Development and application of time-lapse ultrasonic tomography for laboratory characterisation of localised deformation in hard soils / soft rocks

Transcription

1 Development and application of time-lapse ultrasonic tomography for laboratory characterisation of localised deformation in hard soils / soft rocks Erika Tudisco Research Group: Stephen A. Hall Philippe Roux Giulia Viggiani

2 Outline Motivation and objectives Techniques X-Ray tomography Digital Image Correlation (DIC) Ultrasonic tomography Experimental work Results Experimental set-up Rock sample with a known geometry Artificially cemented granular material Conclusions - Perspective 2

3 Motivation and objectives LOCALISATION EXISTS AT DIFFERENT SCALES Conventional Measurements Full Field Measurements In the presence of localized strains, [standard data reduction techniques of element tests are] no longer applicable. In fact, the meaning of stress and strain variables derived from boundary measurements of loads and displacements is only nominal, or conventional. Desrues & Viggiani (2004) Full Field Measurements assign a physical quantity to every point of the space 3

4 Motivation and objectives localisation is linked to different processes occurring at the small scale, depending on the material in the case of rocks it is likely that there will be microcracking phenomena strain localisation can be associated with damage localisation DAMAGE 4

5 Motivation and objectives localisation is linked to different processes occurring at the small scale, depending on the material in the case of rocks it is likely that there will be microcracking phenomena strain localisation can be associated with damage localisation D.I.C. Ultrasonic Tomography Full field measurement of both (strain and damage) during the loading can help to better understand the behaviour of the material This work is focused on development of experimental methods and in particular on Ultrasonic Tomography Technique 5

6 Outline Motivation and objectives Techniques X-Ray tomography Digital Image Correlation (DIC) Ultrasonic tomography Experimental work Results Experimental set-up Rock sample with a known geometry Artificially cemented granular material Conclusions - Perspective 6

7 X-Ray tomography Wilhelm Röntgen:

8 X-Ray tomography Wilhelm Röntgen:

9 Digital Image Correlation (DIC) Vector displacement field Continuum hypothesis Full 2D/3D strain tensor field and strain invariant 9

10 Outline Motivation and objectives Techniques X-Ray tomography Digital Image Correlation (DIC) Ultrasonic tomography Experimental work Results Experimental set-up Rock sample with a known geometry Artificially cemented granular material Conclusions - Perspective 10

11 Outline Ultrasonic tomography Motivations Acquisition device Data analysis 11

12 Ultrasonic tomography - Motivations Full field measurement of ultrasonic waves propagation velocities P waves (f > 20 khz) Equation for P-waves: 2 vol 2 t 2 2 vol Damage causes changes in elastic properties so the propagation velocity is v p 2 M V p M, ρ M = oedometric modules ρ = mass density 12

13 Ultrasonic tomography - Acquisition device source array receiver array 32/64 piezoelectric transducers ( barrettes ) dimensions 10/20 mm x 1,5/0,75 mm characteristic frequency 0,5/1 MHz 13

14 Outline Ultrasonic tomography Motivations Acquisition device Data analysis Double beam forming 0-offset velocities Inversion 14

15 Ultrasonic tomography Double Beam Forming (DBF) + θ 1 time time time θ 2 + θ 1 θ 2 time time 15

16 Ultrasonic tomography Double Beam Forming (DBF) 16

17 Ultrasonic tomography Double Beam Forming (DBF) Two fronts 17

18 Ultrasonic tomography 0-offset velocity profile The 0-offset velocity profile is the simplest and fastest method to analyse barrettes s data Only horizontal paths are taken into account x height (m) x velocity (m/s) The velocity is averaged on the width of the specimen 18

19 Ultrasonic tomography - Inversion Pick all travel-times Propagation models used to construct the matrix M Rays Straight Discretise model space Cubic (using DBF) Curved (Eikonal) Sensitivity Kernels Homogeneous medium Δt = M Δv Inhomogeneous medium Δv =M -1 Δt 19

20 Ultrasonic tomography - Inversion Pick all travel-times Δ v M A P = μ Δ v +(M T C - 1 d M + ε C - 1 m ) - 1 M T C T d ( Δ t - M μ Δ v ) Δ v M A P = μ Δ v + C m M T ( MεC m M T + C d ) - 1 ( Δ t - M μ Δ v ) Inversion parameters: Rearrangement of a row of C m Discretise model space λ x λ y ε spatial smoothing in C m damping λ x λ y Δt = M Δv Δv =M -1 Δt 20

21 Ultrasonic tomography - Inversion Pick all travel-times Δ v M A P = μ Δ v +(M T C d - 1 M + ε C m - 1 ) - 1 M T C d T ( Δ t - M μ Δ v ) Δ v M A P = μ Δ v + C m M T ( MεC m M T + C d ) - 1 ( Δ t - M μ Δ v ) Inversion parameters: num 4 = 5.000e-005 mean velocity 1808 m/s Discretise model space λ x λ y ε spatial smoothing in C m damping heigth (m) width (m) 1700 m/s Δt = M Δv Δv =M -1 Δt 21

22 Outline Motivation and objectives Techniques X-Ray tomography Digital Image Correlation (DIC) Ultrasonic tomography Experimental work Results Experimental set-up Rock sample with a known geometry Artificially cemented granular material Conclusions - Perspective 22

23 Experimental set-up Plane strain compression without confinement (3SR Biaxial apparatus for soils) 2D Ultrasonic tomography Acquisitions every 30/45 sec 2D Displacement / strain field mapping (D.I.C.) High resolution pictures (6080 x Mb) One picture every 2 minutes 23

24 Rock sample with a known geometry Sample preparation X-ray vertical slice 24

25 Rock sample with a known geometry 0-offset velocity profile 25

26 Rock sample with a known geometry Ultrasonic tomography 26

27 Rock sample with a known geometry Ultrasonic tomography 27

28 Rock sample with a known geometry Ultrasonic tomography Evolution (data-based) 28

29 Artificially cemented granular material Ultrasonic tomography / D.I.C. comparison Ultrasonic tomography and D.I.C reveal different phenomena Inside the layer: strain with little damage (until step 160) Outside the layer: damage with little strain Velocity reduction due to cement breakage Ultrasonic tomography does not show the fractures Structure inside the layer below the ultrasonic tomography resolution 29

30 Artificially cemented granular material 2D-D.I.C. / 3D-D.I.C. comparison Slice of 3D D.I.C. Volumetric strain Slice of 3D D.I.C. Shear strain Ultrasonic tomography and D.I.C reveals different phenomena Inside the layer strain with little damage (until step 160) Outside the layer damage with little strain Velocity reduction due to cement breakage Ultrasonic tomography does not show the fractures Structure inside the layer below the ultrasonic tomography resolution 30

31 Outline Motivation and objectives Techniques X-Ray tomography Digital Image Correlation (DIC) Ultrasonic tomography Experimental work Results Experimental set-up Rock sample with a known geometry Artificially cemented granular material Conclusions - Perspective 31

32 Artificially cemented granular material 32

33 Artificially cemented granular material 0-offset velocity profile 33

34 Artificially cemented granular material Ultrasonic tomography before loading 34

35 Artificially cemented granular material Ultrasonic tomography / D.I.C. comparison 35

36 Artificially cemented granular material 36

37 CONCLUSIONS It is important to use a combination of full field measuring techniques to capture all different occurring phenomena Full field mapping of strain and damage during the loading can help to better understand the behavior of a material D.I.C provides the strain map for a loading step Ultrasonic tomography allows mapping of elastic wave velocity field Direct link to mechanical properties High sensitivity to damage

38 CONCLUSIONS Double Beam Forming helps to separate different arrivals and thus to investigate the localised region In situ acquisition during a biaxial test allows differential ultrasonic tomography that is more precise and more detailed than model based tomography Experiments on samples with a know geometry confirm the good resolution of the ultrasonic tomography Ultrasonic tomography reveals material s changes at small strain, below the D.I.C. resolution Velocity perturbations seem to be related to cement breakage Ultrasonic tomography seems to be able to capture the process zone preceding the fracture tip and thus to predict the direction of fracture propagation

39 PERSPECTIVES Enhancements of the ultrasonic tomography technique: Use of multiple arrivals (from DBF) Implementation of double difference approach Anisotropic velocity inversion Sensitivity kernels in inhomogeneous media Full wave form inversion Experiments Analysis of tests performed with load cycling Performing tests under confining pressure Use of obtained data to calibrate constitutive laws with evolving elastic properties, e.g., damage laws