6.6.3 Coupled analysis

In the method just mentioned，analysis is restricted to either drained or undrained analysis.However，real soil behavior is often time related，with porewater pressure response and rate of loading.To account for such behavior，it is necessary to couple the continuity of equation or general consolidation equation with the constitutive and equilibrium equations.The method is then called the coupled analysis，which is subsumed in effective stress analysis，that is，the effective stress parameters are required in analysis.In addition to the parameters of soil models，the coupled analysis also requires the coefficient of permeability and loading time.The coupled method uses displacement and porewater pressure as unknowns and therefore results in both displacement and porewater pressure degrees of freedom at element nodes.

As a result，it can compute the displacements and stresses of a soil element as well as the porewater pressures based on the effective stress.Figure 6.15 shows a commonly used element for coupled analysis.The element has eight displacement nodes，four of which are simultaneously porewater pressure nodes.

Figure 6.15 A commonly used element for the coupled analysis（eight deformation nodes and four porewater pressure nodes）

If using the coupled method to analyze completely undrained behavior，we could simply set the time of loading within a very short time.For example，assume there is a site to be excavated 4 m deep.The coupled method simply sets the 4 m excavation to be finished within a very short time when considering the undrained condition.If considering the drained condition，we can set the excavation time for a very long period.When considering partially drained behavior，set the excavation time in between（the actual excavation time）.