2474
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
2 REVIEW OF DESIGN STANDARDS
The two most common design standards available for the design
of earth embankment on GECs are the British Standard BS
8006 (1995) and the German Standard EBGEO (Chapter 6.9;
2003). Both of them assume the column to be rigid and,
estimate the vertical stress distribution at the base of the
embankment to be independent of the mechanical interaction
with the foundation (i.e. the GEC and the soft soil). From an
engineering point of view, however, the vertical stress
redistribution at the base of the embankment is the main
parameter governing (i) the design of the reinforcement layers
(see Figure 1) and (ii) the evaluation of the differential
settlements.
According to BS8006, the vertical stress redistribution does
not depend on the mechanical properties of the embankment. In
particular, the average vertical stress acting at the column’s top
(in the following this quantity will be called
i
) is determined
only as a function of the geometry (H, S, D), as was suggested
by the approach proposed by Martson (1913) for buried pipes
(see also Jones et al., 1990). The estimation of the average
vertical stress
e
acting on the soft soil is instead obtained by
means of empirical expressions, depending on the full or partial
formation of the arch effect, as a function of the ratio between
height H and difference S-D. According to EBGEO, on the
contrary, a rather complex analytical procedure, based on the
work proposed by Zaeske (2001), is employed to describe the
arch effect. This takes into account the geometry (H, S, D) and
the friction angle of the granular material constituting the
embankment, and imposes the equilibrium of one central slice
of a vault shell of the arch that it is supposed to develop within
the embankment. No estimation of the vertical stress
i
at the
top of the column is provided. For the sake of brevity, the
analytical expressions have not been reported here; for further
details, see BS8006 and EBGEO (Chapter 6.9).
As far as the evaluation of settlements is concerned, the
procedure prescribed by EBGEO follows the work proposed by
Ghionna and Jamiolkowski (1981) and consists in subdividing
the length L of the column in slices (each one of them is then
assimilated to an axisymmetric triaxial soil sample). The
following hypotheses are assumed: (i) the granular soil in the
column is at critical state (i.e. no changes in volume are possible
for the column), (ii) no relative settlement are considered
between the column and the soil. These two hypotheses
introduce very strong simplifications that can lead to unphysical
results. The second one, in particular, makes impossible the
superficial differential settlements to be estimated.
2.1
Parametrical analyses
In this section parametrical analyses on the values of
e
obtained by employing BS8006, as well as some results
concerning the evaluation of the settlement and of the tensile
force in the encasing geo-membrane computed according to
EBGEO, are presented. In particular, the effect of the
embankment height H and of the material friction angle
’ is
investigated for increasing values of the relative spacing S/D,
and by taking into account several diameters D of the column
(the authors are aware of the fact that some values of D and S/D
considered are unrealistic, nevertheless they have been chosen
in order to test even the asymptotic trend of the design
approaches).
2.1.1
Stress on the soft soil at the base of the embankment
Figure 2 shows the values of
e
computed according to BS8006,
and highlights that unphysical results of
e
<0 are obtained for
low values of the relative spacing S/D, independently of the
embankment height H. This result could in general lead to an
overestimation of the arch effect and thus to an unsafe design of
the georeinforcement layers at the base of the embankment.
The arch effect tends to vanish for increasing values of S/D,
and the value of
e
tends to the weight
H of the embankment.
The corresponding values of
i
computed according to BS8006
(not reported here for the sake of brevity) are independent of
S/D, and only slightly dependent on H.
a)
b)
Figure 2. Evaluation of the stress
e
according to BS8006: (a) H=2.5m
and (b) H=10m.
It can be easily demonstrated that
e
and
i
(if computed
according to BS8006) do not even satisfy the total equilibrium
along the vertical direction with respect to the weight of the
embankment, and that the values of the tensile force in the
geosynthetic layers at the base of the embankment computed
according to BS8006 are not continuous with increasing H
(Moraci and Gioffrè 2010).
2.1.2
Settlements and tensile force in the encasing membrane
With reference to the values of the mechanical parameters
listed in Table 1 (taken from an example of application
proposed by EBGEO), in this paragraph a parametrical analyses
on the values of the settlement is presented, for increasing
values of the embankment weight
H and by taking into account
several values of stiffness J of the encasing geomembrane. The
values of the column length L and of the relative spacing S/D
are here considered to be constant and equal to 10 m and 2,
respectively (with D=80 cm and S=1.6m).
Table 1. Values of the mechanical properties of the materials considered
n the analyses.
i
Embankment Column Soft
soil
Unit weight (kN/m
3
)
20
19
15
Friction Angle (°)
-
35
15
Cohesion (kPa)
-
-
10
Young modulus (kPa), at a
reference pressure of 100kPa
-
-
750
Poisson coefficient (-)
-
-
0.4
As it is evident from Figure 3a (where, for the sake of
generality, the value of s has been normalized with respect to
L), the presence of the encasing geomembrane induces a
stiffening effect of the foundation system, thus reducing the
expected value of the total settlement (which is considered,
according to the adopted hypotheses, to be uniform and
coincident with the settlement s at the top of the embankment).
The numerical procedure, however, for low values of
H (i.e.
shallow or light embankments) leads to unrealistic results, for
