ELASTIC WAVES and particulate materials J. Carlos Santamarina - PowerPoint PPT Presentation

In-plane directivity 60 Crosshole tomographic configuration 30 0 0 0 0.05 0.1 0.15 10 20 30 330 40 50 300 60 70 90

Directivity 60 Base-to-borehole tomographic configuration 30 90 70 60 0 0 0.05 0.1 0.15 50 40 30 330 20 10 300 0

Transverse directivity: Side lobe P-wave (specimen size) P-wave P-wave 100 S-wave 80 =0.45 =0.30 Cell radius [mm] 60 =0.15 40 =0.00 R 20 S-Wave H 0 0 20 40 60 80 100 P-Wave Tip-to-tip distance [mm]

Input and output - Convolution Square, f r 4kHz Impulse Sine: f = 40kHz Sine: f = 12kHz Sine: f = 4kHz Sine: f = 1kHz Sine: f = 0.5kHz 0 1 2 3 Time [ms]

Resonant frequency Experimental study Analytical formulation 2 1 . 875 t E f In Air 2 2 L 12 be 1 EI 2 4 2 1 . 875 2 V ( 1 ) L 1 s sl 3 L In Soil f 2 2 btL b L be sl

Operating Frequency - Comparison Analytical Results Experimental Results   100 100 b Frequency [kHz] Frequency [kHz] L Vs=500m/s 10 10 Vs=160m/s In Air Vs=50m/s 1 1 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Cantilever Length [mm] Cantilever Length [mm] Controlling parameter: Short cantilever length Bender element Long cantilever length Soil properties

First arrival? Source Receiver A B C D A: First deflection B: First inflection C: Zero after first inflection D: Second inflection

Multiple Reflection Goals: BE High R-boundaries  No P-wave from side walls  L No uncertainty in length  1 st event 2 nd event Soil No uncertainty in time  BE 1 1 st event Output [Normalized] 2 nd event 0 1 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time [microsec]

Experimental Study - Results Time difference b/w Cross Spectral Density 1 st and 2 nd event 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time [ms] Source Receiver A B C D

Near Field: Signal matching Mathematical Solution Cruse and Rizzo (1968) Stokoe and Sanchez-Salinero (1987) 1.5 1 Dotted line : Measured Procedure: Signal Matching Solid line: Signal Matching 0.5 For given values L and μ S-motion 0 1: Measure the signal S m 0.5 2: Estimate f r and V s 1 3: Compute predicted signal S p = f(V s , f r ) 1.5 0 0.1 0.2 0.3 0.4 0.5 Arrival Time [ms] 4: Change f r and V s until S p ~ S m

Analytical Approach Measured signals Predicted signals 0 0 1 1 ’ increases 2 2 3 3 4 4 5 5 6 6 Meausred Signal Analytical Signal 7 7 8 8 9 9 10 ’ decreases 10 11 11 12 12 13 13 14 14 15 15 16 16 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 Time [microsec] Time [microsec]

P-Transducer

Ultrasound Transducer Electric cable Probe case Insulator Backing block Piezoelectric material Matching layer Damping dependent Heavy Intermediate Light

Ultrasound Transducer Transducer (A3441):  GE Panametrics  Immersion type  To avoid z mismatch with water. High frequency (fr 500kHz)  Goals:   Assess homogeneity Layer detection Position objectives  (e.g., Transducers)

5.00 Directivity 4.00 3.00 2.00 1.00 Fixed axial distance 0.00 -40 -30 -20 -10 0 10 20 30 40 53.3mm 5.00 4.00 Source 3.00 2.00 1.00 0.00 5.00 -40 -30 -20 -10 0 10 20 30 40 4.00 3.00 25.4mm 2.00 1.00 0.00 -40 -30 -20 -10 0 10 20 30 40 25.4mm Receiver Transducer

Directivity Fixed center-to-center distance (=25mm) 90 Source 120 60 150 30 180 0 0 0.5 1 Receiver

Wave Parameters

Velocity and Attenuation A e x 2 A 1 G V S 4 B G M 3 V P

Mechanical Waves attenuation S-waves P-waves

Mindlin contact: Inherently non-elastic (Fretting damage after 10000 cycles - steel) = 20 = 30 N P o P o =0.4N = 60 = 90 0.4 mm (Johnson, 1961)

Photoelasticity and Thermal IR Imaging

Photoelasticity and Thermal IR Imaging

Thermo-mechanical coupling IR image Photoelastic image

Atomic Force Microscopy (AFM) • Surface topography • Surface properties • Forces at nano- scale • Atomic-scale experiments

Environmental chamber (A) and Isolation box Laser beam Photodector Tip radius: 20 nm Stiffness :0.58 N/m

Results of AFM Test • Force curve Pull-out force • Approach 1 Dry, ambient, saturation 25 (6) Retraction (8) 50 (2) (1) (3) (5) 20 30 1 nN C nN 10 A nN 15 B 10 (7) D (9) (4) 30 0 50 100 150 200 nm 10 nm A B C D 1 5 50 Immersed in water 0 60 100 30 Average: 50 Relative humidity (%) nN nN 10 10 500 500 nm 30 0 50 100 150 200 nm nm

Summary D = 0.008 – 0.018 Gravelly Soils D = 0.002 – 0.01 Sand Air-dry D = 0.003 – 0.021 Saturated D = 0.01 – 0.052 Clayey soils D = 0.009 – 0.054 Residual soils Peat (w g 200%) D 0.025

The effect of frequency 3 G max G max 1Hz D min /D min 1Hz 2 D min D min 1Hz 1 G max /G max 1Hz 0 0.01 0.1 1 10 100 Loading Frequency, f, Hz (Stokoe et al.1999)

Mechanical Waves attenuation S-waves P-waves

1: Effective Stress ’=1.4 ’=10.1 ’ increases ’=27.4 ’=62.1 ’=131.5 ’=270.3 ’=409.1 ’=603.9 ’=798.8 ’=1062.5 ’=798.8 ’=603.9 ’ decreases ’=409.1 ’=270.3 ’=131.5 ’=62.1 ’=27.4 ’=10.1 ’=1.4 [sec]

1: Effective Stress V log m s ' ' x y V = S ' 2 P log a kPa Very soft clays exponent 0.30 Sands 0.20 OC clays 0.10 = 0.36 - /700 Cemented soils 0. 100 200 -factor [m/s]