The following figures (Figure 7 to Figure 19) give the QUAKE/W – ProShake comparisons.
-0.80-0.60-0.40-0.200.000.200.400.60
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Acc
eler
atio
n ( g
)
QuakeProShake
Figure 7 Treasure Island surface ground accelerations
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Velo
city
( ft/
sec
)
QuakeProShake
Figure 8 Treasure Island surface velocities
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 7 of 27
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Dis
plac
emen
t ( ft
)
QuakeProShake
Figure 9 Treasure Island surface displacements
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 2.0 4.0 6.0 8.0 10.0
Period ( sec )
Acc
eler
atio
n ( g
)
QuakeProShake
Figure 10 Treasure Island surface spectral accelerations
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 8 of 27
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.0 2.0 4.0 6.0 8.0 10.0
Period ( sec )
Velo
city
( ft/
sec
)
QuakeProShake
Figure 11 Treasure Island surface spectral velocities
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 2.0 4.0 6.0 8.0 10.0
Period ( sec )
Dis
plac
emen
t ( ft
)
QuakeProShake
Figure 12 Treasure Island surface spectral displacements
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 9 of 27
30
50
70
90
110
130
150
170
190
0.00 0.20 0.40 0.60 0.80Peak Acceleration ( g )
Y ( f
t )
QuakeProShake
Figure 13 Treasure Island peak acceleration profile
30
50
70
90
110
130
150
170
190
0.00 1.00 2.00 3.00Peak Velocity ( ft/sec )
Y ( f
t )
QuakeProShake
Figure 14 Treasure Island peak velocity profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 10 of 27
30
50
70
90
110
130
150
170
190
0.00 0.20 0.40 0.60 0.80Peak Displacement ( ft )
Y ( f
t )
QuakeProShake
Figure 15 Treasure Island peak displacement profile
30
50
70
90
110
130
150
170
190
0 2000 4000 6000 8000 10000 12000
Peak Shear Stress ( psf )
Y ( f
t )
QuakeProShake
Figure 16 Treasure Island peak shear stress profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 11 of 27
30
50
70
90
110
130
150
170
190
0.00 0.10 0.20 0.30 0.40Peak Shear Strain ( % )
Y ( f
t )
QuakeProShake
Figure 17 Treasure Island peak shear strain profile
30
50
70
90
110
130
150
170
190
0 2000 4000 6000 8000Equivalent Shear Modulus G ( ksf )
Y ( f
t )
QuakeProShake
Figure 18 Treasure Island equivalent shear modulus profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 12 of 27
30
50
70
90
110
130
150
170
190
0.0 5.0 10.0 15.0Equivalent Damping Ratio ( % )
Y ( f
t )
QuakeProShake
Figure 19 Treasure Island equivalent damping ratio profile
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8 The El Centro Earthquake
The El Centro time-history record is from the Imperial Valley Earthquake (M 7.1) that occurred in May 1940. The shock caused 40 miles of surface faulting on the Imperial Fault, which is part of the San Andreas system in southern California. The predominant period for this record is about 0.85 seconds.
The following figures (Figure 20 to Figure 32) give the QUAKE/W – ProShake comparisons.
-1.0-0.8-0.6-0.4-0.20.00.20.40.60.8
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
time ( sec )
Acc
eler
atio
n ( g
)
QuakeProShake
Figure 20 El Centro ground surface accelerations
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
time ( sec )
Velo
city
( ft/
sec
)
QuakeProShake
Figure 21 El Centro ground surface velocity
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 14 of 27
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
time ( sec )
Dis
plac
emen
t ( ft
)
QuakeProShake
Figure 22 El Centro ground surface displacements
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period ( sec )
Spec
tral A
ccel
erat
ion
( g )
QuakeProShake
Figure 23 El Centro spectral ground surface accelerations
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 15 of 27
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period ( sec )
Spec
tral V
eloc
ity (
ft/se
c )
QuakeProShake
Figure 24 El Centro spectral ground surface velocity
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 2.0 4.0 6.0 8.0 10.0
Period ( sec )
Spec
tral D
ispl
acem
ent (
ft )
QuakeProShake
Figure 25 El Centro spectral ground surface displacement
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 16 of 27
30
50
70
90
110
130
150
170
190
0.0 0.2 0.4 0.6 0.8 1.0 1.2Peak Acceleration ( g )
Y ( f
t )
QuakeProShake
Figure 26 El Centro peak acceleration profile
30
50
70
90
110
130
150
170
190
0.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Velocity ( ft/sec )
Y ( f
t )
QuakeProShake
Figure 27 El Centro peak velocity profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 17 of 27
30
50
70
90
110
130
150
170
190
0.00 0.20 0.40 0.60 0.80 1.00Peak Displacement ( ft )
Y ( f
t )
QuakeProShake
Figure 28 El Centro peak displacement profile
30
50
70
90
110
130
150
170
190
0 2000 4000 6000 8000 10000Peak Shear Stress ( psf )
Y ( f
t )
QuakeProShake
Figure 29 El Centro peak shear stress profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 18 of 27
30
50
70
90
110
130
150
170
190
0.0 0.1 0.2 0.3 0.4Peak Shear Strain ( % )
Y ( f
t )
QuakeProShake
Figure 30 El Centro peak shear strain profile
30
50
70
90
110
130
150
170
190
0 2000 4000 6000 8000Equivalent Shear Modulus G ( ksf )
Y ( f
t )
QuakeProShake
Figure 31 El Centro peak shear modulus profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 19 of 27
30
50
70
90
110
130
150
170
190
0 5 10 15 20 25Equivalent Damping Ratio ( % )
Y ( f
t )
QuakeProShake
Figure 32 El Centro peak damping ratio profile
9 The Saguenay Earthquake
The Saguenay Earthquake (M 5.9) occurred in Quebec, Canada on November 25, 1988. This record is of interest because of its high frequency content. The predominant period for this record is about 0.084 seconds.
The following figures (Figure 33 to Figure 48) give the QUAKE/W – ProShake comparisons.
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Acc
eler
atio
n ( g
) ProShake
Figure 33 Saguenay ground surface acceleration
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 20 of 27
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Acc
eler
atio
n ( g
)
Quake
Figure 34 Saguenay ground surface acceleration
-0.20-0.15-0.10-0.050.000.050.100.150.200.25
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Velo
city
( ft/
sec
) ProShake
Figure 35 Saguenay ground surface velocity
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-0.20-0.15-0.10-0.050.000.050.100.150.200.25
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Velo
city
( ft/
sec
) Quake
Figure 36 Saguenay ground surface velocity
-0.05
0.000.05
0.10
0.15
0.200.25
0.30
0.35
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Dis
plac
emen
t ( ft
)
ProShake
Figure 37 Saguenay ground surface displacements
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-0.05
0.00
0.05
0.100.15
0.20
0.25
0.30
0.35
0.0 10.0 20.0 30.0 40.0 50.0time ( sec )
Dis
plac
emen
t ( ft
)
Quake
Figure 38 Saguenay ground surface displacements
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period ( sec )
Spec
tral A
ccel
erat
ion
( g )
QuakeProShake
Figure 39 Saguenay spectral ground surface accelerations
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period ( sec )
Spec
tral V
eloc
ity (
ft/se
c ) Quake
ProShake
Figure 40 Saguenay spectral ground surface velocities
0.00
0.02
0.04
0.06
0.08
0.10
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period ( sec )
Spec
tral D
ispl
acem
ent (
ft ) Quake
ProShake
Figure 41 Saguenay spectral ground surface displacements
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 24 of 27
30
50
70
90
110
130
150
170
190
0.00 0.05 0.10 0.15 0.20 0.25 0.30Peak Acceleration ( g )
Y ( f
t )
QuakeProShake
Figure 42 Saguenay peak acceleration profile
30
50
70
90
110
130
150
170
190
0.00 0.05 0.10 0.15 0.20 0.25Peak Velocity ( ft/sec )
Y ( f
t )
QuakeProShake
Figure 43 Saguenay peak velocity profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 25 of 27
30
50
70
90
110
130
150
170
190
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35Peak Displacement ( ft )
Y ( f
t )
QuakeProShake
Figure 44 Saguenay peak displacement profile
30
50
70
90
110
130
150
170
190
0 200 400 600 800 1000 1200Peak Shear Stress ( psf )
Y ( f
t )
QuakeProShake
Figure 45 Saguenay peak shear stress profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 26 of 27
30
50
70
90
110
130
150
170
190
0.00 0.01 0.01 0.02 0.02Peak Shear Strain ( % )
Y ( f
t )
QuakeProShake
Figure 46 Saguenay peak shear strain profile
30
50
70
90
110
130
150
170
190
0 2500 5000 7500 10000 12500 15000Equivalent Shear Modulus G ( ksf )
Y ( f
t )
QuakeProShake
Figure 47 Saguenay equivalent shear modulus profile
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QUAKE/W Example File: QUAKE - ProShake comparison.docx (pdf) (gsz) Page 27 of 27
30
50
70
90
110
130
150
170
190
0.0 0.5 1.0 1.5 2.0 2.5 3.0Equivalent Damping Ratio ( % )
Y ( f
t )
QuakeProShake
Figure 48 Saguenay equivalent damping ratio profile
10 Concluding remarks
The agreement between the QUAKE/W and ProShake results is remarkably close, especially when considering the vastly different theories and formulations on which the two products are based.
The one exception where there is some noticeable difference is in the shear stress profile. This is understandable. In QUAKE/W, the base is fixed, and so very slight changes in the motion could cause significant changes in the shear stress. In ProShake, the base is not fixed, and so is slightly more flexible, which could cause the shear stress to be different. When considering that the boundary conditions are so entirely different, it is surprising that the shear stress profiles are as close as they actually are.
The close agreement in the comparisons lends credence to the conclusion that both products are formulated and implemented in accordance with the theory.
Where there are differences, it is not possible to say which product is more correct.
In the end, the comparative study here provides strong evidence that the QUAKE/W formulation and implementation is correct.