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ORIGINAL PAPER
Strutted Excavation in Soft Soil Incorporating a Jet-GroutBase Slab: Analysis Considering the Consolidation Effect
Jose Leitao Borges • Ricardo Gomes Pinto
Received: 1 February 2010 / Accepted: 8 January 2013 / Published online: 19 January 2013
� Springer Science+Business Media Dordrecht 2013
Abstract The influence of the consolidation on a
strutted excavation in soft soil is analysed using
a computer code based on the finite element method.
A base jet-grout slab is considered in order to improve
stability against bottom heave failure and minimize wall
displacements. The numerical model incorporates the
Biot consolidation theory (coupled formulation of the
flow and equilibrium equations) with soil constitutive
relations simulated by the p–q–h critical state model.
Special emphasis is given to the analysis, during and
after the construction period, of the pore pressures, shear
stresses, stress levels and displacements in the ground,
as well as strut compression loads, wall displacements
and bending moments, earth pressures on the wall faces
and compression loads and bending moments on the jet-
grout slab. The safety factor against bottom heave is also
evaluated from the finite element analysis considering
formulations of the critical state soil mechanics, and also
compared to values obtained with traditional methods
that use limit equilibrium approach and bearing capacity
fundamentals.
Keywords Strutted excavation � Soft soil �Base slab � Consolidation � Critical state model �Coupled analysis
1 Introduction
Theoretically, when a strutted excavation is under-
taken in a saturated soft clay and the wall is not
extended below the excavation base, bottom heave
failure occurs if the initial total vertical stress on the
base level is higher than bearing capacity of the
subjacent soil. The two most frequently quoted
methods for analysing bottom heave stability has
traditionally been the limit equilibrium approach
based on Terzaghi (1943) and Bjerrum and Eide
(1956). The latter was calibrated against observed
bottom heave failures.
In order to improve stability against bottom heave
failure, several practical solutions can be considered.
One solution is to extend the wall below the excava-
tion base, usually down into a stronger stratum (hard
stratum). In this case, in simple terms, earth pressure
on the wall, below the excavation bottom, is trans-
ferred to the hard stratum and to the lower strut levels.
However, in practical terms, this solution may not be
practicable if the hard stratum lies deeply.
If this is the case, one possible solution consists of
extending the wall a few meters below the excavation
base and, before excavation, constructing a jet-grout
slab to support the wall below the excavation level.
Another solution consists of using diaphragm walls
to act as cross-walls below the excavation base
(Fig. 1). This concept was firstly developed by Eide
et al. (1972) for constructing a 240 m long section of a
double decked subway and railway tunnel in Oslo,
J. L. Borges (&) � R. G. Pinto
Department of Civil Engineering, Faculty of Engineering,
University of Porto, Rua Dr. Roberto Frias,
4200-465 Porto, Portugal
e-mail: [email protected]
123
Geotech Geol Eng (2013) 31:593–615
DOI 10.1007/s10706-013-9611-0
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Norway. In both base-slab and cross-wall solutions,
the retaining wall can be founded on steel piles
extended to the hard stratum, as shown in Fig. 1.
Another pertinent question in excavations in soft
ground is the excess pore pressure generation during
construction and its dissipation after that period
(consolidation). Basically, during the excavation
period, the variation of the stress state in the ground
consists of a decrease of total mean stress and an
increase of deviatoric stress. In saturated normally
consolidated clays, the decrease of total mean stress
induces negative excess pore pressures whereas the
increase of shear stress gives rise to positive pore
pressures. Therefore, the sign of the excess pore
pressure at the end of excavation may be positive or
negative, depending on the magnitude of the above-
mentioned contrary effects. However, field measure-
ments of a number of excavations suggest that, in
general, excess pore pressure is usually negative at the
end of construction (Lambe and Turner 1970; DiBiagio
and Roti 1972; Clough and Reed 1984; Finno et al.
1989).
Thus, after construction there are pore pressure
gradients in the ground that determine a consolidation
process. This process is clearly dependent on both the
magnitude of excess pore pressure at the end of
construction and the long-term equilibrium conditions
regard to pore pressure. These conditions may corre-
spond to a hydrostatic pore pressure distribution or to a
steady flow state.
In the past, studies of excavations in saturated clays
have majority been based on undrained total stress
analyses. However, despite the importance of such
analyses in practice, a more realistic approach consists
of taking into account the consolidation effect during
and after excavation by performing coupled analyses
with adequate soil constitutive models (Potts et al.
1997).
In the present study, the consolidation effect on an
idealized strutted excavation in soft soil incorporating
a jet-grout base slab is analysed by using a computer
program based on the finite element method. This
program was developed by J. L. Borges and incorpo-
rates, among other features, coupled analysis and the
p–q–h critical state model for soil constitutive behav-
iour simulation. The initial version of the program was
presented in Borges (1995), but several improvements
were posteriorly developed, including a 3D coupled
analysis version (Borges 2004).
The study incorporates the analysis, during and
after the excavation period, of pore pressures, shear
stresses, stress levels and displacements in the ground,
as well as strut compression loads, wall displacements
and bending moments, earth pressures on the wall
faces and compression loads and bending moments on
the jet-grout slab. Comparing to the values obtained
with the methods of Terzaghi (1943) and Bjerrum and
Eide (1956), the safety factor against bottom heave is
also evaluated, at several stages of the excavation and
consolidation, with a computer program, described in
Sect. 3, which uses the results of the finite element
analysis and formulations of the critical state soil
mechanics.Fig. 1 Illustration of diaphragm cross-wall concept as used in
the tunnel of Oslo (1973–1975), Norway
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2 Finite Element Program
Basically, for the present applications, the finite
element program uses the following features:
(a) plane strain conditions; (b) coupled formulation
of the flow and equilibrium equations with soil
constitutive relations formulated in effective stresses
(Biot consolidation theory) (Borges 1995; Borges and
Cardoso 2000; Lewis and Schrefler 1987; Britto and
Gunn 1987), applied to all phases of the problem, both
during excavation and in the post-construction period;
(c) utilisation of the p–q–h critical state model (Borges
1995; Borges and Cardoso 1998; Lewis and Schrefler
1987), an associated plastic flow model, to simulate
constitutive behaviour of soil; (d) use of the 2D elastic
linear model to simulate constitutive behaviour of the
wall (reinforced concrete) and of the jet-grout slab;
(e) utilisation of the 1D elastic linear model to
simulate the constitutive behaviour of the struts;
(f) use of joint elements with elastic perfectly plastic
behaviour to simulate the soil–wall and soil–slab
interfaces.
In the p–q–h model—which is a extension
(improvement) of the Modified Cam-Clay model into
the three-dimensional stress space using the Mohr–
Coulomb failure criteria—the parameter that defines
the slope of the critical state line, M, is not constant
(which happens in the Modified Cam-Clay model), but
depends on the angular stress invariant h and effective
friction angle, /0:
M ¼ 3sin/0
ffiffiffi
3p
cos hþ sin/0sinh
ð1Þ
This defines the Mohr–Coulomb criteria when M is
introduced in the equation of the critical state line
q ¼ M � p ð2Þ
where p is the effective mean stress and q the
deviatoric stress.
This is an important feature of the p–q–h model
because, as shown in triaxial and plane strain tests
(Mita et al. 2004), the soil critical state depends on h.
This means, for instance, that, in the p–q–h model,
M takes different values whether compression or
extension stress paths take place, which does not occur
in the Modified Cam-Clay model. Numerical and
laboratorial results presented by several authors (Potts
and Zdravkovics 1999; Mita et al. 2004) showed that
strain–stress behaviour of the soil in plane strain
analyses is much better simulated if the slope of the
critical state line is defined according to the Mohr–
Coulomb criteria, which happens in the p–q–h model.
Figure 2a shows, in the principal effective stress
space, the yield and critical state surfaces of the p–q–hmodel. In the p–q plane, the yielding function is an
ellipse (Fig. 2b) and, depending on the over-consol-
idation ratio, the p–q–h model simulates hardening
behaviour or softening behaviour. Hardening occurs in
normally consolidated or lightly overconsolidated
clays while softening occurs in medially to strongly
overconsolidated clays.
The accuracy of the finite element program used in
the present study has been assessed against field
measurements (which is the adequate way for complex
problems without theoretical solutions) and used to
analyse a wide range of geotechnical structures
involving consolidation (Borges 1995, 2008; Costa
2005; Domingues 2006; Costa et al. 2007). With
regard to embankments on soft ground, Borges (1995)
compared numerical and field results of two geosyn-
thetic-reinforced embankments, one constructed up to
failure (Quaresma 1992) and the other observed until
the end of consolidation (Yeo 1986; Basset 1986a, b).
The accuracy was considered adequate in both cases.
Using the same computer code, very good agreements
with field measurements were also observed both in an
embankment on soft soils incorporating stone columns
(Domingues 2006) and in a braced excavation in a
very soft ground (Costa et al. 2007; Costa 2005). This
last case study was an excavation carried out in the
City of San Francisco, presented by Clough and Reed
(1984), to install a large sewer culvert. As an example
of the accuracy of the computer code in this kind of
works, comparisons of field and numerical results of
this case study are shown below.
Further details of its numerical simulation can be
seen in Costa et al. (2007). The width and maximum
depth of the excavation (Costa et al. 2007) were
approximately 7.6 and 9 m, respectively. The retain-
ing structure consisted of a steel sheet-pile wall braced
at three or four levels. The behaviours of two sections
were monitored—at Rankin Street and at Davidson
Avenue—and compared with numerical results, as
said above. The typical cross section of the excavation
is presented in Fig. 3. The ground was mainly
composed of rubble fill and soft clay (San Francisco
New Bay Mud); at Davidson Avenue the geotechnical
Geotech Geol Eng (2013) 31:593–615 595
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parameters revealed a weaker soil than at Rankin
Street. At the Davidson Avenue section, two piezom-
eters were installed in the same hole behind the sheet-
pile at depths of 9.1 and 12.2 m. In Fig. 4 numerical
and field results are shown (in y-axis the pore pressure,
u, is divided by the initial pore pressure value, ui, and
in x-axis the evolution of excavation depth is repre-
sented). Although at 9.1 m the computation underes-
timated the decrease of pore pressure, the evolution of
the numerical results was quite similar to the mea-
surements in the field; for the lower piezometer the
agreement was excellent, independently of the exca-
vation depth.
The instrumentation of the excavation also included
some inclinometers, at both Rankin Street and David-
son Avenue sections. Computed and measured hori-
zontal displacements of the wall are shown in Fig. 5.
The behaviour at Rankin Street (Fig. 5a), with small
displacements at the top and tip and a pronounced
convexity of the external face of the wall, was in
agreement with typical patterns observed in similar
works when values of the safety factor against bottom
heave are not low. On the contrary, the pattern of
displacement at Davidson Avenue section (Fig. 5b),
where the soil was weaker, revealed low stability
conditions at the end of the excavation: the external
wall face became concave and the horizontal dis-
placement of its tip reached 23 cm (about 2.5 % of the
excavation depth). At the Rankin Street section, where
field results were available only at the end of the
excavation, a very good similarity of field and
computed results was observed, mainly on the upper
strutted zone of the wall (Fig. 5a). At the Davidson
Avenue section (Fig. 5b), where field measures were
available from stage 2 to stage 4, good agreements
with numerical values were observed, in general. At
stage 2, the computed results were higher than field
values, although a similarity of the curve shape was
(a)
(b)
Originalelasticregion
αp
Criticalstate line
p
ε ( ) qq
ε ( )v
4
3
2
1
Fig. 2 Yield and critical
state surfaces of the p–q–hcritical state model in
a principal effective stress
space and b p–q
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F. L.
Fill
Soft ClayV
aria
ble
3.0
4.5
1.8
4.3
Stage11
Stage
Stage 2
Stage 4
Stage 3
7.6
10.5
m -
R. R
anki
ne
15.0
m -
Dav
idso
n A
v.
Wall bending stiffness:
6.0 x 10 kN/m /m4 2
1st level: 1.3 x 10 kN/m
Axial strut stifness:
2nd/3rd level: 5.8 x 10 kN/m
5
5
Fig. 3 Typical cross
section of the excavation
(Costa et al. 2007)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10
Excavation depth (m)
u/ui
(kP
a)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10
Excavation depth (m)
u/ui
(kP
a)
Measured
Computed D1
(a) (b)
Fig. 4 Comparison between numerical and field results of pore pressures at Davidson Avenue: a depth of 9.1 m; b depth of 12.2 m
(Costa et al. 2007)
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observed; at stages 3 and 4, on the strutted length of the
wall, the similarity is very good, although some
discrepancies had arisen below the excavation bottom.
3 Program of Bottom Heave Stability Analysis
3.1 Preamble
As said above, the two most quoted methods for
analysing bottom heave stability has traditionally been
the limit equilibrium approach based on Terzaghi
(1943), and Bjerrum and Eide (1956). The latter,
which actually stems from Skempton (1951) and was
calibrated against observed bottom heave failures, is
based on the similarity between the bearing capacity of
a deeply embedded footing and a bottom heave failure
of an excavation.
Figure 6 shows the assumed failure surface of the
Terzaghi (1943) approach when the wall is embedded
below the excavation base. In this case, the value of
the safety factor is given by Eqs. 3 and 4, respectively
for Terzaghi (1943) the Bjerrum and Eide (1956)
methods:
0
5
10
15
20-0.08 -0.06 -0.04 -0.02 0.00
Horizontal displacement (m)
Dep
th (
m)
Stage 2 - Computed Stage 3 - Computed
Stage 4 - Computed 3 months - Computed
Stage 4 - Measured
0
5
10
15
20
25
-0.25 -0.20 -0.15 -0.10 -0.05 0.00
Horizontal displacement (m)
Dep
th (
m)
Stage 2 - Computed
Stage 3 - Computed
Stage 4 - Computed
Stage 4 - Measured
Stage 2 - Measured
Stage 3 - Measured
(a)
(b)
Fig. 6 Failure surface of the Terzaghi (1943) method for
bottom heave stability analysis
Fig. 5 Horizontal displacements of the wall. Comparison
between computed and measured results: a at Rankin Street;
b at Davidson Avenue (Costa et al. 2007)
b
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F ¼ð2þ pÞsu þ cd þ 2dsa
B
H c�ffiffi
2p
su
B
� � ð3Þ
F ¼Ncsu þ cd þ 2dsa
B
cHð4Þ
where su: average strength of the soil in the bottom
heave failure zone below the tip of the wall; sa:
average strength of the soil–wall interface over the
embedded depth d; c: unit weight of soil; H: length of
the wall; B: width of the excavation; d: embedded
depth of the wall below the excavation base; Nc:
bearing capacity factor, which depends on the values
of H, B and L (horizontal length of the excavation),
incorporating the effects of the strength of soil above
the excavation base and of the finite length of
excavation.
In the present study, the analysis of the bottom
heave stability is also evaluated by a computer
program that uses the results of the finite element
analysis with formulations of the critical state soil
mechanics, as described in Sect. 3.2. Considering
circular failure surfaces, similar procedures (in terms
of calculation of acting shear stress and shear strength
along a potential failure surface) were used in the
analysis of the overall stability in cut slopes in clayey
soils (Borges 2008) and in embankments on soft soils
(Borges and Cardoso 2002). However, in the present
study, a different type of failure surface is considered
(see below Fig. 7) since the failure mechanism of the
problem is different from those studied in Borges
(2008) and Borges and Cardoso (2002). The type of
surface proposed herein (Fig. 7) revealed to be the
most unfavourable potential failure surface in strutted
excavations, corresponding to the smallest value of
safety factor calculated from the finite element
analysis. As concluded below (Sect. 5.1), where its
results are compared with those of Terzaghi (1943)
and Bjerrum and Eide (1956) methods, this new
methodology for strutted excavations showed to be
very accurate in estimating the safety factor against
bottom heave, both during and after the excavation
period. The program used in the paper corresponds to
an improvement (generalization) of that used in
Borges (2008) and Borges and Cardoso (2002),
incorporating more complex types of potential failure
surfaces and also taking into account that some parts of
the failure surface can coincide with soil-wall inter-
face elements (like for the failure surface of Fig. 7).
3.2 Evaluation of Safety Factor
Using the results of the finite element analysis, the
program of bottom heave stability analysis computes
the safety factor along a defined failure surface, at any
stage of the excavation and consolidation. Figure 7
illustrates the type of failure surface used in the present
study, which is similar to that assumed in the Terzaghi
(1943) approach, except for the line segment above the
wall tip, which is not vertical but inclined 45�. As said
above, this type of surface revealed to be the most
unfavourable potential failure surface, corresponding
to the smallest value of safety factor calculated from
the results of the finite element analysis.
Firstly, the program determines the intersection
points of the failure line with the edges of the finite
Fig. 7 Failure surface of
the program of bottom heave
stability analysis
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elements of the mesh. This way, the failure line is
divided into small line segments, each of them located
inside of only one of the finite elements of the mesh
(Fig. 8).
Afterwards, the average values of the effective
stresses (r0x, r0y, r0z and sxy, normal and shear stresses in
the xyz-space, where xy is the plane of the 2D-finite
element analysis) at each of those segments are
computed extrapolating from stresses at the Gauss
points of the corresponding finite element. Mathemat-
ical procedures of this extrapolation are described in
detail in Borges (2008).
Thus, considering the failure line divided into line
segments, the safety factor is computed as follows:
F ¼
P
N
i¼1
sfili
P
N
i¼1
sili
ð5Þ
where si: acting shear stress at the i-segment (deter-
mined from effective stresses r0x, r0y, and sxy, known
the angle that defines i-segment direction); sfi: soil
shear strength at i-segment; li: i-segment length; N:
number of mesh elements intersected by the failure
line.
Since soil shear strength varies with consolidation
and a critical state model is used in the finite element
analysis, sfi at each stage is calculated by the following
equation of the critical state soil mechanics (Britto and
Gunn 1987):
sfi ¼1
2M � exp
C� vi
k
� �
ð6Þ
where M is given by Eq. 1, and vi, the specific volume
of soil at i-segment, is determined as follows:
mi ¼ C� k ln pi � ðk� kÞ ln api ð7Þ
At i-segment, pi ¼ ðr0xi þ r0yi þ r0ziÞ=3 is the effective
mean stress and api is the p value of the centre of the
yield surface in p–q plane (see Fig. 2b), extrapolated
from ap-values at Gauss points using the same
mathematical procedures as for stresses; k, k and Care parameters of the p–q–h model (soil properties)
whose meanings are indicated in the next section.
4 Description of the Problem
The idealized problem concerns a 10 m deep excava-
tion with width of 12 m (Fig. 9). The retaining
structure consists of a 0.7 m thick diaphragm wall of
reinforced concrete with length of 12.5 m (2.5 m
below the excavation base). Three steel strut levels are
considered at depths of 1, 4 and 7 m. The excavation is
carried out in a total time of 25 days at a uniform rate.
In order to increase stability against bottom heave
failure and minimize the wall displacements, a 1.3 m
thick jet-grout slab is included (constructed by secant
columns) to support the wall below the excavation
base (Fig. 9). Due to hydraulic reasons, ‘‘dissipation
holes’’ in the jet-grout slab (see Fig. 9b) are con-
structed after excavation in order to avoid long-term
over-pressures on the lower face of the slab. There-
fore, it is assumed that, after the end of excavation, the
water flows through the ‘‘dissipation holes’’, being
pumped within the excavated area. This corresponds
to define the boundary condition of pore pressure on
the lower face of the slab equal to 13 kPa (considering
the unit weight of water equal to 10 kN/m3 and that the
thickness of the slab is 1.3 m).
The ground consists of a 30 m thick soft clay
overlying a ‘‘hard stratum’’. The water table is at the
ground surface.
Circular steel tubes, spaced of 2.5 m in the
horizontal direction, are used for the struts. Their
cross sectional area is indicated in Fig. 9.
Figure 10 shows the finite element mesh of the
problem. Two types of the six-noded triangular
element are considered: (1) the coupled element, for
the clay elements where consolidation is considered;
(2) the non-coupled element, for the wall and jet-grout
slab elements, considered as ‘‘impermeable’’. All six
nodes of the coupled element have displacement
degrees of freedom while only the three vertices nodes
Node
Gauss point
Line segment of the slip surface
Fig. 8 Six-noded triangular finite element
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Fig. 9 a Cross section of the strutted excavation; b ‘‘dissipation holes’’ in the jet-grout slab
Geotech Geol Eng (2013) 31:593–615 601
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have excess pore pressure degrees of freedom. The six
nodes of a non-coupled element have only displace-
ment degrees of freedom.
The struts are modeled with three-noded bar
elements with linear elastic behaviour. Six-noded
joint element (three nodes at each face) with elastic
perfectly plastic behaviour are used to simulate the
soil–wall and soil–slab interfaces. Since the jet-grout
slab is constructed after the wall and there is no liaison
(continuity) between them, joint elements are also
considered for slab–wall interfaces, supposing that a
thin portion of soil remains between these two
materials.
Regarding the boundary conditions, no horizontal
displacement is allowed on the vertical boundaries of
the mesh while the bottom boundary is completely
fixed in both the vertical and horizontal directions. The
left vertical boundary corresponds to the symmetry
line of the problem. The right vertical boundary is
located 60 m away from the wall, corresponding to 6
times the excavation depth of the problem. In
hydraulic terms, it is assumed that, in the supported
side, the water level remains on the ground surface
(which is a conservative and simplified assumption
and presupposes that there is a flow that provides water
to the ground) and, in the excavated side, the water
level coincides, at each stage of excavation, with the
excavation base (which means that the water, inside
the excavated area, is assumed to be pumped). A fully
coupled analysis is performed both during and after
the excavation period.
The constitutive behaviour of the clay is modeled
by the p–q–h critical state model (Borges 1995;
Borges and Cardoso 1998; Lewis and Schrefler 1987).
The values of its parameters are indicated in Table 1
(k, slope of normal consolidation line and critical state
line; k, slope of swelling and recompression line; C,
specific volume of soil on the critical state line at mean
normal stress equal to 1 kPa; N, specific volume of
normally consolidated soil at mean normal stress equal
to 1 kPa). Table 1 also shows other geotechnical
properties of the clay: c, unit weight; m0, Poisson’s ratio
for drained loading; /0, angle of friction defined in
effective terms; kh and kv, coefficients of permeability
in horizontal and vertical directions; K0, at rest earth
pressure coefficient; OCR, over-consolidation ratio;
su, undrained shear strength. The values adopted for
the clay are similar to those used by Finno et al. (1991)
regarding an excavation in soft soils constructed in
Chicago, USA.
The reinforced concrete wall is modeled as an
isotropic elastic material with a Young’s modulus
(E) of 18 GPa and a Poisson’s ratio (m) of 0.2.
The isotropic elastic model is also considered for the
Fig. 10 Finite element
mesh
Table 1 Geotechnical properties of the soil
c (kN/m3) K0 OCR k k N C m0 u0
(�)
kx = ky (m/s) su
Clay 16 0.5 1.0 0.18 0.025 3.158 3.05 0.25 26 10-9 0:28r0v0
r0v0, initial vertical effective stress
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jet-grout slab, adopting values of 150 MPa and 0.2 for
E and m, respectively. The value of E is the same as that
referred by Jaritngam (2003) for the jet-grout columns
carried out in a soft soil. The adopted value of E is
assumed as an average value (secant modulus) for the
stress level expected in the jet-grout slab.
The one-dimensional isotropic elastic model is used
in the strut simulation, with a Young’s modulus of
206 GPa for the steel. However, due to the difference
usually observed in practice between theoretical and
effective stiffnesses, the later was considered equal
to half the theoretical stiffness, as suggested by
O’Rourke (1992).
The soil–wall interfaces are modeled with joint
elements with elastic perfectly plastic behaviour
defined in total stresses. Taking into account the
results of laboratorial tests performed by Fernandes
(1983), the soil–wall interface strength was considered
equal to the shear strength of the soft soil. To define the
elastic tangential modulus of the interface, it was
supposed that a tangential displacement of 1 mm is
reached when shear strength is mobilised, also based
on what Fernandes (1983) proposed. Similar criteria
were considered to define the properties of the soil–
slab and wall–slab interfaces. As said above, since the
jet-grout slab is constructed after the wall and there is
no continuity between these two materials, a thin
portion of soil is supposed to remain between them,
which justifies the use of joint elements on the wall–
slab interfaces. A very high value of normal stiffness
in all joint elements was considered, so unrealistic
normal displacements could not be obtained in all
those interfaces.
5 Analysis of Results
5.1 Construction Period
Figure 11 shows results of excess pore pressure at
several stages during excavation. Excess pore pressure
is defined as the difference between pore pressure at a
particular instant and its initial hydrostatic value.
These results show that negative values are generated
during excavation, increasing as excavation pro-
gresses, as expected. Highest absolute value of excess
pore pressure occurs below the excavation base near
the left boundary (symmetry line). This is explained
by the highest decrease of total mean stress associated
to the excavation, which occurs in that zone. On the
supported side of the ground, a tendency of generating
negative excess pore pressure is also observed,
although with lower values than on the excavated
side. This is explained not only by the lower decrease
of total mean stress on that side (because there is no
excavation on the supported side) but also by the
presence of the wall and, mainly, of the base slab,
which decisively contributes to avoid a ground
decompression with similar magnitude to that on the
excavated side. Below the wall tip, this effect does not
take place and consequently higher absolute values of
excess pore pressure are observed on the supported
side.
Principal effective stresses at the end of excavation
are shown in Fig. 12. Rotations of the principal stress
directions on both sides of the wall, mainly below the
wall tip, can be observed in this figure, which means
that large shear stresses (deviatoric stresses) occur on
those zones. This fact is corroborated by the results of
shear stress on horizontal and vertical planes (sxy)
shown in Fig. 13: highest values of sxy are also
mobilised at the end of excavation below the wall tip.
It should be noted that high shear stresses are
observed in the vicinity of the bottom boundary due to
presence of the hard stratum (where displacements are
set as zero because of the very high stiffness of the
hard stratum when compared to the stiffness of soft
soil). These values of shear stress are mainly due to
differential horizontal displacements between the soft
soil and the hard stratum in that zone: as the hard
stratum is modeled without displacements, even small
values of horizontal displacement in the soft soil
determine high values of shear stress in that zone.
Figure 14 shows distributions of stress level in the
ground at several stages during excavation. Stress
level, SL, measures the proximity to the soil critical
state and is defined as follows:
SL ¼ q
pMð8Þ
where p, q and M have the meanings reported in Sect.
3. In normally consolidated soils, SL varies from zero
to 1, the latter being the critical state level. In
overconsolidated soils, because of the peak strength
behaviour, stress level may be higher than 1.
Figure 14 shows that SL significantly increases
during excavation, which is basically related with the
increase of deviatoric stress, q, as commented above.
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At the end of excavation, stress level takes values
close to 1, below the wall tip on both sides of the wall.
Lower values of SL are observed above the wall tip on
both sides of the wall, due to the jet-grout slab which
works as a support of the wall below the excavation
bottom. One can also note that, as the excavation depth
increases, higher values of stress level on the sup-
ported side spread in a direction of approximately 45�with the horizontal direction (which corresponds to the
failure direction for cohesive soils in active limit state,
considering the Mohr–Coulomb failure criterion).
This fact qualitatively indicates that the potential
failure surface takes that direction on that zone, which
was corroborated by the values of F obtained from the
finite element analysis, using the program of bottom
heave stability analysis described in Sect. 3.
Figure 15 shows, at several stages of excavation,
the values of the safety factor calculated by the
Terzaghi (1943) and Bjerrum and Eide (1956) meth-
ods and those obtained from the finite element analysis
along the failure surface defined in Fig. 7. These
results show that the values obtained from the finite
element analysis are very similar to those of the
Bjerrum and Eide (1956) method, at excavation depths
larger than 8 m when F takes smaller values; the
values of Terzaghi (1943) method are slightly higher
at those stages. For smaller depths of excavation
(smaller then 7 m), the values of F obtained from finite
Fig. 11 Excess pore
pressure during excavation:
a 2 m excavated; b 6 m
excavated; c 10 m
excavated (end of
excavation)
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element analysis tend to be higher than those of
Terzaghi (1943) and Bjerrum and Eide (1956) meth-
ods. This is explained by the fact that the application of
the program, calculating F along a potential failure
surface from soil shear strength and acting shear stress,
is less realistic at early stages of excavation when
failure condition is far away. However, the results
show that the program is very accurate [with values
very similar to those obtained by Bjerrum and Eide
(1956) method] when F takes values smaller than 1.5,
which actually corresponds to practical situations
where this stability analysis is more pertinent. At the
end of excavation, F takes the values of 1.145, 1.191
and 1.286 respectively for finite element analysis,
Bjerrum and Eide (1956) method and Terzaghi (1943)
formulation.
Wall horizontal displacements at several stages
during excavation are shown in Fig. 16. Unlike what
usually happens in strutted excavations without a base
slab, Fig. 16 shows that the displacements decrease
with depth at all stages of construction; i.e., the
maximum horizontal displacement takes place on
the top of the wall. This behaviour is obviously due to
the base slab support.
Settlements on the ground surface, on the supported
side, are shown in Fig. 17, for several depths of
excavation. These results show that the maximum
settlement takes place close to the wall, and another
local maximum occurs approximately 20 m away
from the wall. It should be noted that, as said in Sect. 4,
the wall–soil interface reaches its shear strength for
1 mm of tangential displacement, which explains that
high settlements may occur on that interface, as
observed in Fig. 17.
Figure 18 shows the excavation bottom vertical
displacements (on the upper face of the jet-grout slab)
for several depths of excavation. These results show
that upward displacements are higher on the left
boundary (middle of the slab), reaching a value of
11.28 cm at the end of excavation. Near the wall,
upward displacements are smaller, which is justified
by the tangential stress mobilized on the soil–wall
interface. However, this stress does not impede that
high values are also reached on that zone (approxi-
mately 9 cm), since the strength of the interface is
mobilized for a small value of 1 mm of tangential
displacement, as said above.
Strut compression loads for several stages of
excavation are illustrated in Fig. 19. Compression
load of 1st strut level increases with excavation until
2nd strut level is installed. After that, its compression
load decreases. Similar effect is observed on the 2nd
strut level, i.e. its compression load also increases with
excavation, decreasing after 3rd strut level is installed.
The decreasing effect is more expressive on the 1st
level than on the 2nd level.
Fig. 12 Principal effective
stresses at the end of
excavation
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Bending moment diagrams in the wall at several
stages of construction are illustrated in Fig. 20. These
results show that near the excavation base the sign of
the bending moment changes, which is explained by
the base slab support that works as a kind of a fixed
support. Below excavation base, bending moment
increases with excavation whereas above that level the
evolution is different, i.e. the maximum value is
reached at 6 m of excavation and reduces after that.
This reduction is determined by the installation of the
3rd strut level at 7 m of depth.
Compression loads in the jet-grout slab are illus-
trated in Fig. 21. This figure shows that compression
load increases as excavation progresses, as expected,
and does not significantly vary along the slab at each
stage.
Bending moment diagrams in the jet-grout slab are
shown in Fig. 22. These results illustrate that bending
moments also increase with excavation and are higher
at the slab extremities.
It should be noted that, at the end of excavation,
highest values of compression load and bending
moment are applied near the extremities of the slab,
which implies that the minimum and maximum values
of compression stress on the most unfavorable cross
section (extremity of the slab) are 56.06 kPa (lower
fiber) and 857.14 kPa (upper fiber) respectively; the
latter is significantly smaller than the jet-grout strength
Fig. 13 Shear stress on
horizontal and verticalplanes (sxy) during
excavation: a 2 m
excavated; b 6 m excavated;
c 10 m excavated (end of
excavation)
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Fig. 14 Stress level during
excavation: a 2 m
excavated; b 6 m excavated;
c 10 m excavated (end of
excavation)
Fig. 15 Safety factor against bottom heave at several stages of
excavation
-0.04 -0.03 -0.02 -0.01 0.00 0.01
Horizontal displacement (m)
D
epth
(m
)
-12.5
-10.5
-8.5
-6.5
-4.5
-2.5
-0.5
2 m
4 m
6 m
8 m
10 m
Fig. 16 Wall horizontal displacements at several depths of
excavation
Geotech Geol Eng (2013) 31:593–615 607
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0 10 20 30 40 50 60
Distance from the wall (m)
Set
tlem
ent
(m)
-0.030
-0.020
-0.010
0.000
0.010
0.020
0.0302 m
4 m
6 m
8 m
10 m
Fig. 17 Settlements on ground surface at several depths of
excavation
0 1 2 3 4 5 6Distance from left boundary (m)
Ver
tica
l dis
pla
cem
ent
(m)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
2 m
8 m
4 m
6 m10 m
Fig. 18 Excavation bottom heave for several depths of
excavation
0 1 2 3 4 5 6 7 8 9 10
Excavation depth (m)
Co
mp
ress
ion
load
(kN
/m)
0
50
100
150
200
250
300Strut level 1
Strut level 2
Strut level 3
Fig. 19 Strut compression loads during excavation
-12.5
-10.5
-8.5
-6.5
-4.5
-2.5
-0.5
-400-2000200400
Bending moment (kN.m/m)
Dep
th (
m)
2 m
4 m
6 m
8 m
10 m
Fig. 20 Bending moment in the wall at several stages of
excavation
0 1 2 3 4 5 6
Distance from left boundary (m)
Co
mp
ress
ion
load
(K
N/m
)
0
100
200
300
400
500
600
700
2 m
4 m
6 m
8 m10 m
Fig. 21 Compression loads in the jet-grout slab at several
stages of excavation
0 1 2 3 4 5 6
Distance from left boundary (m)
Ben
din
g m
om
ent
(kN
.m/m
)
-120
-100
-80
-60
-40
-20
0
20
2 m
4 m
6 m
8 m10 m
Fig. 22 Bending moment in the jet-grout slab at several depths
of excavation
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values usually reported in bibliography for this kind of
soils. If that was not the case, or traction stress was
detected on the jet-grout slab, the slab thickness
should be enlarged in design.
5.2 Post-construction Period
After construction, the behaviour of the problem is
globally determined by the consolidation process
associated to the dissipation of the excess pore
pressure gradients generated during construction.
Therefore a transient water flow takes place in time
until hydrodynamic equilibrium is reached. In this
case, the long term hydrodynamic equilibrium is
determined by the difference of the hydraulic load of
10 m caused by the water table lowering on the
excavated side.
In the analysis, the three steel strut levels were
maintained in the post-construction period. However,
it should be noted that in building construction, for
instance, it is usual to replace the steel struts by the
definitive concrete slabs of the building in the function
of supporting the wall. Costa (2005) showed that this
replacement, in numerical analysis of this kind of
problems, has insignificant effect on the long term
numerical results that are obtained. Thus, in this study,
Fig. 23 Excess pore
pressure at several stages
after construction: a end of
construction; b 2 years after
end of construction; c end of
consolidation
Geotech Geol Eng (2013) 31:593–615 609
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by simplification, the steel struts are maintained during
all stages of the problem, during and after the
construction period, as said above.
Figure 23 shows results of excess pore pressure at
several stages after excavation. It should be noted that,
as said above, excess pore pressure is considered
herein (as defined in the computer code) the difference
between pore pressure at a particular instant and its
initial hydrostatic value (before excavation), and not
its final value at the end of consolidation. With the
consolidation, the most significant variations are
observed on the excavated side where water pressure
increases (reduction of the absolute value of excess
pore pressure). On the supported side, the evolution is
contrary, although with low magnitude: there is a
small increase of the absolute value of excess pore
pressure which correspond to reduction of the water
pressure (which is related with downward water flow),
especially below the excavation base level. At the end
of consolidation, very typical shapes of isovalue
curves of excess pore pressure are observed. These
curves are normal to the flow lines of the steady flow
reached at end of consolidation (determined, as said,
by the 10 m lowering of the water table on the
excavated side).
Principal effective stresses at the end of consolida-
tion are shown in Fig. 24. Compared with Fig. 12
(principal effective stresses at the end of excavation),
these results show that, with the consolidation, there is
no significant variation of shear stress (directions of
principal stresses remain approximately the same as
after construction) but some variation of mean effec-
tive stress is observed (variation of principal stress
magnitude), corresponding to an increase on the
supported side and a decrease on the excavated side,
below the excavation bottom. Obviously, these vari-
ations are contrary to the pore pressure changes
discussed above, since both phenomena are related.
After construction, stress level (Fig. 25) increases
on the excavated side below the excavation bottom
which is due to the reduction of mean effective stress
on that zone, whereas on the supported side the
contrary effect is observed: stress level decreases,
since mean effective stress increases.
Regarding the bottom stability, Fig. 26 shows the
effect of consolidation on the safety factor, calculated
with the program described in Sect. 3. These results
basically show that F slightly increases with the
consolidation (from 1.145 to 1.207). This small
increase is mainly related to the reduction of stress
level on the supported side, as explained above.
Diagrams of earth pressure (total horizontal stress,
i.e. sum of pore pressure and horizontal effective
stress) on both faces of the wall at ends of excavation
and consolidation are shown in Fig. 27 (pressure on
the excavated face is illustrated with negative sign).
Fig. 24 Principal effective
stresses at the end of
consolidation
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Fig. 25 Stress level at several stages after construction: a end of construction; b 6 months after end of construction; c 2 years after end
of construction; d end of consolidation
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A large increase of earth pressure is observed during
consolidation on the excavated face. This is due to the
swelling effect of the soil (associated to the decrease of
mean effective stress, as seen above) as consolidation
takes place in that zone. The soil swelling is partially
impeded by the wall in the horizontal direction, which
increases the earth pressure on the wall face.
On the supported side, above the excavation level, a
small decrease of earth pressure is observed. This fact
is justified by an effect contrary to what happens on the
excavated side; i.e., as seen above, an increase of
effective mean stress occurs with consolidation on the
supported side, which provokes reduction of the soil
volume and therefore decrease of earth pressure on the
wall.
In overall terms, wall horizontal displacements do
not change significantly with the consolidation, as
shown in Fig. 28. The most expressive variation is
observed below depth of 9 m, where displacements
reduce with consolidation. This effect is explained by
the increase of earth pressure on the excavated face, as
mentioned above.
Diagrams of vertical displacement on the supported
ground surface and on the excavation bottom are
illustrated in Figs. 29 and 30. These results show that,
with the consolidation, there are expressive downward
displacements on the supported ground and upward
displacements on the excavation bottom. These effects
are respectively justified by the reduction and increase
of volume on the supported and excavated soils, as
discussed above.
Diagrams of wall bending moments at ends of
construction and consolidation are illustrated in
Fig. 31. With the consolidation, there is an increase
of bending moment in the upper zone of the wall and a
decrease in the lower zone. This is due to the above-
mentioned increase of earth pressure on the wall on the
excavated side. This provokes the reduction of the
lower ‘‘fixed’’ bending moment (at the jet-grout slab
level) and therefore, due to the equilibrium (since earth
pressure does not change significantly above
Fig. 26 Safety factor against bottom heave at several stages
after the end of excavation
-150 -100 -50 0 50 100 150 200
Earth pressure (kPa)
Dep
th (
m)
-12.5
-10.5
-8.5
-6.5
-4.5
-2.5
-0.5
End of consolidation
End of excavation
Fig. 27 Earth pressure on
the wall faces at ends of
excavation and
consolidation
-12.5
-10.5
-8.5
-6.5
-4.5
-2.5
-0.5
-0.040 -0.035 -0.030 -0.025 -0.020 -0.015 -0.010
Horizontal displacement (m)
Dep
th (m
)
End of excavation End of consolidation
Fig. 28 Wall horizontaldisplacement at ends of
excavation and
consolidation
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excavation level), the increase of moments above the
excavation base.
As for compression loads on the steel struts, the
results of the study showed that there is no significant
variation of their values on the three levels of struts
during consolidation. These results are in consonance
with the small variation of earth pressure on the wall,
above the excavation bottom, as seen above.
Figure 32 shows that during the consolidation the
compression load on the jet-grout slab reduces. This is
due to the increase with consolidation of the earth
pressure (total horizontal stress) on the wall face of
excavated side, as discussed above, which decreases
the load that the wall transfers to the slab. On the other
hand, the reduction of the wall displacements with
consolidation (as seen in Fig. 28) corroborates this
reduction of compression load on the jet-grout slab.
Figure 33 shows that, during consolidation, the
absolute value of bending moment on the jet-
grout slab globally increases, the maximum value
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0 10 20 30 40 50 60
Distance from the wall (m)
Ver
tica
l dis
pla
cem
ent
(m)
End of excavation End of consolidation
Fig. 29 Verticaldisplacement on supported
ground surface at ends of
excavation and
consolidation
0 1 2 3 4 5 6
Distance from left boundary (m)
Ver
tica
l dis
pla
cem
ent
(m)
0.00
0.03
0.06
0.09
0.12
0.15
0.18
0.21
End of excavation End of consolidation
Fig. 30 Verticaldisplacement on excavation
bottom at ends of excavation
and consolidation
-12.5
-10.5
-8.5
-6.5
-4.5
-2.5
-0.5
-400-2000200400Bending moment (kN.m/m)
Dep
th (
m)
End of consolidation End of excavation
Fig. 31 Wall bending moments at ends of construction and
consolidation
0 1 2 3 4 5 6
Distance from left boundary (m)
Co
mp
ress
ion
load
(kN
/m)
0
100
200
300
400
500
600
700
End of consolidation End of excavation
Fig. 32 Compression loads
on the jet-grout slab at ends
of construction and
consolidation
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(at extremities of the slab) increasing 33 % (from
112.819 to 150.137 kN m/m).
6 Conclusions
The influence of the consolidation on a strutted
excavation in soft soil incorporating a jet-grout base
slab was analysed using a computer program based on
the finite element method. The program incorporates
coupled analysis and soil constitutive relations simu-
lated by the p–q–h critical state model. The safety
factor against bottom heave was also evaluated from
the finite element analysis and compared to Terzaghi
(1943) and Bjerrum and Eide (1956) methods. Some
overall conclusions are pointed out below on the
results of the numerical analysis.
1. During excavation, negative excess pore pres-
sures are generated in all zones of the ground. The
highest absolute value of excess pore pressure
occurs below the excavation bottom where the
highest decrease of total mean stress takes place.
After construction, with the consolidation, water
pressure increases on the excavated side and
decreases on the supported side.
2. Stress level of soil significantly increases during
excavation, especially below the wall tip. Lower
values occur above the wall tip on both sides of
the wall due to the jet-grout slab which works as a
support of the wall below the excavation bottom.
After construction, stress level increases below
the excavation bottom, whereas decreases on the
supported side of the wall.
3. Unlike what usually happens in strutted excava-
tions without a base slab, the maximum wall
displacement takes place on the top of the wall at
all stages of excavation and post-excavation.
4. During consolidation, there are expressive down-
ward displacements on the supported ground
surface and upward displacements on the exca-
vation bottom.
5. During construction, below the excavation base,
the wall bending moments increase as excavation
progresses, whereas above that level the maxi-
mum bending moment is not reached at the end of
excavation.
6. During consolidation, there is no significant
variation of compression loads on the struts.
7. With consolidation, the compression load of the
jet-grout slab reduces whereas its bending
moments globally increase.
8. The values of the safety factor against bottom heave
obtained from the finite element analysis are very
similar to those of the Bjerrum and Eide (1956)
method, particularly when F takes values smaller
than 1.5. The values obtained from the Terzaghi
(1943) formulation revealed to be slightly higher.
After construction, the safety factor obtained from
the finite element analysis slightly increases with the
consolidation (from 1.145 to 1.207). This small
increase is mainly related to the reduction of stress
level on the supported side.
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