18?me Congr?s Fran?ais de M?canique Grenoble, 27-31 ao?t 2007
1
On safety of slurry?wall trenches
Brzakala Wlodzimierz & Gorska Karolina
Institute of Geotechnics and Hydroengineering, Faculty of Civil Engineering
Wroclaw University of Technology
Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
brzakala.wlodzimierz@pwr.wroc.pl
Abstract :
The paper focuses on a numerical simulation of ground movements and a stability evaluation during
trench excavation processes (slurry?walls technology). A special attention is paid to modeling of failure
and to defining of safety measures. Numerical calculations are based on the FLAC 3D code. It is found
that the soil kinematics at failure coincides with the literature data. Four kinds of safety factor are
investigated. The results converge if trench is deep enough. The applied probabilistic safety analysis
takes into account the random level of the ground water, as a most important factor, and the soil strength.
The acceptable level of safety is found.
R?sum? :
L?article se concentre sur une simulation num?rique des mouvements du sol et sur l??valuation de la
stabilit? lors du processus d?excavation en tranch?e (parois moul?es). Une attention sp?ciale est attir?e
sur la mod?lisation de d?faillances et sur la d?finition des mesures de s?curit?. Des calculs num?riques
sont bas?s sur le code FLAC 3D. La cin?matique de sol ? la d?faillance co?ncide avec des donn?es dans
la litt?rature. Quatre types des coefficients de s?curit? font l?objet d?une enqu?te. Des r?sultats co?ncident
dans la cas o? la tranch?e est suffisamment profonde. L??valuation probabiliste de s?ret? consid?re une
nappe phr?atique statistique et une r?sistance du sol comme des ?l?ments les plus importants. Un niveau
acceptable de s?curit? a ?t? atteint.
Key-words :
slurry?wall trench; safety measure; numerical simulation
1 Introduction.
An increasing interest towards applications of slurry walls can be observed since the late
sixties. It is so, because geotechnical engineers cope with more and more complicated ground
situations, including water and soil conditions, as well as construction sites situated in urban
regions. Bearing in mind a very limited space in the city infrastructure, deep excavations are
required by needs of underground parking places, protection of existing objects in
the excavation vicinities, large loadings transmitted from the ground and from the structure, etc.,
the concept of vertical reinforced?concrete panels is both technically effective and economically
justified.
The paper focuses on the first phase of the technology when a vertical finite?length trench
element is excavated under a hydrostatic support from inside of a bentonite slurry. It seems that
a little interest is paid to the static analysis and safety margins of the trenches (as well as
a surrounding ground), except for ? but a few ? recent papers. During the trench excavation
some dangerous consequences can occur due to variations of: the groundwater table, the pore
pressure, the soil strength, the slurry level, weak soil lenses, suction forces, etc. All of them are
random, sometimes correlated, and significantly influence the required level of safety.
18?me Congr?s Fran?ais de M?canique Grenoble, 27-31 ao?t 2007
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In the stability evaluation, a half?elliptic sliding block method introduced by Kowalewski
& Piaskowski (1965) is often considered ? Fig. 1a) or a 3D method of columns which
corresponds to the method of 2D slices ? Fig. 1b). Methods resulting from the Janssen silo?
pressure analysis, adopted by Schneebeli, become less popular. Three parameters are very
important for the local stability of the trench: the isotropic supporting stress pz caused by the
bentonite slurry, the hydrostatic pressure pw due to the groundwater table and the effective soil
pressure ?? in soils near a face of the trench. Note that standard engineering measures of safety,
like the local ratios FS = pz/(?? + pw) or FS = (pz ? pw)/??, are not useful in the context of
advanced numerical calculations. Indeed ? the forces acting on all faces of the trench have to be
always in equilibrium (boundary conditions in stresses).
FIG. 1 ? Shape of the sliding wedge by: a) Piaskowski & Kowalewski; b) Tsai & Chang.
A full elastoplastic stability evaluation using the 3D finite difference method for
continuum is the objective of the paper. The shape of the sliding wedge is to be verified and
margins of safety are to be estimated.
2 Assumptions for the numerical study.
A vertical trench, 1m thick and 10m deep (H = 10m), with the typical length 6m (L = 6m),
is considered. Due to two planes of symmetry, only one quarter of the 3D boundary problem is
of interest, Fig. 2a). The soil model corresponds to a macrohomogeneous sand, an elastoplastic
material with the Coulomb?Mohr yield criterion and a nonassociated rule of plastic flow.
The geotechnical parameters are as follows: the unit weight ? = 18,5kN/m3, the earth pressure
coefficient at rest Ko = 0,47, the friction angle ? = 32?, the cohesion c = 0kPa, the dilation angle
? = 0?, Young?s modulus E = 70MPa and Poisson?s ratio ? = 0,25. The groundwater table
varies from 0,5m to 3,0m below the ground surface. It is assumed that there is no hydraulic
contact between the bentonite suspension and the ground water. Neither flow nor changes in the
pore pressure are taken into consideration during the trench excavation.
The model domain is divided into four parts of different zone concentrations: fine ones
near the excavation (minimal mesh distance of 0,5m) and coarse ones near the corners (maximal
mesh distance of 2,0m), Fig. 2b).
18?me Congr?s Fran?ais de M?canique Grenoble, 27-31 ao?t 2007
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FIG. 2 ? The geometric assumptions: a) dimensions of the domain of calculation and boundary
fixities; b) a finite difference mesh.
The excavation process is modelled by a successive removing of 1m ? thick elements from
the mesh. The hydrostatic slurry pressure is taken as an external loading, linearly increasing
with depth, applied to all faces of the trench, including the toe. Calculations were performed in
terms of the effective stress (a fully drained case). Forces which are produced during working
movements of the bucket of a trenching machine are not taken into account; they do not have
much influence, if the length of the bucket is much smaller than the length of the trench
(sometimes, contractors do not agree with this opinion). For simplification, the ground water
pressure is subtracted from the slurry pressure. Thus only the reduced boundary loading from
both fluids is applied to all faces and to the toe of the trench. The bentonite slurry with the unit
weight of 10,5kN/m3 is used as the stabilizing fluid and the value of 10,0kN/m3 is accepted for
the unit weight of water. The slurry level is kept unchanged on the ground surface, i.e. above
the groundwater table. The code FLAC 3D is used for numerical calculation.
3 Deterministic measures of safety.
The stability of the trench is investigated by the reduction of tg? (FS1), by the reduction of
the unit weight of the bentonite slurry (FS2) and by the increase of the unit weight of
the surrounding sand (FS3). Three different factors of safety are proposed, all comparing real
parameters with the reduced (increased) ones at failure:
zredtg
tgFS
?
?=
1 ? reduction of the ground strength parameter (cohesion c = 0),
zzred
zFS
?
?=
2 ? reduction of unit weight of the bentonite slurry,
g
gzwFS
?
?=
3 ? increase of unit weight of the surrounding sand.
The terms ?reduction? and ?increase? mean successive 5% changes of the parameters in
each stage during calculations. The arbitrary 5% level is accepted as a compromise between
time of calculations and required accuracy.
The FS?calculations are executed for every increased trench depth (from 1,0m to 10,0m,
step 1,0m). The response of the trench during every stage of the excavation, i.e. for any fixed
excavation depth, is monitored and the reduction procedure is continued until the trench
collapses. For a ductile elastoplastic behaviour, it is not evident when such a failure takes place.
Therefore, it is assumed that the failure means a ?rapid increase? of displacements of points
18?me Congr?s Fran?ais de M?canique Grenoble, 27-31 ao?t 2007
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selected on the face of the trench. For this purpose, maximal curvature of the subsidence curves
can be used. The points were selected on the plane of symmetry, where the largest
displacements are expected.
Fig.3 presents a dependence of the safety factor on the depth of excavation. For shallow
trenches, the differences between the safety factors FSi are quite significant, but the differences
vanish if the values of FSi become small. The calculations in this section and the results in Fig.3
correspond to the fixed the groundwater table situated 2,0m below the ground surface.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 FS
de
ph
t [m
] FS1
FS2
FS3
FIG. 3 ? The dependence of the safety factors FSi on the depth of excavation [m].
Although based on the same concept, and leading to similar results, the coefficients FS2
and FS3 seem to be more controversial than FS1. Indeed, highly reduced values of tg? are
physically acceptable, in contrast to small values of the unit weight of the bentonite slurry (say,
less than 6kN/m3) or large values of the unit weight of the soil (say, more than 30kN/m3). Note
a kind of (almost) stabilisation of FSi values with depth which can reflect some silo?effects.
A spatial distribution of displacements within the sliding wedge, just before the failure due
to reduction of tg?, is presented in Fig. 4. The results confirm kinematics proposed by Tsai &
Chang (1996), Fig.1b), more than the one used earlier by Kowalewski & Piaskowski (1965),
Fig.1a).
FIG. 4 ? The displacements of the continuum within the sliding wedge near the trench, [m].
4 Reliability index. Calibration.
Assume that the coefficient of friction f = tg? is random, has an expected value ?f and
a standard deviation ?f . Define the following standardized random variable Z1 = (f ? ?f)/?f .
18?me Congr?s Fran?ais de M?canique Grenoble, 27-31 ao?t 2007
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Similarly, Z2 = (t ? ?t)/?t stands for the depth of the random groundwater table, t > 0. If so,
the limit state condition, expressed in terms of the displacements of a representative point, takes
the form U(Z1,Z2) = ulim. Numerical calculations revealed that the dependence on the value of
ulim is not very important, if ulim is large enough (steady plastic?flow zones). The mechanical
assumptions justify a probabilistic simplification that Z1 and Z2 are statistically independent.
Let ?f = 0.55, ?f = 0.055 (the coefficient of variation denoted as ?f = ?f/?f = 0.055/0.50 = 10%)
and ?t = 2.0m, ?t = 0.5 (i.e. ?t = ?t/?t = 0.5/2.0 = 25%). The data can reflect much greater
variability of the water conditions due to ineffective drainage system, floods and so on.
The limit state condition for ulim = 0.015m is plotted in Fig.5, making use of selected results
yielding from the numerical analysis (H = 10,0m).
The shortest distance ? from the origin (0,0) to the limit state line in the space of
the variables (Z1;Z2) is a standard measure of safety, Thoft?Christensen & Baker (1982). Since
the limit state function U is almost linear around the design point D, the probability of failure
can be approximated as:
pf = ?(??), so pf ? 0.0035.
The obtained values of ? and pf are relatively small in the context of standards of structural
reliability, but they seem to be acceptable for short?time construction with ductile behaviour
and plastic reserves of strength.
The design point D(z1d,z2d) determines two design values of the physical parameters:
fd = (tg?)d = ?f + z1d ??f = ?f ??f where:
?f = 1 + z1d ??f = 1 ? ?? ?f ?cos? = 1 ? 1.4?10% = 0.86 = 1/1.16
td = ?t + z2d??t = ?t??t where:
?t = 1 + z2d??t = 1 ? ???t ?sin? = 1 ? 2.3?25% = 0.43 = 1/2.35.
The results in terms of the partial safety factors ?f and ?t need a comment. The dominating
role of the groundwater table localization is evident: ?t << 1. This happens due to the greater
sensitivity of the model subject to changes of the groundwater table than to random fluctuations
of f = tg?.
Formally speaking, this conclusion results from the design?point coordinates for which
|z2d| = 2.3 > |z1d| = 1.4. Furthermore, this is the large variability of the groundwater table depth t
which causes such a conclusion (?t = 25% > ?f = 10%). Apparently, the partial safety coefficient
?t = 0.43 is very low in the considered example. However, this coefficient is to correct the
expected value ?t which is greater than the characteristic value accepted sometimes as a safe
probabilistic quantile. Bearing this in mind, the comparison with the EC7 guidelines becomes
not straightforward, unless a full information on probability distributions is available.
Note that such elements as foundations situated near the trench, random soft?soil lenses,
a pore pressure generation etc. can change the conclusions.
FIG. 5 ? The Hasofer and Lind reliability index ? ? 2.7
and the design point D,
D(?1.4;?2.3) = D(???cos?;???sin?), where ? = 58.6o
-6
-5
-4
-3
-2
-1
0
-3 -2 -1 0 1 2
ulim=0.015m
Z2
Z1
?
D
18?me Congr?s Fran?ais de M?canique Grenoble, 27-31 ao?t 2007
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5 Closing conclusions.
a) The numerical calculations indicate that the safety of the trench supported by the bentonite
slurry decreases with its depth. However, the changes are not very significant below
the depth of 7m and a kind of convergence is observed. Such a finding can correspond to
a silo?effect.
b) Relatively large values of the factors of safety are observed for deterministic situations, like
FS = 2 ? 3 or more. This conclusion can be misleading, because some important factors are
not taken into account: a fluid flow and changes in the pore pressure, technological
excitation by movements of the bucket of trenching machine, soil inhomogeneities,
foundations etc.
c) There is no doubt that the localisation of the groundwater table ? related to the level of
the slurry in the trench ? is the pivotal parameter of the model.
d) The safety factor FS1 (the relative reduction of soil?strength parameters) seems to be
the most coherent and representative for safety estimation within the deterministic
approach.
e) Standard probabilistic analysis of safety, expressed in terms of the reliability index ?,
reveals that the large values of FS in the deterministic approach can be overestimated.
f) The observed kinematics of sliding wedges confirms engineering assumptions within
the limit state approach, especially the ones presented by Tsai & Chang (1996).
Acknowledgement
The cooperation with Dr Marek Ca?a (Polish Academy of Mining and Metallurgy, Cracow)
in numerical modelling using FLAC 3D is appreciated.
References
Piaskowski, A., Kowalewski, Z. 1965 Application of tixotropic clay suspensions for stability of
vertical sides of deep trenches without strutting. 6th Int.Conf.SMFE Montreal, Vol.III, 526-
529.
Thoft?Christensen, P., Baker, M.J. 1982 Structural Reliability Theory and its applications.
Springer?Verlag, Berlin.
Tsai, J.S., Chang, J.C. 1996 Three?dimensional stability analysis for slurry trench wall in
cohesionless soil. Canadian Geotechnical Journal 33, 798-808.
PN?EN 1538 2002 Execution of special geotechnical works ? Diaphragm walls.