## 4 Results and Discussion
### The Raised Effective Formation Level
#### 4.4.1 The Raised Effective Formation Level for Stability Analysis  
To consider the effect of earth berms on the stability of the embedded walls, [PERSON] [27] proposed a modified raised effective formation level approach for use in effective stress analysis, with the raised effective formation level (\(\Delta H\)) given as follows:  
\[\Delta H=W\tan\bigl{(}45^{\circ}-\varphi^{\prime}/2\bigr{)}/\gamma d \tag{3}\]  
where  
\(W\) is the total weight of the berm;  
\(d\) is the wall embedment below the formation level;  
\(\varphi^{\prime}\) is the effective angle of shearing resistance;  
\(\gamma\) is the unit weight of the soil from which the berm is made.  
A series of numerical models were conducted to investigate the raised effective formation level proposed by [PERSON] for stability analysis under both axisymmetric and plane strain conditions.  
Figure 13 illustrates the changes observed in the factor of safety of the PRSS concerning various berm heights and REFL under both axisymmetric and plane strain conditions. Under axisymmetric conditions, the factor of safety initially increases with the increase in berm height, showing a basal heave instability failure mode (as seen in Figure 14a,b). However, when the berm height reaches a certain threshold, the factor of safety decreases, indicating the localized instability of the berm (as seen in Figure 14c). Under plane strain  
Figure 12: Maximum ground surface settlements (**a**) and their locations (**b**) with different berm geometric parameters.  
conditions, the factor of safety remains relatively constant, approximately half of that observed under axisymmetric conditions. The dominant mode of failure is overall instability (as seen in Figure 14d-f). Under axisymmetric conditions and using [PERSON]'s approach to consider the effect of an earth berm on the stability of support structures, the factor of safety increases with the increase in earth berm height, and the failure mode is basal heave instability failure mode (as seen in Figure 15a-c). When the earth berm height is low, the difference in the factor of safety between equivalent and non-equivalent cases is small. However, as the earth berm height increases, the difference between the two cases also increases. This is because the non-equivalent case ignores the possibility of localized instability due to the absence of an earth berm. The factor of safety for the localized stability of the berm decreases with the increase in earth berm height. Under plane strain conditions and using [PERSON]'s approach to consider the effect of an earth berm on the stability of support structures, the factor of safety increases with the increase in earth berm height, but it is about 20% higher than the actual situation. It shows a failure pattern that combines overall instability and basal heave instability (as seen in Figure 15d-f). It is noted that under axisymmetric conditions, [PERSON]'s approach can better consider the effect of an earth berm on the stability of support structures. However, when the height of the earth berm is high, the stability of the earth berm needs to be considered separately. Under plane strain conditions, [PERSON]'s method tends to be dangerous. In circular excavations, axisymmetric conditions should be used to analyze the stability of supporting structures. The use of plane strain conditions will result in overly conservative results.  
Figure 14: Typical shape of the failure surface with berm: (**a–c**) under axisymmetric conditions; (**d–f**) under plane strain conditions.  
Figure 13: Variation in the factor of safety of the PRSS with different berm heights and REFL under axisymmetric and plane strain conditions [33].