Patterns in Geomechanics
Edited by Benjy Marks and Itai Einav

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January 2019

Contents

I

Wednesday, January 30
Evolving patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Cino Viggiani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Julio Valdes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3

Knut Jørgen Måløy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Rheological patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4Anthony Thornton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5

Pierre Rognon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6

Ben Nadler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Thermal patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

Ioannis Stefanou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

8Guillermo Narsilio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

9Elena Pasternak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Fracture patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10Jean-Michel Pereira . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

11

Alexander Scheuermann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

12

Daniel Dias-Da-Costa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

II

Thursday, January 31
Patterns across scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13Jose Andrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

14

Stephen Hall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

15

Stefan Luding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Patterns across scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

Edward Ando . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

17

Mohammad Saadatfar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

18

Giang Nguyen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

III

Friday, February 1
Macro scale patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19Alexander M. Puzrin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

20

Takashi Matsushima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

21

Thierry Faug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Fracture patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

Eleni Gerolymatou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

23

Arcady Dyskin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

24

Ha Bui . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Unsaturated patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Francesca Casini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

26

Jayantha Kodikara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

27

Adrian Russell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

IV

Contact details

I

Wednesday, January 30

Evolving patterns . . . . . . . . . . . . . . . . . . . . . .

1

Cino Viggiani . . . . . . . . . . . . . . . . . . . . . . . . 92

Julio Valdes . . . . . . . . . . . . . . . . . . . . . . . . . 11

3

Knut Jørgen Måløy . . . . . . . . . . . . . . . . . . 13
Rheological patterns . . . . . . . . . . . . . . . . . .

4Anthony Thornton . . . . . . . . . . . . . . . . . . . . 15

5

Pierre Rognon . . . . . . . . . . . . . . . . . . . . . . . 17

6

Ben Nadler . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Thermal patterns . . . . . . . . . . . . . . . . . . . . . .

7

Ioannis Stefanou . . . . . . . . . . . . . . . . . . . . . 21

8Guillermo Narsilio . . . . . . . . . . . . . . . . . . . 23

9Elena Pasternak . . . . . . . . . . . . . . . . . . . . . 25
Fracture patterns . . . . . . . . . . . . . . . . . . . . . .

10Jean-Michel Pereira . . . . . . . . . . . . . . . . . 27

11

Alexander Scheuermann . . . . . . . . . . . . 29

12

Daniel Dias-Da-Costa . . . . . . . . . . . . . . . . 31

1. Cino Viggiani
Localized compaction in Tuffeau de Maastricht
Compaction bands have been observed in different kinds of materials (e.g., rocks, soils, metallic
foams, cellular materials). They are usually promoted by a relatively high porosity, as well as byhigh mean stress levels. However, the inelastic mechanisms controlling localized compaction at
the micro-scale can differ from one material to another. For instance, buckling of thin walls has
been observed in metallic foams or honeycomb structures. In the case of geomaterials, due to theirnatural variability, the microstructural origin of compaction localization is still an open question,
often complicated by the coexistence of multiple inelastic processes (e.g., pore collapse, graincrushing, and degradation of cementation bonds). Full-field nondestructive measurements have thepotential to identify these micro-mechanisms and assess their relative role.
In this talk I will present some selected results from a large experimental study of compaction
banding in Tuffeau de Maastricht, a bioclastic sedimentary limestone exhibiting up to 52% ofporosity. Triaxial compression tests were performed at confining pressures ranging from 1 to 5 MPa,on samples cored perpendicular and parallel to the bedding plane. Systematic use of x-ray micro
tomography combined with the use of advanced image analysis and Digital Image Correlation(DIC) provides quantitative 3D information about the strain field inside a sample and its evolution
during a test.

his talk I will present some selected results from a large experimental stu
paction banding in Tuffeau de Maastricht, a bioclastic sedimentary lime
biting up to 52% of porosity. Triaxial compression tests were performe
10
Chapter 1. Cino
Viggianiining pressures
ranging from 1 to 5 MPa, on samples
coredperpendicularllel to the bedding plane. Systematic use of x-ray micro tomography com
the use of advanced image analysis and Digital Image Correlation
ides quantitative 3D information about the strain field inside a sample anution during a test.

Figure 1: Vertical slices through 3D-DIC based incremental strain fields during a triaxial compression test on
Tuffeau debased
Maastricht
at 4 MPa confinement:(upper row)and volumetricrtical slices through3D-DIC
incremental
strain deviatoricfields during
a triaxial
compression tes(bottomrow).
ffeau de Maastricht at 4 MPa confinement: deviatoric (upper row) and volumetric (bottom ro2. Julio Valdes
Searching for breakage-borne sound patterns in loaded granular media
In a mechanically loaded granular pack, the breakage-borne alteration of the internal structure ofgrains and/or bonds produces elastic waves that propagate through the pack and ultimately reachthe stiff boundaries that confine it. Sensors placed on or near these boundaries capture associatedshort-lived vibrations as acoustic emissions with amplitudes, rates, and frequencies that may beunique to the condition or mechanism in question. Laboratory investigations where breakage-borne
acoustic emission analyses are complementary to load-deformation data are described. Examples
include detecting the yield stress in oedometrically compressed sands, tracking debonding inloaded artificially cemented soils, and characterizing acoustic emission signatures that precede
large localized compaction events in monotonically loaded porous packs.

12

Chapter 2. Julio Valdes

3. Knut Jørgen Måløy et al.∗Pattern formation of frictional fingers in a gravitational potential∗ Jon Alm Eriksen, Renaud Toussaint, Olivier Galland, Bjørnar Sandnes, Eirik Grude Flekkøy andKnut Jørgen Måløy
Aligned finger structures, with a characteristic width, emerge during the slow drainage of aliquid-granular mixture in a tilted Hele-Shaw cell. A transition from vertical to horizontal alignmentof the finger structures is observed as the tilting angle and the granular density are varied. An
analytical model is presented, demonstrating that the alignment properties are the result of thecompetition between fluctuating granular stresses and the hydrostatic pressure. The dynamics is
reproduced in simulations. We also show how the system may explain patterns observed in nature,created during the early stages of a dike formation.

[1] Eriksen J.A., Toussaint R., Måløy K.J., Flekkøy. E.G., Galland O., Sandnes B., Pattern formationof frictional fingers in a gravitational potential. Phys. Rev. Fluids 3, 013801, (2018)[2] B. Sandnes, H.A. Knudsen, K.J. Måløy, and E.G. Flekkøy, Labyrinth patterns in confined
granular-fluid systems. Phys. Rev. Lett. 99, 038001, (2007).

me of air breakthroughat the outlet
for α = fingers
0 , 2 , and. Note the incomplete
Pattern formationof frictionalin a4gravitational
potentialdrainage
ell α = 0◦ . The absence of the height stabilization allows the air fingers to invade in ra
Jon Alm Eriksen,mixture
Renaud Toussaint,
Olivier Galland,
Sandnes, growing finions, leaving pockets of grain-liquid
undisturbed
behindBjørnar
the actively
Eirik Grude
Flekkøy,and Knut Jørgen
Måløythe low-φ to high-α range, hydrostaticheightstabilizationof thereceding interface domi
14
Chapter 3. Knut Jørgen Måløy
The NjordCenter, side-by-side
Department of Physics,
Universityparallelof Oslo, P.O.
Box gravitational
1074 Blindern, 0316
Oslo
ynamics andPoreLab,
the fingers
advance
downward,
to thefield
Norwayell [Fig. 5(a), Supplemental Material (SM) video 1 [39]]. Lateral growth is inhibited b
nce of neighboring fingers on both sides; each finger is confined to downward growth. A fi
erminate its movement if it is bypassed and sealed off by its neighboring fingers. A fi
lso split inAligned
two iffinger
a smallregionwith
along
the finger width,
tip gets
stuck,
andtheeachof thisstructures,a characteristic
emergeduringslowside
drainageof arliquid-granular
mixturein a tilted
Hele-Shawcell.
A transition
from verticalto seems
horizontal
es to separate
fingers. Thistypically
happenswhen
a finger
tip widens,
which
to ha
the finger structures
is observed asfinger.
the tilting
angle terminationand the granulardensityarenjunction alignment
with the ofterminationof a neighboring
Fingerandtip splvaried. An analytical model is presented, demonstrating that the alignment properties are theat approximately
equal frequencies [see Fig. 5(a)], maintaining a steady-state evolution
result of the competition between fluctuating granular stresses and the hydrostatic pressure.
iment andThea constantfinger width.
We notepatterns
looksmayremarkably
dynamicsmean
is reproducedin simulations.
Wethatalsotheseshow howthe system
explain si
terns generated
simulatingof athedewettingsuspensions[40], although thepatternswhen
observed
in nature,retraction
created during
early stagesof a dike formation.
mpletely different.
!

Figure 1: Examples of experimental patterns in a deformable porous medium at different tilt angles.
G. 4. Final Fig.
configuration
ofexperimental
experimental
pattern
at different
anglesα at filling
fraction φ =1. Examples ofpatterns
in a deformableporoustilt
mediumat different
tilt angles.
mage frame is 200 mm wide.

References:

013801-5[1]!Eriksen!J.A.,!Toussaint!R.,!Måløy!K.J.,!Flekkøy!E.,!Galland!O.,!Sandnes!B.,!Pattern!formation!of!frictional!fingers!in!a!
gravitational!potential.!Phys.!Rev.!Fluids!3,!013801,!(2018)!
[2]!B.!Sandnes,!H.A.!Knudsen,!K.J.!Måløy,!and!E.G.!Flekkøy,!Labyrinth*patterns*in*confined*granular5fluid*systems.*Phys.!Re
Lett.!99,!038001,!(2007).!
!

4. Anthony Thornton
Multi-scale modelling of bulbous head and stratification pattern formationin granular avalanches
Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches,
landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at
the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows
is larger than the mean velocity, the larger material is transported to the flow front. This causes
size-segregation in the downstream direction, resulting in a flow front composed of large particles.
Since the large particles are often more frictional than the smalls, the mobility of the flow front isreduced, resulting in a so-called bulbous head. After multiple flows a distinct layered pattern within
the flow depositions is formed. Here we focus on a multi-scale approach where we use informationfrom both continuum models and discrete particle simulations to create prediction parameter freemodels of this complex large scale geophysical pattern forming event.
Continuum methods are able to simulate the bulk behaviour of such flows, but have to makeaveraging approximations reducing the degree of freedom of a huge number of particles to ahandful of averaged parameters. Once these averaged parameters have been tuned via experimental
or historical data, these models can be surprisingly accurate; but, a model tuned for one flow
configuration often has no prediction power for another setup.
On the other hand discrete particle methods are a very powerful computational tool that allows
the simulation of individual particles, by solving Newton’s laws of motion for each particle. With
the recent increase in computational power it is now possible to simulate flows containing a few
million particles; however, for 1mm particles this would represent a flow of approximately 1 litre
which is many orders of magnitude smaller than the flows found in industry or nature.
This talk focuses on the formation and evolution of the bulbous head (see Figure 1a), which weshow to emerge in both a depth-averaged continuum framework and discrete particle simulations(see Figure 1b). Furthermore, our numerical solutions of the continuum model converge to a
travelling wave solution, which allows for a very efficient computation of the long-time behaviour ofthe flow. We use small-scale periodic discrete particle simulations to calibrate (close) our continuum
framework, and validate the simple 1D model with full-scale 3D discrete particle simulations. The
comparison shows that there are conditions under which the model works surprisingly well given
the strong approximations made; for example, instantaneous vertical segregation.
Bulbous head formation in bidisperse shallow granular flow over an inclined plane I.F.C. Denissen,
T. Weinhart, A. Te Voortwis, S. Luding, J.M.N.T. Gray and A.R. Thornton Accepted JFM

16Chapter 4. Anthony Thornton

Figure 1: Top: Experimental debris flow deposit at the USGS flow flume, Oregon, USA, August
2008 (Logan & Iverson 2013). The back of the flow has a constant height, while the front shows
evidence of a bulbous head; the flow is higher near the front than at the back of the flow. Picture
courtesy of USGS. Bottom: Snapshots of discrete particle simulation of a bidisperse chute flow
over a rough bottom. The inflow height is 15 particles diameters, resulting in supercritical inflow
and the mixture is 50/50 large and small particles by volume. Red are the large particles, green
are the small particles. The black lines denote the continuum (DGFEM) solution for the height.
Both x and z are scaled by the large particle diameter in both the discrete particle simulations and
DGFEM solutions. Note, that the x-axis is squeezed by a factor 100 compared to the z-axis, so theindividual particles appear as very thin vertical stripes in this plot.

5. Pierre Rognon
Turbulent-like patterns in sheared granular materials
Granular materials do not flow in a neat and tidy way. Rather, grains spontaneously organise
themselves into chaotic clusters, forming kinematic patterns that are reminiscent of vortices inclassical turbulence. We have been able to measure the size and life-time of these clusters, and toevidence how they underpin macroscopic transport properties (viscosity and diffusion) controllingthe flow and mixing of granular matter. This talk will present these findings and highlight theirimportance to continuum-scale granular flow models.

18

Chapter 5. Pierre Rognon

Figure 1: Turbulent like velocity pattern in granular flows: instantaneous velocity of grains being
sheared between two moving plates (located at the top and bottom) measured in the Stadium Shear
Device.

Rheology of dense ellipsoidal grains
2
6. 1BenNadler,Ben Nadler, Francois
GuillardFrancois, Itai Einav2Guillard and Itai Einav

Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada
E-mail:bnadler@uvic.ca
Rheologyof dense ellipsoidal grains
1

Ellipsoidal grains show a complex microscopic behavior associate with their ability to orient and
Schoolof Civil Engineering, The University of Sydney, NSW 2006, Australiaalign with respect to each other and the flow. These additional microscopic degree of freedom
E-mail: francois.guillard@sydney.edu.au, itai.einav@sydney.edu.au
2

is an evolving property that gives rise to a complex anisotropic rheological response. Available
continuum
tiveflow,modelsof densegrains,
granularshapematerials
typically only consider grain size while
Keywords:
denseconstitugranularellipsoidal
anisotropy
ignoring grain shape, orientation and alignment and their effect on the rheological response.
Ellipsoidal
grainsshow a complex
behavior associate
withrheology
their ability
orient and alignThis
presentation
discusses microscopic
a simple generalizationof the inertia[1] totoellipsoidal
with respect
to
each
other
and
the
flow.
These
additional
microscopic
degreeoffreedom
is an evolving
grains. A continuum model that explicitly accounts for the grain shape and the microscopic
propertythat gives
rise to a based
complexanisotropicrheologicalresponse.
Available
constituarrangement
is proposedon physicalobservations
that areused to motivate
thecontinuum
mathematicaltive models
of
dense
granularmaterials
typically
only
consider
grain
size
while
ignoring
grain
construction of the model. The model consists of a constitutive law that relates the grain shape, shape,orientation
and alignment
and theiron therheologicalmicrostructurearrangement
andeffect
the flow
to thedevelopedresponse.
stresses and an evolution law for theThispresentationarrangement.
discusses a simple generalization of the inertia rheology [1] to ellipsoidal grains. A
microstructure
continuum
modelmeaningfulthat explicitly
accounts forgrain shapeand the microscopicarrangement
is proposed
Limitedexperimental
andthemicro-scale
simulation
data on the mechanics
of ellipbasedsoidal
on physicalthatliterature,are used which
to motivate
theconsists
mathematicalconstructionof theshear
model. The
grain isobservations
available in themainlyof measurementsof simple
model(Couette)consists flowof a constitutive
law datathat isrelatesthedetermine
grain shape,
microstructure
and the flow
[2, 3]. Available
used tothe model
parametersarrangement
and to investigate
to the its
developed
stresses
and an evolution
law for the
microstructurearrangement.
performance.
Comparison
with micro-scale
Discrete
Element Method
simulations shows thatthe model
captures thecomplex mechanicalresponsesimulationthat is induced
shape andthe
Limitedmeaningfulexperimental
and micro-scaledata byon thethegrainmechanics
of ellipsoidal
when
subjected
to simple
shear.
grain microstructure
is available inarrangement
the literature,whichmainlyconsistsof measurements of simple shear (Couette)

flow [2, 3]. Available data is used to determine the model parameters and to investigate its performance.
Comparison with micro-scale Discrete Element Method simulations shows that the model captures the[1] mechanical
P. Jop, Y. Forterre
andO.isPouliquen,
constitutive
lawandforthedense
granular flows,
Nature, whencomplexresponsethat
induced byAthe
grain shape
microstructurearrangement441:727730,
2006.
subjected to simple shear.
0.14

-0.85

0.12

-0.9
DEM
MODEL

0.1

-0.95
0.08
-1

0.06
0.04

-1.05
0

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

0.4

0.5

The macro-scale stress response vs. grain shape for frictionless grains subjected to simple shear
Figure 1: The macro-scale stress response vs. grain shape for frictionless grains subjected to simple
shear.
References[1] P. Jop, Y. Forterre and O. Pouliquen, A constitutive law for dense granular flows, Nature, 441:727730, 2006.
[2] B. Nadler, F. Guillard and I. Einav, Kinematic Model of Transient Shape-Induced Anisotropy in
Dense Granular Flow, Phys. Rev. Lett., 120: 198003, 2018

20

Chapter 6. Ben Nadler[2] B. Nadler, F. Guillard and I. Einav, Kinematic Model of Transient Shape-Induced Anisotropy in
Dense Granular Flow, Phys. Rev. Lett., 120: 198003, 2018[3] D. Nagy, P. Claudin, T. Börzsönyi and E. Somfai, Rheology of dense granular flows for elongatedparticles, Phys. Rev. E, 96: 062903, 2017

7. Ioannis Stefanou, Hadrien Rattez and Jean Sulem
Combined role of the size of the microstructure and of Thermo-Hydro-Mechanicalcouplings on stability and fault reactivation
Fault reactivation depends on many factors involving strain and strain-rate dependency. Here wehighlight the importance of the size of the microstructure and of the various multiphyscial couplings
regarding pre- and co-seismic slip. It is shown that even though the microstructure and THMC
couplings concern a finer length and time scale, they affect considerably the macroscopic behavior
and stability of the system.
We propose a micromechanical, physics-based (Cosserat) continuum model by considering thecharacteristic size of the microstructure and the thermal- and pore-pressure-diffusion mechanismsthat take place in the fault gouge during shearing. It is shown that even for rate-independent
materials, the apparent, macroscopic behavior of the system is rate-dependent. This is due to thecompetition of the characteristic lengths and time scales introduced indirectly by the microstructure
and the thermal and hydraulic diffusivities.
Numerical analyses show that both weakening and shear band thickness depend on the applied
velocity, despite the fact that the constitutive description of the material was considered rateindependent. Moreover the size of the microstructure, which here is identified with the grain size ofthe fault gouge (D50), plays an important role and determines the slope of the softening branch of
the shear stress-strain response curve and consequently influences the transition from aseismic toseismic slip.

Dieterich, J. H. (1979). Modeling of rock friction: 1. Experimental results and constitutive equations.
Journal of Geo-physical Research, 84(B5), 2161. http://doi.org/10.1029/JB084iB05p02161
Scholz, C. H. (2002). The mechanics of earthquakes and faulting (Second). Cambridge.
Stefanou, I., & Sulem, J. (2014). Chemically induced compaction bands: Triggering conditions
and band thickness. Jour-nal of Geophysical Research: Solid Earth, 119(2), 880–899. http://doi.org/10.1002/2013JB010342
Sulem, J., & Stefanou, I. (2016). Thermal and chemical effects in shear and compaction bands.
Geomechanics for Energy and the Environment, 6, 4–21. http://doi.org/10.1016/j.gete.
2015.12.004
Rattez, H., Stefanou, I., & Sulem, J. (2018). The importance of Thermo-Hydro-Mechanicalcouplings and microstructure to strain localization in 3D continua with application to seismic faults.
Part I: Theory and linear stability analysis. Jour-nal of the Mechanics and Physics of Solids, 115,
54–76. http://doi.org/10.1016/j.jmps.2018.03.004
Rattez, H., Stefanou, I., Sulem, J., Veveakis, M., & Poulet, T. (2018). The importance of ThermoHydro-Mechanical cou-plings and microstructure to strain localization in 3D continua with application to seismic faults. Part II: Numerical im-plementation and post-bifurcation analysis. Journal of22

Chapter 7. Ioannis Stefanou

Figure 1: Strain localization inside fault gouge (colours represent Cosserat rotations, wc3 [rad]).
the Mechanics and Physics of Solids, 115, 1–29. http://doi.org/10.1016/j.jmps.2018.03.
003
Rattez, H., Stefanou, I., Sulem, J., Veveakis, M., & Poulet, T. (2018). Numerical Analysis of Strain
Localization in Rocks with Thermo-hydro-mechanical Couplings Using Cosserat Continuum. RockMechanics and Rock Engineering. http://doi.org/10.1007/s00603-018-1529-7

8. G. Narsilio, W. Fei and M. Disfani
Heat transfer in granular materials: unveiling patterns
It has been estimated that a mere 1% of the heat energy stored in the upper 5 kilometres ofAustralia’s landmass could supply Australia’s energy needs for the next 2,600 years. As ‘proof ofconcept’, a demonstration geothermal power plant in the Cooper Basin was designed to produce 50
megawatts, enough to power a neighborhood of 3,000+ homes. In addition, shallow geothermalenergy technology use ground heat exchangers together with heat pumps to provide space heating
and cooling to buildings, there are more than 6 million such installations worldwide collectively
harvesting gigawatts of thermal energy (equivalent to several large cities). Both these deep andshallow geothermal technologies have already demonstrated the promise of a truly sustainable,
emission-free and continuous energy source, with potential to provide Australia’s base-load power
requirements.
At the core of all geothermal projects, fluid flow and heat transfer dominate in design andproduction. The microstructure of geomaterials controls these conduction properties. Indeed, soil
and rock masses comprise complex assemblies of particles, varying in size, shape and mineral compositions, degree of inter-grain cementation and phase, all of which strongly influence macroscopic
response.
Understanding and identifying patterns linking heat transfer in porous media and its microstructure including particle shape and connectivity is thus important for a number of engineering
applications, including geothermal’s. The use of X-ray micro-computed tomography (to extract 3Dfeatures of individual particles) together with Discrete Element method (for generating more irregular particle packings), Finite Element method (for simulating heat transfer) and machine learningtechniques (for investigating the relationship between microstructure and thermal conductivity)
compose our toolbox to unveil patterns related to heat transfer in granular media. In this work, theeffect of particle shape on heat transfer was quantified using 3D physical descriptors and othernon-geotechnical features arising from complex network theory, and this toolbox was used aiming
to unveil patterns or relationships between these features.

24

Chapter 8. Guillermo Narsilio

Figure 1: Heat transfer at the particle scale: (a) FEM mesh generated from a microCT scan anangular sand, (b) temperature and (c) total heat flux distributions arising from the heat transfer
simulation. The process is repeated for other granular assemblies of distinct particle shapes tounveil relationships between microstructural features using physically based machine learningtechniques.

9. E. Pasternak and A. V. Dyskin
Strain localisation as a consequence of elastic instability
Strain localisation in geomaterials under compression is often observed, but its mechanism is notalways apparent. In this presentation we consider a strain localisation mechanism based on theemergence of non-unique elastic solutions in unstable elastic materials.
Incompressible elastic materials and materials with negative stiffness are unstable, which
manifests itself in the non-uniqueness of elastic solution and can produce strain localisation. In
geomaterials incremental (and irreversible) incompressibility can emerge due to dilatancy. The
negative stiffness in the form of incremental negative shear modulus or incremental negative
Cosserat shear modulus are created by rotation of non-spherical grains or clusters thereof in thepresence of compression. We demonstrate that in all these cases there exist solutions that do not
involve unloading and hence just incremental incompressibility or negative stiffness are sufficient
to induce strain localisation.
The existence of non-uniqueness of elastic solution is also controlled by the boundary conditions.
We demonstrate that the emergence of incremental incompressibility or negative Cosserat shear
modulus leave enough free parameters to satisfy the boundary conditions at the lateral surfacesof loaded samples – the only boundary conditions controllable in experiments. We argue that theboundary conditions at the sample ends strongly depend upon the conditions at the contact with theloading platens, which can change during loading and in particular as the result of emergence ofstrain localisation. On the other hand, the non-unique solutions in isotropic materials with negative
shear modulus cannot satisfy the boundary conditions on the lateral surfaces of a loaded sample.
Therefore the uniqueness of elastic solution is maintained and hence excludes strain localisation.

10. A. Alavoine, P. Dangla, J.M. Pereira
Modelling bonded granular materials: an upscaling perspective
Geomaterials in general and granular materials in particular are often encountered in natural
conditions, engineering or industry. In many cases, the particles are bonded by either liquid bridges
or solid bonds. This is the case for instance for unsaturated soils, where these bridges are capillarymenisci. Another example concerns the frozen soils or methane hydrate bearing sediments where
the solid skeleton (the assembly of grains) is cemented by the ice or hydrate phase.
The behaviour of such assemblies of bonded grains is peculiar. In an engineering perspective,
having access to a modelling tool able to predict the macroscopic behaviour of such materials is ofclear interest for many applications. However, bearing in mind the microstructural description of
the material together with the underlying physics behind its basic constituents is clearly a challenge
because of the gap between the scales where physics is better known and where the engineer has its
interests.
In this work, we will present different modelling strategies used to upscale the behaviour ofbonded geomaterials, including their non-linear and irreversible behaviour. A particular focus will
be put on the finite element method and the fast Fourier transform used as tools to reach this goal.

28

Chapter 10. Jean-Michel Pereira

Figure 1: Left: Xenon gas hydrate film growth in sand specimen from (Chaouachi, 2016). Right:
predicted yield criterion using FFT during a triaxial test.

11. A. Scheuermann, et al.∗Hydraulic fracturing of bridle materials: Fracture patterns and characteristics∗ A. Scheuermann, F. Hamidi, S. Behraftar, S.G. Torres, D. Pedroso, H.B. Muehlhaus and L. Li

Hydraulic fracturing is a well-established method in enhanced oil and gas recovery or for deep
geothermal systems for improving the permeability of the reservoir rock. It is also used for thepreconditioning of rocks in mining methods such as block caving and long wall mining. Hydraulicfracturing is there applied to pre-weaken the rock for enhancing the disintegration of the rockwithout creating an uncontrolled rock burst or for intersecting seismically active structures. These
examples clearly show that on the one hand, hydraulic fracturing is a frequently used measure forengineering the properties or the state of a rock to support the targeted application. However, on theother hand there are numerous parameters and conditions influencing the fracture propagation andcharacteristics making the prediction of the outcome of hydraulic fracturing applications difficult oreven impossible.
In order to investigate the influence of the prevailing stress conditions of the host rock and theviscosity of the invading fracturing liquid on the hydraulic fracturing process, experimental investigations with an artificial homogeneous brittle material as a rock substitute have been conducted(Fig. 1d & 1e). A newly developed experimental set-up allowed the implementation of plane strain
hydraulic fracturing tests with circular disc samples. The phases of the fracture development forthe conditions of the test could be characterised using observations with a high-speed camera. A
DEM/LBM code was validated based on Cracked Chevron Notched Brazilian Disc (CCNBD) Tests(Fig. 1a, 1b & 1c).Numerical simulations with this code have been conducted to reveal the influenceof the viscosity on the fracture pattern.
The presentation will introduce the used artificial, rock-like material with the experimental
set-up. Results of the experimental investigations and the numerical study will be presented anddiscussed.

30

Chapter 11. Alexander Scheuermann

Figure 1: a) Comparison between experimental and numerical results for the Crack Mouth Opening
Displacement (CMOD) during CCNBD tests. Result of numerical simulations of CCNBD tests
using the DEM/LBM code for an angle of the crack of b) 28◦ and c) 70◦ . Cracked Straight ThroughBrazilian Disc (CSTBD) Tests with samples made of d) Sand/Epoxy mixture and e) Smash-It.

12. Daniel Dias-Da-Costa
Failure patterns, mechanisms and crack widths in concrete structures: assessment of the uncertainty of a discrete crack model
The ability to accurately predict failure patterns, mechanisms and crack widths in concrete is critical
not only to achieve acceptable serviceability performance, but also to prevent the structural failureof new designs. The interaction of cracks and structural elements can become a highly complex
and non-linear problem, in which case many aspects such as concrete cracking and crushing, steel
yielding and hardening, need to be properly accounted for. For example, in reinforced concrete
members strengthened with FRPs, the stress localisation created by the opening of small cracks canbe enough to initiate debonding of the FRP and sudden structural failure, and this interaction cannot
be analysed by standard models (Figure 1). This presentation assesses the performance of a discrete
crack model in its ability not only to predict failure mechanisms, but also the uncertainty associatedwith crack patterns and widths (Figure 2). Experimental results measured during flexural tests areused for assessing the model uncertainty. The discrete crack model is shown to be a reliable tool topredict the structural behaviour, whilst requiring only a minimum set of material parameters easily
available from design standards as initial input.

Figure 1: Interaction of cracks with FRP and debonding.

32

Chapter 12. Daniel Dias-Da-Costa

Figure 2: Crack pattern from: (a) discrete crack model; (b) smeared model; and (c) experiments.

II

Thursday, January 31

Patterns across scales . . . . . . . . . . . . . . . . .

13Jose Andrade . . . . . . . . . . . . . . . . . . . . . . . 35

14

Stephen Hall . . . . . . . . . . . . . . . . . . . . . . . . 37

15

Stefan Luding . . . . . . . . . . . . . . . . . . . . . . . . 39
Patterns across scales . . . . . . . . . . . . . . . . .

16

Edward Ando . . . . . . . . . . . . . . . . . . . . . . . 41

17

Mohammad Saadatfar . . . . . . . . . . . . . . . 43

18

Giang Nguyen . . . . . . . . . . . . . . . . . . . . . . 45

13. Jose Andrade
Celestial Soil Mechanics: What does it take to create patterns on Mars
The mechanics of regolith (celestial soils) is crucial to creation of natural and man-made patterns
everywhere in the solar system.
In this talk, we will discuss the state of our knowledge about celestial soil mechanics and how
this matters to our current and future exploration of the solar system.
Specifically, the necessary advancements to make infrastructure patterns (e.g., landing pads,
habitats) will be explored. New developments in physics-based simulations, artificial intelligence,robotics, and 3D printing will be touched upon as areas where celestial soil mechanics plays acrucial role.

14. Stephen A Hall et al.∗Following stress, strain and fabric evolution in granular media using x-ray
tomography and 3D x-ray diffraction∗ Stephen A. Hall, Ryan C. Hurley, Jonas Engqvist, Chongpu Zhai, Eric B. Herbold, Marta Majkut& Jonathan Wright
In recent years the combination of grain-resolved 3D x-ray diffraction (3DXRD) and x-ray
tomography have been developed to study details of granular mechanics across three scales; sample,
individual grains and an intermediate, “continuum” scale. Grains stresses, and thus force transfer,can be studied in bulk granular systems using 3DXRD that, along with the granular kinematics andcontact structure from tomography, allowing local comparisons of stress and strain and investigationof local evolution of elasto-plastic properties linked to the underlying granular fabric. Results fromrecent experiments involving confined-1D- and triaxial-compression will be presented to illustrate
the method and the new information that can be gained towards better understanding of granularmechanics.

38

Chapter 14. Stephen Hall

Figure 1: Results from the final load step, after macroscopic failure and before unloading, in a
triaxial test monitored with x-ray tomography and 3DXRD showing the continuum strain andgrain rotations distribution determined from the grain kinematics the grain pressures from the3DXRD-derived grain strains and the contact forces from force inference using the grains stresses
and the contact distribution. The lower plots show spherical distributions of the contact forces,
excluding boundaries forces for the weak and strong forces, respectively. The distribution analyses
were conducted by dividing forces into groups based on force directions and the averaged force
magnitude for forces in each direction is indicated by the colour of the end of each bar. The
red arrows indicate x-axis, y-axis and z-axis with lengths and the probability of force distribution
corresponding to 0.02, 0.02, 0.005, respectively.

15. Stefan Luding
From particle simulations to macro-scale theory:
Applications in geo, civil, mechanical and food processes.
The dynamic behaviour of granular materials and powders is of considerable interest in a wide
range of industries like geotechnics, food, civil, or chemical/mechanical engineering. However, thefull understanding or control of the different phenomena and mechanisms of the particle systems,
natural phenomena, or processes is an essential challenge for both science and application due tothe multi-scale nature from particle contacts via particles, force-chains, and collective macroscopic
flow and structures.
The fundamentals can be studied by direct particle simulation methods, where often the fluid
between the particles is important too, in order to gain a microscopic understanding of the processes
and mechanisms. For large-scale applications, a micro-macro transition towards continuum theory
is necessary, however, only smaller applications can be modeled nowadays directly by discrete
micro-scale methods. Instead, more often meso-scale methods are used where the particles are
up-scaled, representing a certain number of primary particles. As one example for such mesomodels, we use experiments and discrete particle simulations (DEM) to investigate the dosingof cohesive fine food-powders. Other applications involve avalanches or chute flows, ring-shear
rheology testing of granular flows as well as the study of the elastic, or elasto-plastic solid-likematerial behavior.
As alternative multi-scale approach, the micro-macro transition from discrete particulate systems to continuum theory involves a mathematical homogenization or coarse-graining that translatesparticle-positions, -velocities and -accelerations into density-, stress-, and strain-fields, by statisticalspatial- and temporal averaging. The macroscopic fields are compatible with the conservation
equations for mass and momentum of continuum theory, and also the fluctuating kinetic energy
provides a measure for the importance of fluctuations in those systems. The ultimate goal is tofind constitutive relations that contain information about the micro-structure and -fluctuations, andto solve those on the macro-level for solving application and optimization problems. Examples
considered are chute-flows down slopes, ring-shear testers as well as rotating drums, where thesame local rheology models all should work, independent of the geometry.

16. E. Ando, J. Desrues and G. ViggianiExperimental observations of emergence of shear bands at different scales
The geomaterial pattern that is studied in this work is the emergence of strain localisation in granular
media under quasistatic triaxial loading.
X-ray tomography has been used with great success, since the end of the 1980s to reveal 3D
structures and processes in geomaterials. At the beginning of this adventure, spatial resolution in
medical x-ray scanners was not sufficient to resolve individual sand grains (0.3mm size in thisstudy), however important findings regarding the local significance of the value of critical state void
ratio were made, e.g., in Desrues et al. 1996.
Synchrotrons and laboratory x-ray scanners now offer high spatial resolutions. However, theusual trade-off between spatial resolution and field-of-view still applies, so to take advantage ofthe gain in spatial resolution, experiments have had to be miniaturised. In this case, specimens ofsand (always 0.3mm size) for triaxial compression have been reduced to cylinders 11mm diameterand about 22mm height, containing tens of thousands of grains. Experiments performed on suchsmall speicmens have allowed the patterns of grain scale kinematics during the emergence of strain
localisation to be measured.
In this work we return to larger specimens (70mm diameter and 140mm height) and always intriaxial compression study the complex patterns and elusive emergence of strain localisation whenmillions of grains are present in a sample.
The ability to test large specimens significantly facilitate the grain size dependence in shear
bands with coarser grains, some preliminary results will be presented.

dy), however important findings regarding the local significance of the value of critical statd ratio were made, e.g., in Desrues et al. 1996.
Synchrotrons and laboratory x-ray scanners now o↵er high spatial resolutions. However, th
al trade-o↵ between spatial resolution and field-of-view still applies, so to take advantage
42
Chapter 16. Edward Andogain in spatial resolution, experiments have had to be miniaturised. In this case, specimens
d (always 0.3mm size) for triaxial compression have been reduced to cylinders 11mm diamete
about 22mm height, containing tens of thousands of grains. Experiments performed on suc
all speicmens have allowed the patterns of grain scale kinematics during the emergence of strai
alisation to be measured.
In this work we return to larger specimens (70mm diameter and 140mm height) and always ixial compression study the complex patterns and elusive emergence of strain localisation whelions of grains are present in a sample.
Preliminary results of deviatoric strain calculated fromincremental kinematics measured on a grid close to the stresspeak for a dense sand under triaxial compression"grain scale"

Initial height = 140mm

Initial height = 22mm

intensity of rotation

Incremental grain rotations in the residual stressstate for a dense sand.
Note this is just a qualitative comparison ofkinematics, and means in no way to imply thatthe large specimen is locally undergoing the samestress path as the small specimen

Lab Specimen scale
Deviatoric Strain
0

5%

Figure showing
1: Illustrationstrain
showinglocalisation
strain localisationpatterns
patterns fromlarge large(complexpattern) and pattern)smallure 1: Illustration
from(complexand smalscale (simple pattern) triaxial compression tests performed with x-ray tomographye (simple pattern) triaxial compression tests performed with x-ray tomography

The ability to test large specimens significantly facilitate the grain size dependence in shea
ds with coarser grains, some preliminary results will be presented.

117. Mohammad Saadatfar
Patterns in sphere packings: a multi-scale view of the compaction process
The arrangements of particles and forces in granular materials have a complex organisation on
multiple spatial and temporal scales that range from local structures to mesoscale and system-wide.
This multiscale organisation can affect how a material responds or reconfigures when subject toexternal perturbations.
At the grain-scale, we identify four grain-scale deformation mechanisms that highlight basic grain-scale rearrangements underpinning sphere packing and granular compaction (Fig.a-d).
Through these grain-scale pattern selection, we recover the connection between topological featuresof sphere packings and their mechanical stability. At the intermediate scale i.e. meso-scale; we finddensely packed tetrahedral patterns of grains (Fig.e-f) that form polytetrahedral clusters (Fig.g-h).
We show that sphere packing compaction is fundamentally connected to the disappearance of
these polytetrahedral clusters . Finally at the global scale of the entire system; we utilise network
analysis tools to show that the structural origin of the jamming transition in jammed sphere packing
emerges as sudden appearance of k-cores at certain coordination numbers which are related not to
the isostatic point, but to the emergence of the 3- and 4-cores as given by k-core percolation theory.

Mohammad Saadatfar
Department of Applied Mathematics, The Australian National University

The arrangements of particles and forces in granular materials have a complex organisation on multiple
spatial and temporal scales that range from local structures to mesoscale and system-wide. This multiscaleorganisation can affect how a material responds or reconfigures when subject to external perturbations.

44

Chapter 17. Mohammad Saadatfar

At the grain-scale, we identify four grain-scale deformation mechanisms that highlight basic grain-scale
rearrangements underpinning sphere packing and granular compaction (Fig.a-d). Through these grain-scalepattern selection, we recover the connection between topological features of sphere packings and theirmechanical stability. At the intermediate scale i.e. meso-scale; we find densely packed tetrahedral patternsof grains (Fig.e-f) that form polytetrahedral clusters (Fig.g-h). We show that sphere packing compaction isfundamentally connected to the disappearance of these polytetrahedral clusters . Finally at the global scaleof the entire system; we utilise network analysis tools to show that the structural origin of the jamming
transition in jammed sphere packing emerges as sudden appearance of k-cores at certain coordination
numbers which are related not to the isostatic point, but to the emergence of the 3- and 4-cores as given byk-core percolation theory.

Figure 1: (a-d) Grain-scale deformations scenarios representing tetrahedral (a-b) and octahedral cavities that drive densification in spherepacking.
of polytetrahedralclusters in jammed
sphere packing.
(h) Visualizationsof the topology
of polytetrahedral
Figure(e-g)
1: Formation(a-d) Grain-scale
deformations
scenarios
representing
tetrahedral(a-b)
and octahedral
aggregates. Polytetrahedral clusters are represented as networks in which each vertex (blue nodes) is a dense tetrahedron and each bondcavitiesthat drive
spherepacking.
(e-g)ofFormation
polytetrahedral(whitetube) represents
two densification
tetrahedra sharing ain
face.
(i-j) Network
representation
sphere packingsof
showing
the formation of aclusters
giant
percolatingclustersphereof grains. packing. (h) Visualizations of the topology of polytetrahedral aggregates.
in jammed

Polytetrahedral clusters are represented as networks in which each vertex (blue nodes) is a dense
tetrahedron and each bond (white tube) represents two tetrahedra sharing a face. (i-j) Network
representation of sphere packings showing the formation of a giant percolating cluster of grains.

18. Giang Nguyen and Ha H Bui
Localisation — Material & Structural — Space & Time
Localisation of deformation destroys the assumption on the homogeneity of materials. The behaviour of the volume element in such cases depends on the size and orientation of the localisation
zone inside it, which is usually at a much lower scale, their corresponding mechanical responses
and interactions, besides the boundary conditions as usual. In short it should be considered as a“structural” problem given the heavy involvement of geometrical properties. The evolutions of thematerial responses inside and outside the localisation zone generally follow their own time scales,
regardless of how the macro (and controlled) loading is. We present our attempts and preliminary
results in tackling this significant difference in space and time evolutions in constitutive modellingand SPH simulations of problems involving localised failure (Figs. 1ab). Some interesting preliminary results in controlling the time evolution of inelastic behaviour inside the localisation zone,
through the Brazilian disc tests on rocks (that usually fail instantly under quasi-static loading,leaving no time for the measurements; Fig. 1c), are also presented.

Localisation – Material & Structural – Space & Time
Giang D. Nguyen1*, Ha H. Bui2

46

Chapter
18.Australia
Giang Nguyen
School of Civil, Environmental and Mining Engineering, Universityof Adelaide,2
Department of Civil Engineering, Monash University, Australia

1*

Corresponding author: g.nguyen@adelaide.edu.au / giang.nguyen@trinity.oxon.org

Abstract
Localisation of deformation destroys the assumption on the homogeneity of materials. The behaviourof the volume element in such cases depends on the size and orientation of the localisation zone insideit, which is usually at a much lower scale, their corresponding mechanical responses and interactions,besides the boundary conditions as usual. In short it should be considered as a “structural” problem
given the heavy involvement of geometrical properties. The evolutions of the material responses
inside and outside the localisation zone generally follow their own time scales, regardless of how themacro (and controlled) loading is. We present our attempts and preliminary results in tackling thissignificant difference in space and time evolutions in constitutive modelling and SPH simulations ofproblems involving localised failure (Figs. 1ab). Some interesting preliminary results in controlling
the time evolution of inelastic behaviour inside the localisation zone, through the Brazilian disc tests
on rocks (that usually fail instantly under quasi-static loading, leaving no time for the measurements;
Fig. 1c), are also presented.
Key words: constitutive modelling, localisation, space and time.

(a)

(c)
(b)

Figure 1: Localised failure: constitutive modelling (a), SPH simulations (b), and space & time
Figure 1: Localised failure:modelling(a), SPHtechniques
simulations
relativeconstitutive
to capabilities
of experimental(c).(b), and space & time
relative to capabilities of experimental techniques (c).

III

Friday, February 1

Macro scale patterns . . . . . . . . . . . . . . . . . .

19Alexander M. Puzrin . . . . . . . . . . . . . . . . . 49

20

Takashi Matsushima . . . . . . . . . . . . . . . . . 51

21

Thierry Faug . . . . . . . . . . . . . . . . . . . . . . . . . 53
Fracture patterns . . . . . . . . . . . . . . . . . . . . . .

22

Eleni Gerolymatou . . . . . . . . . . . . . . . . . . . 55

23

Arcady Dyskin . . . . . . . . . . . . . . . . . . . . . . 57

24

Ha Bui . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Unsaturated patterns . . . . . . . . . . . . . . . . . .

25

Francesca Casini . . . . . . . . . . . . . . . . . . . . 61

26

Jayantha Kodikara . . . . . . . . . . . . . . . . . . 63

27

Adrian Russell . . . . . . . . . . . . . . . . . . . . . . . 65

19. Alexander M. Puzrin and Andreas Stöcklin
Understanding geomorphological patterns in submarine landslides
The paper presents recent advances in analytical and numerical modelling and understanding ofunderlying mechanisms of spreading and ploughing failure, leading to observed geomorphologicalpatterns in gigantic submarine landslides.

50

Chapter 19. Alexander M. Puzrin(a) Seafloor geomorphology(b) Landslide simulations

Figure 1: (a) Seafloor ripples in the Glencoe landslide offshore Western Australia (after Hengesh etal., 2013); (b) Equivalent plastic strain and cross section with localized shear surfaces for spreadingand ploughing patterns of a submarine slope failure.

20. Takashi Matsushima
Patterns of landforms: A numerical study of fluvial geomorphological processes
Geomorphology is a scientific study to understand various landforms on/near a planetary surface.
In particular, this study focuses on the fluvial processes, which is regarded as a primary geomorphological processes on the earth (Figure 1). It includes the erosion, transport, and deposition of
granular geomaterials by surface water flow. Its first principle is the grain-scale dynamics involving
complicated interaction between water flow and soil grains. The resulting collective sediment behavior leads to the topographic evolution from meter scale to kilometer scale during several to morethan hundred years. This study attempts to simulate such complicated fluvial geomorphologicalprocesses using a depth-integrated particle method. Each computational particle represents a unit
water mass that can take in and out the sediment mass as a suspended load from the bed surface.
The bottom shear stress of each numerical particle is evaluated by the modified Manning’s formulaconsidering the threshold slope angle of flow (similar to Bingham fluid). Fluid pressure gradient ismodeled by two-body interaction between numerical particles similar to Discrete Element Method.
The effect of grain size is also incorporated into the model, which enables us to reproduce theresulting geological layers. Some examples of landforms are demonstrated (Figure 2) and its
features are discussed in the presentation.

Figure 1: Left: Gully formation (Kumamoto, Japan). Right: Example of numerical simulation.

21. Thierry Faug
Snow and avalanche patterns: a wide range of grain sizes and time scales
Snow refers to the myriad of ice crystals that form in the atmosphere under varying air saturation,
temperature and moisture conditions, then precipitate and finally undergo changes once they reach
the Earth’s surface (inset of figure 1).
After deposition on the ground, the coherent porous structure formed, which is made of moreor less sintered ice crystals, alters. Because it is close to its melting temperature, seasonal snow on
the ground changes constantly. The alteration is known as metamorphism. In addition, the weightof the overlying snow layers and the wind come into play. The mechanical and thermodynamicalactions that snow experiences give rise to a rich variety of snow patterns, covering a broad range ofscales in space from the millimeter (snow grain) to the large kilometer-scale in mountains.
Several situations may lead to the mechanical failure of the snowpack and then trigger
avalanches. There are various expressions to characterize the rapid motion of snow masses: slab
avalanche, loose avalanche, glide avalanche, dense/flowing avalanche, powder avalanche (aerosol),cold avalanche, warm avalanche, dry avalanche, wet/humid avalanche, granular avalanche, etc.
There’s no end of words to describe the perceptions of avalanches by high mountain guides, by ski
resorts’ managers, by snow scientists, etc., or by any observer who practices recreation activities inthe snowy slopes. Those words refer to various complicated physical processes which take placewhen the avalanche initiates, then propagates along the slope and finally come to standstill. The
prints and deposits left by avalanches (example in figure 1) reflect another rich variety of snow
patterns.
The time scales of seconds to a few minutes for the snow mass motion during an avalanche areat odds with the time scales of hours to weeks involved in the alteration of snowpack, and the rangeof grain sizes largely extends when the avalanche propagates, especially when the water gets into
the game. I will describe some amazing snow patterns by trying to explain their physical origin.

54

Chapter 21. Thierry Faug

Figure 1: Non uniform and rough snow avalanche deposits (source: Irstea). Inset: digital composite
of snowflakes and frost (adapted from jefunne/shutterstock.com).

22. Eleni Gerolymatou
Crack interaction and coalescence: peak and residual strength
It is a well-known fact that the strength of rock mass is mainly dominated by the strength of its
discontinuities. The shear strength of continuous joints has been investigated extensively in thelaboratory, in situ and from a constitutive point of view. The strength of discontinuous rock joints
on the other hand has not been systematically examined. Not a lot of works have been performedin this area. The existing ones are mostly concerned with laboratory tests on artificial or natural
material with cracks under uniaxial, triaxial or shear conditions.
This work presents experimental results of shear tests at different normal pressures, bothconcerning the peak and the residual shear strength. The tests were performed on gypsum specimens
created with intermittent cracks at different inclinations with respect to the shearing direction. The
tests were interrupted just after the peak shear stress was observed to register the coalescencepatterns formed by the cracks. The tests were then continued to relatively large displacements,
exceeding the spacing between neighboring cracks. Both the patterns formed at crack coalescenceand the peak and residual shear strengths were significantly influenced by the original inclinationof the intermittent joints, as shown below.
To capture the peak strength observed several alternatives were tried, such as modificationsof the law of Patton for discontinuous cracks and linear elastic fracture theory. It was found thatthe maximum circumferential strain criterion reproduced with satisfying accuracy both the peakstrength and the wing crack angle. The consideration of fracture interactions was found to further
improve the result, though the difference was not very large.
The residual strength was found to also vary significantly with the inclination of the initial
cracks, in some cases being significantly lower than the residual strength of horizontal continuous
joints. The phenomenon can be linked to rotations of the fragments resulting from the crack
coalescence and is only apparent for a narrow band of initial inclinations. The same phenomenon
has been also observed in shear tests performed by other authors. It is much harder to observe undersymmetrical loading conditions, such as those of uniaxial and triaxial tests.

Gerolymatou.aspx

eywords: intermittent joints, crack coalescence, shear strength56

Chapter 22. Eleni Gerolymatou

ABSTRACTs a well-known fact that the strength of rock mass is mainly dominated by the strength of its discontinuiti
e shear strength of continuous joints has been investigated extensively in the laboratory, in situ and from
nstitutive point of view. The strength of discontinuous rock joints on the other hand has not be
stematically examined. Not a lot of works have been performed in this area. The existing ones are mosncerned with laboratory tests on artificial or natural material with cracks under uniaxial, triaxial or she
nditions.
is work presents experimental results of shear tests at different normal pressures, both concerning the ped the residual shear strength. The tests were performed on gypsum specimens created with intermittent cracdifferent inclinations with respect to the shearing direction. The tests were interrupted just after the peak she
ess was observed to register the coalescence patterns formed by the cracks. The tests were then continued
atively large displacements, exceeding the spacing between neighboring cracks. Both the patterns formed
ack coalescence and the peak and residual shear strengths were significantly influenced by the origin
clination of the intermittent joints, as shown below.

Figure 1 Coalescence patterns for different initial fracture orientations, in order of appearance 45, 75, 90, 135 and 165
FigureCoalescencefor differentconstant,initial fractureorderdisplacedof appearance
45,right.
degrees.
The1:bottom
platepatterns
was maintained
whileorientations,the top onein wasto the75, 90, 135 and 165 degrees. The bottom plate was maintained constant, while the top one wasdisplaced to the right.

capture the peak strength observed several alternatives were tried, such as modifications of the law of Patt
discontinuous cracks and linear elastic fracture theory. It was found that the maximum circumferential straterion reproduced with satisfying accuracy both the peak strength and the wing crack angle. The considerati
fracture interactions was found to further improve the result, though the difference was not very large.
e residual strength was found to also vary significantly with the inclination of the initial cracks, in some cas
ing significantly lower than the residual strength of horizontal continuous joints. The phenomenon can
ked to rotations of the fragments resulting from the crack coalescence and is only apparent for a narrow ba
initial inclinations. The same phenomenon has been also observed in shear tests performed by other authors
much harder to observe under symmetrical loading conditions, such as those of uniaxial and triaxial tests.

23. A. V. Dyskin and E. Pasternak
Patterns of fracture growth under compression
Fracture growth in geomaterials under compression is one of the mechanisms of failure including
such dangerous types of failure as rockbursts. Observations reveal three types of fracturing undercompression: (a) splitting or column fracture observed in uniaxial compression when the sample
is split along the compressive (major principal) axis; (b) spallation observed in samples undercompression and underground excavations near a free surface; (c) “shear” failure whereby the
sample is broken by formation of an oblique fracture inclined to the major principal axis.
The common understanding of the mechanics of fracture growth parallel to the axis of uniaxial
compression causing splitting or spallation is based on the observations made on growth of throughfractures or pores in plates or rectangular samples. In these, essentially 2D configurations, the initialdefect sprouts secondary crack or wings growing extensively parallel to the direction of uniaxial
compression. The real defects are however mostly internal defects. Experiments on transparent
materials show that the initial cracks or pores produce wings that wrap, which arrests their further
growth. We show that the extensive fracture growth can happen in two cases: (1) when there areseveral interacting wing cracks which produce a new extensively growing fracture; (2) when there
exists biaxial stress state (this for instance happens near an excavation wall). It is the action ofwhat can be termed intermediate principal stress that prevents wing wrapping thus enabling theirextensive growth. It is interesting that the magnitude of the intermediate principal stress needed toensure extensive fracture growth is about 6% of the major principal stress.
“Shear” fracture propagation happens in its own plane resembling that of a Mode II (shear)crack, which gave the name “shear”. However all direct experiments on Mode II fractures showthat they cannot propagate in their own plane. Instead they kink producing the wing cracks. In
order to resolve this conundrum we note that the “shear” fracture is observed at the peak load when
the concentration of accumulated damage is sufficient to produce near zero effective stiffness. It isthen natural to assume that the accumulated damage also permits independent rotations of grains orother constituents of the geomaterial. The presence of rotations induces a special mechanism ofMode II fracture propagation based on bending failure of remaining bonds between the rotating
grains. This leads to a band-like planar propagation of the fracture. We formulate a criterion of
fracture growth of this type.

24. Ha H. Bui and Giang Nguyen
Failure mechanism of highly porous cement-based materials
Highly porous cement-based materials compose of solid phases and air pores formed through the
Failure mechanism of highly porous cement-based materials
solid phases. The existence of a large amount of air pores in these materials causes their mechanicalresponses highly dependent on the density and the stress state, and their failure mechanisms to be
1* other solid materials.
complicated and significantly different
fromHa H. Bui
and Giang D. Nguyen2 In particular, the constitutive
responses and failure mechanisms
thisEngineering,material arehighlycontrolled
by the competition of the1
Department ofof
Civil
MonashUniversity,
Australia
2
shear failure andpore
collapse.
In this work,
we present
our primarily
results
on theinvestigations of
Schoolof Civil,
Environmental
and Mining
Engineering,
University of
Adelaide,
Australia*
the failure mechanisms of this material
underauthor:
the true
triaxial stress conditions. The experimentally
Corresponding
ha.bui@monash.edu
validated discrete element method (DEM) is utilised to explicitly describe the internal pore-structure,
while the cemented phase is modelled at theAbstract
micro/meso-scale using a cohesive-frictional model.
Someinsights
intothemechanisms
ofshear
failurepore
collapse
theformed
failure process,theHighly porous cement-based materials compose ofand
solidphasesand during
air pores
through thetransition
frombrittlefailuretoductile,andtheyield/failuresurfacesofatypicalhighlyporoussolid phases. The existence of a large amount of air pores in these materials causes their mechanicalmaterial
be presented
responseswill
highlydependentand
ondiscussed.
the density and the stress state, and their failure mechanisms to becomplicated and significantly different from other solid materials. In particular, the constitutive
responses and failure mechanisms of this material are highly controlled by the competition of theshear failure and pore collapse. In this work, we present our primarily results on the investigations of
the failure mechanisms of this material under the true triaxial stress conditions. The experimentally
validated discrete element method (DEM) is utilised to explicitly describe the internal pore-structure,
while the cemented phase is modelled at the micro/meso-scale using a cohesive-frictional model.
Some insights into the mechanisms of shear failure and pore collapse during the failure process, thetransition from brittle failure to ductile, and the yield/failure surfaces of a typical highly porous
material will be presented and discussed.
Key words: porous material, triaxial, constitutive behaviour

(a)

(b)

(c)

Density 1300 kg/m3

Figure 1: Behaviour of a highly porous material: (a) Effect of confining stress, (b) influence of
Figure 1: Behaviourof a highly(a) Effectof confining
stress, (b) influence ofmaterial
density porousand (c) material:
meridian curveof yield-failuresurfaces.
material density and (c) meridian curve of yield-failure surfaces.

25. Francesca Casini
Placing the Fluid Retention Curve as the core of multiphase soils response
under environmental loading
The presentation aims at providing a fundamental understanding of fluid retention curve effects on
the mechanical behaviour of multiphase soils. In particular, the influence of the void ratio on thesoil-water retention curves is discussed for a silty sand retrieved from a steep forested instrumented
slope. The interpretation of a wide set of triaxial tests performed on the silty sand with different
water content and obliquity are interpreted by means of a critical state constituive model extended
to unsaturated conditions. Finally, it is presented and interpreted the hydro-mechanical of thesteep forested slope during an artificail rainfall, which triggered a shallow slope failure fifteen
hours after rainfall initiation. Coupled hydro-mechanical finite element analyses, using a criticalstate constitutive model and extended to unsaturated conditions, are used to interprete the in field
response.
Further, it is presented the influence of a proper definition of the fluid retention curve (FRC) on
the mechanical response of the frozen soils by means of the interpretation of the frost-heave tests.
The evolution of the frost-heaving mechanism is discussed based on the definition of the FRC.

62

Chapter 25. Francesca Casini26. Jayantha Kodikara
Travelling with soil particles from sedimentation, consolidation, decohesion, re-compaction and environmental stabilisation
Soils are the most abundant naturally formed geomateirals on earth available for a geotechnicalengineer to discharge his duties to make human habitat better. Although it can be just ‘dirt’ to alayman, it generally conforms to a complex three-phase particulate system with its highly variableinterstitial pore spaces filled with water and (or) air giving different consistencies ranging fromliquid-like soil to completely dry soil. In its natural form, soil can be subjected to internal stresses
arising from gravity and other physico-chemical forces such as due to water surface tension andsalts, commonly referred to soil suction. Then, in geotechnical engineering applications, soil canbe completed reworked, compacted and consolidated through external forces, in addition to being
subjected to sustained atmosphere/soil interaction. Tracking and modelling of soil behaviour inthese processes generally is very complex, hence engineers have devised constitutive models subject
to various approximations and limitations. This modelling complexity is further enhanced due todifficulty input parameter measurement, and the variability and uncertainty of the soil conditionsin the field. None the less, as engineers, we need robust but (naked) physics-based tools that areeasy to use yet capture most important phenomenological features of soil behaviour. This need
will become increasingly important as the digital and automation age advances with intelligent
robots and IoT. For example, we will need such tools to make intelligent robots to compact soil for
performance-based specifications.
Following the above engineering need, the presentation will focus on tracking and modellingof soil behaviour in a framework developed by the author (i.e., MPK framework; Kodikara, 2012)and subsequently extended to develop a generalised model with his co-workers. The framework isbased on macroscopic representation of soil system through state variables ν, νw , s, p and q, which
are specific volume, specific moisture volume, mean net stress and deviator stress respectively.
The novel feature of the model is that it has used the phenomenological volumetric behaviourin ν, νw , p space to build and relate the other state variables through classical plasticity theory
approaches. While ν, νw , p volumetric space is a different way of looking at a four dimensional(when s is included) system with two independent variables, it offers a clear ease of input parameter
determination and a direct link to the well-known (Proctor) compaction curve, which is routinely
used in geotechnical engineering practice. When it is coupled through a volumetric plastic strain
dependant water retention curve that evolves with internal and (or) external loading, most field
stress paths may be modelled including wet/dry cycling in soil/atmosphere interaction. This multidimensional space then can be further extended to incorporate deviator loading to cater for generalloading conditions.
Kodikara, J.K. (2012). New framework for volumetric constitutive behaviour of compacted
unsaturated soils, Canadian Geotechnical Journal, Vol. 49, pp. 1227-1243.

64

Chapter 26. Jayantha Kodikara

Figure 1: Generalized MPK Volumetric Surface in the ν–νw –p space (Kodikara, Jayasundera andZhou, 2019)27. Adrian Russell
Uniqueness of pore geometry in soils
Understanding pore geometry in soils is important when characterising water retention and flow
as well as describing compression behaviour, strength and stiffness. Here it is shown how poregeometry exhibits uniqueness. It may be described using functions, analytically derived, which
incorporate soil density and particle size distribution. Demonstrations will be given for well-graded‘fractal’ soils and poorly-graded ‘monodisperse’ soils.

66

Chapter 27. Adrian Russell

Figure 1: Left: Cumulative distribution of normalised pore volume for random assemblies ofmonodisperse spheres. Right: Rescaled cumulative distribution showing uniqueness, fitted witha k-Gamma function. (Sufian et al., 2015, Pore shapes, volume distribution and orientations
in monodisperse granular assemblies, Granular Matter, 17:727-742. http://dx.doi.org/10.
1007/s10035-015-0590-0).

IVContact details

69

List of Speakers
Edward Ando edward.ando@3sr-grenoble.fr
Jose Andrade jandrade@caltech.edu
Ha Bui ha.bui@monash.edu
Francesca Casini francesca.casini@uniroma2.it
Daniel Dias-da-costa daniel.diasdacosta@sydney.edu.au
Arcady Dyskin arcady.dyskin@uwa.edu.auThierry Faug thierry.faug@irstea.fr
Eleni Gerolymatou eleni.gerolymatou@chalmers.se
Stephen Hall stephen.hall@solid.lth.se
Jayantha Kodikara jayantha.kodikara@monash.edu
Stefan Luding s.luding@utwente.nl
Knut Jørgen Måløy k.j.maloy@fys.uio.noTakashi Matsushima tmatsu@kz.tsukuba.ac.jp
Ben Nadler bnadler@uvic.ca
Guillermo Narsillio narsilio@unimelb.edu.au
Giang Nguyen g.nguyen@adelaide.edu.au
Elena Pasternak elena.pasternak@uwa.edu.au
Jean-Michel Pereira jean-michel.pereira@enpc.fr
Alexander Puzrin alexander.puzrin@igt.baug.ethz.ch
Klaus Regnauer-Lieb klaus@unsw.edu.au
Pierre Rognon pierre.rognon@sydney.edu.au
Adrian Russell a.russell@unsw.edu.au
Mohammad Saadatfar mohammad.saadatfar@anu.edu.au
Alexander Scheuermann a.scheuermann@uq.edu.au
Ioannis Stefanou ioannis.stefanou@enpc.fr
Anthony Thornton a.r.thornton@utwente.nl
Julio Valdes jvaldes@mail.sdsu.edu
Cino Viggiani cino.viggiani@3sr-grenoble.fr

Organisers
Itai Einav itai.einav@sydney.edu.au
Benjy Marks benjy.marks@sydney.edu.au