Numerical modelling for optimizing shoring wall performance in deep urban excavations

Soil nailing and anchoring are effective methods for reinforcing the soil in situ, providing internal support that enables the earth to sustain itself during and after excavation. To ensure optimal performance, it is essential to monitor the behavior of the soil nail walls throughout the excavation and after completion, so that the SOE system design can be improved. This study presents a comprehensive survey of the design and performance of soil nail walls in deep urban excavations at depths ranging from 19.5 to 29.3 m. After construction, the lateral deformations of the soil nail walls varied significantly from 69% to 222% of the initial deformations observed immediately after completion. Numerical analyses were used in the design process to accurately predict the wall performance and determine the design characteristics to identify appropriate design parameters and predict the wall behavior. Several numerical models using different modelling approaches are examined, and the results demonstrated that post-construction deformation rates can vary between walls based on factors such as the soil nail and anchor system design and geotechnical conditions at the excavation site. A thorough understanding of these variables is crucial for optimizing the performance of SOE systems in deep urban excavations.


Introduction
In recent years, soil-nail walls have been extensively employed in the city of Tehran as temporary retaining walls to allow a higher number of basements below high-rise structures.Soil nailing is an in-situ earth reinforcement method that reinforces the soil or rock mass internally and enables an earth mass to support itself through the introduction of driven or grouted steel bars into the mass during and after the excavation process.
Soil nailing is a versatile excavation retaining system for deep excavations in urban areas surrounded by major structures and infrastructure, provided that the limiting lateral displacements are not exceeded.For the adjacency of urban excavation projects to facilities, buildings, and roads, the deformation of walls is one of the most important criteria for acceptable performance of the support system.Therefore, monitoring systems are typically used to record the deformations of excavation walls.
The monitoring data demonstrated the performance of the wall during excavation and after its completion.Durgunoglu et al. [1] studied the performance of nail walls in Istanbul and discussed the relationship between nail arrangement and wall deformations.In this study, the performance of the walls was monitored using laser total station recordings obtained at certain time intervals parallel to the excavation process.Numerical analysis is generally applied in the soil nail wall design process to specify the proper design characteristics and predict the wall performance.The results of the numerical models, applying different modeling approaches developed using Plaxis 2D [2], were surveyed in this study.
Plaxis 2D is a finite element software that can be used to create numerical models for simulating soil nail walls (for example [3]- [5]).
The simulation of the soil nail wall construction process was conducted considering a sequence of construction stages.To verify the results of the models, a polyclinic wall in Seattle was modelled, and the horizontal deformation of the model was compared with the field data reported in [6].The results verify the applicability of the modeling approach.
The walls of the Yas Project were simulated using a verified modeling approach.The simulation results were analyzed and compared with the field data obtained by monitoring.

General specifications
In this section, the general specifications of soil-nailed walls are introduced.Yas (walls Y1 and Y2), Eram (wall E1) and Baran (wall B1) were surveyed.Figures 1 and 4 illustrate the perspectives of walls Y1, Y2, E1, and B1.Table 1 presents the height of the walls and density of the soil nailing systems.The nail density was calculated as Nail density = (/ ) /, where  is nail length,  is horizontal nail spacing, and  is wall height.Adjacent 2 to 4-story residential and administrative buildings were located approximately 30 m from the excavation line.The East wall was located directly in the vicinity of several stores.Type Y1 was considered for the North and the West walls, and Type Y2 was considered for the east wall of the Yas project.The groundwater level was below the excavation level.

Eram project
The Eram project site is located West of Tehran.Eram had a more conservative design.The excavation depth of this project was initially considered to be approximately 24 m at first, and the excavation was stopped at a depth of 19.5 m , following revisions of the project's specifications.The critical design profile, Type E1, consists of a cut with a 19.5 m depth.After 3-meter layer of filling soil, geotechnical investigations have intersected layers of residual soil with cohesion of 30 to 40(kPa), internal friction of 36-38 (degree), and Young's modulus of 40 to 50(MPa), which vary with depth.In Type E1, some 5-story residential buildings were located approximately 7 m from the project line.The average depth of the groundwater table in the Type E1 was 17.5 m.Table 3 presents details of the performed soil nailing system for E1. Figure 7 illustrates the arrangement of the soil nails for E1.

Baran project
The Baran project is located along Shariati Street in the center of Tehran.The critical design profile, Type B1, comprised an outer cut from the top elevation to a depth of 10 m to the first 2-m-wide horizontal bench.Then, a 6.4-m-high middle cut down to the second 2-m-wide horizontal bench, and an 11-m-high inner cut down to the bed elevation, which resulted in an equivalent batter of 8.3 degrees.The inclinations of the soil nails with respect to the groundwater level were increased to strengthen the soil against local instability.
After the layer of filling soil, some layers of residual soil with cohesion of 28 to 35 kPa, internal friction of 25-35 degrees, and Young's modulus of 25 to 60 MPa, which vary with depth, were recognized in geotechnical investigations.
Figure 8 illustrates the arrangement of the soil nails for B1, and table 4 presents the corresponding details of the soil nailing system.The average groundwater table level in the Type B1 was approximately 18.2 m.A sixstory administrative building and several three to four-story residential and administrative buildings are located at 12 m from the project line.

Monitoring results
An instrumentation program was established to monitor the performance of the soil-nail system and provide early detection of deflections that could potentially damage adjacent structures in all of these projects.
The performance of the walls was monitored by laser total station recordings from the reflectors installed on the top nail rows, parallel to the excavation progress, and in service at the perimeter of the project line.
The displacements of the reference points were read at scheduled times during the excavation.The measured horizontal displacements from some reflectors of Y1 are presented in figure 9 [7].The maximum measured value of the average cumulative horizontal displacement (Ux) of approximately 35 mm occurred along Y1.
Prior post-construction monitoring of soil nail wall displacements shows that these movements tend to continue after wall construction for up to six months, depending on the ground type.
The monitoring results presented in figure 9 indicate that the maximum measured horizontal displacements were approximately 219% larger than the measured horizontal displacements immediately after the completion of the excavation at the end of Feb-2010.For Y2, this increase was approximately 167% after the excavation was completed.Similarly, for walls E1 and B1, the increases were 222% and 69%, respectively.
The maximum reported horizontal deformation (  ) and maximum horizontal deformation at wall completion () are presented in table 5.
Post-construction monitoring of soil nail wall displacements shows that these movements tend to continue after wall construction for up to six months, depending on the ground type.
The FHWA [3] states that post construction deformation typically increases by up to 15% of the deformations observed soon after construction.Where, Ti is the interval between the time of wall accomplishment and the last reading.As shown in table 5, all wall horizontal deformations were significantly lower than 0.005H, as suggested by the FHWA as the upper limit of acceptable performance.
The reported post-construction deformations of the walls varied from 69% to 222% of the deformations observed soon after construction; these amounts were significantly higher than the value stated by the FHWA (15%).

Analysis
The soil nail wall systems were numerically simulated using a two-dimensional finite element code (Plaxis 2D version 8.2) to provide information on the performance of the soil nail wall.The program can analyze either plane-stain or plane-stress problems.
The plane strain mesh was defined by 15-node triangular elements with 12 Gaussian points, and the soil layers were modelled using the elastic-plastic Mohr-Coulomb model.
In the used finite element program, the soil nail and shotcrete wall were modelled using elastic plate elements, and a fixed connection was used between the wall and nails.The plates were structural elements with bending and axial stiffness.The most important parameters of the plates were the flexural rigidity (bending stiffness) EI and axial stiffness EA.
The equivalent nail and grout parameters are calculated according to the following equations. =  ( /) +   /  =  / ( /4)  = (/ℎ)( /64) , where Eg is the elasticity modulus of the grout material, En is the elasticity modulus of the nail, A is the total cross-sectional area of the grouted soil nail, Ag is the cross-sectional area of the grout cover, An is the cross-sectional area of the reinforcement bar, DDH is the diameter of the drill hole, and Sh is the horizontal spacing between the soil nails.
The Shotcrete facing wall of 10-cm thickness, reinforced with welded wire mesh, was modelled as elastic plate elements of EA = 2.1 × 106 kN/m and EI = 1750 kN/m /m.
Several phases were used to model the staged construction: the first phase was to apply the initial conditions, and the other phases were used to simulate the construction sequences of the soil nail wall.
Updated mesh analysis is a type of calculation provided in Plaxis 2D that considers the effects of large deformations, and all the analyses were performed using the updated mesh option.

Results
Models were developed to obtain the final monitored results for the walls.The results of the models are presented in this section.Figure 10 shows the resulting horizontal displacement shadings of Y1.The value of extreme horizontal displacement at the location of the installed reference points for Y1 was 35.4 mm.
The construction of other soil-nailed walls was simulated in a similar manner.Table 6 presents the maximum horizontal deformations at the locations of the installed reference points after wall construction.The results of the models were close to the monitored data for maximum horizontal deformations, but the monitored deformations of the wall at the completion of the wall construction were smaller than the maximum values.
The post-construction deformations continue after wall construction is completed until the unbalanced forces are completely released and the soil-nailed system reaches a balance.Therefore, when the wall construction is accomplished, there are some unreleased forces.To simulate the conditions of the soil nail system at the completion of wall construction, we can reduce the percentage of load relaxation in modelling the construction stage of the walls.
Figure 11 shows the effect of load relaxation factor variation on the final resulting horizontal deformations at the locations of the installed reference points for the walls.
As shown in the graph, the variation in the horizontal deformations had a near-linear relationship with the load relaxation factor.The results of these variations are listed in Table 7.As shown in Table 9, walls Y1 and Y2, which have similar geotechnical situation and construction process, did not have a similar rate of post construction.Furthermore, they did not result in similar load-relaxation factors.These differences show that the load relaxation factor is a subject of the soil nail system design and is not related to geotechnical conditions.By contrast, walls Y1 and E1 had similar rates of post construction, but their load reduction factors were different.1336 (2024) 012004 IOP Publishing doi:10.1088/1755-1315/1336/1/0120049

Conclusion
The lateral deformation of soil-nailed walls in urban projects is very important because of the presence of adjacent buildings and installations.For the soil-nailed walls of deep excavations, the post-construction deformation after accomplishment of the wall can be even higher than the deformations that occurred until the wall was construction.These deformations may affect adjacent buildings and installations.Therefore, it is important to accurately predict these factors.
The difference between the final deformations and the deformation immediately after wall completion for several soil-nailed walls was simulated in this study.To achieve this difference, we reduced the percentage of the relaxation factors at each stage of construction.Thus, some of the deformations that resulted from the excavation of each stage wall occurred during the next stages and after the completion of the wall.
These case studies indicate that the rate of post-construction deformations can differ from wall to wall, and it is a subject of several factors, such as the soil nail system design and geotechnical conditions.Although numerical modelling can estimate the deformation of soilnailed walls, it seems necessary to improve the model with the results of continuous monitoring of the walls and experience of similar projects.

Figures 5
Figures 5 and 6 illustrate the arrangement of the soil nails for walls Y1 and Y2, respectively.

Figure 9 .
Figure 9. Horizontal displacement trend of the soil-nail wall at the post-construction condition-Y1

Figure 11 .
Figure 11.Variation of the horizontal displacement with load relaxation factor.

Table 1 .
Wall height and nail density

Table 3 .
Arrangement of soil nails on E1.

Table 4 .
Arrangement of soil nails for B1 walls.

Table 5 .
Monitored horizontal deformation of the walls.