ppt_damage and fracture in geomaterials

8/10/2019 PPT_Damage and Fracture in Geomaterials

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ALERT Doctoral School 2007 Damage and Fracture in Geomaterials

Damage and Fracture in Geomaterialsan overview of the phenomena and

mechanisms to be dealt with

Cino ViggianiLaboratoire 3S-R (Sols, Solides, Structures - Risques)

University of Grenoble, France

RR


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pipes

"La Trahison des Images" ("The Treachery of Images") by Ren Magritte, 1928

TRUE: the painting is not a pipe, but rather an image of a pipe


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and fractures

Ceci nest pas une fracture


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outline

(a few) important concepts- damage and fracture, a matter of scale- tensile vs. shear fracture

(a few) examples of experimental observations- various materials, various mechanisms, a few tools


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fractures: are they simple?


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John Rudnicki says

Multi-axial constitutive relations Coupling of mechanical response with fluid flow and chemistry

Fracture growth, interaction and network development Earthquake dynamics


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scientific statements and spectacular cracks

Because the applied principal stresses are almost always compressive, the tensile stresses driving opening cracks are necessarily local and, hence, crack growth is, at least initially, stable (Rudnicki 2000)

This is said to be the world's largest free-standing boulder. It's called Giant Rock (California)


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scientific statements and spectacular cracks

Because the applied principal stresses are almost always compressive, the tensile stresses driving opening cracks are necessarily local and, hence, crack growth is, at least initially, stable (Rudnicki 2000)

On 26 March 2000, we received a communication from Doug H., who wrote: () Ended up at Giant Rock about duskand discovered that Giant Rock is now Giant Rocks () Unfortunately nobody was hurt in the "accident

http://www.deuceofclubs.com/rv/cal230b.htm

fracture propagation


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spectacular, large scale discontinuities

example of fracture complexities: Nash Point, South Waleslocal perturbations and superposition of deformation phases

Helen Lewis and Gary Couples, Heriot-Watt University


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back to basics: modes of fracture

Shear Fracture the relative

displacement is parallel to thefracture surface

(the dominant mode of macroscopicbrittle failure in triaxial compressiontests at all but the lowest confiningpressures)

conventional distinction (Griggs & Handlin 1960, Paterson & Wong 2005)

two principal modes of brittle fracture

Extension Fracture separation

normal to the fracture surface(best known from its occurrence in theuniaxial tension and compression test)


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the mode of fracture depends on mean normal stress


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But, all this is at the macro level

Triaxial compressionon Vosges Sandstone(Bsuelle 1999)


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looking at the local (micro) level mode I

Interactions between the fracture path,initiating from the notch tip (top), and

the mineral boundary contact type

Chevron Cracked Notched BrazilianDisc specimen (diameter 20 cm)

Westerly granite


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Nasseri & Mohanty (2007) - Fracture toughness anisotropy in granitic rocks. International Journal of Rock Mechanics & Mining Sciences (in press)

Fracture propagation normal (left) and parallel (right)to normal to pre-existing preferably oriented microcracks in Barre granite


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Fracture propagation normal (left) and parallel (right)to normal to pre-existing preferably oriented microcracks in Stanstead granite


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Fracture propagation in Bigword granite

Left: normal to pre-existing preferably oriented mesocracks

Right: curvilinear morphology of the test cracks following the curvilinear path ofmesocracks and recrystallized quartz-feldspatic minerals

ramping up of the test crack along a steep mesocrack


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looking at the micro level does mode II exist?

" even cracks which seem to be favourably oriented formode II growth might extend in mode I by kinking "

Melin (1986) - When does a crack grow under mode II conditions? Journal of Fracture, 30: 2

" in materials with the properties of crystalline rock, mode II fracture does not exist "" sliding along pre-existing fracture surfaces, in conjunction with eventual type I (new) fractures "

Doz & Rierab (2000) - Towards the numerical simulation of seismic excitation. Nuclear Engng. and Design, 196:3

.


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looking at the micro level does mode II exist?

"en chelon " pattern (a set of offset normal cracks): theoverall direction of the set of cracks, not the individualfissures, marks the trace of the fault

(Hayward Fault in Oakland, California)

Post-mortem X-ray micro tomographic images of shear fractures in Beaucaire Marl (Marello et al. 2003)


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Morgenstern & Tchalenko Gotechnique 1967

Sequence of shear induced displacement discontinuities in kaolinspecimens sheared in 6 cmx 6 cm conventional shear box normal todirection of preferred orientation of original fabric


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Morgenstern & Tchalenko Gotechnique 1967


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weve been talking of fractures what about damage?

Westerley granite

Intergranular vs intragranular (andtransgranular) cracks

Crack density

defining Damage = setting the scalefor modeling (and observations)

KONDO dixit: " the main objective ofstandard Continuum Damage Mechanicsis to propose a continuum-mechanicsbased framework allowing tocharacterize, represent and model at

the macroscopic scale the effects ofdistributed defects and their growth onthe material behavior "


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back to basics: types of geomaterials, types of cracks

Compact rocks "the sources of microcrack initiation are themselves microcracksalready present in the rock. Irreversible deformation involvesthe growth of stress-induced extensile microcracks "

Porous rocks crack initiation also at pores (in weak porous rocks ).Intergranular bonding strength is also important (in strongporous rocks )

it is commonly considerered that (Paterson & Wong 2005)

what about concrete ?similar mechanisms, concrete is also a cohesive-frictional material !(concrete is nothing but a synthetic conglomerate)

for soil ? the standard thought: plasticity, not damage and fracture !saturated fine-grained clays crack as they dry and shrink shear bands / fissures are observed upon shearing+ grain crushing for coarse-grained (and fine-grained?) soils

Crystalline rocks


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grain crushing upon 1D loading Bolton 2003


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grain crushing upon 1D loading


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i hi 1D l di


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d l ?


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and clay ?

Is clay "clastic"?

il l ti it i t d th il l ti it


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soil clasticity instead than soil plasticity

Malcolm Bolton viewpoint

A fundamental reappraisal of the strength and stiffness of soils is under way, relating the properties of the aggregate to

the strength and stiffness of its constituent grains. A statisticaldescription of the successive fracturing of particles shows

promise for the understanding of self-similarity in a widerange of materials from tectonic mlanges to sedimentedclays

"Plastic yielding" on what Schofield and Wroth call the "wet side" of critical states may then be seen asclastic yielding (Chambers: clastic - fragmented, especially applied to a rock composed of fragments of pre-existing rocks) with the voids ratio reducing as the breaking fragments fit more neatly into the voidsbetween the pre-existing grains.

fracture and damage in sandstone (1)


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7 MPa confining pressure 42 MPa confining pressure

El Bied et al. (2002) - Microstructure of shear zones in Fontainebleau sandstone. IJRM, 39:7



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7 MPa confinementgrains cracked,

not crushed

28 MPa confinementintense crushing

and pulverisation



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7 MPa confinementgrains cracked,

not crushed

28 MPa confinementintense crushing

and pulverisation



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g ( )



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g ( )

fracture and damage in concrete


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g

transverse and longitudinal slices through concrete cylinders after loading. Magnetic ResonanceImaging allows us to see the fractures (and to carry out measurements on fracture patterns)

Marfisi & Burgoyne, Cambridge University Engineering Dept.

X-ray micro tomography damage in mortar


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Magnetic resonance imaging of concrete

Landis et al., Engineering Fracture Mechanics 2003; Landis, Geox 2006


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X-ray micro tomography damage in mortar


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fracture and damage: fissured clay vs. mortar


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Plane strain compression of intensely fissured clays (Vitone 2007)

"listening" to fractures (AE) rocks cry when they crack


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development of failure in quasi-brittle materials is associated with microcracks,

which release energy in the form of elastic waves called acoustic emission

Lockner & Byerlee

"listening" at fractures (AE) rocks cry when they crack


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Stanchits & coworkers, GFZ Potsdam

an even more "exotic" tool: infrared radiation (2)


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an even more "exotic" tool: infrared radiation (1)


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Wu et al., IJRM 2006

from my personal experience: fractures in clay shales


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fracture development in Callovo-oxfordian argillite undertriaxial compression studied by X-ray micro tomography

with Nicolas Lenoir, Jacques Desrues, Pierre Bsuelle, Michel Bornert *

* LMS-X Palaiseau, France

Triaxial testTomography

3D Volumetric DIC

motivation : damage in the EDZ around radioactive wasteunderground storage galleries

Callovo oxfordian argillite

1


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Callovo-oxfordian argilliteFrom the Borehole EST261 (depth 476m) of

the Underground Research Laboratory of

Bure (ANDRA)

URL in Bure (France) , depth: 490m

a few characteristics

Clay content : 40 %Water content : 6 %Permeability : 10 -20 to 10 -22 mIn situ vertical stress? effective 10 MPa total 6 MPa

Excavation Damaged Zonediffuse or localised ?effect on permeability ?

recording attenuation profiles through aspecimen slice under different angular

basic principle X-ray micro tomography (CT)


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specimen slice, under different angularpositions, using a CT scanner

reconstructing a radiograph of the slice

repeating to get a complete set of slicesover the specimen

reconstructing a 3D image of the internal

structure of the specimen from the spatialdistribution of the linear attenuationcoefficient

Otani 2000

X-ray white beam to have a high photon flux X-ray energy: 50 to 70 keV spatial resolution: 14 m (voxel size) time for scanning: 40 second for one scan

X-ray characteristics

ESRF, Grenoble (France)

The triaxial compression test is performed in situ on the beam lin

X i h k d i h

xper men a se -up


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X-ray micro tomography scans are taken during the test

x-ray sourceX-ray source

x-ray imagingsystem

fast shutter

mirror

fast shutter

X-ray imagingsystem

Frelon camera

positioning system

loading system

displacement controlled loading ( 1 to 100 m/min) max axial load: 7.5 kN

1 xper men a se -up


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Specimen

Confining cellX-Ray beam

Triaxial cell + XR scan set-up

Imager

max cell pressure:

10 MPatests on

Callovo-Oxfordian

argillite specimens

10 mm in diameter

Results


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Two undrained triaxial tests presented : Low confining pressure (1 MPa) High confining pressure (10 MPa) Stress-strain response + direct CT scan

observations ;

Refined analysis of the deformationprocess in the 2 tests, using 3D

volumetric DIC : Mode II versus mode I crack development

25 horizontal cut

2 Argillite Low confinement test (1 MPa)Mechanical Response


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0 0.01 0.02 0.03

Dformation a xiale

0

5

10

15

20

D e v

i a t e u r

( M P a )

1

2

3

4

5

Specimen after the test

30 Mechanical Response

Argillite High confinement test (10 MPa)Horizontal cut

5


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0 0.02 0.04 0.06 0.08

Dformation axiale

0

10

20

D e v i a t e u r

( M P a )

1

2

3

4

6

7

5

Specimenafter test

10 mm

20 mm

30 Vertical cutMechanical response

Argillite High confinement test (10 MPa)


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0 0.02 0.04 0.06 0.08

Dformation axiale

0

10

20

D e v i a t e u r

( M P a )

1

2

3

4

6

7

5

Specimenafter test

10 mm

20 mm

Preliminary conclusions


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Confining pressure plays a major role oin fracture development :

Low CP : overall fracturation, a lot of openfractures -> permeability increase

High CP : less fractures, open in mode Ionly at de-confinement (CP release)

Can we obtain more information from theCT scan images ?


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impressive, huh ?

Can we obtain more from these images ?


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Micro tomography :

Improved resolution

if density fieldchanges !

What if density does not change ?Mode II or III cracks, shear band with

isochoric deformation (pure shear)

X-ray tomography + 3D DIC

3D - Digital Image Correlation : 8


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Bay et al 1999, Verhulp et al 2004, Bornert et al 2004

(almost) straightforward extension of 2D DIC (Sutton et al. 1989)

basic principle of Image Correlation

two 3D-images of a specimen at two steps of loading


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-

x (x)

D

f(x )

(D)

g( (x))

transformation ?

is determined at x to optimize a correlation function in

order to get g(

(x)) in

(D) the most likely to f(x) in D

D : subset around the material point

f(x) : gray level distribution inside D - characterizes the material point

g( (x) ) : gray level distribution inside (D) in the deformed image

test ESTSYN01 (10 MPa confining pressure)

Deviatoric Incremental Strain field before after peak 1


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0 0.02 0.04 0.06 0.08

Axial strain

0

10

20

30

D e v

i a t o r i c s

t r e s s

( M P a

)

Vertical cut along the axis

Horizontal cut close to the bottom end

Deviatoric Incremental Strain field before peak1


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Incremental strain field Radiographic cutat the peak

Element size280 mIncremental strain field Radiographic cut

at the peak

Vertical cut along the axis

Horizontal cut close to the bottom end

Deviatoric Incremental Strain field after peak


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Incremental strain field Radiographic cutafter the peak

Incremental strain field Radiographic cutafter the peak

from my personal experience: fractures in volcanic rock

Single daisy growing in crack in rock outcropping


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Analysis of fracture in a soft rock using digital image correlation with displacementdiscontinuity quantification

Steve Hall, Cino Viggiani & Pierre BsuelleLaboratoire 3S-R, Grenoble

Acknowledgements: Fiorenza de Sanctis & Gabriela Chacon

R

the material: Tufo di Napoli (Neapolitan Yellow Tuff)

soft rock originating from the lithificationof pyroclastic soils produced during theactivity of the Phlegrean Fields


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L a

b o r a

t o i r e

3 S - R :

E q u

i p e

G D

y g

fine grained but with soft and hardinclusions of various sizes

forms much of the foundation of Napoli

contains many cavities which are prone

to collapse

R

xper menta proce ure: ax a apparatus- unconfined plane-strain compression


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L a

b o r a

t o i r e

3 S - R :

E q u

i p e

G D

D R

specimen description prismatic blocks

100 mm x 50 mm x 35 mm

preexisting slits made using a


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L a

b o r a

t o i r e

3 S - R :

E q u

i p e

G D

45

50 mm

1 0 0 m m

35 mm

12 m m

8 / 12mm

preexisting slits made using a

diamond wire sawlength = 12 mmaperture = 0.4 mmInclination = 45

rock bridge angle, : 45 -120

(displacement rate =3 m/min)

45

45 45

60

45

75

45

90

Non-overlapping slits

Overlapping slits45

105

45

120

D R


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L a

b o r a

t o i r e

3 S - R :

E q u

i p e

G D

no slits:axial splitting

single slit =45 =105 =120

Wing Cracks

Secondary Cracks

failure mechanismdepends on


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D R

photographic analysis deformation tracked using

high resolution digital photographs 13.5 mega-pixels


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L a

b o

r a t o i r e

3 S - R :

E q u

i p e

G D

through transparent side-walls of load cellidentification and tracking of fracture development

D R

Photographic analysis


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L a

b o

r a t o i r e

3 S - R :

E q u

i p e

G D

D R

: ur met o oto arp


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L a

b o

r a t o i r e

3 S - R :

E q u

i p e

G

D

Best correlationdisplacement vector(integer - pixel) Sub-pixel refinement

- search peak of functiondescribing local cross-correlation variation

Vectorial conditioning-to edit poor points-sensitive to correlationstrength-prevents folding of fieland other inconsistenci

Vector-displacement fieldwith sub-pixel accuracy Tensor strain field

Continuumhypothesis

2 images of specimenat different load states

D R

: ur met o oto arp


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L a

b o

r a t o i r e

3 S - R :

E q u

i p e

G

Best correlationdisplacement vector(integer - pixel) Sub-pixel refinement

- search peak of functiondescribing local cross-correlation variation

Vectorial conditioning-to edit poor points-sensitive to correlationstrength-prevents folding of fieland other inconsistenci

Vector-displacement fieldwith sub-pixel accuracy

Quantification of displacement

jumps

2 images of specimenat different load states

D R

Discontinuous deformation (fracture): Displacement discontinuity quantification


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L a

b o

r a t o i r e

3 S - R :

E q u

i p e

G

Displacement jumpalong fracture

[u N] & [u T]

DIC

d

dx

dz

dx

dz

dNdT

dTdN

D R

PhotoWarp

Tffds32: =45: DIC strain


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L a

b o

r a t o i r e

3 S - R :

E q u

i p e

GPhotoWarp(DIC-2D)

0

2

4

6

8

10

12

0 1 2 3 4 5

time (hours)

V e r

t i c a

l f o r c e

( k N )

Mshst

D R

ongoing work further development of DIC-discontinuity method and analysisof tests to analyse failure processes


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L a

b o

r a t o i r e

3 S - R :

E q u

i p e

G

PhD T. Backers

(unconfined) plane-strain punch-through shear:

+ Ultrasonic, AE and DIC monitoring

Triaxial PTS test in tufo (collab. 3S-R - GFZ)

the end (of this lecture)



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Thank you for your attention .


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and good luck with the following lectures!

Climbing the Yosemite crack

cvcvcvc


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cvcvcvc


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This book derives from the symposium held in September 1993. The contributions discuss recent advances in fracture mechanics studies of concrete, rock, ceramics and other brittle disorderedmaterials at micro and structural levels. It draws together research and new applications in continuum, damage and fracture mechanics approaches.Introduction. Keynote paper : the scaling laws andrenormalization group in the mechanics and micromechanics of fracture. Fracture in brittle matrix composites. Fracture mechanics of concrete. Fracture mechanics of rock. Fracture mechanics of ceramics. Continuum models. Discrete crack models. Micromechanisms and micromechanical models. Damage, localization and size effect. Application of fracture mechanics.

ppt_damage and fracture in geomaterials

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