6.6.4 Plane strain analysis and three⁃dimensional ...

6.6.4 Plane strain analysis and three⁃dimensional analysis

Though in general engineering practice，plane strain analysis is capable of obtaining a rational result，the wall deflection and ground settlement on the section of the shorter side［B⁃B section in Figure 6.1（a）］or that near the corner are three⁃dimensional behaviors and plane strain analysis would overestimate the deformation or settlement.Three⁃dimensional analysis can solve the problems.Figure 6.16 shows wall deformation at the comer in the Haihaw Financial Center excavation from plane strain analysis，three⁃dimensional analysis and field measurement.As shown in the Figure，plane strain analysis will overestimate；whereas three⁃dimensional analysis will obtain rational results.Besides，the wall deformation and ground surface settlement in excavations with soil improvement or property protection measures such as counterfort walls or cross walls also constitute three⁃dimensional behavior.In such cases，only three⁃dimensional analysis can obtain rational results.

Figure 6.16 Comparisons of the wall deflection from plane strain analysis，three dimensional analysis and field measurement，respectively in a corner of the Hai Haw Financial Center excavation

In three dimensional analysis，the stress state at a point has six components：σxx，σyy，σzz，xy，yz，zx.The theories of finite element analysis，the soil models，and others are all similar to those for the plane strain analysis.In practice，the element of the retaining wall and soil used in the three⁃dimensional analysis is usually an 8⁃noded low order hexahedron element，which is called a H8（8⁃noded hexahedron）element，the solid element，or brick element，as shown in Figure 6.17（a）.A 20⁃node high order element［Figure 6.17（b）］，though more accurate，is usually not adopted because it requires too much computer memory and is very time consuming in computation.

Figure 6.17 Three dimensional elements