6.4         Dynamic Stress Reduction

A two bay frame bridge was modeled twice, using both a finite difference analysis technique and a finite element method. The purpose is to compare the two methods for solving soil structure interaction problems experiencing small strains under dynamic loading. Both models have the same grid as shown in figure 6-12a. A simple harmonic wave was applied to the model. The problem was solved for two cases, a case without geofoam as shown in figure 6-12b and the case with geofoam blocks arranged as shown in figure 6-12c. Damping ratio was taken two percent for both the sand and the geofoam to see the effect of adding a lightweight fill on the response of a statically indeterminate structure. The analysis was done after that with different values of damping ratios for foam and maintaining the damping ratio for the sand at 2%. FLAC, the finite difference software, as well as ANSYS (ANSYS Inc., 1997), the finite element software, were used to model the problem at the case of 2% damping for both the foam and the sand. Comparison between the solutions for both methods shows matching in both the stresses and the displacement. ANSYS was used to model the cases where the damping ratio is different for both the sand and the geofoam. 

Figure 6-13 shows the results for the difference in the bending moment in the case of foam backfill from the case of sand backfill in the middle column obtained from the finite element analysis. Results show that the lightweight fill by itself will not decrease the dynamic response unless the difference in the damping ratio between the sand and the foam is taken into consideration.  

Figure 6‑1 Two Bays Frame: a) The Mesh b) Sand Backfill c) with Geofoam

Figure 6‑2 Mid Support Bending Moment from Finite Element Analysis