# Ground Deformation Associated with Deep Excavations in Beijing, China
## 3 Characteristic Analysis of Deformation
### Deformation Development  
Based on the time series of the real deformation, which is associated with the progress of the construction process, the development of surface deformation is analyzed. The time series of several typical cases are shown in detail (Figure 6).  
The ground movements exhibit reasonable consistency, although there are significant differences in terms of the deformation of different sites (Figure 6b). At the beginning of stage 1, minor deformations occur due to the shallow depth of the excavation, showing  
Figure 5: Probability distribution of the final ground surface deformation.  
Figure 6: Time series of monitoring ground surface deformations; time is normalized during the construction period. (**a**) Layout of monitoring points; (**b**) Time-history curve of the deformation process.  
upheaval or settlement (<5 mm) to be recorded. During the installation of the first supports, the strata exhibit an uplift tendency under the action induced by larger supporting forces; the ground points exhibit enhanced uplift or a weakened settlement. As the level of excavation continuously rises, the excavation in stage 2 starts with the installation of the second strut of the support system. This process continues in stages as the excavation process develops. Particularly at the onset of drainage consolidation in stage 2, the rate of settlement and cumulative settlement progressively increase. The deformation tends to stabilize or slightly reverse once the internal structure is completed in structure operating stage.  
The maximum vertical displacement (\(\delta\)\(v\)m) occurs during the demolition of the first and second struts above the bottom, and not when excavating to the bottom, or during bottom slab casting. In fact, when the bottom struts are demolished, due to the high soil pressure and the reduced internal stiffness, the ground settlement developed continuously. This is noteworthy because many studies in the literature conclude by describing how surface deformation occurs during the process of excavation to bottom slab construction, and they do not reflect the maximum surface deformation. Furthermore, we detected the difference in deformation values (\(\Delta\delta\)\(v\)) before and after the demolition of last struts to clarify responses in different sites.  
Remarkable differences are observed between points when comparing \(\Delta\delta\)\(v\) values (Figure 7). The strongest response, with an average \(\Delta\delta\)\(v\) of 2.8 \(\pm\) 0.75 mm, was found at the middle transverse section along the long edge. The response of points situated at the transverse section of the 1/4 long edge have an average of \(\Delta\delta\)\(v\) of 1.5 \(\pm\) 0.7 mm, whereas those found at the middle transverse section of the short edge have an average \(\Delta\delta\)\(v\) of 1.0 \(\pm\) 0.4 mm. Corner points show the weakest response, having an average \(\Delta\delta\)\(v\) of only 0.6 \(\pm\) 0.4 mm. The final settlements of the ground surface (\(\delta\)\(v\)) are slightly lower than \(\delta\)vm, and the disparity is negligible (<5 mm). This may be because, with the completion of the internal structure, it has a larger stiffness in order to effectively bear the soil pressure acting upon it, thereby reducing deformation and encouraging convergence.  
The largest values (\(\delta\)\(v\)m and \(\delta\)\(v\)) can be observed on the middle transverse section along the long edge, followed by a section on the 1/4 long side, and then, on the mid-transverse sections along its short sides. The smallest deformation is observed at the corner. This is likely because the corner is subjected to significant confinement effects by the soil on both sides, thus, the maintenance structure, and the purlin around the corner, is also more constrained.  
Figure 7: Box-plots of \(\Delta\delta\)\(v\)m values of different sites.