In John's  and Rogbeck et al.'s  methods for plane strain condition, the load acting on the reinforcement was assumed to be vertical and uniformly distributed along the deflected length, and the resultant deflected shape of the geosynthetic reinforcement was catenary.
In the BS8006 method , the deflected shape of the geosynthetic reinforcement is approximated as a parabola, and the strain and tension are computed using the following:
It can be seen that the deflected shape of the geosynthetic reinforcement can be adequately described by both the parabolic and circular geometries.
Because the current design methods do not represent the true 3D deformation nature of the geosynthetic reinforcement, 3D finite element analyses were conducted to get a better understanding of the deflected shape and the corresponding tensile forces developed in the geosynthetic reinforcement.
It was found that for two-dimensional problem, the deflected shape of the geosynthetic can be adequately described by both the parabolic and circular arc geometries.
Based on the numerical results, a new deformation model was suggested to model the three-dimensional deflected shape of the geosynthetic reinforcement, and then the corresponding governing equation was derived and solved based on the membrane theory.