International Workshop of

Young Doctors in
Geomechanics

Ecole Nationale des Ponts et Chaussées

Champs-sur-Marne, France
December 4 - 6, 2002

V. De Gennaro & P. Delage, editors

Ecole Nationale des Ponts et Chaussées, France
PROCEEDINGS OF THE INTERNATIONAL WORKSHOP OF YOUNG DOCTORS IN GEOMECHANICS
W(H)YDOC 02 / CHAMPS-SUR-MARNE / DECEMBER 4 - 6, 2002

International Workshop of
Young Doctors in
Geomechanics

V. De Gennaro & P. Delage, editors

Ecole Nationale des Ponts et Chaussées, France

ALERT
Alliance of Labora- Agence Nationale pour Degradation and Instabilities Ecole Nationale Institut de Radio-
tories in Europe for la Gestion des Déchets in Geomaterials with Application des Ponts et protection et de
Research and Radioactifs to Hazard Mitigation Chaussées Sûreté Nucléaire
Technology

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 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

Table of contents

Foreword IX

THM coupling in geomaterials

Temperature effects in high porosity chalk 3

M.V. Madland, R. Risnes

Modelling of unsaturated chalk: from experiment to reservoir 7

F. Collin, Ch. Schroeder, R. Charlier, V. De Gennaro

Thermally dependent constitutive model for soils 11

C. Cekerevac, L.Laloui

A double structure model for expansive clays 15

M. Sanchez, A. Gens, S. Olivella

A re-examination of swelling pressures of compacted bentonites from 17

Gouy-Chapman diffuse double layer theory
S. Tripathy, T. Schanz

Time dependent changes of microstructure of a compacted MX80 21

Bentonite at constant volume
D. Marcial, P. Delage,Y.J. Cui, X. Ruiz

Determination of structural porosity in red mud suspensions 23

G. Bartholomeeusen, G.C. Sills

A correlation between clay mineralogy and Atterberg limits 27

R.M. Schmitz, Ch. Schroeder, R. Charlier

Constitutive modelling in geomaterials

On Casagrande & Carrillo induced & inherent anisotropy concept 33

M.Arroyo

V
Quasi-static shear deformation characteristics of granular systems: 35
insights from dem simulations
S. J. Antony

Numerical modelling of damage and permeability in claystone: application 37

to underground radioactive waste storage
K. Maleki, P. Berest, A. Pouya, P. Dangla

Contribution to the inverse subsidence diffusion-convection problem in 41

geostructures
E. Vairaktaris, I. Vardoulakis, E. Papamichos, V. Dougalis

Experiments on the mechanical behaviour of geomaterials

Effect of principal stress rotation on the behaviour of natural soils 47

K. Nasreddine

Weathering effects on the mechanical behaviour of soft rocks: an 51

experimental study
R. Castellanza, R. Nova

An experimental study on influence of the hydromechanical behaviour on 55

flow and transport of contaminants
R.L. Rodríguez-Pacheco, L. Candela, A. Lloret

A new peak shear strength criterion for rough rock joints 57

G. Grasselli

Mechanical behaviour of geotechnical structures

Experimental and numerical approaches to the study of the behaviour of 63

micropile groups and networks subjected to vertical or horizontal loading
R. Estephan, R. Frank

Coupled seismic response of deep saturated soil deposit in Shanghai 65

Y. Huang, W.-M. Ye, Y.-Q. Tang, Z.-C. Chen

New design criteria for piled rafts and related methods of analysis 67
L. de Sanctis

Study on stability and displacements of DMP retaining wall in soft soil 69

J. Xiong, M. Yang

Stability analysis and Tunnels

Effects of embedded diaphragm walls on mouvements induced by tunnel 75

excavation
E. Bilotta

VI
Optical fibre sensors for remote tunnel displacement measurements 77
N. Metje, C. Rogers, D. Chapman, S. Kukureka

Simulation of pipeline behaviour on liquefied seabed: numerical study 79

P.L. Vun, A.H.C. Chan, S. Dunn

Numerical Photogrammetry in laboratory experiences on 2D slopes 83

F.Froiio, G. Viggiani, F. Laouafa

Modelling lanslides in volcanic soils: las colinas landslide 87

(El Salvador, February 2001)
J.A. Fernandez-Merodo, M. Pastor, P. Mira

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 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

Foreword

The scope of W(H)YDOC 02 (Paris, December 4 - 6, 2002) was to bring together young
geotechnical doctors within an informal three days invited Workshop, so as to allow for the
presentation of researches carried out during their PhD thesis. Students completing their last PhD
year were also welcomed. Several senior researchers from various European Universities acted as
discussion leaders during the sessions. The Workshop aimed at favouring informal and
constructive exchanges about recent research results and ideas.

The Universities that agreed to participate to W(H)YDOC 02 are listed below; various of them are
already partners within the ALERT and DIGA European networks:
Bauhaus University of Weimar (D), University of Bristol (UK), C.E.D.E.X. Madrid (SP), University of
Birmingham (UK), Ecole Centrale de Nantes (F), University of Leeds (UK), Ecole Nationale des
Ponts et Chaussées (F), Université de Liège (B), LMS-G3S Ecole Polytechnique (F), Università di
Napoli "Federico II" (I), Ecole Polytechnique de Lausanne (CH), University of Oxford (UK), Imperial
College of Science, Tech. and Med. (UK), Universitat Politecnica de Catalunya (SP), Institut
National Polytechnique de Grenoble (F), Università di Roma "Tor Vergata" (I), Laboratoire Central
des Ponts et Chaussées (F), University of Stavanger (NO), National Technical University of Athens
(GR), University of Swansea (UK), Politecnico di Milano (I), University of Tongji (China),
Universidad Central de Venezuela (V), Università di Trento (I).

A total of 27 contributions coming from 11 countries were presented during the three days
Workshop. This book contains the summaries of these contributions, outlined in a short paper
provided by the authors. They would be useful for all researchers to have an idea of the ongoing
research activities in the field of geomechanics.

We are grateful to the people who ensured the scientific co-ordination of the Workshop, namely:
Prof. David Muir Wood (University of Bristol, UK), Prof. Roberto Nova (Politecnico di Milano, I),
Prof. Gyan N. Pande (University of Swansea, UK), Prof. Manuel Pastor (C.E.D.E.X. Madrid, SP),
Prof. Rasmus Risnes (Stavanger University, NO), Prof. Felix Darve (Institut National Polytechnique
de Grenoble, F).
We are grateful too, to all the "young doctor contributors", who have animated the three days
meeting. Thanks are due also to their Tutors, who accepted to cover part of their fees of
attendance.

We acknowledge Prof. D. Muir Wood, Prof. G.N. Pande and Prof. M. Pastor for their kind
acceptance to held the keynote lectures presented during the three days of the Workshop.

This Workshop would not have been possible without the sponsorship of: ANDRA (Agence
Nationale pour la Gestion des Déchets Radioactifs, F), DIGA (Degradation and Instabilities in
Geomaterials with Application to Hazard Mitigation) EC Research Training Network, ENPC (Ecole
Nationale des Ponts et Chaussées, F) and IRSN (Institut de Radioprotection et de Sûreté
Nucléaire, F). Their support is here acknowledged.

Vincenzo De Gennaro
Pierre Delage
Champs, December 2002

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THM coupling in geomaterials
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

TEMPERATURE EFFECTS IN HIGH POROSITY CHALK

Merete V. Madland (merete.v.madland@tn.his.no), Rasmus Risnes

Stavanger University College, Stavanger, Norway.

ABSTRACT. The objective of the present project was to study how high temperatures affect the
different mechanical parameters of chalks. The general result is that both cohesion and the
hydrostatic yield stress are typically reduced about 20 % in going from 20 to 130 oC, but the
magnitude of this reduction may be chalk type dependent.

1. Introduction

During the last decades, mechanical behavior of porous chalks has been extensively studied in
order to understand the mechanisms behind well instability, compaction and subsidence
experienced in the North Sea chalk reservoirs. However, most of the laboratory work performed,
has been carried out at ambient temperature. This greatly facilitates laboratory studies, and
temperature effects on mechanical properties of chalks have received limited attention.
So far only few studies on temperature effects in chalks have been reported and the results
point in different directions. The objective of this present study is to investigate how the different
mechanical parameters, like cohesion, friction angle and hydrostatic yield, are affected by
temperature.

2. General chalk properties and test equipment

For high porosity chalks, it has been shown (Risnes et al., 2000) that the Mohr circle corresponding
to the Brazilian test results fits very closely to the Mohr Coulomb line derived from conventional
compressive test data. This fact makes the easily performed Brazilian test useful for estimation of
the chalk cohesion. Combined with uniaxial compressive tests, estimates for friction angle may also
be obtained. To explore this potential it was decided to develop a test cell where the Brazilian test
could be performed up to reservoir temperatures and later this cell has been modified to allow also
uniaxial compressive tests. In addition tests were also run in a standard triaxial cell equipped with a
heat regulating system.
The chalks used in this study were high porosity outcrop chalks, which have similar
mechanical properties as reservoir chalks. Both water and glycol was used as saturating fluids and
in addition some test series on dry samples were performed. Glycol is fully miscible with water and
this property assures no capillary effects if some water should remain in the chalk before saturation.

3. Test results

Four types of tests have been performed in this study: Standard triaxial compressive tests with
different confining pressures, quasi-hydrostatic tests (K=0.9) and Brazilian (ToB ) – and uniaxial
compressive (Co) tests. The test series were performed at ambient and reservoir temperatures.

Brazilian and uniaxial tests

A summary of the results from water and glycol saturated Aalborg chalks are presented in Table 1.
As can be seen from the tabular data the resistance for water saturated chalk is reduced by around 20 %,
while the temperature effect is even more pronounced with glycol both in Brazilian and uniaxial tests, the
changes being in the range of 30-40 % as temperature increases from 20 °C to 130 oC. The friction angle
(ϕ) seems less affected, but there is a slight tendency towards decreasing friction angle with increasing
temperature for both water and glycol saturated chalks.

3
 Fluid Water Glycol
T (oC) 20 130 20 130
ToB (MPa) 0.65±0.06 (10) 0.54±0.03 (10) 1.08± 0.09 (11) 0.76± 0.03 (13)
Co (MPa) 3.91±0.65 (4) 3.18±0.51 (4) 9.77± 0.62 (9) 5.84± 0.46 (9)
So (MPa) 1.12 0.94 2.00 1.33
ϕ (degree) 30.5 28.9 45.7 40.8
Table 1. Results from Brazilian and uniaxial tests, water and glycol saturated Aalborg chalk.

The results obtained with a series of "dry" chalk show a strengthening tendency with
increasing temperature. The magnitude of the changes is somewhat less compared to the
preceding cases, only around 10 %. The reason for this behavior may be drying effects, as the
water content was not controlled during the heating of the samples. In this case there is also a very
slight increase in friction angle.

Complete yield curves from triaxial and brazilian tests

To determine a complete yield curve, a series of triaxial compressive tests is needed, with different
confining pressures in the interval between zero and the hydrostatic yield stress value. In addition a
series of Brazilian tests is useful for determination of the Mohr-Coulomb parameters. The results of
such test series with water and glycol saturated Liège chalks are presented in Figure 1 and Table
3.

14

12

10 Glycol, 20 oC
q (MPa)

8
Glycol, 130 oC
6

2 Water, 20 oC
0 Water, 130 oC
0 2 4 6 8 10 12 14 16 18
p`(MPa)

Figure 1. Yield curves for water and glycol saturated Liège chalk.

Fluid Water Glycol

T (oC) 20 130 20 130
ToB (MPa) 0.37 (22) 0.36 (21) 0.86 (16) 0.69 (15)
So (MPa) 0.69 0.59 1.5 1.2
ϕ (degree) 34.6 35.0 37.5 39.7
σh (MPa) 10.3 8.5 16.0 14.0

Table 2. Results from testswith water and glycol saturated Liège chalk.

On the shear failure side a reduction of 15 to 20 % is observed in cohesion (So) for both fluids, while
the friction angle shows only a very slight increase with increasing temperature. On the end-cap
side the hydrostatic yield values (σh) show the same tendency as seen for cohesion with increasing
temperature.

4. Conclusions

With "dry" chalk as an exception, all tests, both Brazilian and triaxial tests show a decreasing
resistance with increasing temperature. The overall typical result is strength reductions around 20
% in going from 20 to 130 oC. The strength reduction seems to be an overall effect. It affects both
cohesion and hydrostatic yield stress.

4
5. References

Charlez Ph.A., Heugas O., Shao J.F (1992). Effect of temperature on mechanical properties of chalk. Fourth
North Sea Chalk Symposium, Deauville, France.
Addis, M.A. (1989) The behaviour and modeling of weak rocks. Rock at great depth.Vol.2, pp 899-914, A.A.
Balkema, Rotterdam.
Risnes R., Berg T., Paulsen T. (2000). Tensional failure and solid-fluid interactions in high porosity chalk. The
Fourth North American Rock mechanics Symposium, Seattle, USA, Pacific Rocks 2000 pp205-212
Balkema, Rotterdam

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 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

MODELLING OF UNSATURATED CHALK: FROM EXPERIMENT TO RESERVOIR

Frédéric Collin (f.collin@ulg.ac.be), Christian Schroeder, Robert Charlier

Dept. GEOMAC, University of Liège, Belgium.
Vincenzo De Gennaro
CERMES, Ecole Nationale des Ponts et Chaussées-LCPC, France.

ABSTRACT. Chalk is the constituent material of numerous oil reservoirs in North Sea. The
mechanical behaviour of a saturated chalk has been largely studied and different mechanical
models have been proposed. However, different aspects of its behaviour are not yet well
understood: one of them is the water-sensitivity of material characteristics. On one hand, an oil
saturated chalk is stiffer and stronger than a water saturated one. On the other hand, during water
injection in reservoir (waterflooding), compaction of production layers is observed implying seabed
subsidence. The paper presents the different models developed in the framework of the
“Pasachalk 1” EC “Thermie” Project.

1. Introduction

As chalk in oil reservoir is generally saturated by two or more fluids (oil, connate water, gas), the
basic idea of this project is to apply some approaches of the unsaturated soil mechanics to the
study of the mechanical behaviour of chalk submitted to waterflooding (Delage et al., 1996).
A constitutive law is proposed for the modelling of the mechanical behaviour of chalk. The
effects of the suction (related to some specific forces, including capillary actions) are taken into
account. They are considered as an independent variable, as in the Barcelona’s basic model
developed for unsaturated clay (Alonso et al., 1990). In the model, the experimental results have
lead to consider internal friction and pore collapse as independent mechanisms.
The experimental work is focused on one hand on tests at different suction levels and on the
other hand on the determination of the parameters of the failure mechanisms, including hardening
law, for the two extreme saturation conditions (oil and water).
Validation of the numerical model is achieved thanks to waterflooding experiment. Finally
results of an academic reservoir model are presented to show the ability of the numerical tool to
reproduce the in situ observations.

2. Chalk behaviour: experimental evidences

The experiments on water and oil saturated sample show clearly two plastic mechanisms: the pore
collapse for high mean effective stresses and a frictional failure for high deviator stresses (Figure
1).
24

22 pl as tic W a t er s a tu ra te d sa m p le s

20
s he ar ( br ittle)

18
pl as tic ( br ittl e)
16

U CS
14
69
q (M P a)

72 68
12

5 8b 67
10
65 64
04
8 07
62 61 70
66
6 09
58
63 60
4
59
2

70 66/67 72 69 E 20 E30
0
64/68 58/65
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

p ' (M P a)

Figure 1. Yield points for water saturated samples (Schroeder et al., 2000).

7
 Results refer to tests on Lixhe chalk, an outcrop chalk belonging to the same formations as
the reservoir chalk layers. Few results allow for the determination of traction strength, but the yield
limit for extension path predicted by a frictional model usually overestimates the actual value. In the
reservoir chalk, suction effects develop between oil (non-wetting fluid, like air in unsaturated soils)
and water (wetting fluid, like in unsaturated soils). Suction controlled oedometer tests confirm the
strengthening influence of the suction: results show the evolution of preconsolidation pressure from
a water saturated chalk to an oil quasi-saturated one which is stronger and stiffer.
In order to better understand the compaction phenomenon during water injection in the
reservoir, waterflooding experiments are achieved under controlled pressure and stress reservoir
conditions. Experimental results show that compaction appears in the direction of the major stress
and deformations follow the water front displacement.

3. Finite element modelling

In order to carry out fully coupled simulations of waterflooding experiments on Lixhe chalk, a
suction dependent cap model coupled with a multiphase flow model have been implemented in the
CONVILAG finite element code (Collin et al., 2002). The parameters of the models are determined
using results of experiments performed on Lixhe chalk.

Saturated chalk sample & waterflooding experiment

In a first attempt, the goal of simulations is the validation of our models. Thus, experiments on
saturated chalk are modelled in order to check the ability of the constitutive laws to reproduce the
different plastic mechanisms of the material. The computations of waterflooding tests in isotropic
and anisotropic stress state are presented. Comparisons between numerical and experimental
results are made in terms of fluid volume exchanges and local and global deformations
measurements (Figure 2).
25

7
20

6
Axial deformation [°/°°]

15
G1 - Exp
5
Gauge 1
Volume [cm³]

10 G2 - Exp
4 Injected water Gauge 2
G3 - Exp
Expelled Soltrol
3 5 Gauge 3
Expelled water G4 - Exp
2 Gauge 4
LGIH-Injected Water 0
0 500 1000 1500 2000 2500 3000 3500
1
-5
0
0 500 1000 1500 2000 2500 3000 3500 4000
-10
Time [sec] Time [sec]

(a) (b)

Figure 2. (a) Fluid exchange during water flooding, (b) axial strains at the four gauges (Charlier et al., 2002).

Academic reservoir simulation

Once the validation issue addressed, a simplified reservoir model is used in order to simulate the
production and injection phases. The fully coupled models allow to reproduce the fluid flows and
the compaction observed during the reservoir history.
These computations show the ability of the numerical models to reproduce the experimental
observations. They confirm also the validity of the assumptions we made to better understand
compactions during water injections in the reservoir.

4. Perspectives

An important aspect of chalk behaviour is not taken into account in the model: the time-dependent
response of the material. This is one of the topics of the currently running "PASACHALK 2" Project.

8
 Also, reservoir simulations dealing with more complex formations properties and a fully
coupled 3D model will be tackled.

5. Acknowledgements

The authors want to acknowledge the EU project Degradation and Instabilities in Geometerials with
Application to Hazard Mitigation (DIGA) in the framework of the Human Potential Program,
Research Training Networks.

6. References

Alonso E.E., Gens A., Josa A. (1990). A constitutive model for partially saturated soils. Géotechnique, 40(3):
405-430.
Delage P., Schroeder Ch., Cui Y.J. (1996). Subsidence and capillary effects in chalk. Eurock 96 proceedings,
Turin, Italy: 1291-1298.
Charlier, R., Collin, F., Schroeder, Ch., Illing, P., Delage, P., Cui, Y.-J., De Gennaro, V. (2002). Constitutive
modeling of chalk - application to waterflooding. Proc. 2nd Biot Conference, Grenoble, France, in print.
Collin F., Cui Y.J., Schroeder Ch., Charlier R. (2002). Mechanical behaviour of Lixhe chalk partly saturated by
oil and water: experiment and modelling. Int. J. of Num. and Anal. Meth. in Geomechanics, 26: 897-924.
Schroeder Ch., Bois A.-P., Charlier R., Collin F., Cui Y.J., Delage P., Goulois A., Illing P., Maury V. (2000).
PASACHALK project (Partially saturated chalk) : Constitutive modelling, determination of parameters
using specific stress paths and application to the waterflooding (Extended abstract & Posters). JCR V
Symposium Brighton.

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 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

THERMALLY DEPENDENT CONSTITUTIVE MODEL FOR SOILS

Cane Cekerevac (Cane.Cekerevac@epfl.ch), Lyesse Laloui

Swiss Federal Institute of Technology, EPFL, Lausanne, Switzerland.

ABSTRACT. This paper presents part of an extensive thermo-mechanical experimental study

performed on CL clay (Kaolin). It proposes a simple method to incorporate thermal effects in
constitutive modelling, motivated by a rational engineering consideration: accurate results need to
be obtained with the least possible number of parameters. To reach this aim, an isotropic thermo-
plastic model is proposed based on considerations of the thermal effects on the preconsolidation
pressure.

1. Introduction

Thermal effects in geomechanical problems are important for many specific applications. Recent
research is mainly concerned with nuclear waste isolation and the use of soil deposits for heat
energy storage. Other applications are related to geothermal structures, petroleum drilling etc.
To account for thermal strains and changes in the material state induced by heating, an
analysis of the isotropic behaviour has been made. The main considered parameter is the
preconsolidation pressure, which controls the size and evolution of the yield limit. In the following
sections, the thermal effect on this parameter will be analysed and a mathematical formulation for a
thermo-plastic constitutive model will be deduced.

2. Experimental results

An experimental study was carried out using a GDS triaxial cell modified to manage temperature
(Cekerevac et al., 2001). The required heat was obtained by circulating water through metal tubes
placed spirally around the sample. The hot water came from a bath, placed outside the triaxial cell,
went through the tube inside the cell around the sample and returned to the bath. Two
thermocouples were placed around the sample: the first one gave a feed-back signal to the
heater/cooler and the second one was used for data acquisition. The system employed allowed
temperature control in the range of 5°C to 150°C with an accuracy of ±0.15 °C. All units of the
equipment were managed by a personal computer.

Temperature induced changes in preconsolidation pressure

This experimental study was performed on Kaolin (Cekerevac et al., 2002). Three consolidation
tests were carried out at different constant temperatures: 22°C (Test 1), 60°C (Test 2) and 90°C
(Test 3). The results, in Figure 1, show that the preconsolidation pressure decreases with an
increase in temperature. Several results from the literature show the same pattern of behaviour, a
decreasing of the preconsolidation pressure with increasing temperature.
Each set of experimental results has roughly the same shape and it appears that the σ′c − T
relationship for the clays can be normalised: σ′c (T ) with respect to the preconsolidation pressure at
a reference temperature σ′c (T0 ) , and T with respect to the reference temperature T0, assumed
here to be the minimal testing temperature. This relationship is essentially linear and can be
expressed by the following equation:

σ′c (T ) = σ′c (T0 ){1 − γ [log ((T0 + ∆T ) / T0 )]} (1)

11
3. Constitutive modelling

The thermal effect on the preconsolidation pressure can be introduced in the constitutive modelling
by an isotropic thermo-plastic mechanism. In isothermal conditions, the isotropic yield limit can
simply be expressed as:

fiso = p'−σ 'c (2)

The preconsolidation pressure can be related to the volumetric plastic strain by:

σ′c = σ′c 0 exp (βε pv ) (3)

Preconsolidation pressure [kPa]

700

Test 1
600 Test 2 Test 3

500
0 25 50 75 100
Temperature, T [°C]
Figure 1. Influence of temperature on the preconsolidation pressure.

100
Temperature, T [°C]

80

60
γ=0.4
γ=0.3
40 γ=0.15
γ=0.075
20
70 80 90 100 110
Preconsolidation pressure, σ' [kPa]
c

Figure 2. Shape of the isotropic thermo-mechanical yield limit for the different values of the parameter γ .

where σ 'co is the initial value of preconsolidation pressure; β the plastic compressibility and ε Pv the
plastic volumetric strain. The complete expression of the isotropic thermo-plastic mechanism is:

( )
fiso = p'−σ 'co exp β ε Pv ⋅ {1 − γ [log ((T0 + ∆T ) / T0 )]} (4)

Figure 2 shows the shape of the yield limit (Eq. 4) for different values of the parameter γ.

12
4. Typical numerical responses

Isotropic consolidation after heating up to two different temperatures is shown in Figure 3. The path
at a higher temperature (C – D) exhibits a lower elastic domain (i.e. lower preconsolidation
pressure).
Isotropic consolidation after heating-cooling path is analysed in Figure 4. As can be seen, the
settlement induced by heating (A→A1) produces an increase of the isotropic yield limit. The
mechanical re-loading from point A first remains within the elastic domain before reaching the yield
limit ( σ'c1 ) and then becomes plastic again.

0.02
Path C - D

0 Path A - B
Void ratio change [-]

-0.02 T
C
T D
2
-0.04
A
T B
1

-0.06 p'

σ'
c0
-0.08
1 10
log p' [MPa]
Figure 3. Isotropic re-consolidation after heating the sample.

-0.02
Void ratio change [-]

-0.04 T A

T1 A1 A1 A'
-0.06

A A'
-0.08 p'
σ'c0 σ'c1
-0.1
1 10
log p' [MPa]

Figure 4. Isotropic re-consolidation after a heating-cooling cycle.

5. References

Laloui L., Cekerevac C., Vulliet L. (2001). Thermo-Mechanical modelling of the behaviour of MC clay.
Computer Methods and Advances in Geomechanics, (ed) C. S. Desai, Balkema, Tucson, USA: 829-835.
Cekerevac C., Laloui L. Vulliet, L. (2002). Dependency law for thermal evolution of preconsolidation pressure.
Eighth International Symposium on Numerical Models in Geomechanics - NUMOG VIII, Rome, Italy, 687-
692.
Cekerevac C., (2003). Thermo-mechanical behaviour of saturated soils - application to thermal piles, Doctoral
thesis, Swiss Federal Institute of Technology, Lausanne, (in prep.).

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 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

A DOUBLE STRUCTURE MODEL FOR EXPANSIVE CLAYS

M. Sánchez (marcelo.sanchez@upc.es), A. Gens, S. Olivella

Dept. of Geotechnical Engineering and Geosciences, Technical University of Catalunya

ABSTRACT. In this work a double structure model specially developed for the treatment of
problems involving expansive materials is presented. An important part of the formulation is the
mechanical constitutive model, that considers explicitly the two dominant structural levels present in
the expansive soils. In addition a double structure Thermo-Hydro-Mechanical (THM) formulation
has been developed, that allows the consideration of the strong coupling between phenomena,
characteristic of this kind of materials. The paper includes the experimental validation of the model
and a number of application cases.

1. Introduction

The possible use of expansive clays as engineered barriers and seals in radioactive waste
repositories has led to an increased knowledge of the behaviour of expansive soils under a wide
range of testing conditions, in particular the THM behaviour has been the object of special
attention. As a consequence it is necessary to develop constitutive models that take into account
the major features of THM behaviour and incorporate, to some extent, the main physical
phenomena relevant to this type of soils.
The behaviour of expansive clay is potentially very complex since it results from the
interaction between the volume change of aggregates made up of a highly expansive clay mineral
(microstructural level) and the rearrangement of the granular-like skeleton formed by the
aggregates (macrostructural level). In this work a mechanical constitutive model for these kinds of
materials has been developed using concepts of generalised plasticity and classical plasticity
theory, the BExM has been considered as the starting point (Gens & Alonso,1992). In the barrier
and the near field, significant thermo-hydro-mechanical (THM) phenomena take place, that interact
in a complex way. A good understanding of THM issues is therefore necessary to ensure a correct
performance of engineered barriers and seals. A formulation that expresses, in a mathematical
way, the various THM phenomena considered relevant as well as their main interactions is a basic
requirement for advancement. Availability of such a formulation is necessary if the various aspects
of THM behaviour are to be considered in an integrated way. A double structured THM formulation
developed with this objective is described.
The proposed model has been implemented in the program Code_Bright, Olivella et al, 1996,
which is a tool designed to handle coupled THM problems in geological media. The code solves in
a coupled way: the momentum balance for the medium, the internal energy balance, the water, air
and solid mass balance. Finite elements in space and finite differences in time are used for the
discretization of the system of equations. Finally the model has been applied to different problems
related to the behaviour of expansive materials.

2. Brief model description

The mechanical model considers explicitly the two structural levels present in expansive clays. The
inclusion of the microstructural level allows the consideration, in a consistent way, of the physico-
chemical phenomena occurring at particle level, which are the main responsible of the expansive
behaviour of this soils. As pointed out above, the macrostructural level corresponds to the granular-
like arrangement of particle aggregates and macropores. This structural level is modelled using the
BBM (Barcelona Basic Model), Alonso et al.,1990. The BBM uses two basic stress variables: the
net stress, and the matric suction. BBM extends the concept of critical state for saturated soils to
the unsaturated conditions, including the dependence of yield surface with suction.

15
 Regarding the microstructural level it is assumed that the deformation behaviour is reversible
and not affected by the state of the macrostructure. Although the behaviour of the microstructure is
expected to be independent of the macrostructure, there is an important influence of the
microstructure on the macrostructural level, where it can induce significant plastic strains. The
magnitude of the interaction depends on the current stress state and on the density of the
macrostructure.
In order to integrate the mechanical model a framework of multidissipative materials have
been adopted; in which a classical elastoplastic model, for the macrostructure, is combined with a
generalised plasticity model that takes into account the interaction between the macrostructural and
the microstructural level. The aim is to achieve a more general interpretation of the phenomena that
take place in an expansive soil and provide an increased flexibility and robustness to the model.
Relating to the THM behaviour a double structure formulation has been developed as an
extension of that proposed by Olivella et al 1994 for a single porosity medium. The extension of the
formulation was carried out with the aid of double porosity theory (Wilson & Aifantis 1982). The
theoretical framework is composed of three main parts: balance equations, equilibrium restrictions
and constitutive equations. The problem is formulated using a multi-phase, multi-species approach
for each media.

3. Experimental validation and application cases

In the context of the Febex project a wide experimental study has been carried out on a heavily
compacted bentonite (LLoret et al. 2002). The testing programme has been carried out using
oedometers in which a combination of loading paths (up to 10 MPa) at constant suction and wetting
and drying paths (up to 550 MPa) at constant load were applied. The experimental study also
include swelling tests under constant volume conditions in order to determine the swelling pressure
and the stress path followed during wetting. These two kinds of tests provide the opportunity to
examine the behaviour of the model over a wide range of stress paths. In the paper the model
results of constant load tests, constant suction tests and swelling pressure tests are examined and
discussed taking into account the role of the soil fabric. The aim of this modelling exercise is the
experimental validation of the model and to use the constitutive model as a consistent tool to gain a
better and more founded understanding of the behaviour of the soil and of the mechanisms that
underlie it. It can be observed that major features of behaviour are correctly reproduced, including
the stress path dependency of volumetric strains observed in the tests.
Also, the model has been applied to analyze the behaviour of an expansive clay, submitted to
a complex THM stress path in a large scale heating test, that simulate an engineered barrier in a
radioactive waste disposal scheme. It has been shown that the model is able to reproduce the
major features of the observed mechanical behaviour in response to a complex history involving
temperature and suction changes. The consideration of the two levels of structure (really existing in
the material) and the interactions between them plays a crucial role in the reproduction of the
irreversible effects affecting the observed behaviour of the swelling pressure.
Finally, the model has been applied to simulate the hydration of a clay material that can
potentially be used to construct engineered barriers and seals in radioactive waste repositories.

4. References

Alonso E.E., Gens A., Josa A. (1990). A constitutive model for partially saturated soils. Géotechnique 40,
Nº3, 405-430.
Gens A., Alonso E.E. (1992). A framework for the behaviour of unsaturated expansive clays. Can. Geotech.
Jnl, 29, 1013-1032.
Lloret A., Villar M., Sánchez M., Gens A., Pintado X., Alonso E.E. (2002). Mechanical behaviour of heavily
compacted bentonite under high suction changes. Accepted in Géotechnique.
Olivella S., Carrera J., Gens A. & Alonso E. (1994). Non-isothermal multiphase flow of brine and
gas through saline media. Transport in porous media, \/ 15: 271-293.
Olivella S., Gens A., Carrera J., Alonso E.E. (1996). Numerical formulation for a simulator
(CODE_BRIGHT) for the coupled analysis of saline media. Eng. Computations, 13(7), 87-112.
Wilson R., Aifantis E. (1982). On the theory of consolidation with double porosity. Int. J. Engng Sci.
Vol. 20, No. 9: 1019-1035.

16
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

A RE-EXAMINATION OF SWELLING PRESSURES OF COMPACTED BENTONITES

FROM GOUY-CHAPMAN DIFFUSE DOUBLE LAYER THEORY

Snehasis Tripathy (snehasis.tripathy@bauing.uni-weimar.de), Tom Schanz

Bauhaus-Universität Weimar, Germany

ABSTRACT. In this paper the swelling pressures of several bentonites (MX80, Febex, Montigel)
proposed to be utilised as barrier material in storing high-level radio active waste in many countries,
were determined from the Gouy-Chapman diffuse double layer (DDL) theory. The swelling
pressures thus determined from the theory were compared with the reported experimental swelling
pressures of the bentonites. Three different new equations were proposed on the basis of the DDL
theory to compute the swelling pressures of bentonites. The proposed equations are based on the
experimental u-Kd relationships and hence take into account the apparent discrepancies in the
theory at low and high bentonite dry densities. The suitability of the equations was also verified
using the experimental results of a few other bentonites, namely Kunigel, Kunigel V1, and Bentonite
S-2. A very good agreement between the theory and experiment was found in all the cases with the
new equations. The use of the proposed swelling pressure equations is based on the weighted
average valency of cations present in bentonites.

1. Introduction

The Gouy-Chapman DDL theory (Gouy 1910; Chapman 1913) has been the most widely used
approach to relate clay compressibility and the swelling pressure to basic particle-water-cation
interaction (Sridharan and Jaydeva 1982; Gens and Alosnso 1992; Marcial et al. 2002). According
to this theory, the interaction force between two double layers depends on the ion concentration, n,
at the midplane between two adjacent parallel clay platelets and is given by the osmotic pressure,
p, in that plane (Bolt 1956). Therefore, for any given separation distance, d, between two clay
platelets the osmotic pressure can be determined from the theory and vice versa.
Swelling pressure determination is an important aspect of all the high-level radioactive waste
projects. Laboratory swelling pressure tests on compacted bentonites have been carried out by
many researchers in the past (Bucher and Müller-Vonmoos 1989; Komine and Ogata 1994; Japan
Nuclear Cycle report H12 1999; ENRESA 2000). The swelling pressure tests have been for the
confined situation, where the volume change of specimen was not permitted. This paper reports an
extensive investigation that compared the swelling pressures of several bentonites obtained from
the Gouy-Chapman DDL theory with the reported experimental swelling pressures of the
bentonites.

2. Theory

Sridharan and Jaydeva (1982) have given the procedure to determine the swelling pressure of
clays using the Gouy-Chapman DDL theory. The swelling pressure is determined from Langmuir’s
equation (Equation 1). To compute p for a given pore fluid medium, the midplane potential function,
u, must be known. For a given double layer distance, d (where e = G Sγwd), a relationship between
u and d should be established prior to computing u. Sridharan and Jaydeva (1982) have given such
relationship in the form of a table, a chart and even an equation to determine u for any given value
of ion concentration, n, and distance function, Kd. However, the information is for clays with
monovalent cations. For clays with mixture of monovalent and bivalent cations, actual properties
can be considered to establish such relationships.
In this study, the u-Kd relationship was established from several considerations for the
bentonites. It was found that there can be a minimum and a maximum u value from the theoretical
consideration. The minimum u value can be obtained by considering the actual pore fluid properties
and the range of pressure within which the swelling pressure is expected to be varied. The
maximum u value can be determined by considering a pressure range of 50 kPa to 400 kPa for a

17
set of n values. In both the cases the actual clay properties were considered. For any given dry
density of bentonites, Equation (1) was then used to determine the swelling pressure.

p = 2nkT (cosh u − 1) (1)

3. Experimental and theoretical swelling pressures

The experimental swelling pressures and swelling pressures obtained from the theory, for MX80,
Febex and Montigel bentonites are shown in Fig. 1(a). As can be seen from the figure, the overall
agreement between experiment and theory is good. However, in general the experimental values
are less than their theoretical counterparts at low pressure range, whereas reverse is the trend at
higher pressures. The primary reasons for the differences between theory and experiment are due
to the mechanical effects arising at low dry densities and the hydration effect at high dry densities
of the bentonites that have been not considered in the theory. There are also many other factors
responsible for the differences and have been stated by Gens and Alonso (1992) and Sridharan
and Choudhury (2002).

Corrected midplane potential function and distance function relationships

An attempt was made to account for the differences between the theoretical and experimental
swelling pressures of the bentonites. For the experimental swelling pressures, the u values were
back-calculated using Equation (1). Knowing the Kd value for any given dry density, the
experimental u-Kd relationships were established for MX80, Febex, and Montigel. These bentonites
cover a wide range of cation valency and clay properties. The relationships thus obtained were
substituted in Equation (1) for u, to obtain the swelling pressure equations. The swelling pressure
equations are thus for cation valency, v, of 1.14, 1.73 and 1.97. These valencies are the weighted
average valency of the cations present in the bentonites. The equations were then verified for
swelling pressures of another three bentonites namely, Kunigel V1, Kunigel, and Bentonite S-2
having cation valency of 1.46, 1.5 and 1.66, respectively.
Figure 1(b) shows the experimental and swelling pressures obtained by using the new
equations for the six bentonites considered in this study. A much better agreement between the
experimental swelling pressures and the swelling pressures obtained using the new equations can
be clearly seen in Fig. 1(b).
100 100
Experimental swelling pressure (MPa)

Experimental swelling pressure (MPa)

10 10

Bentonite:
MX80
1 MX80 bentonite 1 Febex
Montigel
Febex bentonite
Kunigel V1
Montigel bentonite
Kunigel
Bentonite S-2
0,1 0,1
0,1 1 10 100 0,1 1 10 100
Theoretical swelling pressure (MPa) Swelling pressure (MPa) (from new equations)

Figure 1. Experimental and theoretical swelling pressures of bentonites (a) from Gouy-Chapman DDL
theory,and (b) using new swelling presure equations (based on experimental data and
Gouy-Chapman DDL theory).

4. Conclusions

Experimental swelling pressures of several bentonites were compared with the theoretical swelling
pressures derived from the Gouy-Chapman DDL theory. Three new swelling pressure equations
were proposed that have theoretical background. The proposed equations are applicable to several
bentonites proposed to be used as a barrier material in storing high-level radioactive waste. The
use of the equations is based on weighted average valency of the cations in the bentonites.

18
5. References

Bolt G.H. (1956). Physico-chemical analysis of the compressibility of pure clays. Geotechnique 6, No. 2, 86–
93.
Gens A., Alonso E.E. (1992). A framework for the behaviour of unsaturated expansive clays. Canadian
Geotechnical Journal 29:1013-1032.
Marcial D., Delage P., Cui Y.J. (2002). On the high stress compression of bentonites. Canadian Geotechnical
Journal 39: 812-820.
Sridharan A., Jayadeva M. S. (1982). Double layer theory and compressibility of clays. Geotechnique, 32 (2):
133–144.
Sridharan A., Choudhury D. (2002). Swelling pressure of sodium montmorillonites. Geotechnique, 52 (6),
459–462.

19
20
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

THE TIME DEPENDENT CHANGES OF THE MICROSTRUCTURE OF A COMPACTED

MX80 BENTONITE AT CONSTANT BULK DENSITY

Duilio MARCIAL
Universidad Central de Venezuela, IMME, Apt. 50.361, Caracas 1050-A, Venezuela
Pierre DELAGE, Yu Jun CUI
Ecole Nationale des Ponts et Chaussées, 6-8 Av. B. Pascal, 77455 Marne la Vallée cdx 2, France
Xavier RUIZ
Universidad Politécnica de Catalunya, Gran Capitán s/n, Modulo D2, 08304 Barcelona, España

ABSTRACT. It is suspected that the as-compacted state of heavily compacted clays used for
engineered barriers for nuclear waste disposal is not stable and that some further change may occur in
the material, even at constant water content and density (see Gehling et al. 1995). Obviously, this
observation is of particular interest in the design of engineered barriers and in the prediction of their
behaviour during the life time of the repository. This paper presents an investigation conducted at the
microstructure level on samples of MX80 compacted at various dry densities and water contents, using
mercury intrusion pore size distribution (PSD) measurements and scanning electron microscope (SEM).
To account for time effects, the samples were compacted into specially designed cells in which they
were kept afterwards during various periods of time to allow for ageing at constant volume and water
content. After ageing, the microstructure of the samples was investigated. A significant change in
microstructure with time was observed (Figures 1 and 2), characterised by a decrease in the inter-
aggregate porosity and an increase in the thinner porosity not intruded by mercury (r < 3.7 nm). The
former observation is similar to that observed during hydration with swell prevented and is related to the
filling of inter-aggregate pores by exfoliation. The latter observation is related to the changes that occur
in smectite platelets when suction is reduced, interpreted in the light of a recent detailed investigation
carried out on MX 80 compacted samples using low angle X ray diffraction (Saiyouri et al. 1998). The
changes in the very thin porosity is governed by the progressive placement of inter-layers water
molecules inside the platelets together with the division of platelets that gives rise to an inter-platelets
porosity that develops inside the aggregates.

0.7

0.6
Intruded mercury void ratio, em

0.5

0.4 e = 1.008 ; w = 28.5 %

90 days
30 days
0.3

e = 0.646 ; w = 8.2 % 1 day

0.2
90 days
30 days
0.1

1 day
0
0.001 0.01 0.1 1 10
Porous radius (µm)
Figure 1. Changes in PSD curves with time

21
 A B

C D
Figure2. SEM pictures of the looser sample: e = 1.008 ; w = 28.5% (picture width is 40 mm). A and B
correspond to the initial state; C and D correspond to a 90 days ageing time.

References
Ahmed S., Lovell, C. W. and Diamonds S. (1974). Pore sizes and strength of compacted clay. ASCE J.
Geotechnical. Eng. 100, 407-425.
Calvet R. (1972). Adsorption de l’eau sur les argiles; Etude de l’hydratation de la montmorillonite. Bull. Soc.
Chimique de France 8, 3097-3104.
Cui Y.J, Loiseau C. & Delage P. (2002). Microstructure changes of a confined swelling soil due to suction
controlled hydration. Proceedings of the 3nd International Conference on Unsaturated Soils, UNSAT’2002 (2),
593-598, Recife, Brazil, Balkema.
Delage P. & Graham J. (1995). The mechanical behaviour of unsaturated soils. Proceedings of the 1st
International Conference on Unsaturated soils, Vol. 3, 1223-1256, Paris, Balkema.
Delage P., Audiguier M., Cui Y. J. and Howat M. D., (1996). Microstructure of a compacted silt. Canadian
Geotechnical Journal 33, 150-158.
Gehling W. Y. Y., Alonso E. E. and Gens A. (1995). Stress-path testing of expansive compacted soils.
Proceedings of the first international conference on unsaturated soils, Paris, France, Balkema.
Marcial D., Delage P. & Cui Y. J. (2002). On the high stress compression of bentonites. Canadian Geotechnical
Journal 39, 1-9.
Push R. (1982). Mineral-water interactions and their influence on the physical behavior of highly compacted Na
bentonite. Canadian Geotechnical Journal. 19, 381-387.
Saiyouri N., Hicher P. Y. and Tessier D. (1998). Microstructural analysis of highly compacted clay swelling.
Proceedings of the Second International Conference on Unsaturated Soils 1, 119-124, Academic publishers,
Beijing, China.
Saiyouri N., Hicher P.Y. & Tessier D. (2000). Microstructural approach and transfer water modelling in highly
compacted unsaturated swelling clays », Mechanics of Cohesive and Frictional Materials 5, 41-60.
Tessier D. (1990). Matériaux Argileux, Structure, Propriétés et Applications. Ed. A. Decarreau, Société Française
de Minéralogie et Cristallographie, Paris, France. 1, 387-445.
Wan A. W. L., Gray M. N. and Graham J. (1995). On the relations suction, moisture content, and soil structure in
compacted clays. Proceedings of the First International Conference on Unsaturated Soils. Paris, France,
Balkema.

22
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

DETERMINATION OF STRUCTURAL POROSITY IN RED MUD SUSPENSION

Gert Bartholomeeusen (gert.bartholomeeusen@eng.ox.ac.uk), Gilliane C. Sills

Department of Engineering Science, University of Oxford, UK

ABSTRACT. Structural porosity is defined as the porosity at which effective stresses in a soil
suspension start to develop. In this paper it is shown that the structural porosity is not unique, but
can be determined from the flux function of a material.

1. Introduction

The settlement curve of a dilute suspension is marked by a fast and constant settling rate in the
beginning, which suddenly decreases when the sediment-water interface meets an upward
travelling porosity step. Figure 1 depicts data of a Brazilian Red mud suspension (RM5 after Alves
(1992)) from which a sedimentation and consolidation zone can be identified. In the sedimentation
zone, the settlement is controlled by the local porosity (Kynch, 1952), and the soil particles are fluid
supported with total stress equal to pore water pressure (σv = uw). In the consolidation zone
effective stresses, calculated as the difference between total stress and pore water pressure
(σ'v = σv - uw), control the settlement (Gibson et al., 1981). It can be concluded that the
characteristic line of porosity n equal to 0.92 marks the transition between sedimentation and
consolidation. Therefore this porosity is called the structural porosity as below this value effective
stresses exist. This paper presents sedimentation analysis of suspensions to determine the
upwards travelling porosity step, and the associated structural porosity.

1.00

Surf. settle.
Char. Line, n=0.92
0.75 Data Pts., n=0.92
Height [m]

Overlying
0.50 Water

Sedimentation
zone
0.25

σ = uw Consolidation zone
σ' = σ-uw
0.00
0 20 40 60 80
Time [hours]

Figure 1. Surface settlement curve of Red Mud suspension (hi=0.989 m and ni=0.97)

2. Sedimentation and non-convex flux function

Soil sedimentation is describe by the continuity equation:

∂ n ∂ f (n)
+ =0
∂t ∂t

23
where f(n) is the flux function. Porosity steps occur in soil sedimentation problems with non-convex
flux functions (Bartholomeeusen et al., 2002). Figure 2 shows flux data of Red mud, and and a
fitted flux function. Initial porosities which are higher than the porosity of the inflection point, see
Figure 2, jump to a lower porosity on the flux function during sedimentation. The size and the
speed of the discontinuity or shock wave can determined from the flux function by drawing the
tangent line from the initial flux to the inside of the curve, as illustrated for two initial porosities (ni1
and ni2). The speed of the shock wave is simply the gradient of the tangent line, while the size of
the jump is the difference between the initial porosity (ni) and the porosity at the tangent point. The
porosity at the tangent point is the structural porosity and these two examples show that it is not
unique.

9.0E-04

Red Mud
RM - Flux Func.
Infl. Pt.
Volume flux [m/hour]

6.0E-04

Tangent
points
n T2
3.0E-04
n T1

0.0E+00
0.88 0.92 0.96
n i2 n i1 1
Porosity [-]

Figure 2. Flux function with illustration of tangent lines

3. Numerical predictions

In order to numerically approximate the solution of equation (1), a conservative finite difference
scheme or a finite volume method (FVM) is required to deal appropriately with the propagation of
discontinuities. Figure 3 shows experimentally measured X-ray-porosity profiles of a settling
column experiment on Red mud from Brazil and associated numerical predictions with a FVM
scheme and the non-convex flux function, depicted in Figure 2. Experiment and model prediction
are very close at all times. Consequently, the the speed and the size of the shock wave are
modelled well.

1
Time elapsed in hours:
6
0.75 24
32
Height [m]

0.5

0.25

0
0.8 0.85 0.9 0.95 1
Porosity [-]

Figure 3: Experimental and numerical porosity profiles of a Red mud suspension (hi=0.989 m and ni=0.97)

24
4. Conclusions

It has shown that the porosity jump during soil sedimentation varies in size and propagation speed
depending on the form of the flux function and the initial porosity. The proposed theoretical
implementation is compatible with experimental data which suggest that the structural porosity is
not unique, but resides in a narrow region of porosities. Numerical modelling of the sedimentation
process realistically simulates the propagation of shock waves.

5. References

Alves M.-C. (1992). Compartemento de sedimentaçăo e adensamento de uma lama vermelha. PhD Thesis,
Pontificia Universidade Católica do Rio de Janeiro.
Bartholomeeusen G., De Sterck H., Sills G.C. (to appear). Non-convex flux functions and compound shock
waves in sediment beds. Proceedings of the Tenth International Conference on Hyperbolic Problems,
International series of numerical mathematics.
Gibson R.E., Schiffman R.L., Cargill K.W. (1981). The theory of one-dimensional consolidation of saturated
clays. 2. Finite non-linear consolidation of thick homogeneous layers. Canadian Geotechnical Journal, 18:
280-293.
Kynch G.J. (1952). A theory of sedimentation. Transactions Faraday Society, 48: 166-176.

25
26
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

A CORRELATION BETWEEN CLAY MINERALOGY AND ATTERBERG LIMITS

Robrecht Schmitz (RM.Schmitz@ulg.ac.be), Christian Schroeder, Robert Charlier

Dept. GEOMAC, University of Liège, Belgium.

ABSTRACT. Clay is and was deposited in those regions were most people live. Nowadays
civilisation is associated closely with infrastructure, like buildings, roads and tunnels, therefore a
civil engineer cannot avoid constructing in, on, or with clay. The mechanical properties of clays are
rather complex; they depend on the fluid content and the fluid chemistry. Therefore it is difficult to
predict their behaviour when environmental conditions change. Geological analogues can however
be of help because they have been well studied by clay mineralogists over the years. In this
contribution it is shown how these aspects can be used to help geotechnical engineers for instance
in the framework of storage of radioactive waste1.

1. Correlation between mineralogy and Atterberg properties

When in geotechnical literature reference is made to clay mineralogy and the aspect of sample
preparation for X-ray diffraction analysis (XRD) is discussed, the fact that usually only the fraction
smaller than 2 µm is analysed is defended with the proclamation that Smectites (or Illite-Smectite
mixed layer) are: (i) the most dominant clay mineral, and they are (ii) nearly completely present in
the smaller than 2 µm fraction.
Hypothesis 1: LL is a function of the Smectite content
Therefore we tested the hypothesis that the liquid limit depends only on the Smectite (or Illite-
Smectite mixed layer) content. This relationship is plotted in Figure 1 (the names of the clays, their
origin, clay mineral composition and consistency limits are given in Table 1).

Figure1. The Smectite content alone, does not account for all clay reactivity expressed in terms of LL

It is obvious (Figure 1) that this assumption is a too large generalisation for two reasons: (1)
the Soignies (tertiary natural clay) and (2) Kruibeke (tertiary natural clay from the same formation
as the famous Boom clay) samples, show a large difference in LL although their relative Smectite
content is comparable. When the reference Kaolinite is considered we can see that this clay,
consisting almost completely of Kaolinite, has a fairly large liquid limit, which is not taken into
account when the focus is on Smectite only. Thus not only Smectite is a reactive clay mineral, the
other clay minerals need to be considered as well.

1
Abbreviations and symbols are given in part 5

27
 Figure 2. The amount of clay minerals plotted versus the liquid limit, LL

Hypothesis 2: LL is a function of the amount of clay minerals present in the sample

If only the amount of clay minerals is considered irrespective of possible differences between
these minerals we obtain a situation that exists when the activity of the clays is determined
according to Skempton (1953). This is shown (considering only the liquid limit and not the plasticity
index) in Figure 2. In this case the same liquid limit is expected for the reference Kaolinite and the
reference Smectite, which obviously, is not true.
These examples show that it is not sufficient to consider only the Smectite content or the total
amount of clay minerals present in the sample. A formulation needs to include at least, information
on the: (a) clay mineralogy qualitatively, (b) clay mineralogy quantitatively
Before it is explained how these two properties were combined in one formulation, we are
going to have a look at the importance of taking interlayer reactivity in clay minerals into account.

Figure 3. The equivalent basal spacing versus the liquid limit, LL

2. Equivalent basal spacing (EBS)

What is so special about interlayer reactivity of clay minerals? In these interlayers clay mineral
alterations take place, which can change the geotechnical properties to a large extend. In contrast
to cation exchange, changes within the interlayer space are not always reversible. Interlayer
reactivity depends directly on the clay composition:
In Kaolinites, the intercrystalline reactivity is limited to intercalation of neutral organic
molecules. In three layer clay minerals (like Smectites) the intercrystalline reactivity includes e.g.:
- The exchange of interlayer cation by organic or inorganic cations

28
 - The absorption of organic substances in-between the layers (Lagaly & Köster 1993)
Even important processes like Illitisation and Smectisation, are strongly related to the
presence or absence of K+ (or other “small” ions like NH4+) in the interlayer space. Acknowledging
the importance of interlayer space, it is not a surprise that a technique like X-ray diffraction, which
gives a direct measure of this property (measurement of the basal spacing), has become so
popular.
Hypothesis 3: LL is a function of the equivalent basal spacing
To make the link between what we see with X-ray diffraction and the Atterberg tests we need
to take a look at the interlayer distance as well. To relate the interlayer space of a polymineral clay
to the liquid limit, we introduce the concept of equivalent basal spacing:

EBS = TCF TR P
⋅
∑ CF
i =1
i
FOA
⋅ BS (i 001)FOA (1)

The relative amount of a clay mineral is multiplied with the basal spacing (Å) of this mineral
known from literature (e.g. Mitchel 1995). This step is repeated for all measured clay fractions, and
then these values are summed. This sum is then corrected for the total amount of clay minerals in
the sample.
An example: If the sample consists only of Smectite: Then the TCFTRP = 1, the CFSmectiteFOA=1
and the BSSmectite(001)FOA = 15Å, therefore the EBS will be 15Å as well. If the sample consists only of
sand: Then the EBS=0 Å. In Figure 3 the EBS is plotted versus the liquid limit of the same samples
(Casagrande cup). If a linear correlation is assumed then: EBS = (0.0236 ⋅ LL + 5.4262 ) . With a
coefficient of correlation equal to 0.94.

3. Using mineralogy to predict geotechnical properties example I

Imagine that nuclear waste is isolated using a Bentonite plug and that the temperature rises locally
up to 500°C. What will the undrained shear strength be? What will the coefficient of correlation be?
It is difficult to tell but a clay mineralogist knows what happens. A standard test during XRD
analysis is the heating of the clay sample to 500°C during 4h. This will result in a collapse of
predominantly Smectite minerals form 14-15 Å to 10 Å whereas the other clay minerals remain
stable. Using the following variables we can predict the LL of the reference Smectite (original value
liquid limit = 385%) :CFSmectiteFOA= 1, BSSmectite(001)FOA = 10 Å, TCFTRP = 1 This results in a LL =
194%. Using the following relationship: C C = 0.009 ⋅ (LL − 10) a decrease from 3.4 to 1.7 is expected
although the residual friction angle remains fairly equal (<10°) (Terzaghi et al. 1996). To check if the
predicted Atterberg results obtained were reliable, several hundred gram of the reference Smectite
were heated to 500°C during 4 hours, the Atterberg limit was determined: LL = 191% identical to
the predicted value!

4. Conclusion

With the concept of equivalent basal spacing a new tool has been created which provides a direct
link between clay mineralogy and geotechnical properties. When, in future, the mineralogical
composition of a clay is available a quick assessment of its engineering properties can be made. In
addition it possible to quantify the engineering significance of any known clay mineral alteration
process.

5. Acknowledgements

The research work described in this paper was supported by a grant from the Belgian National
Fund for Scientific research (FNRS) based on the 'Action de Recherche Concertée' of the 'Communauté
Française de la Belgique', convention n° 99/04-243, entitled "Confinement de centres d'enfouissement
technique à l'aide de barrières argileuses". The support of the FNRS and that of the Communauté Française
de la Belgique were gratefully acknowledged. The reference Smectite, product name: Colclay A-90, was
donated by Ankerpoort N.V. Maastricht, The Netherlands. Additionally we would like to express our sincere

29
gratitude for the execution and analysis of the clay mineralogy by the Liege Clay Lab, its professor J. Thorez
and its assistant D. Dosquet.
The authors want to acknowledge the EU project Degradation and Instabilities in
Geometerials with Application to Hazard Mitigation (DIGA) in the framework of the Human Potential
Program, Research Training Networks.

6. References

Lagaly, g., Köster, h.m. (1993). Tone und tonminerale. Tonminerale und tone, k. Jasmund and g. Lagaly
Eds., steinkopff verlag darmstadt.
Manwal (2001). Manuel relatif aux matiéres naturelles pour barrières argileuses ouvragées pour c.e.t.
(centres d'enfouissement technique) et réhabilitation de dépotoirs en région wallonne. Version 1. editors:
Marcoen J.M., Tessier D., Thorez J., Monjoie A., Schroeder Ch. (Eds.), Published by: Ministère de la
Région Wallonne, Direction Générale des Ressources Naturelles et de l'Environnement, Office Wallon des
déchets. 40 pp.
Mitchel J.K. (1993). Fundamentals of soil behaviour. Second edition, John Wiley & Sons inc.
Skempton A.W. (1953). The colloidal “activity” of clays”. Proceedings, 3rd International Conference of Soil
mechanics and Foundation Engineering, vol.1: 57-61.
Terzaghi K., Peck R.B., Mesri G. (1996). Soil mechanics in engineering practice. Third edition, John Wiley &
Sons, inc.
Thorez J., Dosquet D., Illing P., Schroeder, Ch. (2001). Behaviour of two tertiary clayey materials leached
with a complex domestic waste fluid under high pressure: triaxial permeability, and qualitative and semi-
quantitative clay mineral changes. Proc. 6th KIWIR International Workshop on Key Issues in waste
isolation research, Ecole Nationale des Ponts et Chaussèes.
Van Paassen l. (2002). The influence of pore fluid salinity on the consolidation behaviour and undrained
shear strength development of clayey soils. Memoirs of the centre of engineering geology in the
Netherlands, no. 216, issue 1386-5072, TU-Delft, Delft.

Appendix
(%)

(%)
(%)

(%)
(%)
(%)

(%)

EBS (Å)
FOA

FOA
FOA
FOA
LL (%)

FOA
FOA

TRP
CF(10-14m)

CFKaolinite
CF(10-14c)

CFChlorite
CFSmAl
CFIllite

TCF

Appendix
Kaolinite 62 0 100 100 7,2
Luxemburg clay 35 67 2,4 14 9,9 6,5 71 8,1
Kruibeke average 63 28 18 17 5 13 19 65 7,7
Tournai average 116 16 7,5 68 9,0 61 8,5
Soignies average 35 33 15 16 6,4 20 10 52 5,8
Smectite 385 100 100 15

Table 1. The clay mineralogy was determined (except Kaolinite see van Paassen 2002) using the Liege Clay
Lab sample preparation method (see the complete description in: ManWal 2001) avoiding any pre-treatment
of the samples and taking the total clay fraction into account (not only the fraction smaller than 2µm). Tournai,
Soignies and Kruibeke clay are natural tertiary clays. Colclay (reference Smectite) and Speswhite (reference
Kaolinite) are industrial clays used as reference material.

Abbreviations and symbols:

BSi(001): The basal spacing of an oriented clay sample that can be found in literature (e.g. Mitchel 1993) [unit length].
CFiFOA: Fraction of a clay mineral species (with respect to the total amount of clay minerals) determined during the XRD
analysis of a forced oriented aggregate [fraction].
EBS: Equivalent basal spacing, determined using formula (1) [unit length].
FOA: Forced oriented aggregate, an oriented sample used for XRD analysis taking the whole clay fraction into account
(not only the fraction smaller than 2µm)
LL: Liquid limit (% fluid content).
TRP: Total random powder, the non oriented sample used for XRD analysis
TCFTRP: Total amount of clay minerals determined during XRD analysis of a not oriented total random powder sample.
XRD: X-ray diffraction.
(10-14m): Illite-Smectite mixed layer.
(10-14c) Illite-Chlorite mixed layer.
SmAl Al-hydroxilised Smectite.

30
Constitutive modelling in geomaterials
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

ON CASAGRANDE & CARRILLO INDUCED & INHERENT ANISOTROPY CONCEPT

Marcos Arroyo (marroyoa@iberinsa.es)

Iberinsa, Madrid, Spain (formerly at University of Bristol, UK)

ABSTRACT. There is general agreement amongst the soil mechanics community about the
anisotropic nature of most aspects of soil behaviour. There is less agreement about how to model
and formulate this feature. Some clarity is to be gained in this issue if, as pioneered by Boehler,
algebraic methods are systematically employed to check and develop the relevant formulations. An
example is given here using a classical paper by Casagrande & Carrillo.

1. Introduction

A pervading feature in soil literature dealing with anisotropy is the distinction between induced and
inherent anisotropy. The idea could be traced back to Casagrande & Carrillo who proposed it in
1944. It is worth to quote them exactly: “….If the anisotropic distribution of strength, exhibited by the
material at failure, is due exclusively to the strain associated with the applied stresses, the material
will be said to possess induced anisotropy. If, in the other hand, the non-isotropic behaviour
observed in a test is a physical characteristic inherent in the material, and entirely independent of
the applied strains, the material will be said to possess inherent anisotropy.”
The definition looks deceptively simple. In what follows it would be shown that their proponents
failed to give it the intended meaning. This purpose is best served when some algebra is addedd to
their reasoning. Casagrande & Carrillo dealt with strength anisotropy. Their explicit aim was to
generalise the Mohr-Coulomb criteria for purely cohesive and purely frictional materials. Here we shall
take a closer look to their proposal for an anisotropic purely cohesive material, within a plane stress
context, which is simpler and good enough for our purpose. A purely cohesive Mohr-Coulomb criterion
it is usually known by the name of Tresca. It is sometimes employed to model the undrained strenght
of clays.
Anisotropy is a directional dependence of some particular test result. Therefore, an
anisotropic undrained strength criteria should predict different results when the same undrained
strength measurement is taken in different directions. This kind of measurement will be obtained,
for instance, if a vane blade is pushed into the soil in different directions or if UU tests are
performed onto samples trimmed in different directions. Note that as Wood (1990) shows,
anisotropy is not necessary to justify or explain how different undrained strength values are
obtained in different tests.

2. Anisotropic or not?

The usual isotropic Tresca criterion could be written as:

max (λ ) n(λ ) ⋅ T ⋅ t (λ ) ≤ c (1)

Where T is the stress tensor, n the generic unit normal to a plane (identified by λ) and t a generic unit
vector orthogonal to n. What is written means that the maximum tangential stress in any plane is
limited by a constant value, c. A straightforward development shows that this maximum corresponds to
a plane at 45° with the principal axis of T.
Casagrande & Carrillo arguments are expressed in graphical form, but they could
nevertheless be interpreted as follows. A “cohesion tensor”, C, is proposed1, such that cohesion in
any plane, cλ, will be obtained as:

1
Although the term tensor is never used, an explicit parallel is traced with the small deformation tensor in elasticity theory.

33
 c λ = n(λ ) ⋅ C ⋅ n(λ ) (2)

When this equation is expressed in the principal axes of C the strength distribution function
employed by Casagrande & Carrillo is recovered2

c λ = c 2 + (c 1 − c 2 ) sin 2 (λ ) (3)

and now λ denotes the offset angle of a generic vector from the principal axes of C. The generalised
Tresca criterion proposed compares, at each plane, its shear strength or cohesion, cλ, with the
tangential stress acting on that plane. This could be written as:

max (λ ) n(λ ) ⋅ T ⋅ t (λ ) − n(λ ) ⋅ C ⋅ n(λ ) ≤ 0 (4)

It is at this point where the distinction between inherent and induced anisotropy is introduced.
According to Casagrande & Carrillo in a material with induced anisotropy “…the principal strengths
develop in the planes of principal stress”. We can rephrase this in algebraic terms saying that for
induced anisotropy C and T share principal axes –i.e. they are coaxial- whereas for inherent
anisotropy C and T do not share principal axes -i.e. they’re non-coaxial.
After maximisation of (4) some results are obtained in the paper for the coaxial or “induced”
case: λc, critical value of λ, angle between the failure plane and C principal axes; cλ cohesion value
in that plane; and rλ, radius of the corresponding Mohr circle.

c2
tan 2 α c =
c1
2c 1c 2
cα = (5)
c1 + c 2
r α = c 1c 2

But now a problem appears. Note that the principal values of C will be obtained by measuring
rα and αc in any test reaching failure. The initial orientation of the sample with respect to any fixed
reference is immaterial. If the theory is employed to interpret the undrained strength of a clay
deposit it would predict the same strength for all sample orientations. The effect of the so called
“induced anisotropy” is to modify the failure angle plane and the value of the deviatoric failure
stress, with respect to the case where c1=c2 but, perhaps surprisingly, the resulting failure criteria is
isotropic !

3. Conclusion

Coaxiality is the critical step where anisotropy got lost. This aspect is also relevant for more
complicated modelling endeavours like those related to stiffness anisotropy, where as Arroyo
(2001) shows it can shed a new light onto this traditional dichotomy between induced and inherent
anisotropies.

4. References

Arroyo M. (2001). Pulse tests in soil samples. PhD thesis, Dept. of Civil Engineering, University of Bristol.
Boehler J.P. (ed.) (1987). Applications of tensor functions in solid mechanics. CISM Series 292 Springer-
Verlag.
Casagrande A., Carrillo N. (1944). Shear failure of anisotropic materials. Proc. Boston Soc. Civ. Engrs. 31,
74-87.
Wood D.M. (1990). Soil behaviour and critical state soil mechanics. CUP.

2
There is a small change in the simbology: they use α instead of λ

34
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

QUASI-STATIC SHEAR DEFORMATION CHARACTERISTICS OF GRANULAR

SYSTEMS: INSIGHTS FROM DEM SIMULATIONS

S. Joseph Antony (s.j.antony@leeds.ac.uk)

School of Process, Environmental and Materials Engineering, University of Leeds, U.K.

ABSTRACT. In this presentation, the evolution of contact structure in a three-dimensional granular

assembly subjected to quasi-static shearing is presented. They provide insights on the influence of
force net works that develop within the granular assembly on the macroscopic shear strength.
The macroscopic shear strength of the granular system seems to depend on the ability of the
material to form strongly anisotropic fabric structures. These strongly anisotropic contact
structures, carrying greater than average normal contact force, are aligned along the major
principal stress direction.

1. Introduction

Granular materials are composed of a large number of solid particles that interact with each other
at contact points when loaded at the boundary. In granular media, the transmission of forces from
one boundary to another can occur only via the interparticle contacts. Hence the distribution of
contacts will determine the distribution of forces within the system of particles. These forces will not
be necessarily distributed uniformly, even for an isotopic and homogeneous assembly of particles
subjected to homogeneous applied load. This important qualitative observation of stress
distribution can be seen in photoelastic studies of two-dimensional disks reported by several
investigators [1-4].
The inhomogeneous distribution of optical fringe patterns in these studies, even for a
homogeneous applied load, reveals that the load is transmitted by relatively rigid, heavily stressed
chains of particles which form a relatively sparse network of greater than average normal contact
force. The groups of particles separating the strong force chains are only lightly loaded.
Although a consensus on the nature of the distribution of contact forces in granular media and
a “perfect” physical model to capture the force distribution is far from achieved, recent numerical
simulations on a two-dimensional [5-8] and three-dimensional system of particles [8-12] under
quasi-static shearing have revealed some exciting features. It has been shown that the normal
force contribution is the major contribution to the total stress tensor and the spatial distribution of
normal contact forces can be divided into two sub-networks, viz., (i) the contacts carrying less than
the average force (forming ‘weak force chains’) and (ii) the contacts carrying greater than the
average force (forming ‘strong force chains’). The contacts that slide are predominantly in the weak
force chains and they contribute only to the mean stress while their contribution to the deviator
stress (shear strength) is negligible. The contribution of the strong force chains to the deviator
stress is the dominant contribution. Hence, the weak force chains play a role similar to a fluid
surrounding the solid backbone composed of the strong force chains. It is important to verify these
findings through 3D experimental investigations, though the method of measurement will remain as
an open challenge for quite some time to come. In this presentation, based on discrete element
method simulations, we look into the effect of shape and size of the individual grains on the micro-
macroscopic shear deformation characteristics of granular assemblies subjected to quasi-static
shearing.

2. References

Drescher A., de Jong J. (1972). Jl. Mech. Phys. Solids, 20: 337-351.
Oda M., Konish J. (1974). Soils and Foundations, 14, 25-38
Liu C., Nagel S.R., Schecter D.A., Coppersmith S.N., Muajumdar S., Narayan O., Witten T.A. (1995).
Science, 269: 513-515.
Howell D.W., Behringer R.P., Veje C.T. (1999). Chaos, 9(3): 559-572.

35
Radjai F., Wolf D.E., Roux S., Jean M., Moreau J.J. (1997). Powders and Grains 97, R.P Behringer and J.T.
Jenkins Eds. (Balkema, Rotterdam): 211-214.
Radjai F., Jean M., Moreau J.J., Roux S. (1996). Phys. Rev. Letts., 77(2): 274-277.
Radjai F., Wolf D.E., Jean M., Moreau J.J. (1998). Phys. Rev. Letts., 80(1): 61-64.
Radjai F., Wolf D.E. (1998). Granular Matter, 1: 3-8.
Radjai F., Roux S. Moreau J.J. (1999). Chaos, 9(3): 544-550.
Antony S.J. (2001). Physical Review E, American Physical Society, 63(1), No. 011302.
Antony S.J., Ghadiri M. (2001). Journal of Applied Mechanics, American Society of Mechanical Engineers,
68(5): 772-775.
Thornton C., Antony S.J. (1998). Phil. Trans. Roy. Soc. Lond. A, 356: 2763-2782.

36
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

NUMERICAL MODELLING OF DAMAGE AND PERMEABILITY IN CLAYSTONE:

APPLICATION TO UNDERGROUND RADIOACTIVE WASTE STORAGE

Keyvan Maleki (maleki@g3s.polytechnique.fr)

G3S-LCPC, Palaiseau, France
Ahmad Pouya, Patrick Dangla
Laboratoire Central des Ponts et Chaussées, Paris, France.
Pierre Berest
G3S - Ecole Polytechnique, Palaiseau, France.

ABSTRACT. This paper presents a numerical modelling of damage and permeability in claystone
with microcrack growth. The damage is modelled as a crack network and each crack is assumed to
be a circular disc in space. All co-ordinates of the disc, including radius, thickness and orientation
are obtained according to the type of mechanical loading (compression or tension) by using the
microcrack density distribution function. Porosity of the initially undamaged media is assumed to be
a regular connected crack network. The superposition of discs on this initial porosity induces an
increase of permeability, particularly when the percolation threshold is reached. The geometrical
parameters are compared with in-situ observation and laboratory results. The damage tensor is
calculated based on the fabric-tensor of each crack density. Finally, the relationship between the
calculated values of damage and permeability tensor is employed to establish a macroscopic
model, used in a structural calculation code.

1. Introduction

The excavation of galleries and wells in a radioactive waste storage site can generate damage in
the rock. This damage can change the geotechnical properties of rock, particularly the permeability.
The relationship between the permeability and rock damage in this excavation disturbed zone
(EDZ) is important from the point of view safety analysis around the storage structure.
Study of this phenomenon is the principal objective of a collaboration between the Ecole
Polytechnique (Laboratory G.3S), Agence Nationale pour la gestion des Déchets Radioactifs
(ANDRA), Electricité de France (EDF R&D) and Laboratoire Central des Ponts et Chaussées
(LCPC). The storage zone, considered in this work, is located in a deep clay foundation.
Nevertheless the proposed approach should also apply to granite.

2. Crack Superposition in porous media

In the analysis of damage porous media, we need to know how we can create the crack. Micro-
Cracks are modeled as discs in space. It is suppose that cracks are uniformly distributed. It means
that the center of coordinate for each crack is based on a uniform probability distribution law.
However, for thickness and radius, a logarithmic distribution law is employed:

1 -x
F( x ) = exp ( ) (1)
λ λ
where F is the distribution function and λ is the mean value of x. In fact, the possibility of
having a large value of x (thickness or radius) is lower than the possibility of having a small value of
x (micro crack). In order to obtain the direction of the unit vector in disc, a trigonometric law can be
employed, thus:

E(θ) = A Cos² (θ) (in Tension) ; E(θ) = A Sin² (θ) (in Compression) (2)

Where θ is the angle between unit normal vector of disc and the vertical axis and A is a constant.

37
 It indicates that in the tensile case, most of cracks appear in the horizontal direction (θ ≅ 90°)
and in compression case, most of them are in the vertical direction (θ ≅ 0°).

n
m

Figure 1. Representation of the angle θ

(a) (b)
Figure 2. (a)Tension and (b) Compression trigonometric distribution of the angle θ

3. Damage-Permeability tensor analysis

The damage tensor according to the Fabric-tensor idea can be calculated by:

r
dij = ∫ s2 E(n) ni n j dS2 (2)

Where E(ñ) is the general crack distribution law and ni - nj are two space vectors.

7E-14
Tractionn
6E-14
5E-14
Trace K

4E-14
3E-14
Compression
2E-14
1E-14
1E-20
0 0,2 0,4 0,6 0,8 1
Trace D
Figure 3. Permeability and damage evolution with crack density

38
 Figure 3. Permeability and damage evolution with crack density

The permeability is calculated by using the Poiseuille equation for plane type crack. The initial
porosity is also considered as a regular crack network, in which the thickness and the distance
between the cracks provide the initial permeability.
At last, when the crack density changes (like number of crack in unit of volume or rise the
radius of cracks) we can obtain a damage-permeability relationship. Furthermore the percolation
threshold can be obviously observed in this evolution.

4. Conclusion

In this paper, a simple relationship has been established between permeability and the associated
damage stage based on microcrack theory in a Claystone EDZ. This relation also shows that there
is a percolation threshold for the density of cracks. Finally the numerical model is calibrated with the
real observations and can be useful for structural calculation.

5. References

Lubarda V.A. Krajcinovic D. (1993).Damage tensors and the crack density distribution. Int J. Solids
Structures, Vol.30, page 2859-2877,.
Oda M. (1984). Similarity rule of crack geometry in statistically homogenous rock masses. Mechanics of
Materials, Vol 3, Page 119-129,
ThikhomiroV D., Neikamp R. et Stein E. (2001). On three-dimensional microcrack density distribution.
Math.Mech. Vol 81, page 3-16,

39
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

CONTRIBUTION TO THE INVERSE SUBSIDENCE DIFFUSION-CONVECTION

PROBLEM IN GEOSTRUCTURES

E. Vairaktaris (mvairak@mail.ntua.gr), I. Vardoulakis

N.T. University of Athens, Greece
E. Papamichos
SINTEF Petroleum Research, Norway
V. Dougalis
University of Athens, Greece

ABSTRACT. Compaction of a collapsible substratum due to effective stress increase may give rise
to the formation of the well-known trap-door mechanism (Terzaghi 1936, Vardoulakis et al. 1981).
According to early works, large-scale subsidence over a yielding underground geostructure is seen
as a stochastic (Markov) process (Litwinszyn 1974, Dimova 1990). This process leads to Einstein-
Kolmogorov integral equation. Under certain physical conditions and transformations of the
coordinate system the E-K integral equation satisfies some partial differential equation of parabolic
type, where the vertical coordinate replaces time. Initial condition of the direct problem is the
underground subsidence and solution considers surface subsidence. The solution depends on a
diffusivity coefficient, which determines the formation of the subsidence trough inside the body as
well as in the surface. This is considered as the Subsidence-Diffusion problem. In this work the
inverse S-D problem using two kinds of regularization is presented, considering results of the direct
S-D problem (Lattès and Lions, 1969). In particular Lion’s uxxxx method is compared to the presently
proposed uzzz method. Stability, in the sense of the von Neumann condition is ensured where the
amplification factor depends on the regularization parameter ε. A first approach to convergence is
done in the sense of the norm of the amplification factor. Another convergence is studied in terms
of the truncation error (Richtmyer and Morton, 1967).

1. Introduction

Compaction of a collapsible substratum due to oil-production (effective stress increase) and/or

water-injection (capillary action) may give rise to the formation of the well-known trap-door
mechanism (Terzaghi 1936, Vardoulakis et al. 1981). According to early works, large-scale
subsidence over a yielding underground geostructure is seen as a stochastic (Markov) process
(Litwinszyn 1974, Dimova 1990). This process leads to Einstein-Kolmogorov integral equation.
Under certain physical conditions and transformations of the coordinate system the E-K integral
equation satisfies some partial differential equation of parabolic type, where the vertical coordinate
replaces time. This is considered as the Subsidence-Diffusion problem. Below we show a typical
computational example, concerning the numerical solution of the i.b.v. problem, inside a prescribed
trough (H, 2B, and β) (Figure 1).

Direct SDC

0,74
0,59
0,44
z/H

0,29
0,15
0,00
-0,15
0 0,2 0,4
x/B*

41
 Figure1. Results of the direct problem

2. Inverse SDC Problem

Oil-production or water injection in situ, results in surface subsidence that can be large enough to
cause severe damages in the surface constructions. The difficulty in large-scale problems lies in
the fact that for given surface subsidence the corresponding base displacement is not known. The
problem of computing the base displacement using as "initial" conditions the surface subsidence
corresponds to the solution of inverse in "time" (depth) SDC problem.
Inverse problems are in general mathematically ill-posed, which means that existence,
uniqueness and stability of the solution cannot be ensured. Several regularization methods have
been developed for this kind of problems. Due to the dual nature (diffusion-convection) of the
considered problem we introduce here mainly two methods of regularization (uxxxx, uzzz) of the
Inverse Subsidence Diffussion-Convection problem (ISDC). Below we show in Figure 2,3 typical
numerical examples of the numerical solution using the above mentioned regularization methods.

Method uxxxx, ε=1.*10^-2

0.18

0.15

0.11
z/H

0.07

0.04

0.00

-0.04
0 0.1 0.2 0.3 0.4 0.5
x/B*

Figure 2. Comparison of direct and inverse subsidence solution using uxxxx regularization

Method uzzz , ε=3.1

0,74

0,59

0,44
z/H

0,29

0,15

0,00

-0,15
0 0,1 0,2 0,3 0,4 0,5
x/B

Figure 3. Comparison of direct and inverse subsidence solution using uzzz regularization

42
3. Stability of the numerical algorithm and truncation error

The von Neumann condition claims that the stability of the numerical solution, can be insured, if,
under certain conditions which depend on the numerical parameters of the problem, holds
(Richtmyer and Morton, 1967). It is applied to the numerical algorithms for both regularization
methods. Stability is ensured due to right choices of ε and "time" b of the problem that affects the
parameter Ln. Convergence in the terms of the Truncation error, is satisfactory except of the
boundary x=1, where both regularization methods have significant differences concerning the
solution of the direct problem.

4. Acknowledgements

The authors want to acknowledge the EU project Degradation and Instabilities in Geometerials with
Application to Hazard Mitigation (DIGA) in the framework of the Human Potential Program,
Research Training Networks.

5. References

Terzaghi K.V. (1936). Stress distribution in dry and saturated sand above a yielding trap door. Proc. Int. Conf.
Soil Mech., Cambridge Mass., I: 307-311.
Vardoulakis I., Graf B. and Gudehus G. (1981). Trap-door problem with dry sand: A statical approach based
upon model test kinematics. Int. J. for Num and An. Methods in Geomech., 5: 57-78.
Papamichos E., Vardoulakis I., Heil L.K., (2000). Overburden Modelling Above a Compacting Reservoir Using
a Trap Door Apparatus. Phys. Chem. Earth (A), 26
Dimova V.L. (1990). Some Direct and Inverse Problems in Applied Geomechanics. University of Mining &
Geology, Sofia.
Litwinszyn J. (1974). Stochastic Methods in the Mechanics of Granular Bodies. Springer-Verlag, Wien.
Tikhonov A.N., Samarskii A.A. (1963). Equations of Mathematical Physics. Dover.
Vardoulakis I., Vairaktaris E. (2002). Modelling Subsidence Diffusion-Convection in Geostructures. Int. J. for
Num. and An. Methods in Geomech., (to appear), J. Wiley and sons.
John F. (1982). Partial Differential Equations. Springer-Verlag
Lattés R. and Lions J.L. (1969). The method of quasi-reversibility. American Elsevier Pub. Co., New York.
Richtmyer R.D., Morton K.W. (1967). Difference methods for initial-value problems. J. Wiley and sons.

43
Experiments on the mechanical behaviour of geomaterials
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

EFFECT OF PRINCIPAL STRESS ROTATION ON THE BEHAVIOUR OF NATURAL

SOILS

Khaldoun Nasreddine (nasredin@lcpc.fr)

LCPC, Paris, France.

ABSTRACT. In this paper, a methodology for the determination of soil behaviour parameters based
on tests performed by means of a hollow cylinder apparatus is presented. Several possible types of
constitutive models taking into consideration the principal stress rotation are checked by analysing
the experimental results. This paper also presents the consequences that this variation can have
on the estimation of the safety of the structures within the practice of the engineer. We show that
2D and 3D numerical modelling confirm the lack of precision due to not taking into consideration
the intermediate principal stress in the expression of the plasticity criteria.

1. Introduction

In many geotechnical problems, soil loading is multiaxial and may also be accompanied by rotation
of principal stress directions. In most models of soil behavior, principal stress rotation effects are
generally ignored. Thus, studies concern the influence of the intermediate principal stress on the
yielding criteria and not the material or stress anisotropy. Therefore, there is a need for laboratory
testing techniques wich can follow stress paths similar to those wich soils undergo in nature. The
classical tests such as the direct shear and standard triaxial compression are popular because of
their simplicity and the important need for strength data for limit equilibrium analysis; however,
these tests do not provide data adequate for all deformation behavior analyses. Since the early 30’s
of the last century, the hollow cylinder triaxial apparatus (HCTA) has been designed, built and
developed to provide data from tests with firstly manual and more recently automatic stress path
control. A complete history of test techniques and devices has been published elsewhere
(Reiffsteck and Nasreddine, 2002). The HCTA can also serve to explore material behavior under
various radial stress gradients and it can be employed for a variety of standard tests.

2. The Laboratoire Central des Ponts et Chaussées hollow cylinder triaxial apparatus

The hollow cylinder test specimen is 10 cm external diameter, 7 cm internal diameter and 15 cm
high. These dimensions were selected after giving appropriate considerations to keeping stress
inhomogeneities within acceptable levels. The apparatus contains four step-motors that permit the
application of cell pressure, pore pressure, vertical force and torque (Figure 1).

Ucp 9
Mt 4

LabVIEW LabWindows M

CVI A
Pi
M
1
A 10
5 et 6
5

M
Pe 3
A
2
A B M 7
5
A
M
générateur de pression
A
M

A
Ucp F
M
5

écrans déportés A 8
M

5
A
M
volumètre
A

Figure 1. HCTA system architecture

47
 There are 14 transducers such as cell pressure, pore pressure, displacement and rotation
transducers. A cupboard contains the different conditioning and command racks. Two computers
using the software LABWINDOWS CVI of National Instruments drive the motors to follow the
imposed stress path.

3. Testing program and results

The imposed stress paths are similar to the paths that often occur in the field involving
combinations of vertical normal and horizontal shearing stresses. These tests are used to study
both the characteristics and the behavior of the material. In particular, the effect of the reorientation
of principal stresses on the soil friction angle is studied to develop a constitutive model that takes
into account the stress rotation. Several series of drained and undrained torsion shear tests have
been carried on natural clay using the HCTA. Figure 2 shows a combined compression-torsion
drained test

120
q kPa (deviatoric stress)

100 0,6

torsion angle (rd)

80
0,4
60
40
0,2
20
0 0
0 25 50 75 0 30 60 90 120
P kPa (mean stress) q kPa (deviatoric stress)

(a) (b) (c)

Figure 2. (a) deformed specimen, (b) followed stress path, (c) deviatoric stress Vs . angle of torsion

(c)

Figure 3. (a) 3D representation, (b) 2D, axisymmetric and 3D modelisations, (c) modified yield surface

4. Application

To show the importance of taking into account the rotation of principal stresses in the classical
plasticity criterias, we study a real circular foundation in the west of Paris. The 3D and 2D numerical
analyses have been carried out using the CESAR-LCPC finite element program.

48
From the bibliography and the results of our tests we conclude a relation between the parameter M,
which is function of the angle of friction (M = 6 sinϕ/(3-sinϕ)), and the principal stress rotation.
Using this relation, we introduce the stress rotation angle in the modified Cam-Clay plasticity
q2
criteria: p.( 2 2 + 1) = p 0 developed by (Roscoe et al., 1958).
M .p
We study some particular points under the foundation where remarkable stress rotations may take
place. Then, we compare their yielding (failure) by two means: CESAR-LCPC which uses a yield
surface that doesn’t take the stress rotation into consideration and the modified 3D Cam-Clay
criteria that considers the effect of the rotation of stress. A difference in soil behaviour is concluded.
This study has been reproduced on a retaining wall and an embankment.
The comparison of the responses of classical soil behaviour laws and the proposed model
able to take into account the rotation of principal stress confirms the consequences of this stress
rotation on the estimation of the safety of the structures.

5. References

Reiffsteck Ph., Nasreddine K. (2002). Cylindre creux et détermination de paramètres de lois de

comportement des sols. Int. PARAM 2002: .
Roscoe K.H., Schofield A.N., Wroth C.P. (1958). On the yielding of soils. Géotechnique, 8 (1): 22-53.

49
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

WEATHERING EFFECTS ON THE MECHANICAL BEHAVIOUR OF SOFT ROCKS: AN

EXPERIMENTAL STUDY

Riccardo Castellanza (rcaste@stru.polimi.it), Roberto Nova

Milan University of Technology (Politecnico), Italy.

ABSTRACT. Soft rocks are subjected to progressive degradation of their mechanical

characteristics due to weathering. This phenomenon may have an engineering relevance since it
induces settlements of foundation, progressive failure of slopes, pressure increase on tunnel liners.
For studying weathering effects at laboratory time, oedometric tests have been conducted on
specimens of calcarenite and artificially cemented silica sand. Weathering was simulated by means
of percolation of an acid solution. Under constant loads, the recorded progression of settlements
with time ends with an horizontal asymptote when only bonds are destroyed (cemented sand),
while it results steadily increasing when also the grains are degraded (calcarenite).
For determining the stress state variation induced by weathering, a special oedometer was
designed. Allowing a very small lateral deformation of the ring, its circumferential stretching was
measured and correlated with the lateral pressure exerted by the specimen. In all cases
considered, the horizontal stress increases remarkably during weathering at constant vertical load

1. Experimental set-up: The Weathering Test Device.

In order to study the effects of weathering, it was first necessary to design a special type of
apparatus called Weathering Test Device (WTD) (Castellanza, 2002) (Fig. 1). It is a variation on the
theme of the so-called "Soft Oedometer" (Kolymbas and Bauer, 1993), in which an acid solution is
forced to seep through by a set of peristaltic pumps. The thin ring of the oedometer allows very
small lateral strains to occur so that the horizontal stresses can be derived from the measurement
of the circumferential strains. The thickness of the ring was chosen in such a way that the
circumferential strains generated by the horizontal pressure exerted by the specimen on the ring
are measurable by strain gauges, but very small, so that quasi-oedometric conditions are ensured.

1) LOADING PHASE
σv

Specimen C o ns t ant
v e r ti ca l
load

RIGID PERMEABLE
S t r ai n
2) W EATHERING PHASE g a u g es
S p e c im e n

Acid
flo w

A c id F lo w
a) b) c)
Figure 1. (a) Weathering Test phases (b) Schematic view of the WTD; (c) pictures of the ring and top cap.

To keep a constant flow of the acid solution, the hydraulic circuit is equipped with three
peristaltic pumps. The flow is directed from bottom to top, in order to allow an easy expulsion of the
carbon dioxide produced by the chemical weathering reactions.
The weathering test consists of two phases. In the first one the vertical load is increased as in
any oedometric test. During this phase, the specimen is dry. In the second part of the test, an acid

51
solution is allowed to seep through the rock pores, while the vertical loading is kept constant and
horizontal strains are (almost) zero. The porosity of the specimen and the grain size are so large
that it is assumed that the excess pore water pressure dissipates in a negligible time lag, so that
effective stresses can be assumed to be equal to total stresses at all times

2. Experimental results

Firstly an artificially cemented sand has been tested; it is obtained by mixing a fixed amount
of silica sand with hydraulic lime. Quartz grains are not attacked by acid. Complete weathering is
obtained, therefore, when all the calcareous bonds are destroyed. Different types of artificial rocks
can be obtained by testing the specimens after different curing time.

500 D 0,12
B’ OD: Loading Phase
axial stress σa(kPa), radial stress σr (KPa)

B (with 2 unload-reload cycles) F

0,1 DE: Creep Phase
400 EF: Weathering Phase
Axial Stress (percolation of an acid solution)
Radial Stress axial strain εa 0,08
300

F 0,06

200
0,04
B B’ D E
100
B B’ D E
0,02
A
O a) A b)
C O C
0 0
0.00 2.00 4.00 6.00 8.00 0.00 2.00 4.00 6.00 8.00 10.0
time (hours) time (hours)

Figure 2: Weathering test on silica cemented sand: evolution of axial and radial stress (a) and of axial strain
(b) with respect to time during all phases of the weathering test

A selected test on a specimen of artificially cemented sand in which the time allowed for
curing was short (68 hour) is shown in Figure 2. The bond strength is lesser than in the case of
complete curing, so plastic strains take place even in the first loading phase. A sharp kink is
recorded in the stress path (point A), in fact, by unloading σa to zero (point C), permanent axial
strain as well as radial stress are recorded. The vertical stress is then increased again up to point
D. Since point D is associated to a vertical load lower than that of point B at which unloading
started, the rock specimen is still within the elastic domain at the end of this phase and practically
no creep occurs, if the vertical load is kept constant for four hours (D=E ). At point E the weathering
phase starts.

B
B’

D,E

G
A F

O,O’

C c)

00

Figure 2: Weathering test on silica cemented sand: stress path in q:p’ plane for all the test phases in Figure 2.

As the acid solution is allowed to seep through the pores, vertical strains take place and
horizontal stresses increase. This process continues until point F is reached, corresponding to a

52
horizontal asymptote of the vertical strains; now unloading from F to zero vertical load, the stress
path followed is similar to that of an uncemented sand with linear reloading branch and curved
unloading branches.
The same type of tests were conducted also on specimens of a natural calcarenite The
results have much in common with those already presented in Figure 2; in this case, however,
since the acid solution attacks both the bonds and the grains, a horizontal asymptote of vertical
strains is not reached, vertical strains continue indefinitely until the entire specimen is dissolved.

3. Conclusions

A new apparatus, called Weathering Test Device, was designed. For all cases considered the
horizontal stress increases remarkably during weathering at constant vertical load. For the
cemented silica sand the vertical strains stop when debonding is complete. Differently, for the
calcarenite they increase linearly with time until the entire specimen is dissolved, since both bonds
and grains are made of soluble material.
This kind of results have been modeled by a chemoplastic strain hardening model presented
in Nova and Castellanza (2001); with this model it has been possible to study boundary value
problems where the weathering effects cannot be neglected (Castellanza 2002, Castellanza et al.
2002).

4. Acknowledgements

The authors want to acknowledge the EU project Degradation and Instabilities in Geometerials with
Application to Hazard Mitigation (DIGA) in the framework of the Human Potential Program,
Research Training Networks.

5. References

Castellanza, R. (2002), Weathering effects on the mechanical behaviour of bonded geomaterials: an

experimental, theoretical and numerical study. PhD Thesis, Politecnico di Milano.
Castellanza R., Nova, R., Tamagnini, C. (2002) Weathering induced subsidence of a circular foundation.
Proc. VIII Int. Symp. on Num. Models in Geom. (NUMOG VIII), Rome, Pande&Pietruszczak (eds), Swets
& Zeitlinger, Lisse, 407-413.
Kolymbas, D., Bauer, E. (1993), Soft oedometer – A new testing device and its application for the calibration
of hypoplastic constitutive laws. Geotechnical Testing Journal, 16, no2, 263-270.
Nova R., Castellanza, R. (2001), Modelling weathering effects on the mechanical behaviour of soft rocks.
Proc. Int. Conf. on Civil Engineering, Bangalore, India, Interline Publishing, 157-167.

53
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

AN EXPERIMENTAL STUDY ON INFLUENCE OF THE HYDROMECHANICAL

BEHAVIOUR ON FLOW AND TRANSPORT OF CONTAMINANTS

Roberto L. Rodríguez-Pacheco (Roberto.Rodriguez-Pacheco@upc.es), L. Candela, A. Lloret

Department of Geotechnical Engineering & Geosciences, University Polytechnic of Catalonia, Spain.

ABSTRACT. The environmental impact of mining and metallurgical activities, the waste generated
by them have become of special interest to the studies of environmental problems affecting the
marine and continental water masses. Nevertheless, the influence of the hydromechanical
behaviour on flow and transport of contaminants has not been systematically investigated for
mining-metallurgical wastes. The main aim of this work is to study the physical, hydromechanical,
hydrogeological and geochemical factors and conditions that influence flow and transport of metals
(Cr, Ni, Mn) in mining wastes.

1. Introduction

The material used in the present study is a waste material from the Cuban nickel industry (ACL
waste). The original material is treated with ammonium carbonate in an industrial leaching process
in order to obtain nickel and cobalt oxides. With this purpose an extensive experimental programme
has been developed, which has allowed to know the behaviour of the material under saturated and
non-saturated conditions.
The waste is composed of heavy metals and iron minerals, organic matter content is about
4.6% due to the presence of aliphatic products incorporated in the oil combustion process. Average
particle density is 3.97 g/cm3. Grain size distribution is poorly graded with a value of D50 about 0.02
mm. This material has a liquid limit of 43.9, a plastic limit of 39.9 and may be geotechnically
classified as ML. Water permeability, retention curve and vapour diffusivity are the most relevant
material properties controlling desiccation rate. Saturated water conductivity is highly dependent on
void ratio ( 3 10-7 m/s for e=3.8; 10-10 m/s for e= 1.8 and 2 10-12 for e=0.9).
The hydromechanical characterization tests show that, the resistance to direct and indirect
traction, to simple compression, the rigidity of the material and the hydraulic conductivity are very
dependent on the degree of saturation. Volume changes due to retraction and the variation in the
degree of saturation induce a decrease in the hydraulic permeability, whereas the desiccation
cracks in the material under the retraction process induce an increase in the hydraulic conductivity
higher than two orders of magnitude when compared with the homogeneous porous media.

2. Hydromecanical behaviour

In order to study the hydro-mechanical behaviour of the mining wastes and their influence on flow
and solute transport, a fully equipped column was built with diverse sensors able to automatically
control the changes in different parameters over time, which in turn control the hydro-mechanical
behaviour of the waste (Figure 1).
During the test it is possible to measure the vertical retraction, the suction, the temperature,
the relative humidity and the volumetric water content in the matrix of the porous medium with
depth and also at the sample surface. It also allows to perform flow and solute transport tests in
homogeneous and as well in cracked porous media.
Finally the influence of the hydro-mechanical behaviour of the ACL waste on the flow and
solute transport of three solutes, a conservative pentafluorobensoate (PFBA) tracer, a fluorescent
tracer Na-fluorescein and Ni, were studied in the saturated porous medium with preferential flow in
a waste column of 28.5 cm diameter and 31.5 cm height with stratification and desiccation cracks.
The hydraulic conductivity of the column (5.26x10-6 m/s) is more than twice that of the
homogeneous porous media. The hydraulic conductivity of the column (5.26x10-6 m/s) is more than
twice that of the homogeneous porous media.

55
3. Conclusions

The results of flow and solute transport tests with tracer and reactive solutes are coherent with the
conceptual flow and advective transport model along the desiccation cracks, combined with the
diffusion of the solute in the relatively non-mobile water which occupies the matrix of the porous
medium. This is confirmed by the characteristics of the breakthrough curves of PFBA and nickel,
which have an almost vertical and rapid increase during the adsorption process and a big tail during
the desorption process. This double process is also present with the Ni concentration measured in
the adjacent matrix of the crack zone, where the adsorbed mass of Ni decreases exponentially with
the distance of the sampling point to the crack, and with the distribution of the Na-fluorescein in the
crack zone.
Simulations of breakthrough curves of PFBA and nickel with a model of equivalent porous
media are not comparable with experimental results whereas the simulations with two region model
(double porous media) resulted in a good comparison with the experimental results.

B
T EV V
TDR
SP V
V
SP
T
SP TDR
I TDR T
SP
SP
SP
T SP

CC

VE
SA

B
II

EV T
12 F
11 LVDT
10
9
8
TDR 7
6
5
4 EA
SP 3 TDR V
2
1 M NA
TDR
T
III
PP
T
TN

CC
0 cm 10 20 30

Figure. 1. Schematic diagram of instrumented laboratory column: I-Distribution of sensors. II- Data acquisition
System III) 3-D representation of column. The numbers indicate the position of waste layer. Sensors were
placed as they are in I. CC: load cell; TN: tentiometer; PP: porous plate; M: membrane; TDR: Time Domain
Reflectometry; T: Thermometer; SP: psychrometer; V: hygrometer; EA: input of air; SA: output of air; NA:
water level; F: cotton filter; VE: ventilator; B: light; LVDT: transducer of displacement;
EV: electric valve; P: piezometer.

4. References

Rodríguez-Pacheco R.L. (2002). Estudio Experimental de Flujo y Transporte de Cromo, Níquel y Manganeso
en Residuos de la Zona Minera de Moa (Cuba): Influencia del Comportamiento Hidromecánico. Ph.D.
Thesis. University Polytechnic of Catalonia (UPC), Barcelona, Spain.

56
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

A NEW PEAK SHEAR STRENGTH CRITERION FOR ROUGH ROCK JOINTS

Giovanni Grasselli (G.Grasselli@ic.ac.uk)

Imperial College, London, UK.

ABSTRACT. Strength, deformability and fluid flow properties of rock joints are to a great extent
controlled by the surface roughness. The roughness parameters classically proposed in literature,
such as the JRC or the fractal dimension D, are usually estimated from the analysis of single linear
profile. Three-dimensional characterisation of the surface morphology would obviously yield more
information. This paper briefly describes a new methodology for quantifying the influence of the
joint roughness on the hydro-mechanical properties of the fractures.

1. Introduction

The assessment and management of risks associated with natural hazards play a crucial role for
the sustainable development of a liveable and safe environment. One of the major problems for
efficient risk management is the current lack of a thorough understanding of the physical processes
involved in most kinds of natural instabilities. Undoubtedly, among all factors that influence the
behaviour and the stability of rock masses, fractures play a major role. Therefore, their full
understanding is important in all fields of rock mechanics (i.e. tunnelling, rock slope stability,
foundations in rock, etc.). Moreover, the scientific interest of studying fractures in rock must also be
related to the strong need of practicing engineers for reliable solutions concerning the hydro-
mechanical behaviour of fractured rock masses.
The geometry of joint-surface roughness greatly influences the size and distribution of contact
areas during shearing, therefore, it has to be considered the most important geometrical boundary
condition for explaining this process under low normal load conditions. In addition, the size, shape,
and spatial distribution of damaged areas depend on the shear direction, the degree and
distribution of stress, and horizontal displacement. It is obvious that damage increases with
increasing stress and displacement. The common characteristic among all damaged areas is that
they are without exception located in the steepest zones facing the shear direction. The shape of
the damage zones depends on the local geometry of the fracture surface, including the size and
shape of the asperities, as well as on the mechanical parameters of the rock.

2. Three-dimensional parameters for the description of the surface roughness

In the present research a large number of surfaces have been digitised and reconstructed using a
triangulation algorithm. This approach results in a discretisation of the joint surface into a finite
number of triangles, whose geometric orientations have been calculated. Furthermore, during
shear tests it was observed that the common characteristic among all the contact areas is that they
are located in the steepest zones facing the shear direction. Based on these observations and
using the triangulated surface data, it is possible to describe the variation of the potential contact
area versus the apparent dip angle with the expression

C
 θmax
*
− θ* 
A θ* = A o   (1)
 θ* 
 max 

where A0 is the maximum possible contact area, θ∗max is the maximum apparent dip angle in
the shear direction, and C is a “roughness” parameter, calculated using a best-fit regression
function, which characterises the distribution of the apparent dip angles over the surface (Grasselli
et al. 2002a).

57
3. Map of surface anisotropy

The surfaces of four joints of different rock types were analysed with the purpose of estimating the
anisotropic distribution of the roughness of the surface, and of quantifying the influence of the
morphology on the shear strength of the joint. In order to visualise and compare the anisotropy of
different rock joints, for each surface the parameters A0, C and θ∗max were calculated all around the
average-plane of the joint in steps of 5 degrees, and the values of ratio θ∗max/C, obtained for each
direction, were plotted in polar diagrams (Figure 1) (Grasselli et al. 2002b).

S2
θm ax / C 90
20
120 60

15

150 30
10

0 180 0

10
210 330

15

240 300
20
270

Figure 1. Anisotropical distribution of values θ∗max/C for a surface of Valtellina serpentinite (sample S2)

4. New empirical shear strength criterion for rough rock joints

The dependence of the shear strength on the direction of the motion was studied by shearing
identical surfaces in different directions. A good correlation was found between the shear strength
values obtained during laboratory tests, and the morphological parameters that were calculated
from three-dimensional surface measurements. The experimental results confirmed that the shear
strength of rock joints is direction-dependent, and show that the new surface parameters to can be
used to estimate the anisotropy in the shear strength of a fracture.
Based on these observations, and on the results of more than 50 laboratory tests, a new
empirical criterion for the estimation of the peak shear strength has been proposed by Grasselli &
Egger (2002):

 −  max n  
 θ* σ 
 9 A Cσ 
τp = σn tan φ 1 + e  o t  
*
(2)
γ

 

where τp is the peak shear strength of the joint, σn is the applied average normal stress, σc is
the compressive strength of the intact material obtained from a standard uniaxial test, and φr* is the
residual friction angle (measured after a standard displacement of 5 mm).

5. Conclusions

The most important aspect of this model is the introduction of quantitative three-dimensional
surface parameters into the peak shear strength criterion. The contribution of the roughness to the
shear strength of the joint is, indeed, captured by parameters that are calculated on the entire joint
surface, and not only on single profiles.

58
6. References

Grasselli G., Egger, P. (2002). Constitutive law for shear strength of rock joints based on quantitative 3-
dimensional surface parameters,. Int J Rock Mech Min Sci in press.
Grasselli G. et al. (2002a). Quantitative three-dimensional description of a rough surface and parameter
evolution with shearing. Int J Rock Mech Min Sci 39 (6): 789-800.
Grasselli G. et al. (2002b). Functional parameters for quantifying the surface anisotropy of rock
discontinuities. Proc. Eurock2002. Funchal (Madeira Island), Portugal: in press.

59
Mechanical behaviour of geotechnical structures
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

EXPERIMENTAL AND NUMERICAL APPROACHES TO THE STUDY OF THE

BEHAVIOUR OF MICROPILE GROUPS AND NETWORKS SUBJECTED TO VERTICAL
OR HORIZONTAL LOADING

Roger Estephan (estephan@cermes.enpc.fr), R. Frank

CERMES, Ecole Nationale des Ponts et Chaussées-LCPC, France.

ABSTRACT. Two approaches are used to analyze the behavior of micropile groups and networks
subjected to vertical or horizontal loading. In the first approach, we present some results obtained
by experimental tests realised on full and reduced scale model of micropile groups and networks. In
the second approach, the load transfer function method is used by the mean of GOUPEG program.
Numerical results are then compared to those obtained by the experimental approach. A parametric
numerical study is finally presented in this paper, giving interesting results on micropile inclination
effect within a group/network subjected to vertical or horizontal loading.

1. Introduction

Micropile bearing capacity is usually developed by shaft resistance, their tip resistance is relatively
small due to the small micropile section. When used within a group or a network, micropile-soil-
micropile interaction should be considered. This interaction generally depends on the geometry of
the group (micropile spacing and inclination), on the soil characteristics, and on the method of
installation of the micropiles.
Many experimental tests were realized to study the group and network effects (Lizzi and
Carnevalle, 1979; Frank and Zhao, 1982). Recently, the french national research project on
micropiling systems led to considerable conclusions on group and network effects (FOREVER,
2002).

2. Experimental tests results

We analyze in this first part the results of some series of tests realized within the national research
project on micropiles (FOREVER). These tests were realized on reduced scale models of micropile
groups and networks: in calibration chambers at the CERMES (Le Kouby et al., 2001), in
experimental cuve at L3S laboratory (Foray and Estephan, 2001); and on full scale tests: at the
CEBTP experimental site (Gangneux et Plumelle,1997).
The main characteristics of the experimental tests are given in the following table:

CEBTP L3S CERMES

Test type Full scale Experimental Cuve Calibration chamber
Number of micropiles 4 18 5

Relative spacing 4/12/17 3,5/7 4

Micropile inclination (network) 20° 20° 15°

Soil type and relative density Sand (ID = 0,57) Sand (ID = 0,4 to 0,55) Sand (ID = 0,70)

Loading type Vertical / Horizontal Vertical Vertical

Table 1. Characteristics of experimental tests

63
3. Load transfer function method

In this part, the numerical approach is used to analyze the behavior of a double A-shaped micropile
network, and an equivalent group of 4 vertical micropiles (similar to the full scale group and network
tested on the CEBTP experimental site).
The GOUPEG program combines load transfer method to calculate the group behavior
(Degny et Romagny, 1989) and the continuum elastic method to determine pile-soil-pile interaction
factors by using Mindlin’s equations (Mindlin, 1936; Perlo et al., 1999; Estephan and Frank, 2001).
Figure 1 shows the use of Mindlin’s equations to evaluate the effect of induced displacement due to
pile-soil-pile interactions.

X
Y

Z
w0 own displacement
c
P ix δw induced displacement

i z
P iy
P iz

δ u ou δ v own displacement
r u0 ou v0 induced displacement
Pile I Pile J

Figure 1. Application of Mindlin’s equations to evaluate pile-soil-pile interacion

4. Parametric study

The parametric study concerns the effect of micropile inclination within a group. GOUPEG program
is used to simulate micropile group and network behavior under vertical and horizontal loading. This
study was realized for 5 inclination of the micropiles: 0°, 10°, 20°, 30° and 40°.

5. References

Degny E., Romagny Ph. (1989). Présentation du programme de calcul général des groupes de pieux
GOUPIL. Bulletin de liaison du Laboratoire Central des Ponts et Chaussées, n°162, juil-août 1989, p3-12.
Estephan R., Frank R. (2001). Analyse du comportement de groupe et de réseaux élémentaires de
micropieux sous chargement vertical et horizontal. Applications aux essais de chargement du réseau de
Saint-Rémy-lès-Chevreuse. Rapport FOREVER N°FO/98-99/06.
Foray P., Estephan R. (2001). Synthèse des essais de chargement vertical de groupe et de réseaux
élémentaires de 18 micropieux (modèle de Lizzi) réalisés sur des modèles réduits de micropieux en dans
une grande cuve expérimentale . Rapport FOREVER No. FO/98-99/09.
Frank R., Zhao S.R. (1982). Estimation par les paramètres pressiométriques de l’enfoncement sous charge
axiale de pieux forés dans des sols fins. Bull. Liaison Laboratoire des Ponts et Chaussées, 119, pp. 17-24
FOREVER (2002) Document de synthèse et de recommandations du Projet National de recherche sur les
micropieux. Irex.
Gangneux P., Plumelle C. (1997) Expérimentation en vraie grandeur de réseaux de micropieux. Exécution
des micropieux. Rapport FOREVER No FO/96/09.
Le Kouby A., Canou J., Dupla J.C. (2001) Etude comparative du comportement mécanique de groupes et de
réseaux de micropieux modèles en chambre d’étalonnage. Rapport FOREVER N°FO/98-99/05.
Lizzi F., Carnevale G. (1979). Les réseaux de pieux racines pour la consolidation des sols. Aspects
théoriques et essais sur modèles. Colloque Fondations profondes, Paris, pp. 317-324.
Mindlin R.D. (1936). Force at a point in the interior of a semi-infinite solid. Physics – Volume 7, pp. 195-202.
Perlo S., Degny E., Frank R. (1998). Analyse du comportement des groupes de micropieux sous charge
transversale- application au site expérimental de Saint Rémy-Lès-Chevreuse (essais réalisés en 1995),
thème 3.6 . Rapport FOREVER No FO/97/04.

64
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

COUPLED SEISMIC RESPONSE OF DEEP SATURATED SOIL DEPOSIT IN

SHANGHAI

Yu Huang (yhuang@mail.tongji.edu.cn), Wei-Min Ye, Yi-Qun Tang, Zhu-Chang Chen

Department of Geotechnical Engineering, Tongji University, Shanghai, P. R. China.

ABSTRACT. The Quaternary deposits in Shanghai are horizontal soil layers of depth up to
270~290 m or so at cantonal area with annual groundwater table at 0.5~0.7 m from the surface.
Therefore, the soil deposit of Shanghai is deep and fully saturated and has important influences
upon earthquake response of soil layers. Based on the dynamic coupled theory, the saturated soil
is modelled as a two-phase porous media system consisting of solid and fluid phases. A new
numerical model for predicting the seismic response of Shanghai soil layers is developed to
describe the characters of deep saturated soil deposits. Then the seismic response of Shanghai
horizontal soil layer of depth 280 m, which is subjected to four base excitations (El Centro, Taft,
Sunang and Tangshan Earthquakes), is studied in terms of dynamic coupled computation with the
proposed model. The calculation results of acceleration, pore water pressure and earthquake
subsidence are also investigated.

1. Introduction

Shanghai is located on the east coast of China at the mouth of the Yangtze River at the Donghai
Sea. It is the biggest city in China, where over 14 million people live in 2000. Although Shanghai is
not a typical seismic area, there are several seismic sources within a range of 200-300 km. The
earthquake influencing Shanghai was firstly recorded in A.D. 288. Several moderate earthquakes
have affected Shanghai in the past twenty years, such as Liyang Earthquake in 1979 (M = 6.0),
South Huanghai Sea Earthquake in 1984 (M = 6.2), Changshu-Taicang earthquake in 1990 (M =
5.1) and South Huanghai Sea Earthquake in 1996 (M = 6.1). The alluvial soil deposit of Shanghai is
150-400m deep. The average thickness is 270-290m deep at city centre. The soil deposit is fully
saturated and particularly with an about 100m thick saturated soft soil, which has a large water
content and a high compressibility.
There are major differences in responses between shallow and deep deposits. The deep soil
deposit has lower resonant frequency than that of a shallow soil deposit. Among deeper soil
deposits, the difference in amplification ratios within and at the surface of the deposit is small,
whereas the resonant frequency depends on the thickness of soil deposit. Therefore, it has a great
meaning to predict the earthquake response of Shanghai deep saturated soil deposit.

2. Analysis method

The behaviour of geomaterials, and in particular of soils, is governed by the interaction of their solid
skeleton with the pore fluid. The behaviour of soils under dynamic loadings can only be achieved
through coupled analysis for the interaction of the soil skeleton and the pore fluid. The interaction of
the pore water with the solid soil skeleton belongs to the Class II coupled problems. The coupling
occurs through the governing differential equations of both solid mechanics and transient seepage.
The Class II coupled problems can be solved numerically under given boundary and initial
conditions by the finite element method (Zienkiewicz et al. 2000). This paper is concerned with the
dynamic interaction of the pore water with the solid soil skeleton under fully saturated conditions.

3. Dynamic coupled constitutive model

A hierarchy of constitutive models is available for the dynamic response of soils to earthquake
loading. The models range from the relatively simple hysteretic nonlinear models to complex
elastic-kinematic hardening plastic models. On the basis of an extensive experimental data, a

65
dynamic coupled constitutive model is proposed in this paper, which is a modified equivalent
viscoelastic model including a set of relationships of stress, strain, pore water pressure and
earthquake subsidence (Huang et al. 2000). Compared with elastoplastic models, the model
simulates the soil dynamic behaviour in a cycle of loading as a whole, not in detail.

4. Application

A sample geology profiles of the Shanghai deep saturated soil deposit of depth 280m, which is
subjected to 4 base motions of the first 10s component of the El Centro, Taft, Sunang and
Tangshan Earthquake respectively with the maximum acceleration scaled to 0.1g, is studied in
terms of the dynamic calculation model. The ground and bedrock response spectra with 5 percent
damping ratio are shown in Figure 1. The results indicate that the deep soil deposit acts as a filter
when the bedrock earthquake acceleration is transmitted through it. Moreover, the soil deposit
filters out a significant portion of the high frequency content of the bedrock acceleration. Figure 2
shows the earthquake subsidence development of soil ground under 4 earthquakes. The calculated
maximum earthquake subsidence is about 48.5mm subjected to El Centro earthquake until the
dissipation of pore water pressure completes.

3.0 3.5 Taft

2.5 El Centro 3.0
Bedrock
2.0 Bedrock 2.5
β
Ground
2.0
1.5 Ground
β

1.5
1.0
1.0
0.5 0.5
0.0 0.0
0 1 2 3 4 5 0 1 2 3 4 5
Period (s) Period (s)

3.0 2.5 Tangshan

2.5 2.0 Bedrock
Sunang
β

2.0 Ground
Bedrock 1.5
1.5
β

Ground 1.0
1.0
0.5 0.5

0.0 0.0
0 1 2 3 4 5 0 1 2 3 4 5
Period (s) Period (s)

Figure 1. Response spectra of bedrock and ground surface

Time (s)
0.1 10 1000 105 107 109
0
1 Sunan
Subsidence (cm)

2
Taft
3
Tangshan
4
5 El Centro

Figure 2. Predicted earthquake subsidence development of soil ground

5. References

Zienkiewicz O.C., Taylor R.L. (2000). The finite element method. Vol. 1: The basis, Fifth Edition, Butterworth-
Heinemann, Oxford.
Huang Y., Tang Y-Q., Ye W-M., Chen Z-C. (2000). A dynamic calculation model of Shanghai saturated soft
soil. Proceedings of 7th International Conference on Recent Advances in Structural Dynamics,
Southampton, UK: 1027-1035.

66
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

NEW DESIGN CRITERIA FOR PILED RAFTS AND RELATIVE METHODS OF ANALYSIS

Luca de Sanctis (luca.desanctis@unina2.it)

PhD, University of Napoli Federico II, Napoli, Italy

ABSTRACT. Simple numerical codes for the analysis of soil structure interaction in the case of piled raft
foundations are available. A proper idealisation and geotechnical quantification of the subsoil profile is of
main concern. Firstly, recent research work on the problem of piled foundations embedded in layered
soils is reported. In the second part of the paper innovative design criteria for piled rafts are discussed. It
is argued that for a proper application of innovative concepts the safety factor of a piled raft has to be
defined. To this aim 3D finite element predictions of the ultimate vertical load of a piled raft will be
presented.

1. Introduction

As early as 25 years ago, Burland et al. (1977) pointed out that, in the majority of practical cases, the
primary reason for adopting a piled foundation is to reduce settlement. The usual design approach, on
the contrary, is based on bearing capacity and neglects the contribution of the raft. As a consequence,
piled rafts are usually designed by overconservative criteria and their settlement is uselessly small.
Since then, a number of interesting contributions to the analysis of piled rafts have been published
and considerable attention is being dedicated to the optimisation of the design (Horikoshi & Randolph,
1997; Russo & Viggiani, 1998; Prakoso & Kulhawy, 2000; Viggiani, 2001; de Sanctis et al., 2002).
Reliable procedures of analysis are needed to predict the response of the foundation as required
by the existing regulations, but also to explore innovative design criteria.

2. Methods of analysis for piled rafts

The most widespread techniques for the analysis of pile groups and piled rafts are based on the
Boundary Element Method (Butterfield & Banerjee, 1971). Computer programs for the analysis of piled
foundation based on BEM has been developed at Department of Geotechnical Engineering in Napoli.
The program ‘Gruppalo’ (Mandolini, 1994) allows for the prediction of the settlement of pile groups while
the program ‘Napra’ (Russo, 1996) accounts for the full pile-soil-raft interaction.
They are based on the interaction factors methods and solve simplified models with approximate
numerical procedures. The overall reliability of the algorithms has been thoroughly checked against
benchmark solutions, nearly always limited to foundations embedded in elastic halfspace.
One of the key features of these codes is their capability to handle horizontally layered profiles.
These are solved via the so called Steinbrenner approximation. A thorough and extensive check of this
procedure has been carried out using FEM to supply benchmarks where closed form solutions are not
available. In this connection some expedients for a proper application of this approximate solution have
been found and the overall procedure of analysis employed in Napra has been slightly improved (de
Sanctis, 2001).
In the case of soil stiffness decreasing with increasing depth serious errors may occur (de Sanctis
et al., 2002). The most critical step is the analysis of the single pile. On the contrary the interaction
factors are practically unaffected by the method of analysis and depend on the type of subsoil profile
rather than on the absolute value of the stiffness.
It is suggested to use the stiffness of a single pile as deduced by a full scale test, which is often
available for important projects. This is a key step of the standard procedure defined by Mandolini e
Viggiani (1997). The success achieved in the interpretation of the behaviour of full scale pile foundations
(Viggiani, 2001) demonstrates that satisfactory predictions may be obtained by the existing codes,
provided they are properly applied.
Should the pile load test not be available it is suggested to use the stiffness of the single pile as
obtained by a finite element analysis, which is relatively simple from a computational point of view
because of axial symmetry. This procedure, however, is affected by heavy uncertainties for the

67
difficulties of evaluating the relevant soil parameters and for the influence of the installation method
adopted for the piles.

3. Innovative design concepts

The availability of satisfactory procedures of analysis makes possible the search for optimum design
criteria. An optimum design may be defined as a design achieving maximum economy, while keeping a
satisfactory behaviour. In the design of a piled raft an assessment of the behaviour can be referred to
different quantities, such as the mean settlement, the differential settlement, the stress in the raft. In
order to get some insight into the optimisation of design, Russo & Viggiani (1998) suggested to group
piled foundations in two broad categories: small and large piled rafts. For the purpose of the present
work, they are defined as follows:
Small piled rafts are those in which the bearing capacity of the unpiled raft is not sufficient to carry the
total load with a suitable factor of safety. The primary reason to add piles is thus that of achieving a
sufficient factor of safety. In this case limitations of mean settlement is the main design requisite;
Large piled rafts are those whose bearing capacity is sufficient to carry the applied load with a
reasonable margin of safety, so that the addition of piles is essentially intended to reduce settlement.
The flexural stiffness of the raft cannot be but rather small, and the requisite for an optimum design is the
limitation of the mean and the differential settlement. In general the width of the raft is large in
comparison to the length of piles (B/L ≥ 1).
At present, the design of a piled raft is essentially capacity based, and neglects the contribution of
the raft; this is still the content of codes and regulations all over the world.
In a draft revision of the Italian regulation some considerations is allowed of the load sharing
between raft and piles. To this aim, a preliminary analysis of the interaction between these elements is
required. Once the loads acting on the raft and on the piles have been determined, they are separately
checked for a safety factor against a bearing capacity failure.
In any case, to assess in a rational way the safety of a piled raft, its bearing capacity has to be
defined (Viggiani, 2001). This matter will be discussed on the basis of 3D finite element predictions of the
ultimate vertical load of piled rafts.
Finally a further innovative design introduced by the draft Italian regulation is reported. If the piles
are intended to control the settlement of the foundation, the bearing capacity of the latter can be
evaluated referring only to the raft, without accounting for the piles. This indication seems to be suitable
for large piled rafts. In this case, indeed, the bearing capacity of the unpiled raft is already sufficient.

4. Reference

Burland J.B., Broms B.B., De Mello V.F.B. (1977) Behaviour of foundations and structures. State-of-the-Art Report,
IX ICSMFE, Tokyo, vol. 2, 495-546
Butterfield R., Banerjee P.K. (1971) The problem of pile group – pile cap interaction. Géotechnique, vol. 21, n. 2,
135-149
de Sanctis L. (2001) Modellazione ed analisi di piastre su pali. PhD Thesis, University of Napoli Federico II
de Sanctis L., Mandolini A., Russo G., Viggiani C. (2002) Some remarks on the optimum design of piled rafts. Deep
Foundations 2002, GeoInstitute of the ASCE, Geot. Special Publication No. 116, 405-425, Orlando, Florida
th
de Sanctis L., Russo G., Viggiani C. (2002) Piled rafts on layered soils. Proc. of the 9 Intern. Conf. on Piling and
Deep Foundations, DFI 2002, 279-285, Nice, France
Horikoshi k., Randolph M.F. (1997) Optimum design of piled raft foundations. Proc. XIV ICSMFE, Hamburg, vol. 2
Mandolini A. (1994) Cedimenti di fondazioni su pali. PhD Thesis, University of Napoli Federico II
Mandolini A., Viggiani C. (1997) Settlement of piled foundations. Géotechnique, vol. 47, n. 4, 791-816
Poulos, H. G. (1968) Analysis of settlement of pile groups. Géotechnique, vol. 18, No. 3, 449-471
Prakoso W. A., Kulhawy F. H. (2000) Contribution to piled raft foundation design. Journ.
Geotechnical and Geoenvironmental Engineering, vol. 127, n.1, 17-24
Russo G. (1996) Interazione terreno struttura per piastre su pali. PhD Thesis, University of Napoli Federico II
Russo G., Viggiani C. (1998) Factors controlling soil-structure interaction for piled rafts. Proc. Int. Conf. on Soil-
Structure Interaction in Urban Civil Engineering, Darmstadt, 297-322
Viggiani C. (2001) Analysis and design of piled foundation. First Arrigo Croce Lecture. Rivista Italiana di
Geotecnica, n. 1, 35-63

68
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

STUDY ON STABILITY AND DISPLACEMENT OF DMP RETAINING WALL IN SOFT

SOIL

Juhua Xiong (xjhwwww@sohu.com), Min Yang

Tongji University, Shanghai, China

ABSTRACT. In this paper some data of 17 practical DMP (deep mixing pile) retaining walls are
analysed. The relationship between stability and displacement is discussed. A new method for the
calculation of the stability factors of DMP retaining wall is put forward.

1. Introduction

The DMP retaining wall is widely used in soft soil area such as Shanghai. Generally, the stability
factors should be determined during the designing process. But it was found illogical that the Kq
(stability factor of overturn) decreased as the length of piles increased. Meanwhile it is difficult to
predict the displacement of a DMP retaining wall.

2. Relationships between stability and displacement

Based on the monitoring data of 17 projects with DMP (deep mixing pile) retaining walls, the
relationships between stability factors and the displacement of retaining wall are shown in Figures 1
and 2. It clearly shows that the displacement (y) decreases as the stability factors, such as K (the
stability factor of integer), Ks (the stability factor of upheaval), Kh (the stability factor of slippage),
increase. But, for Kq, the result is totally different (Figure 2b).

y/mm y/mm

250 250

200 200

150 y = 127.2K -2.223 150

100 R = 0.734 y = 143.66KS-1.467

100
R = 0.727
50 50

0 0
0.5 1 1.5 2 2.5 K
0.5 1 1.5 2 2.5 3 3.5 4 KS

(a) (b)
Figure 1. (a) Relationship between K and y, (b) Relationship between Ks and y

y/mm
y(mm)
250 240

200 200

160
150 -1.887
y = 111.03Kh
120
100 R = 0.779
80
50 40

0 0
0.5 1 1.5 2 2.5 Kh 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Kq

(a) (b)
Figure 2. (a) Relationship between Kh and y; (b) Relationship between Kq and y

69
3. Analysis and discuss

The main reason for what happened to Kq, which is Kq decreases as the length of pile increases
(shown in Figure 5), may because of the assuming conditions for the calculation of Kq is not so
reasonable. As you know, the assumption for the calculation (Equation 1) is that the DMP retaining
wall will overturn at its toe. In fact, the DMP retaining wall would probably overturn at its toe, heel or
some point nearby lower part of the pile. So Kq should be calculated by Form 2 (shown in Figure 3).

K q = (E p h p + 0.5 Wb ) / (E a h a ) （1）

K 'q = (E p h p + 0.5 W1b1 + F1b1 + F2b 2 + 0.5Pu b 2 ) / (E a a + 0.5 W2 b 2 ) （2）

4.5

3.5 c=10kPa • =10°

c=0kPa • =20°
3 c=0kPa • =10°

2.5
Kq

1.5

0.5

0
0 2 4 6 8
h0(m)

(a) (b)
Figure 3. (a) Relationship between Kq and h0; (b) Sketch map of Kq’

With equation 2, the result is reasonable that Kq’ increases as the length of pile increases (shown in
Figure 4a). Furthermore, the relationship between Kq’ and y drawn again shows the same regularity
that the displacement decreases as Kq’ increases, the same as K, Ks, Kh and y (shown in Figure
4b).
4.5

4 y/mm

3.5 c=10kPa • =15°

c=0kPa • =20° 250
3 c=0kPa • =10°

2.5
200
Kq'

2
150 -1.656
y = 101.76Kq
1.5
100 R = 0.749
1

0.5 50
0
0 2 4 6 8 0
h0(m)
0.5 1 1.5 2 2.5 Kq’
(a) (b)
Figure 4. (a) Relationship between Kq ’and h0; (b) Relationship between Kq’ and y

4. Conclusions

The displacement of the retaining wall would decrease as the stability factors increase. The
displacement could also be predicted by the relationship between K, Ks, Kh and yo.

70
 The Kq calculated by the former method is not so reasonable mainly because of the assuming
condition that the DMP retaining wall will overturn at its toe and the consideration of no friction
between the wall and soil is some unreasonable. The Kq calculated by proposed method herein is
reasonable.

5. References

Huang Q. (1995). Design Technology of Retaining Structure in Foundation Pits. (in Chinese)
Beijing: China Architecture & Building Press, 160-161
South China University of Technology, Southeast University, Zhejiang University, Hunan University
(1991), Soil and Foundation (in Chinese), Beijing: China Architecture & Building Press: 151-152

71
Stability analysis and tunnels
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

EFFECTS OF EMBEDDED DIAPHRAGM WALLS ON MOVEMENTS INDUCED BY TUNNEL

EXCAVATION

Emilio Bilotta (bilotta@unina.it)

University of Napoli Federico II, Naples, Italy.

ABSTRACT. In this paper the use of embedded diaphragm walls as a protective measure of buildings
from damages occurring from tunnel excavation is analysed. A set of centrifuge tests has been carried
out and some of the results are shown. The influence of various geometrical parameters (i.e., the length
and the thickness of the wall, its distance from the tunnel axis, the roughness of the soil-wall interface)
has been studied.

1. Introduction

The development of new railways and mass transport system in urban areas often involves the
excavation of tunnels that may be large, relatively shallow and under or near existing buildings. A
growing issue of concern in the design is the protection of buildings from damages occurring from
tunnel excavation.
A possible remedial measure uses structural elements in the ground that work as a barrier to the
movements between the tunnel under construction and the building to be protected. Such a restraint
might be provided by an embedded diaphragm wall which is neither attached to the building nor a
structural part of the tunnel excavation.
It is hard to find out in published references pieces of information on the effectiveness of such
kind of measure as well as objective design criteria: hence, the need of setting up a data base of ‘case
histories’ to calibrate a numerical model of the problem.
To this aim, a series of tests on reduced scale models of tunnelling has been carried out at the
Centrifuge Laboratory of the City University London.

2. Centrifuge testing

The tests were carried out on a kaolin clay model. Ground movements in the plane strain model
are determined from analysis of digital images obtained from a CCTV camera during each test (Grant &
Taylor, 2000).
The models were prepared from a slurry which is one-dimensionally consolidated in a strong box
to a pressure of 350 kPa and then swelled back to a pressure of 150 kPa: this process takes several
days. On the day of the test the container was removed from the press and the model was prepared by
removing the front wall of the strong-box, cutting and lining the 50 mm diameter tunnel cavity, inserting
the targets for image-processing in the front face and bolt a Perspex window to the box to allow viewing
by the CCTV camera. These operations were performed quickly with the drainage taps closed and
sealing with oil the air-exposed clay surface in order to minimise clay swelling and shrinkage.
The model was placed onto the centrifuge swing and accelerated to 160 g. At the same time the
air pressure in the bag was increased to balance the overburden pressure. As spinning up increases
the total stress distribution, a period of about six hours was needed to achieve effective stress
equilibrium. The steady state water table was fixed by feeding water in the model using a standpipe and
the equilibrium checked by a couple of miniature pore pressure transducers embedded into the model
at different depths. After equilibrium was reached, the excavation was simulated by reducing the air-
pressure at the rate of around 100 kPa per minute, thus achieving a largely undrained response. During
this phase, pictures of the model were taken by the digital camera about every second and stored for
later image processing.
A couple of tests were carried out where no diaphragm wall was put into the model. These tests
were performed to determine a reference displacement field in order to compare it with measured
displacements from the model with diaphragm walls. The tunnel has a diameter of 50 mm (which
corresponds to 8 m at the prototype full scale) and the cover C in most of the cases equals the
diameter.
A series of tests was performed in which an aluminium wall is installed. The wall geometry
parameters vary over the set of models. In particular, the length of the wall L, its thickness t (which
75
corresponds to certain stiffness) and its offset d from the tunnel axis were varied according to the test
programme shown in Table 1. Most of the walls were actually thick.

D (mm) C/D L (mm) t (mm) d (mm)

50 0.9 - 1 70 - 120 0.8 - 10 50 - 75

Table 1. Characteristics of the wall in the centrifuge tests.

The diameter of the tunnel is the same in all the tests. The length of the wall varies between two
values corresponding to a short and a long wall. The offset of the wall from the tunnel axis is either 1D
or 1.5D. The two values of wall thickness correspond to a very flexible and a nearly rigid wall. Finally,
the influence of the roughness of the wall will be investigated as well, by testing models with the same
geometry but different interface with the clayey soil. Fig. 1 shows a digital image of a model.

Figure 1. Model with a stiff and short wall installed one diameter away from the tunnel axis

-200 -150 -100 -50 0 50 100 150 200

0

-0.05

-0.1
settlement (mm)

-0.15

-0.2

-0.25 short & thin C/D=0.9

-0.3 no wall C/D=0.9 ∆p/p o = 40%

-0.35
distance from axis (mm)

Figure 2. Comparison between test EB2 and EB3 at 40% of air pressure reduction

As an example of results, Fig. 2 shows the settlements close to the surface during the tests EB2 (in
free-field conditions) and EB3 (where a flexible and short wall was installed on the right side, one
diameter away from the tunnel axis) at a value of air pressure 40% less of the original one.
In this case the effect of the wall is to reduce settlements at its back.

3. Concluding remarks

Embedded diaphragm walls can provide a restraint to movements induced by tunnelling. This issue
could be useful in order to reduce the damage on existing buildings due to tunnel construction. The
results of the centrifuge testing programme performed show the influence of the length of the wall, its
distance from the tunnel, its thickness and of the roughness of the interface between soil and structure
on the behaviour of the wall. These results form a rich data base aimed to well calibrate a numerical
analysis. In fact, numerical analyses are in progress to study in details the influence of the various
above mentioned parameters.

4. References

Grant, R.J. & Taylor, R.N., (2000). Tunnelling-induced ground movements in clay. Proc. ICE Geotech. Engng,
143, Jan., 43-55.

76
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

OPTICAL FIBRE SENSORS FOR REMOTE TUNNEL DISPLACEMENT

MEASUREMENTS

Nicole Metje (n.metje@bham.ac.uk), Chris Rogers, David Chapman, Stephen Kukureka

The University of Birmingham, Birmingham, UK

ABSTRACT. Monitoring the movement of existing tunnels during the construction of new tunnels is
very important. Present techniques such as electrolevels and theodolites are very cost and labour
intensive. Further, they can only be used while there are no trains running. The present project
concentrates on the investigation of the use of fibre optic sensors to measure tunnel movements.
The present paper outlines the first results and the research proposal for this project.

1 Introduction

The movement of existing tunnels when new tunnels are driven in their close proximity is important
to tunnel owners when developing new tunnelling systems in urban areas. From the point of view
of existing tunnel owners, there is an ongoing need for remote monitoring of railway tunnels both
during and after adjacent construction works to ensure that tunnel displacements do not
compromise train operations. There is an equally important need to monitor the displacement of
tunnels in the long term in order that the asset can be adequately maintained and managed.
Existing manual monitoring systems, although considered most reliable, require access to the
tunnel during engineering hours (1 a.m. to 4.30 a.m.) and thus only provide measurements during a
limited time of the day and under non-operational conditions. Although remote monitoring based
upon electrolevels is available, there have been operational difficulties with such systems,
necessitating back up by manual monitoring, and comprehensive data are expensive to obtain.

2 Project Aim

The aim of this project is to develop a remote system of tunnel settlement, rotation and distortion
monitoring using fibre optic sensors. This will yield deformation plots for periodic examination by
maintenance contractors as well as providing continuous monitoring during adjacent construction
operations (e.g. new tunnelling, deep excavations, compaction grouting for control of
surface/building settlements) and warnings when ‘trigger values’ are reached in any of the
measured parameters. This will represent a major advance for tunnel owners by allowing them to
assess the potential damage to the tunnel linings and to take measures to avoid it as a result of
accurate and precise real-time monitoring. Another important advance sought from this project is
economy in relation to existing ring monitoring systems.
The remote monitoring system will exploit the accuracy and reliability of optical fibre systems.
Smart Fibres will provide the expertise in optical fibre technology. The Civil Engineering
Department at the University of Birmingham provides expertise in tunnelling and sub-surface
ground displacement, while the Metallurgy and Materials Department covers the mechanical
performance of optical fibres and composite materials.

3 Detailed Objectives of the Project

1. Via analysis of existing research data, determine general guidelines for the monitoring of tunnel
linings for different adjacent construction operations, and, for the specific cases to be studied in
the fieldwork, produce designs for standard and prototype research monitoring instrumentation.
2. Design and manufacture an array of optical fibre sensors that can be fixed at discrete points to
tunnel linings; are able to measure accurately, reliably and economically tunnel strains and
displacements associated with settlement, rotation and distortion; and are suited to the
environmental conditions. Their operational efficiency will be determined in extensive
laboratory tests and a field trial.

77
3. Determine how best to mount and protect the sensors in the operational environment.
4. Examine the short- and long-term mechanical performance of the fibres and sensor systems,
both in the laboratory and after installation and operation in a live railway environment.
5. Develop a remote means of data retrieval and transmission from the sensor systems.
6. Develop a means of visual representation of the data that will facilitate both immediate action if
‘trigger levels’ are exceeded and maintenance and asset management strategies to be
implemented.

4 First Results

In order to understand the behaviour of an existing tunnel during the construction of a new tunnel in
its vicinity, semi-empirical equations are employed. These equations were taken from Mair et al.
(1993) and determine the movement of discrete points around the tunnel lining. The equations are
based on the assumption that the transformed shape, or settlement profile, transverse to the tunnel
is a normal distribution curve and the longitudinal shape is a cumulative distribution curve.
Figure 1 gives a schematic of a typical tunnel layout forming the basis for the analysis. Figure 2
shows an example of the movement of the existing tunnel during a number of advancing stages of
the new tunnel, which in this example passes underneath the existing tunnel. The new tunnel
advances in steps of 10 m.

6
Ori g in a l Tu n n e l

x dist x_dist r new= 4.5m

n e w tu n n e l fa ce :
n e w tu n n e l fa ce :
10 m
20 m
n e w tu n n e l fa ce : 30 m
r old= 2.095m n e w tu n n e l fa ce : 40 m
cross section 4 z new= 26.11m n e w tu n n e l fa ce : 50 m
n e w tu n n e l fa ce : 60 m
z old= 10.9m n e w tu n n e l fa ce : 70 m

Xs 1 Xf 1 a
n e w tu n n e l fa ce :
n e w tu n n e l fa ce :
80 m
90 m
n e w tu n n e l fa ce : 100 m
y_dist b 2 Scale: 10 mm
h
45
c
y [m ]

new g 0

tunnel

skew d
y f -2
angle
y_dist
e

-4

cross
x section old
tunnel
-6
-6 -4 -2 0 2 4 6
X [m ]

(a) (b)

Figure 1. (a) Schematic of Typical Tunnel Layout; (b) exaggerated Movement of a Tunnel Cross-Section
during Different Advancing Construction Stages of a New Underlying Tunnel.

3 References

Mair R.J., Taylor R.N., Bracegirdle A. (1993). Subsurface settlement profiles above tunnels in clays.
Geotechnique 43 (2): 315-320.

78
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

SIMULATION OF PIPELINE BEHAVIOUR ON LIQUEFIED SEABED: NUMERICAL

STUDY

Pui Lee Vun (plv126@bham.ac.uk), Andrew H. C. Chan

University of Birmingham, Birmingham, United Kingdom.
Scott Dunn
HR Wallingford Ltd., Wallingford, United Kingdom

ABSTRACT. Numerical study of the wave induced liquefaction problem, i.e. a seabed with a
pipeline laying on the top subjected to cyclic loading due to the ocean wave, is presented in this
paper. Some of the results of the numerical analyses performed via finite elements are compared to
the available experimental findings. Besides, the numerical solutions are compared to the analytical
solutions based on poro-elastic theory. The influence of various assumptions such as boundary
conditions, meshing, constitutive model is presented and discussed.

1. Introduction

The cyclic loading due to the severe wave could induce excessive pore pressure built up and lead
to the occurrence of liquefaction to the seabed. This is similar to the case where the ground is
subjected to cyclic loading during earthquake. Hence, the dynamic finite element program originally
developed for earthquake problems namely SWANDYNE II (Zienkiewicz et al., 1999) was modified
and used in this study.
The structures situated either on the seabed and in the seabed could encounter severe
damage during the liquefaction. Hence the dynamic stability of a seabed has very important impact
in the stability of an offshore structure founded either in or on it.
Some experimental works have conducted by means of geotechnical centrifuge testing and
wave flume testing (1g test) to investigate the soil response subjected to two-dimensional wave
excitations such as Sassa and Sekiguchi (1999) and Teh et al. (2002). Some constitutive models
have also been developed, for example Pastor and Zienkiewicz (1986), Pastor et al. (1990) and
Sassa and Sekiguchi (2001), to predict the occurrence of liquefaction due to cyclic loading using
finite element method. In order to assess the applicability of the program SWANDYNE II,
comparisons have also been made with available analytical solution by Hsu and Jeng (1994).

2. Experimental result

The behaviour of pipeline on a seabed under different progressive wave conditions has been
investigated using wave flume experiment (Teh et al., 2002). The experiment was carried out at HR
Wallingford Ltd. The pipeline and the seabed were modelled by rubber tube and silt respectively.
The variation of pore pressure of the silt bed and the vertical displacement of the pipeline were
recorded during the test.

3. Finite element modelling

The numerical analyses performed under plane strain conditions and based on the experimental
conditions have been carried out using the SWANDYNEII finite element program. This program has
been improved to enable the loading effect induced by water wave to be modelled.
Linear elastic model and Pastor-Zienkiewicz Model Mark-III (PZ3) model (Pastor and
Zienkiewicz, 1996) were used to predict the linear elastic and the elasto-plastic behaviours of the
silt deposit. PZ3 model was developed based on the Generalised Plasticity Concept.
The pipeline was simply modelled using point loading in this study. The wave pressure
applied to the surface of the seabed was estimated based on the first order of the short-crested
wave theory, which is given by

P = p 0 cos(kx − ωt ) (1)

79
 γ wH 2π 2π
Where p 0 = ; k= ; ϖ= and L is the wave length; x is the horizontal
2 cosh kd L T
distance; T is the wave period; t is the time; H is the wave height; d is the thickness of seabed.

Both consolidation and dynamic analyses were carried out in this study.

Finite element meshes and boundary conditions

The main results of the numerical analyses performed using finite elements are here compared to
the experimental findings from the wave flume test. The effects of various assumptions such as
choice of boundary conditions, meshing, constitutive modelling, are presented and discussed.
Eight-node quadratic elements have been used for all the calculations. Due to limited
available information of the silt used in the test, parametric study on the soil parameters was carried
out using the PZ3 model. One of the finite element meshes used for the simulations of the wave
flume test as well as the boundary conditions is shown in Figure 1.

Weight of Pipeline
L/2
Wave Pressure (P)
(without adding hydrostatic pressure)
0

0.3

1.6

Figure 1. (a) Dimension of the wave flume, (b) Finite element mesh (c) Loading conditions

80
4. Analytical solution

The analytical solution based on the poro-elastic theory can be obtained using the model
developed by Hsu and Jeng (1994). The model is capable to calculate the variation of effective
stresses, shear stress and pore pressure in either infinite and finite thickness soil under two-
dimensional and three-dimensional wave conditions. The analytical solutions are used here to
compare with the numerical solutions produced using linear elastic model to assess the
performance of the numerical model.

5. References

Hsu J. R. C., Jeng D. S. (1994). Wave-Induced Soil Response in an Unsaturated Anisotropic Sea of Finite
Thickness”. Int J. Numer. Anal. Methods Geomech.18: 785-807.
Pastor M., Zienkiewicz O. C., Chan A. H. C. (1990). “Generalized Plasticity and the Modelling of Soil
Behaviour”. Int J. Numer. Anal. Methods Geomech.14, pp. 151-190.
Pastor M., Zienkiewicz O. C., (1986). A Generalised Plasticity, Hierarchial Model for Sand under Monotonic
and Cycle Loading. I.N.M.E. University College of Swansea.
Sassa S., Sekiguchi, H. (1999). Wave-Induced Liquefaction of Beds of Sand in a Centrifuge. Geotechnique
49, No. : 621-638.
Sassa S. and Sekiguchi H. (2001). Analysis of Wave-Induced Liquefaction of Sand Beds. Géotechnique 51,
No. 2, pp. 115-126.
Teh T. C., Palmer, A. C. and Damgaard J. S. (2002). Experimental Study of Marine Pipelines on Unstable
and Liquefied Seabed. Submitted.
Zienkiewicz O. C., Chan A. H. C., Pastor M., Schrefler B. A., Shiomi T. (1999). Computational Geomechanics
with Special Reference to Earthquake Engineering. Pub: Wiley.

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 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

NUMERICAL PHOTOGRAMMETRY IN LABORATORY EXPERIENCES ON 2D SLOPES

Francesco Froiio (froiio@ing.uniroma2.it)

DIC, Università di Roma - Tor Vergata, Italy
Gioacchino Viggiani
Laboratoire 3S (CNRS – UJF – INPG), Grenoble, France
Farid Laouafa
DRS-INERIS, Verneuil en Halatte, France

ABSTRACT. In this preliminary study a numerical photogrammetry system was tested in

measuring incremental displacement fields in slope models realised with analogous Schneebeli
material. Two tests were performed corresponding to different sets of boundary conditions on the
displacements; controlled and uncontrolled deformation scenery were experienced. The resulting
measures showed efficiency, limits and perspective of this measuring technique.

1. Introduction

Current modelisation is not yet retained to be exhaustive to interpret some collapse phenomena
and subsequent shallow flows observed in natural slopes of granular material (Darve and Laouafa,
2000). The need of a better understanding of these phenomena, starting from their kinematics, and
the recent consistent improvements in numerical photogrammetry techniques motivated this
preliminary work. It was carried out at the Laboratoire 3S in order to test how efficiently Particle
Image Velocimetry can be used to measure incremental displacement or velocity fields in
laboratory experiments on slope models.
PIV is a numerical photogrammetry technique originally developed to measure plane velocity
fields in fluids, gases and flames: laser, optic and information technology being interfaced; this work
is an attempt to optimise PIV on specimen realised with Schneebeli analogue material; thus, the
starting point was not a real case to be modelled with small-scale experimentation. Analogous 2D
granular material has already been extensively used with the 1γ2ε apparatus (Joer, 1992): these
being the ingredients, one tried out to qualitatively reproduce and measure the kinematics of some
interesting phenomena: collapse triggering in the slope, granular flow or simply large unrecoverable
deformation where experienced. This aims to be the base for a further true-small-scale
experimentation program.

2. Experimental apparatus and test procedures

Two slope models, shown in Figure 1 and 2, were realised inside the 1γ2ε apparatus; this is a
system of extensible bars connected by hinges, computer controlled, designed to apply
displacement or pressure boundary conditions to specimens realised with Schneebeli analogue
material: in this case an assembly of 60mm-long cylindrical rods with diameters 1.5mm, 3mm, and
3.5mm, made of PVC (Figure 3).
In the first test the model was prepared with a slope angle of 23.6°; a constant c.c.w. angular
velocity around the base hinges of 5⋅10-4rad/s was assigned to the lateral bars; the specimen first
underwent controlled not-localised deformations; when the slope angle got about 26.0°, a relevant
collapse was observed, turning into a quick surface flow that dropped the slope angle down to
21.9°. In the second test, the initial slope was 24.3°; during the test a plate pushed downward on
the top of the specimen with a constant velocity of 8.62⋅10-2mm/s; the control on the deformation
was never lost, except some irrelevant surface slides.
For images acquisition, it was required a much lower technological effort than in the
conventional PIV applications on fluids: no laser technology was necessary; a professional digital
video camera was used, that allowed a maximum acquisition frequency of 25 images per second.
To compute the incremental-displacement-fields measures on the images sequences, the software
Davis 6.0 (La Vision, 2001) was used, that implements the PIV image-correlation algorithm.

83
 (a) (b)
Figure 1. Specimen in test 1 (a) and 2 (b) (squares on the backgorund: 20x20mm)

3. Measures

Some characteristics of the measures are reported in Table 1: the images acquisition frequencies,
the magnitude order of the maximum involved velocities and displacements, and the accuracy of
the PIV algorithm following La Vision (2001), in terms of how it effects the incremental displacement
values.
The measures relative to the phase preceding collapse in the first test, and those relative to
the second test, were found to be in very good agreement with the visual observation of the motion,
and were confirmed by some “hand made” measures of the rods displacements performed on the
images. Even at the velocities rise due to the collapse in the first test, the measured vector fields
followed reasonably the observed motion; but less clear results were obtained: nonsense measures
had to be corrected with a very human-time-consuming procedure.

SEQUENCE ACQUISITION VELOCITIES DISPLACEMENTS QUALITATIVE

ACCURACY
DESCRIPTION FREQUENCY MAGNITUDE MAGNITUDE AGREEMENT
test 1: controlled deformation 1 image / 5s 2.5⋅10-1 mm/s 1.2 mm 0.13mm very good
test 1: collapse triggering 25 images / 1s 2.9⋅10 1 mm/s 1.2 mm 0.13mm good
test 1: shallow granular flow 25 images / 1s 1.4⋅10 2 mm/s 5.6 mm 0.13mm not always satisfying
test 2 1 image / 10 s 7.2⋅10-1 mm/s 7.2 mm 0.11mm very good
Table 1. Characteristics of the measures.

Figure 3. (a) Schneebeli material, (b) Incremental displacement field.

84
4. Conclusions

Testing Particle Image Velocimetry on laboratory slope models realised with analogue Schneebeli
material indicated this coupling to be a powerful tool to investigate the kinematics of many
phenomena of interest in slope stability studies. This being a preliminary study, the range of
amelioration is consistent; rods size, material pigmentation, images-acquisition frequency and
image definition will be optimised to get more trustful measures.

5. References

Darve F., Laouafa F. (2000). Instabilities in granular materials and application to landslides. Mech. Choes.
Frict. Mater. 5 (8): 627-652.
Joer H. A. (1992). 1γ2ε: une nouvelle machine de cisaillement pour l’étude du comportement des milieux
granulaires. PhD. Thesis.UJF, Grenoble.
La Vision (2001). Davis Software Manual. Göttingen, Germany.

85
 International Workshop of Young Doctors in Geomechanics - W(H)YDOC 02
De Gennaro & Delage (eds) 2002, ENPC Champs-sur-Marne

MODELLING LANDSLIDES IN VOLCANIC SOILS: LAS COLINAS LANDSLIDE (EL

SALVADOR, FEBRUARY 2001)

Manuel Pastor, Jose A. Fernández-Merodo, Pablo Mira (mpastor@cedex.es)

CEDEX, Madrid, Spain.
Laura Tonni
Università di Bologna, Bologna, Italy.

ABSTRACT. A numerical model is presented to simulate landslides in volcanic soils. The failure
mechanism of Las Colinas landslide (El Salvador), during the February 2001 earthquake is
analysed. A suitable constitutive model able to reproduce the behaviour of cemented soils is
introduced in the finite element code GeHomadrid for dynamic analysis. Special attention is paid to
the numerical treatment of the implicit integration of the constitutive law and the boundary
conditions.

1. Introduction

Catastrophic landslides are one of natural hazards taking an important toll in human lives and
causing major economic damages throughout the world. The landslide of Las Colinas (El Salvador),
which occurred during the February 2001 earthquake is a dramatic example of this phenomenon,
Figure 1.

Figure 1. Las Colinas landslide (El Salvador, February 2001)

Numerical models are a most important tool to assess the safety of a particular site,
estimating under which conditions a landslide can take place.

2. Model for cemented soils

A constitutive law developed within the framework of the Generalized Plasticity theory (Pastor et al.
1990) and improved with the results obtained by Lagioia and Nova (1995), is used to represent the
behaviour of cemented soils.

3. Implicit integration of the proposed model

The reliability and robustness of the numerical analysis, even more for dynamic problems, strongly
depend on the accuracy and robustness of the algorithm used for the integration of the constitutive
rate equations. An implicit integration scheme for the proposed model, developed by Tonni (2002),
is used.
87
4. Finite element modelling of Las Colinas landslide

The numerical analysis of the Las Colinas landslide is carried out using the GeHoMadrid finite
element program. Plane strain condition and eight-node elements are used for the calculations.
The specified earthquake motion and the radiation boundary condition for the unbounded
media are defined imposing dashpots in the tangential and normal direction at any position of the
boundary.
The results of the numerical computation are analysed and compared with the observed
mechanism of failure.

5. Acknowledgements

The authors want to acknowledge the EU project Degradation and Instabilities in Geometerials with
Application to Hazard Mitigation (DIGA) in the framework of the Human Potential Program,
Research Training Networks.

6. References

Pastor M., Zienkiewicz O.C., Chan A.H.C. (1990). Generalized plasticity and the modelling of soil behaviour.
Int. J. Numer. & Anal. Meth. Geomech., vol. 14: 191-207.
Lagioia R., Nova R. (1995). An experimental and theoretical study of the behaviour of a calcrenite in triaxial
compression. Geotechnique 45, Nº 4: 633-648
Tonni L. (2002). Modellazione numerica di terreni granulari con la plasticità generalizzata. Tesi di dottorato
del Politecnico di Torino, 2002.
Fernandez Merodo J.A. (2001) Une approche à la modélisation des glissements et des effondrements de
terrains: initiation et propagation. Thèse de l’Ecole Centrale Paris, nº 2001-33.
Mira P. (2002) Análisis por elementos finitos de problemas de rotura de geomateriales. Tesis Doctoral ETSI.
Caminos, Canales y Puertos UPM, 2001.

88