2.1 Introduction

Failures or collapses of excavations are disastrous at excavation sites.At worst，they endanger the safety of workers and the adjacent properties.Their influential zones are usually so large that much ground settlement may be introduced and adjacent properties within the influential zone of settlement may be damaged significantly.Due to its significant damage，to avoid failures or collapses is of vital importance and stability analyses are therefore firstly required.

Failure of an excavation may arise from the stress on the support system exceeding the strength of its materials when，for example，the strut load exceeds the buckling load of struts or the bending moment of the retaining wall exceeds the limiting bending moment.Failure can also arise from the shear stress in soil exceeding its shear strength.

When the shear stress at a point in soil exceeds or equalizes the shear strength of soil at the point，the point is in the failure or the impending state.When many failure points connect and form a slip line，the failure surface is thus produced.Once the failure surface is produced，the excavation failure or collapse will occur.This is called the overall shear failure.

Basal heave and the push⁃in are two main overall failure modes of excavation.As shown in Figure 2.1（a），the push⁃in is caused by the excessive earth pressures，reaching the limiting state on both sides of the retaining wall，which is thereby moved a large distance toward the excavation zone（especially the part embedded in soil）until reaching the full⁃zone failure.The analysis views the retaining wall as a free body and the external forces on the wall and internal forces of the wall are in equilibrium.The factor of safety against push⁃in or penetration depth of the wall can thus be obtained.When push⁃in is caused，with different extents of movement of the embedded part of the retaining wall，the earth pressure on the retaining wall varies.Thus there are fixed earth support method and free earth support method for analysis.

The basal heave arises from the weight of soil outside the excavation zone exceeding the bearing capacity of soil below the excavation bottom，causing the soil to move and the excavation bottom to heave so much that the whole excavation collapses.Figure 2.1（b）is a possible form of basal heave.When analyzing the basal heave，we should assume several possible basal heave failure surfaces and find their corresponding factors of safety according to mechanics.The surface having the smallest factor of safety is the most likely potential failure surface or critical failure surface.With the variable forms of critical failure surfaces，there exist many analyzing methods.

Figure 2.1 Overall shear failure modes

As discussed above，the mechanisms of push⁃in and basal heave are different.Basically，push⁃in refers to the stability of the retaining wall.Push⁃in also causes soil near the wall to heave.Basal heave refers to the stability of the soil below the excavation bottom，and its failure surface may pass through the bottom of the retaining wall or through the soil below the bottom of the retaining wall.When basal heave occurs，the soil around the excavation bottom will mostly heave.Nevertheless，when it occurs to a soft clay ground，the earth pressure on both sides of the wall may also reach the limiting state，from which a push⁃in failure is also possible.