3.1 Introduction
Problems of deep excavation，whether stability analysis，stress analysis or deformation analysis，entail the distribution of earth pressures.Though introductory books on soil mechanics or foundation engineering have discussed quite a few earth pressure theories along with many examples，a systematic organization is lacking，and some important points may not be sufficiently emphasized.In actual analyses，a wrong choice of earth pressure theory may lead to an uneconomical or even unsafe design.This chapter is going to do a systematic organization and to simplify the complicated calculations for excavation analyses and design.Most of the methods introduced here have been frequently used in engineering practice though they have not been introduced in general textbooks.
Other than the gravity retaining walls（the retaining wall alone can rarely resist the lateral pressure），supplementary strutting systems are also required.The selection of the strutting system depends on not only the magnitude of lateral pressure，but also the period it will take to install the strutting system and the obstruction it may bring about on the construction.A strutting system comprises either horizontal struts or anchors，which contribute to the resistance to the lateral earth pressure generated by excavation.The struts are the most important elements in a braced excavation.Deformation and stress being analyzed，the type and size of the struts are accordingly decided.The data on the strut load are necessary for the detailed design of struts or anchors.To design a strutting system，one should first analyze the load on the strut during excavation.
The strut load can be calculated following the finite element method，the beam on elastic foundation method，or the apparent earth pressure method，the last of which will be introduced in this section.
The design pressures acting on a braced retaining wall are very different from those computed from conventional walls where the pressure distribution is usually triangular.Because of the redistribution due to arching and the incremental nature of excavation and strut installation，the pressure distribution does not linearly increase with depth.
When excavation proceeds，the pressure distributions during different excavation stages are shown in Figure 3.1，which states as follows：
Stage 1：The wall is subjected to an active earth pressure and the wall deforms.
Stage 2：A strut is installed and preloaded.Generally，the wall and soil will not be pushed back to its original position，but since the strut force is larger than the active pressure，this causes an increase in the wall pressure.
Stage 3：The excavation in stage 3 causes a new lateral displacement.The soil moves out of the zone behind the first strut into the displacement between b and c.
Stage 4：The installation of the second strut in stage 4 will result in similar changes to the earth pressures.
Figure 3.1 Pressure distributions during different excavation stages