6.5.3 Boundary conditions

If considering the symmetry of an excavation and taking a half for analysis as shown in Figure 6.1，the symmetric boundary［line B′⁃B′in Figure 6.1（b）］should be equipped with rollers to restrain the lateral displacement and allow vertical displacement.According to Ou and Shiau（1998），to analyze movement in an excavation，rollers will be more efficient than hinges placed on line C′⁃C′［Figure 6.1（b）］.Also，the rollers should be placed at a distance more than three excavation depths from the retaining wall for the analysis of wall deformation.To analyze ground settlement，the rollers should be placed at a distance of more than four excavation depths from the retaining wall.In principle，the farther the boundary is to the retaining wall，here designated as C′⁃C′，the better the analysis results are，though it takes more computation time.On the base，either rollers or hinges can be placed.In general，the hinges or rollers should be placed on hard soils or several meters below the retaining wall bottom.

The location of the boundary of mesh can also be determined from convergence study of the finite element analysis.As shown in Figure 6.1（b），assume the boundary is line G′⁃G′，and then carry out the analysis.Extend the boundary to line H′⁃H′and perform the analysis again.If the two analyses come out similar in stress，strain，or displacement along，for example，X′⁃X′，it means that the boundary can be set at G′⁃G′or H′⁃H′.Otherwise，the boundary should be moved to C′⁃C′.