Study of Convex Corners' Effect on the Displacements Induced by Soil-Nailed Excavations

In deep excavations, because of time, budget, and computational tools limitation, two-dimensional analyses (plane strain analyses) rather than three-dimensional ones are often used for controlling factors of safety and displacements. In most excavation projects, the excavation plan includes convex and concave corners. Unlike concave corners, the use of two-dimensional analysis for convex corners is non-conservative. In the present study, by using three-dimensional numerical modellings and comparing 3D and 2D results, the e ects of convex corners on the displacements induced by soil-nailed excavations are studied for two types of soil: sand (granular soil) and clay (cohesive soil). The results of the study indicate that the length of the zone a ected by the convex corner (the zone along the wall and around the convex corner where the values of the displacements are greater than the corresponding two-dimensional values) is about 0.75 to 1 times the excavation's depth. The results also show that although the horizontal soil nails are executed easier and prevent interference of nails which cross, but applying an appropriate angle over the horizon (about 10 degrees) to the soil nails can reduce the wall displacements. Furthermore, it was found that applying azimuth to the soil nails in the area a ected by the convex corner, signi cantly increased the displacements of this area. Lastly, it has been suggested that to reduce the displacements in the zone a ected by the convex corner, increasing the length of the soil nails is more e ective than decreasing their horizontal spacing.

In deep excavations, because of time, budget, and computational tools limitation, two-dimensional analyses (plane strain analyses) rather than three-dimensional ones are often used for controlling factors of safety and displacements. In most excavation projects, the excavation plan includes convex and concave corners. Unlike concave corners, the use of two-dimensional analysis for convex corners is non-conservative. In the present study, by using three-dimensional numerical modellings and comparing 3D and 2D results, the eects of convex corners on the displacements induced by soil-nailed excavations are studied for two types of soil: sand (granular soil) and clay (cohesive soil). The results of the study indicate that the length of the zone aected by the convex corner (the zone along the wall and around the convex corner where the values of the displacements are greater than the corresponding two-dimensional values) is about 0.75 to 1 times the excavation's depth. The results also show that although the horizontal soil nails are executed easier and prevent interference of nails which cross, but applying an appropriate angle over the horizon (about 10 degrees) to the soil nails can reduce the wall displacements. Furthermore, it was found that applying azimuth to the soil nails in the area aected by the convex corner, signicantly increased the displacements of this area. Lastly, it has been suggested that to reduce the displacements in the zone aected by the convex corner, increasing the length of the soil nails is more eective than decreasing their horizontal spacing. 1 This study aims to assess the eect of con-

Results and discussion
After determining properties of soil and used elements and characteristics of the models, threeand two-dimensional analyses were done. Fig. 8 shows the soil's total displacements in 3D and 2D models, for sand. As it can be seen, soil displacements around the convex corner are greater rather than areas which are not aected by it.
In Fig. 9, the horizontal displacement of the corner in 3D analysis was compared to the hori-  where the values of the displacements are greater  can be a better approach rather than decreasing their horizontal spacing.

Conclusion
This study aimed to evaluate the eect of convex corners on the displacements induced by • Although the horizontal soil nails are executed easier and prevent interference of nails which cross, but applying an appropriate angle over the horizon to the soil nails can reduce the wall displacements. It was found that an angle of about 10 degrees can be the most ecient.
• Applying azimuth to the soil nails in the area aected by the convex corner, signicantly increases the displacements. Hence, applying azimuth to the nails is not recommended at all. The results indicate that the amount of increase in displacements is more in granular soils rather than cohesive ones.
• For reducing the displacements in the zone aected by the convex corner, increasing the soil nails length can be more eective than decreasing their horizontal spacing.
Studying the convex corners' eect on the displacements induced by anchored excavations and the eect of soil relaxation due to the partial excavation's steps in each level on the displacements can be the possible future works.
To investigate the latter topic, it can be studied, for example, by comparing 3D analyses and 2D ones with dierent Mstage factors using PLAXIS software.