203
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
1
Methods of determination of K
0
in overconsolidated clay
Méthodes de détermination de K
0
dans une argile surconsolidée
Boháč J., Mašín D., Malát R., Novák V., Rott J.
Charles University in Prague, Faculty of Science, Albertov 6, 12843 Praha 2, Czech Republic
ABSTRACT: In situ effective stresses, expressed usually by the at rest coefficient K
0
, influence the mechanical behaviour and thus
any geotechnical analysis. In normally consolidated soils K
0
can be computed according to the Jáky formula. For overconsolidated
clays however neither a general formula nor a general experimental procedure are available. The paper summarizes briefly the
available methods and then presents some methods in more detail. First the use of flat dilatometer is discussed. Further, K
0
is
determined by back analysing the convergence of a circular test gallery. Finite element analysis using the hypoplastic constitutive
model to represent the clay behaviour is adopted in the analyses.
RÉSUMÉ : Les contraintes effectives in situ, exprimées habituellement à travers le coefficient des terres au repos K
0
, ont une
influence sur le comportement mécanique des sols, et donc, sur toute analyse géotechnique. Dans les sols normalement consolidés, K
0
peut être calculé à partir de la formule de Jáky. Pour les argiles surconsolidées cependant, il n’existe ni formule générale, ni procédure
expérimentale reconnue pour évaluer ce paramètre. La communication présentée résume brièvement les méthodes actuellement
disponibles, puis présente quelques méthodes plus en détail. D'abord, l’utilisation du dilatomètre plat et d'une cellule de pression en
forme de pelle est discutée. En outre, K
0
est déterminé à partir de l’analyse en retour de la convergence d'une galerie d’essai circulaire.
Une approche en éléments finis, basée sur l’utilisation d’une loi de comportement hypoplastique pour modéliser le comportement des
argiles, est adoptée dans l’analyse.
KEYWORDS: clay, earth pressure at rest, horizontal stress, anisotropy, hypoplasticity, tunnelling.
MOTS-CLÉS : argile, pression des terres au repos, contrainte horizontale, anisotropie, hypoplasticité, tunnel
1
INTRODUCTION
The in situ effective stresses represent an important initial
condition for geotechnical analyses. Typically, the horizontal
stress is computed from the vertical stress using the coefficient
of earth pressure at rest K
0
=σ
h
'/σ
v
', where σ
h
' and σ
v
' are
effective horizontal and vertical stresses, respectively. In the
case of deep foundations (friction piles), retaining structures and
tunnels, K
0
influences the mechanical behaviour dramatically.
Franzius et al. (2005) made a direct investigation into the
influence of K
0
conditions in 3D finite element analysis of a
tunneling problem using K
0
= 1.5 and K
0
= 0.5. The
unrealistically low K
0
value for London Clay led to better
predictions: the normalised settlement trough was narrower and
deeper. In absolute values, however, low K
0
caused
overprediction of surface settlements by a factor of 4. With
K
0
= 1.5 the predicted trough was too wide and vertical
displacements were underpredicted by the factor of 4.
For normally consolidated soils the estimation of horizontal
stresses is not a major problem. Jáky's equation in its usual
simplified form of K
0nc
=1-sinφ
c
' may be used in determining the
K
0nc
for normally consolidated soils (Jáky, 1948; φ
c
' is the
critical state friction angle). There is a lot of experimental
evidence throughout the literature that the Jáky formula
represents the at rest coefficient of normally consolidated soils
well provided the critical state effective friction angle φ
c
' is used
(Mesri and Hayat, 1993; Mayne and Kulhawy, 1982).
For overconsolidated clays however neither a general
formula nor a generally applicable experimental procedure for
determining the initial stress are available to date. In
summarising the knowledge about the mechanical behaviour
and characterisation of a typical example of overconsolidated
clays – the Tertiary London Clay, which has been a subject of
very intensive research for many decades, Hight et al. (2003)
noted: „Still the most difficult parameter to determine for the
London Clay is K
0
“.
1.1
Direct methods of K
0
determination
Horizontal stress in clay is most often determined by selfboring
pressuremeter (e.g., 'Camkometer' - Wroth and Hughes, 1973),
by the flat dilatometer (Marchetti, 1980), or different types of
pushed-in spade-shaped pressure cells (e.g., Tedd and Charles,
1981). The use of push-in instruments in stiff clays is often
questioned due to possible problems with the installation and
due to the soil disturbance. The latter reason together with the
possibility of imperfect fit in the borehole seems to have
disqualified the Menard-type pressuremeter in stiff clays. A
good agreement of K
0
values obtained by push-in spade-shaped
pressure cells and Camkometer for London Clay was reported
by Tedd and Charles (1981), the 'spade' producing a smaller
scatter and better reproducibility. Hamouche et al (1995)
reported results by Marchetti dilatometer consistent with those
obtained with the self boring pressuremeter in overconsolidated
sensitive Canadian clays.
A hydraulic fracturing technique for clays for measuring the
horizontal total stress was developed by Bjerrum and Andersen
(1972). The method is based on measuring the stress at closing
of a vertical crack that had previously been formed by
pressurised water. The method can hardly be used under the
condition of K
0
> 1 as a horizontal crack would be formed
instead of the vertical one, and „...the method will just measure
the weight of the overburden...“ (Bjerrum and Andersen, 1972).
A recent 2D numerical study by Wang et al (2009) also
considers horizontal cracks being formed in the case of K
0
>1,
i.e. in overconsolidated clays. However, Lefebvre et al. (1991)
