Slide 1

Wave Travel and Attenuation and Machine Foundations Richard P. Ray, Ph.D., P.E. Civil and Environmental Engineering University of South Carolina

Slide 2

Topics for Today Waves in Elastic Media Waves in the Earth Surface Excitations Machine Foundations

Slide 3

Waves Rayleigh, R Surface (2-D) Shear,S Secondary (1-D) Compression, P Primary (1-D) http://paws.kettering.edu/~drussell/demos.html

Slide 4

Resonant Column - MOC - Wavelets Discrete Properties

Slide 5

Resonant Column - MOC - Wavelets Rock Motion Soil 1: G 1, 1, 1 Soil j: G j, j, j Soil m: G m, m, m............................ Surface Block Mass Horizontal Polarization Vertical Propagation Computational Reaches Nodes z n-1 z 1 z i i,Vii,Vi A B P t=0......1.......2......3

Slide 6

Resonant Column - MOC - Wavelets t C + characteristic: C - characteristic: =shearing stress; V=particle velocity. S =phase (shear wave) velocity; =mass density; t=time; B5B5 C1C1 z3z3 z2z2 z1z1 z4z4 A1A1 A2A2 A3A3 B2B2 B3B3 B4B4 C2C2 C3C3 C4C4 A4A4 C5C5 P1P1 P2P2 P3P3 P4P4 P5P5 C-C- C-C- C-C- C-C- C+C+ C+C+ C+C+ C+C+

Slide 7

Resonant Column - MOC - Wavelets S time P B A B2 A2 CC2C3 B3 A3 C + C - t z R time R space S space Nonlinear Interpolation

Slide 8

Resonant Column - MOC - Wavelets zz 30 31

Slide 9

Resonant Column - MOC - Wavelets

Slide 10

Slide 11

Slide 12

Cumulative Hysteretic Energy Time (sec) Reach Number Strain 400Hyst 400

Slide 13

A1A1 A2A2 A3A3 A4A4 Wavelets

Slide 14

Resonant Column - MOC - Wavelets

Slide 15

Profile View

Slide 16

MEMS Accelerometer

Slide 17

Data Acquisition

Slide 18

Resonant Column - MOC - Wavelets Wavelets

Slide 19

Resonant Column - MOC - Wavelets Wavelets

Slide 20

Resonant Column - MOC - Wavelets By varying the wavelet scale s and translating along the localized time index n, one can construct a picture showing both the amplitude of any features versus the scale and how this amplitude varies with time. Wavelet Scale Localized Time Index Fourier Transform Wavelet via Fourier Transform

Slide 21

Resonant Column - MOC - Wavelets

Slide 22

Wavelets

Slide 23

r -2 r -0.5 r -1 r Shear wave Vertical component Horizontal component Shear window Rayleigh wave Relative amplitude + + + + - - + + Wave TypePercentage of Total Energy Rayleigh67 Shear26 Compression7 Waves Fundamentals-Modeling-Properties-Performance

Slide 24

Free-Field Analytical Solutions urur uzuz Fundamentals-Modeling-Properties-Performance

Slide 25

Free-Field Analytical Solutions urur uzuz Fundamentals-Modeling-Properties-Performance

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Karlstrom and Bostrom 2007 Trench Isolation Fundamentals-Modeling-Properties-Performance

Slide 32

Chehab and Nagger 2003 Fundamentals-Modeling-Properties-Performance

Slide 33

Celibi et al (in press)

Slide 34

ATST Telescope and FE Model Fundamentals-Modeling-Properties-Performance

Slide 35

Summary and Conclusions (Cho, 2005) 1.High fidelity FE models were created 2.Relative mirror motions from zenith to horizon pointing: about 400 m in translation and 60 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 (dynamic) 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. Dynamically stiff enough to hold the optics stable 3. Not significantly vulnerable to wind loadings Fundamentals-Modeling-Properties-Performance

Slide 36

Foundation Movement X Z Y Fundamentals-Modeling-Properties-Performance

Slide 37

Design Questions (1/4) How Does It Fail? Static Settlement Dynamic Motion Too Large (0.02 mm) Settlements Caused By Dynamic Motion Liquefaction What Are Maximum Values of Failure? (Acceleration, Velocity, Displacement) Fundamentals-Modeling-Properties-Design-Performance

Slide 38

Velocity Requirements Massarch (2004) "Mitigation of Traffic-Induced Ground Vibrations" Fundamentals-Modeling-Properties-Performance 0,40

Slide 39

Fundamentals-Modeling-Properties-Performance 300800

Slide 40

Design Questions (2/4) What Are Relations Between Loads And Failure Quantities? Loads -Harmonic, Periodic, Random Load Structure Foundation Soil Neighboring Structures Model: Deterministic or Probabilistic Fundamentals-Modeling-Properties-Performance

Slide 41

Design Questions (3/4) How Do We Measure What Is Necessary? Full Scale Tests Prototype Tests Small Scale Tests (Centrifuge) Laboratory Tests (Specific Parameters) Computer Model Fundamentals-Modeling-Properties-Performance

Slide 42

Slide 43

Design Questions (4/4) 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

Slide 44

r -2 r -0.5 r -1 r Shear wave Vertical component Horizontal component Shear window Rayleigh wave Relative amplitude + + + + - - + + Wave TypePercentage of Total Energy Rayleigh67 Shear26 Compression7 Waves Fundamentals-Modeling-Properties-Performance

Slide 45

r -2 r -0.5 r -1 r Shear wave Vertical component Horizontal component Shear window Rayleigh wave Relative amplitude + + + + - - + + Wave TypePercentage of Total Energy Rayleigh67 Shear26 Compression7 Waves Fundamentals-Modeling-Properties-Performance

Slide 46

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

Slide 47

Lumped Parameter m G k m c r Fundamentals-Modeling-Properties-Performance

Slide 48

Single Degree of Freedom k m c z

Slide 49

c=0Undamped c=2mCritically Damped c