Technical Paper by A. Fakher and C.J.F.P. Jones WHEN THE ...

FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
G
E
= ------------------- ( = 1.2 × 10
21 ( + ν)
7 Pa)
(1)
E
K = ---------------------- ( = 4.1 × 10 (2)
31 ( – 2ν)
7 Pa)
The elastic properties of super soft clays are difficult to measure; however, experimental
studies have shown that the elastic modulus of the super soft clay is not significant
in the problem (Fakher 1997). Based upon experimental findings the shear
modulus and bulk modulus of the super soft clay were assumed equal to 42 and 20
MPa, respectively. The shear strength of the super soft clay was assumed to be 50 Pa
for the majority of the analysis, but was increased up to a value of 1,000 Pa to illustrate
the influence of stronger and stiffer soil. An elastic-perfectly plastic behaviour was
assumed for the soils in order to simplify the analyses.
2.3 Geosynthetic Reinforcement
The reinforcements were modelled in two ways in order to investigate the effects of
reinforcement bending stiffness on the bearing capacity of the super soft clay:
1. As cable elements, with no bending stiffness. This method is frequently used to
model geosynthetic reinforcements when bending is considered unimportant. The
cable elements used in the analyses were one-dimensional axial elements described
in terms of cross-sectional area, elastic modulus, and yield strength of the cable.
2. As beam elements with elastic bending stiffness. The beam elements used in the
analyses were two-dimensional elements with three degrees of freedom at each
node providing displacement in two perpendicular directions and rotation. The
beam elements were described in terms of cross-sectional area, elastic modulus,
second moment of area (moment of inertia), and plastic moment. The moment
capacity was assumed to be infinite.
The reinforcements were fixed to the line of symmetry (Figure 1). However, they
were not fixed to any other vertical boundary so as not to cause an unrealistic pull-out
resistance. The length of the geosynthetic reinforcement was 2 × 7B, where B is the
width of the footing. In view of the low value of the shear strength of super soft clay, it
was assumed that perfect adherence existed between the clay and the reinforcement.
The elastic modulus and cross-sectional area of the reinforcement were assumed to
be equal to 1 × 10 5 Pa and 0.0033 m 2 , respectively. The second moment of area, I, of
the beam elements was assumed to be equal to 7.64 × 10 -7 m 4 . However, this value was
varied from 1 × 10 - 8 to 2.15 × 10 - 6 m 4 in order to study the effect of bending stiffness,
EI. The bond stiffness and the bond strength of the element-soil interface and the yield
strength of the cable elements were assumed to be 3 × 10 7 N/m/m, 4.5 × 10 4 N/m, and
6.8 × 10 3 N, respectively for all the analyses. Details of the material properties used in
the different analyses are shown in Table 1.
448 GEOSYNTHETICS INTERNATIONAL • 2001, VOL. 8, NO. 5