6.4 Modeling of an Excavation Process
The conception of simulating excavations using the finite element method can be illustrated by Figure 6.12.As shown in Figure 6.12（a），before excavation，the initial stresses of the soil are in equilibrium.Once excavation is started，the stresses on the excavation surface and the wall above the excavation surface shall become 0.Thus，an excavation simulation can be described as follows：
•Compute the initial stress state on the designed excavation surface［Figure 6.12（b）］.
•According to the stress state obtained above，compute the equivalent nodal force（Peq）.
•Load forces of－Peq on the excavation surface.
•Reduce the stiffness of the soil that is to be excavated to 0（or to a very low value）.
•Compute the displacement，stress，and strain in the unexcavated area caused by－Peq.
Following Brown and Booker's study（1985），the equivalent nodal force on the excavation surface in Step 2 can be computed as follows：
where
Peq＝the equivalent nodal force on the excavation surface；
i＝the present excavation stage；
i－1＝the previous excavation stage；
Vi＝the volume in the present excavation stage；
σi－1＝the stress in the previous excavation stage.
Figure 6.12 Simulation of excavation
The first item in the above equation represents integration of the nodal forces derived from the stresses at the integration points in the previous excavation stage（the stresses before excavation）over the volume in the ith stage（the volume after excavation）.The second item represents integration of the nodal forces derived from gravity over the volume in the ith stage（the volume after excavation）.Subtract the latter from the former，and we can then obtain the equivalent nodal forces on the excavation surface.If dewatering is carried out in the excavation zone，due to the change of the water pressure before and after excavation，a stress increment｛U｝will be generated.The stress increment can be transformed into the equivalent nodal force.Eq.6.24 can then be rewritten into the following：
where U＝change in the water pressure due to dewatering.
The equivalent nodal forces can thus be obtained from Eq.6.24，The changes of stresses and strains for soil elements can be obtained by loading the equivalent nodal forces on the excavation area and perform finite element analysis.