Richard P. Ray, Ph.D., P.E.
Civil and Environmental Engineering
University of South Carolina
USC

Thanks To:
Prof. Richard D. Woods, Notre Dame Univ.
Prof. F.E. Richart, Jr.
USC

 Fundamentals
 Modeling
 Properties
 Performance
USC

Z
Y
θ
φ
X
ψ
Fundamentals -Modeling-Properties-Performance USC







How Does It Fail?
Static Settlement
Dynamic Motion Too Large (0.02 mm is large)
Settlements Caused By Dynamic Motion
Liquefaction
What Are Maximum Values of Failure?
(Acceleration, Velocity, Displacement)
Fundamentals -Modeling-Properties-Design-Performance USC

Fundamentals
Massarch (2004) "Mitigation of Traffic-Induced Ground Vibrations"
-Modeling-Properties-Performance USC

Fundamentals -Modeling-Properties-Performance USC

 What Are Relations Between Loads And
Failure Quantities
 Loading -Machine (Periodic), Impluse, Natural
 Relations Between Load, Structure, Foundation,
Soil, Neighboring Structures
 Generate Model: Deterministic or Probabilistic
Fundamentals -Modeling-Properties-Performance USC

 How Do We Measure What Is Necessary?
 Full Scale Tests
 Prototype Tests
 Small Scale Tests (Centrifuge)
 Laboratory Tests (Specific Parameters)
 Numerical Simulation
Fundamentals -Modeling-Properties-Performance USC

USC

 What Factor of Safety Do We Use?
 Does FOS Have Meaning
 What Happens After There Is Failure
 Loss of Life
 Loss of Property
 Loss of Production
 Purpose of Project, Design Life, Value
Fundamentals -Modeling-Properties-Performance USC

r -2 r -2 r -0.5
+
Rayleigh wave
Vertical component
Horizontal component
+
r -1
+
Shear wave
+
-
Relative amplitude
Shear window r -1
+
Waves
Fundamentals -Modeling-Properties-Performance
+ r
Wave Type Percentage of
Total Energy
Rayleigh
Shear
Compression
67
26
7
USC

 Lumped Parameter (m,c,k) Block System
 Parameters Constant, Layer, Special
 Impedance Functions
 Function of Frequency (ω), Layers
 Boundary Elements (BEM)
 Infinite Boundary, Interactions, Layers
 Finite Element/Hybrid (FEM, FEM-BEM)
 Complex Geometry, Non-linear Soil
FundamentalsModeling -Properties-Performance USC

P

P o sin(
 t ) r m m c
G
ν ρ k m  z   c   kz

P
0 sin(
 t )
FundamentalsModeling -Properties-Performance USC

SDOF
Mag

A dynamic
A static

1



1




 n


2



2



2 D

 n


2
FundamentalsModeling -Properties-Performance USC

Z m z
 z   c z z   k z z

P
0 sin(
 t )
C z
I
ψ ψ
K z m
K x
 n

X k m
C x
K
ψ
D
 c c cr
C
ψ
/2 C
ψ
/2
FundamentalsModeling -Properties-Performance c cr

2 k m
USC

Lumped Parameter Values
Mode Vertical Horizontal Rocking Torsion
Stiffness k
Mass Ratio m
ˆ
Damping
Ratio, D
Fictitious
Mass
4 Gr
1
 m ( 1

 
4
 r
3
)
0 .
425
ˆ 1 / 2
0 .
27 m
8 Gr m
2
( 2




8
 r
3
)
0 .
288
ˆ 1 / 2
0 .
095 m
8 Gr
3
3 ( 1
3 I


( 1

)
 
8
 r
5
)
( 1

0 .
15
ˆ
)
ˆ 1 / 2
0 .
24 I x
16 Gr
3
3

I
 r 5
0 .
50
1

2
0 .
24 I z
D=c/c cr
G=Shear Modulus ν=Poisson's Ratio r=Radius
ρ=Mass Density I
ψ
,I
θ
=Mass Moment of Inertia
USC FundamentalsModeling -Properties-Performance

FundamentalsModeling -Properties-Performance USC

VERTICAL COMPRESSOR
Unbalanced Forces
•Vertical Primanry = 7720 lb
•Vertical Secondary = 1886 lb
•Horzontal Primary = 104 lb
•Horizontal Secondary = 0 lb
Operating Speed = 450 rpm
Wt Machine + Motor = 10 900 lb
DESIGN CRITERION:
Smooth Operation At Speed
Velocity <0.10 in/sec
Displacement < 0.002 in
Jump to Chart
Soil Properties
Shear Wave Velocity V s
= 680 ft/sec
Shear Modulus, G = 11 000 psi
Density, γ = 110 lb/ft 3
Poisson's Ratio, ν = 0.33
USC FundamentalsModeling -Properties-Performance

A zs

Q
0 k z

0 .
002 " r

72 .
8 "

6 .
07 '

( 1
 
) Q
0
4 Gr

0 .
667 ( 7720

1885 )
4

11 000
 r
Try a 15 x 8 x 3 foundation block, Area = 120 ft 2 and r = 6.18 ft
Weight = 54,000 lb Total Weight = 54 000 + 10 900 = 64 900

( 1
 
) W
4 r
3 g
 g

0 .
67
4


110

64 900
6 .
18

3

0 .
42
D

0 .
425

0 .
66 M z

1 .
0
1
2 D
Jump to Figure
A z dynamic

A z static

0 .
002 "
FundamentalsModeling -Properties-Performance USC

34'
18'
Design Example - Table Top
W=550 000 lb
Q
0
=400 lb
I
ψ
=2.88 x 10 6 ft-lb-sec 2
18'
11'
Soil Properties
Shear Wave Velocity V s
= 770 ft/sec
Shear Modulus, G = 14 000 psi
Density, γ = 110 lb/ft 3
Poisson's Ratio, ν = 0.33
ψ
DESIGN CRITERION
0.20 in/sec Horizontal Motion at
Machine Centerline
Ax = 0.0015 in. from combined rocking and sliding
Speed = 160 rpm
Slower speeds, Ax can be larger
USC FundamentalsModeling -Properties-Performance

Horizontal Translation Only
Equivanlen t r

D

0 .
288
ˆ 1 / 2

0 .
465
4 cd


4

18

34


Mag x

1 .
0

13 .
96 ft
A x static

Q
0 k x

Q
0
8

2
 
2
 
8
Gr m
 r
3

0 .
38

3 .
0

10

5 in
Rocking About Point "O"
Equivalent r

4
16 cd
3
3


4
16

17

9
3
3


12 .
0 ft
 
120 rpm

12 .
5 rad / sec k


D


2
8 Gr
 

8

( 14 000

144 )

12 .
04
2

0 .
33

2 .
90

10
8 lb / ft
 n
 k

I


2 .
90

10
8
2 .
88

10
6

10 rad / sec

3 ( 1
 
)
8
I

 r
5

3 ( 0 .
67 )
8
2 .
88

10
6
110
32 .
2
( 12 .
04 )
5

0 .
83

( 1

0 .
15

)


0 .
09

Mag


5 .
6 Static Moment

M o

400

18

7200 ft
 lbs .
FundamentalsModeling -Properties-Performance USC

Static Angular Deflection
  s

M o k


7200

3 ( 0 .
67 )
2 .
9

10
8

0 .
50 rad
10
6
Horizontal
At
Motion
Resonance


A xs
  s
5 .
6 ( 1 .
0

10

4
)
 h


0 .
50
( 18

12 )
10
6
5 .
6

10

4 in .

1 .
0

10

4 in
6
5
4
3
2
1
0
0
Damping = 9%
0.5
1
OmegaRatio
1.5
FundamentalsModeling -Properties-Performance
2 2.5
USC

 Based on Elasto-Dynamic Solutions
 Compute Frequency-Dependent Impedance
Values (Complex-Valued)
 Solved By Boundary Integral Methods
 Require Uniform, Single Layer or Special Soil
Property Distribution
 Solved For Many Foundation Types
USC FundamentalsModeling -Properties-Performance

P

P o e i
 t 
P o
 cos(
 t )
 i sin(
 t )

S z
S z

R z
A z

K
 i

C


K
STATIC
 k (

)

 i


 C

2 K

D
SOIL


Radiation Damping
Jump Wave
FundamentalsModeling -Properties-Performance
Soil Damping
USC

Impedance Functions a
0
  r

G

 r
V s
ψ
Luco and Westmann (1970)
FundamentalsModeling -Properties-Performance USC

FundamentalsModeling -Properties-Performance USC

ψ
FundamentalsModeling -Properties-Performance USC

Boundary Element
Stehmeyer and Rizos, 2006
FundamentalsModeling -Properties-Performance USC

B-Spline Impulse Response Approach
FundamentalsModeling -Properties-Performance USC

   

      e i
 t

    e i
 t
 
 
2
   then
   
Finite/Hybrid
Model
G *

G 1


2

2 
2 i

1
 
2

FundamentalsModeling -Properties-Performance USC

Dynamic p-y Curves
FundamentalsModeling
Tahghighi and Tonagi 2007
-Properties-Performance USC

 Shear Modulus, G and Damping Ratio, D
 Soil Type
 Confining Stress
 Void Ratio
 Strain Level
 Field: Cross-Hole, Down-Hole, Surface
Analysis of Seismic Waves SASW
 Laboratory: Resonant Column, Torsional
Simple Shear, Bender Elements
Fundamentals-ModelingProperties -Performance USC

Oscilloscope
ASTM D 4428
Pump
 t
Shear Wave Velocity:
V s
=
 x/
 t
Test
Depth
Downhole
Hammer
(Source) packer
Note: Verticality of casing must be established by slope inclinometers to correct distances
 x with depth.
Slope
Inclinometer
PVC-cased
Borehole
 x
Velocity
Transducer
(Geophone
Receiver)
PVC-cased
Borehole
Slope
Inclinometer
USC

Resonant Column Test
G, D for Different γ
Fundamentals-ModelingProperties -Performance USC

Schematic Stress-Strain
Fundamentals-ModelingProperties -Performance USC

Hollow Cylinder RC-TOSS
Fundamentals-ModelingProperties -Performance USC

TOSS Test Results
Fundamentals-ModelingProperties -Performance USC

Steam Turbine-Generator
(Moreschi and Farzam, 2003)
Fundamentals-Modeling-PropertiesPerformance USC

Machine Foundation Design Criteria
 Deflection criteria: maintain turbine-generator alignment during machine operating conditions
 Dynamic criteria: ensure that no resonance condition is encountered during machine operating conditions
Jump to Resonance
 Strength criteria: reinforced concrete design
Fundamentals-Modeling-PropertiesPerformance USC

STG Pedestal Structure
Fundamentals-Modeling-PropertiesPerformance USC

Vibration Properties Evaluation
 Identification of the foundation natural frequencies for the dominant modes
 F requency exclusion zones for the natural frequencies of the foundation system and individual structural members (±20%)
 Eigenvalue analysis: natural frequencies, mode shapes, and mass participation factors
USC Fundamentals-Modeling-PropertiesPerformance

Finite Element Model
Structure and Base
Fundamentals-Modeling-PropertiesPerformance USC

Low Frequency Modes
1 st mode
6.5 Hz
95 % m.p.f.
2 nd mode
7.2 Hz
76 % m.p.f
Fundamentals-Modeling-PropertiesPerformance USC

High Frequency Modes
28 th mode
46.3 Hz
0.3% m.p.f
Excitation frequency: 50-60 Hz
42 nd mode
64.6 Hz
0.03% m.p.f
USC Fundamentals-Modeling-PropertiesPerformance

Local Vibration Modes
 Identification of natural frequencies for individual structural members
 Quantification of changes on vibration properties due to foundation modifications
Fundamentals-Modeling-PropertiesPerformance USC

Fundamentals-Modeling-PropertiesPerformance USC

 Optics Lab mass/Instrument weight = 228 tons
 Wind mean force = 75 N, RMS = 89 N
 Ground base excitation PSD = 0.004 g 2 /hz
 Concrete Pier
 High Strength Concrete (E=3.1

10 10 N/m 2 ,

=0.15)
 Soil Stiffness, k

Four different values using Arya & O’Neil’s formula based on the site test data (Shear modulus:30~75ksi, Poisson’s ratio:0.35~0.45)
USC Fundamentals-Modeling-PropertiesPerformance

Frequency vs Soil Stiffness
Stiffness units = SI, frequency mode (hz)
MODE
1
2
3
4
5
6
Stiffness
Kx
Ky
Kz
Krx
Kry
Krz min m in+33.3% m in+66.6% max
1.19E+10 1.83E+10 2.48E+10 3.12E+10
1.19E+10 1.83E+10 2.48E+10 3.12E+10
1.48E+10 2.45E+10 3.41E+10 4.38E+10
1.34E+12 2.21E+12 3.09E+12 3.96E+12
1.34E+12 2.21E+12 3.09E+12 3.96E+12
1.74E+12 2.61E+12 3.49E+12 4.36E+12
6.3
7.0
7.4
7.5
6.4
9.4
7.1
9.7
7.5
9.9
7.7
10
9.4
10.4
11.2
10.3
11.9
13.0
11.1
12.6
13.6
11.8
13.3
13.7
• Soil property range: Shear modulus (30~75ksi), Poisson’s ratio (0.35~0.45)
• Pier Footing: Diameter (23.3m)
• “min” for shear modulus of 30 ksi; “max” for 75 ksi
Fundamentals-Modeling-PropertiesPerformance USC

Summary and Conclusions (Cho, 2005)
1.
High fidelity FE models were created
2.
Relative mirror motions from zenith to horizon pointing: about 400 m m in translation and 60 m rad in rotation.
3.
Natural frequency changes by 2 hz as height changes by 10m.
4.
Wind buffeting effects caused by dynamic portion (fluctuation) of wind
5.
Modal responses sensitive to stiffness of bearings and drive disks
6.
Soil characteristics were the dominant influences in modal behavior of the telescopes .
7.
Fundamental Frequency (for a lowest soil stiffness):
OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz
8.
A seismic analysis was made with a sample PSD
9.
ATST structure assembly is adequately designed:
1.
Capable of supporting the OSS
2.
3.
Dynamically stiff enough to hold the optics stable
Not significantly vulnerable to wind loadings
Fundamentals-Modeling-PropertiesPerformance USC

Free-Field Analytical Solutions u z u r u z
( r ,

, 0 )
  i



2

L
0
V
3


 R
V
( a
0
) H
0
2


 r
C
R

 u r
( r ,

, 0 )
 i



2
M

3
0
V


 R
V
( a
0
) H
1
2


 r
C
R


Fundamentals-Modeling-PropertiesPerformance USC

Fundamentals-Modeling-PropertiesPerformance USC

Fundamentals-Modeling-PropertiesPerformance USC

Fundamentals-Modeling-PropertiesPerformance USC

Fundamentals-Modeling-PropertiesPerformance USC

Fundamentals-Modeling-PropertiesPerformance USC

Trench
Isolation
Karlstrom and Bostrom 2007
Fundamentals-Modeling-PropertiesPerformance USC

Fundamentals-Modeling-Properties-
Chehab and Nagger 2003
Performance USC

Celibi et al (in press)
USC

 Questions?
USC

r -2 r -2 r -0.5
+
Rayleigh wave
Vertical component
Horizontal component
+
Shear window r -1
+
r -1
+
Shear wave
+
-
Relative amplitude
+ r
Wave Type Percentage of
Total Energy
Rayleigh
Shear
Compression
67
26
7
USC

Rayleigh, R
Surface
Shear,S
Secondary
Compression, P
Primary
USC

Machine Performance Chart
0.002
Performance Zones
A=No Faults, New
B=Minor Faults ,
Good Condition
C = Faulty, Correct
In 10 Days To Save
$$
D = Failure Is Near,
Correct In 2 Days
E = Stop Now
450
USC