Numerical Analysis of the Influence of Deep Excavation on Nearby Pile Foundation Building

Abstract

In this paper, a numerical simulation is used to establish a three-dimensional model, which considers the height of buildings, the relative position between buildings, and foundation pits. These were studied in detail to investigate the changes in settlement of adjacent buildings and the displacement and internal force of piles caused by deep foundation pit excavation. The results indicate that the number of floors in the building, along with the angle and distance between the building and the excavation pit, have a significant impact on the settlement of the building and the deformation and internal force variation in the piles. For example, when D = 0.1 H, with the increase in the number of floors, the increase in the bending moment of pile 1 at the pile shaft is 62.63 kN·m, and the increase in the bending moment at the pile head is 224.72 kN·m. At this point, the maximum horizontal displacement of the pile shaft occurs at approximately 1.27 H. When $\theta$ = 45${}^{\circ }$, the maximum difference between the maximum and minimum deformations of the building is 9.71 mm. When D ≤ 1.0 H, the majority of the building is in the primary influence range of surface settlement behind the wall, and the building undergoes a combined deformation of ‘upper convex’ and ‘concave’. When D > 1.0 H, the building predominantly resides in the secondary influence range, and the building undergoes a deformation of ‘upper convex’.

1. Introduction

With the improvement of living standards, more and more people are flocking to big cities. To meet the housing needs of the population, there is a requirement for constructing residential buildings in the city. However, urban construction land is limited. As a result, high-rise buildings have emerged, which can significantly enhance the utilization of urban land resources [1]. The foundation-bearing capacity requirements of high-rise buildings cannot be met by natural soil, leading to the adoption of pile foundations in engineering as the basis for high-rise constructions. Pile foundations are extensively applied in building construction due to their excellent stability and strong bearing capacity [2,3,4]. With the increase in urban population, ground transportation has become increasingly congested. To meet the needs and convenience of people, the development of underground spaces and the construction of more and taller buildings and underground passages are necessary. Deep excavation is considered the optimal solution for addressing these issues [5]. However, the construction of new deep excavation projects inevitably comes close to existing high-rise buildings [6,7]. The excavation of deep foundations will inevitably disrupt the original stress equilibrium of the soil layers, resulting in the generation of additional internal forces, extra settlement, and complex soil–structure interactions in neighboring buildings, and even leading to structural damage [8,9,10]. Therefore, understanding the potential risks to neighboring buildings during excavation is crucial for the safety of the excavation process. The public is also increasingly concerned about the issues arising from excavation activities on adjacent structures [11]. Additionally, due to uncertainties about the underground engineering, determining the exact causes of the impacts on neighboring buildings during excavation is not easy, as it may be influenced by geological conditions. This can lead to incidents such as a crack [12,13,14], damage [15], and dumping [6] in buildings during the construction process.

In the study of the impact of excavation construction on surrounding buildings, some scholars have simplified the buildings. For instance, methods such as the overload method [16], the equivalent elastic beam method [17,18], and the building structural method [19,20,21] have been employed. Among these methods, the latter can effectively consider the influence of building structural stiffness on the research results [22]. The interactions between the upper structure of the building, the pile foundation, and the surrounding soil layers are comparatively complex, and this mechanism is much more intricate than that of shallow foundations. Currently, research on this topic has not been conducted in-depth [23,24,25]. Ding et al. [24] investigated the influence of factors such as the number of building floors, types of building foundations, and the relative position between tunnels and buildings on the three-dimensional structural characteristics of neighboring buildings during tunnel excavation. The results indicate that the type of building foundation has a significant impact on the deformation characteristics of the structures. Feng et al. [25] considered factors such as the relative position between the excavation pit and buildings and the method of pit construction. They studied the mutual interactions between the excavation pit and neighboring buildings and established a multi-angle safety assessment method for evaluating the impact of excavation on neighboring structures. Abdelatif et al. [26] employed a model of soil–structure interaction to investigate the displacement response of neighboring isolated foundation buildings caused by soil excavation. The results indicate that the most significant impact occurs between the foundation and the first floor, rather than at the top of the building.

Although the relative position between buildings and excavation pits has been considered to some extent in previous studies, in some research, buildings have been significantly simplified, which hinders the detailed analysis of neighboring buildings. Furthermore, the above-mentioned results indicate that the impact of excavation on neighboring buildings largely depends on the type of building foundation. Therefore, the analysis should encompass the interactions between soil, structure, and piles [27,28,29,30,31,32]. Additionally, when assessing the influence of certain parameters on buildings, such as building height, the angle between a building and the excavation pit, and depth of excavation, 3D models are required for research [22,33]. For engineering construction in the core urban areas, mitigating the impact on neighboring pile foundation buildings is a significant challenge during excavation.

A complete understanding of the response behavior of neighboring pile foundation buildings to excavation-induced displacements is still lacking due to the complexity of interactions between the upper structure of buildings, pile foundations, and excavation activities. Therefore, the study of the interactions between pile foundation buildings and excavation pits is considered highly necessary for modern engineering. In this study, firstly, an excavation project with a long-deep foundation pit was introduced, including the pit’s linear dimensions, geological conditions, and position relative to neighboring buildings. Then, a three-dimensional numerical model considering the interaction among buildings, piles, and soil was established. The reliability of the model was validated using empirical formula data. Without considering the effects of pit spatial behavior and mutual influences of neighboring buildings, a comprehensive investigation was conducted on the variations in settlement of neighboring buildings and the displacements and internal forces of pile foundations induced by pit excavation, considering factors such as building height and the relative position between the building and the excavation pit (including horizontal distance and angle). The research results provide a more accurate depiction of the internal forces and displacements by adjacent pile foundation structures due to excavation; this serves as a basis for safeguarding the neighboring pile foundation structures to a certain extent.

2. Project Profile

Figure 1 illustrates the surrounding buildings of a deep excavation project. The environment around the excavation site is shown in Figure 1a, with the pit being 700 m long and 18 to 22 m wide, and the excavation depth ranging from 8 to 12 m. The area is densely populated with large commercial and residential buildings. Building 1 has a minimum of 5 floors while Building 2 has a maximum of 17 floors. The closest distance between the buildings and the excavation pit’s edge is 5.6 m, and both buildings are founded on pile foundations. Figure 1b presents the site plan of the surrounding environment of the excavation pit, showing varying angles and distances between the buildings and the excavation pit. Therefore, during the process of pit excavation, pile foundation buildings will inevitably be affected, and the project may encounter construction and safety risks.

3. Establishment and Validation of the Numerical Model

The settlement and deformation of the surrounding soil layers and buildings are influenced by the presence of corner portions in the excavation pit. Additionally, the existence of corners in the excavation pit renders the settlement and deformation characteristics of the buildings more complex [34,35]. Therefore, in order to have the research focus concentrated on the impact of excavation on neighboring buildings, the influence of pit spatial behavior and mutual interactions among neighboring buildings on the research results needs to be avoided. Hence, considering the characteristics of the actual project’s surrounding environment and the research objectives of this study, the actual building complex and pit shape are simplified, while other parameters are sourced from the actual engineering.

3.1. Establishment of Soil Layers and Support Structure

A three-dimensional numerical simulation analysis was conducted in this study using finite difference software. The numerical model was established to represent the characteristics of the excavation pit, building, and soil layers, as shown in Figure 2a. The planar monitoring section is illustrated in Figure 2b. The model dimensions were 200 m × 200 m × 60 m, with the outer boundary of the model being 90 m away from the excavation pit, which is approximately 8.2 times the excavation depth. The area below the pit bottom was 49 m, which is approximately 4.5 times the excavation depth, ensuring that the boundary conditions did not influence the model. The model is constrained with normal displacement boundaries around its perimeter and fixed constraints at the bottom. In order to achieve accurate computational results, the model contains about 340,000 zone elements of hexahedral elements with a size of about 1 m. The excavation pit profile and the profile of neighboring buildings are shown in Figure 3. The soil parameters are presented in

Table 1. Geotechnical parameters of the soil strata.

NO.	f (${}^{\circ }$)	c (kPa)	$\mathit{\nu }$	E${}_{\mathit{s}}$ (MPa)	$\mathit{\rho }$ (kN/m${}^3$)
➀	5	5	0.35	5	1800
➁	18	10	0.31	8.25	1910
➂	19	11	0.30	11.89	1860
➃	16	26	0.34	5.12	1940
➄	28	0	0.25	16.5	1850
➅	18	14	0.30	14.06	1930
➆	32	0	0.25	25	1960
➇	17	19.5	0.31	9.1	1960

. In the table, $\mathit{f}$ indicates the internal friction angle, $\mathit{c}$ indicates the cohesion, $\nu$ indicates the Poisson’s ratio, E${}_s$ indicates the deformation modulus, and $\rho$ indicates the density of the soil. The excavation depth of the pit is 11.0 m. The retaining structure is simulated using Shell elements with a wall thickness of t = 0.8 m and a depth of ${\mathit{H}}_1$ = 22.0 m. The support structure is simulated using Beam elements. The first layer consists of concrete supports with a cross-section size of 800 mm × 800 mm and a spacing size of 6.0 m. The density $\rho$ is 2500 kg/m${}^3$, and the elastic modulus E is 30 GPa with a Poisson’s ratio $\nu$ of 0.3. The second and third layers are steel supports with a cross-section diameter of 609 mm and a wall thickness of t = 16 mm, spaced at 6.0 m intervals. The density $\rho$ is 7850 kg/m${}^3$, and the elastic modulus E is 200 GPa with a Poisson’s ratio $\nu$ of 0.3.

3.2. Parameters of the Building Model

As shown in Figure 4, the building model only considers floor slabs, columns, beams, and piles. The floor slabs are simulated using Shell elements with a thickness of t of 0.12 m. The density $\rho$ is 2500 kg/m${}^3$, and the elastic modulus E is 30 GPa with a Poisson’s ratio $\nu$ of 0.3. Columns and beams are simulated using Beam elements. The column dimensions are 800 mm × 800 mm, and the beam dimensions are 500 mm × 600 mm. The density $\rho$ is 2500 kg/m${}^3$, and the elastic modulus E is 30 GPa with a Poisson’s ratio $\nu$ of 0.3. Piles are simulated using pile elements with a diameter of d is 1 m. The density $\rho$ is 3000 kg/m${}^3$, and the elastic modulus E is 30 GPa with a Poisson’s ratio $\nu$ of 0.3. All structural elements of the above buildings are considered to be ideal elastic bodies [8]. Due to the elongated shape of the excavation pit, deformations along the long side of the pit are relatively complex [25,36]. Based on the actual engineering characteristics introduced in Section 2, the research in this paper considers the impact of different distances, angles, and floors between buildings and the excavation pit on the interaction between the building and the pit excavation. Taking the corner point ‘O’ of the building as the reference point, as shown in Figure 4, the distances of this reference point from the edge of the excavation pit, denoted as D, are set to 0.1 H, 0.5 H, 1.0 H, 1.5 H, 2.0 H, 2.5 H, and 3.0 H, where H represents the depth of the excavation pit. The angles ($\theta$) between the longitudinal wall of the building and the edge of the excavation pit are set to 0${}^{\circ }$, 30${}^{\circ }$, 45${}^{\circ }$, 60${}^{\circ }$, and 90${}^{\circ }$. The number of floors in the building is varied as 3, 5, 7, and 9 floors, respectively.

3.3. Numerical Model Simulation Process

The simulation process is consistent with the actual construction process, including the following steps: (1) equilibrating the ground stresses and resetting the displacements to zero; (2) activating the building model to generate the self-stresses of the building and the stresses on the soil under the influence of building gravity, and resetting the displacements to zero; and (3) excavating the foundation pit at depths of −2.00 m, −5.00 m, −8.00 m, and −11.00 m with support positions at 0.00 m, −3.00 m, and −6.00 m. In order to better represent the actual engineering conditions, the numerical model assumes that the ground and soil layers are uniformly distributed, and a Mohr–Coulomb constitutive model with full elastoplastic characteristics is adopted for modeling. This is due to the lack of detailed field survey data, and the advantage of this model is that it requires fewer soil parameters. Therefore, this relatively simple constitutive model is used [20,33,36]. Although more advanced constitutive models could be employed, there are no reliable data available for calibrating the model [37].

3.4. Validation of the Numerical Model

To verify the accuracy of the model, the horizontal displacements of the ground surface after excavation without buildings are compared with the empirical curve of horizontal displacements proposed by Schuster et al. [38]. This comparison is shown in Figure 5a, where $\delta$${}_{hm}^1$ represents the maximum horizontal displacement of the ground surface without buildings and $\delta$${}_h$ represents the horizontal displacement of the ground surface. The settlement displacements of the ground surface after excavation without buildings are compared with the empirical curve of settlement displacements proposed by Hsieh et al. [39]. This comparison is shown in Figure 5b, where $\delta$${}_{vm}$ represents the maximum settlement displacement of the ground surface without buildings and $\delta$${}_v$ represents the settlement displacement of the ground surface. From the above two figures, it can be observed that the simulated results of horizontal and settlement displacements are in good agreement with the empirical curves. The settlement trough consists of the main influence area (0 ≤ D ≤ 2 H) and the secondary influence area (2 H ≤ D ≤ 4 H); H represents the depth of foundation pit excavation. Therefore, it can be concluded that the model used in this study is reliable and the parameters and simulation process can accurately describe the displacement of the soil behind the wall after excavation. Moreover, there is a certain range of uplift in the soil behind the wall in the secondary influence area, which is consistent with the findings of Tao et al. [40].

4. Analysis of the Results

4.1. Displacement and Moment Variation of Piles Included in Monitoring Section

In urban core areas, nearby existing buildings are inevitably affected by excavation projects for foundation pits. Especially with the development of cities, the possibility of encountering pile foundation buildings increases as well. Excavation of foundation pits can induce horizontal displacement of retaining structures and the soil behind the walls, causing horizontal displacement of piles and significant internal forces (moments). Therefore, this study first investigates the response behavior of pile foundation buildings at different floors (three floors, five floors, seven floors, and nine floors) located at the same distance and angle from the excavation pit.

The horizontal displacement and bending moment variation curves of different floor buildings’ piles are shown in Figure 6 and Figure 7 when D = 0.1 H and $\theta$ = 0${}^{\circ }$. In this study, the horizontal displacements of piles and retaining structures are normalized by $\delta$${}_{hm}$, which represents the maximum horizontal displacement of the retaining structure on the non-building side. From Figure 6a–d, it can be observed that when the distance between the building and the excavation pit’s edge remains constant, the horizontal displacements of the retaining structure on the building side and piles are continuously increased with the increase in the number of building floors. Additionally, the magnitude of displacement increase becomes larger as the number of building floors is increased. The maximum horizontal displacement of pile 1 at nine floors is approximately 1.52 times that of it at three floors, 1.28 times that of it at five floors, and 1.12 times that of it at seven floors. From the displacements at different locations along the pile shaft, it can be observed that the maximum deformation of the pile decreases with an increase in the distance from the excavation pit’s edge. Additionally, the overall deformation trend of each pile is consistent with the deformation trend of the retaining structure. Due to the connection of the pile head to the building structure, the horizontal displacements at the bottom of the buildings (pile head positions) are essentially consistent. Additionally, it can be observed from the graph that the maximum displacement along the pile shaft is always greater than the maximum displacement at the pile head. The displacement variation curves of pile 1 at different floor levels are compared in Figure 6e. It can be observed that the variation in floor levels has a minor influence on the horizontal displacement at the pile head but a significant impact on the displacement along the pile shaft. Additionally, the location at which the maximum pile horizontal displacement occurs is generally consistent with the location of the maximum horizontal displacement of the surrounding retaining structure, which is about 1.27 H.

The bending moment variation curves of piles at different locations are compared, as shown in Figure 7. Positive values of the bending moment indicate tensile stresses on the surface of piles closer to the excavation pit, while negative values indicate tensile stresses on the surface of piles farther from the excavation pit. Based on Figure 7a–d, it can be observed that when the distance between the building and the excavation pit remains constant, the increase in the number of floors leads to a continuous increase in the building’s weight, resulting in the gradual increment of additional bending moment on the pile shaft. By comparing the bending moment variation curves of piles at different locations but at the same floor level, it can be deduced that the bending moment on the pile shaft gradually decreases as the distance from the excavation pit edge increases. Additionally, the bending moment trends of piles at different locations show a basic consistency with the variation in depth. Due to the proximity of pile 1 to the excavation pit, it is subjected to the greatest impact from the pit excavation, making it relatively more hazardous compared to other pile locations.

Therefore, by comparing the bending moments of pile 1, as shown in Figure 7e, it can be observed that the location of the maximum bending moment on the pile shaft is generally consistent and corresponds to the location of the maximum horizontal displacement of the pile. Furthermore, with the increase in the number of floors, the increment of the bending moment of pile 1 is 62.63 kN·m. Among these, the maximum bending moment of pile 1 at nine floors is approximately 1.28 times that of it at three floors, 1.18 times that of it at five floors, and 1.08 times that of it at seven floors. Moreover, the increment of the bending moment at the pile head is 224.72 kN·m. Among these, the maximum bending moment value at the pile head of pile 1 at nine floors is approximately 1.75 times that of it at three floors, 1.39 times that of it at five floors, and 1.15 times that of it at seven floors. Therefore, as the number of floors increases, not only should the increase in the bending moment of the pile shaft be given special attention, but also the variation in the internal forces at the pile head should be closely monitored.

4.2. The Horizontal Displacement and Bending Moment Variations of Pile 1

As indicated in Section 4.1, it has been found that pile 1 experiences the most significant response to the excavation. Therefore, in this study, the displacement variation curves of pile 1 for the nine-floor building at different distances from the excavation edge are compared and analyzed, as illustrated in Figure 8. The pile horizontal displacement curves at different distances from the excavation edge are compared, and it is observed that, as the value of D decreases, the maximum horizontal displacement of the pile shaft gradually increases, and the position where the maximum value occurs is close to the position where the maximum displacement of the retaining structure occurs. By comparing the displacement of the pile head, it can be observed that regardless of the floor height, the sequence of pile head displacement is as follows: D = 1.0 H, D = 1.5 H, D = 0.5 H, D = 0.1 H, D = 2.0 H, D = 2.5 H, D = 3.0 H. This is consistent with the research results obtained by Schuster et al. [38] that the maximum horizontal displacement occurs at 1.0 H from the ground surface.

The curve of normalized maximum displacement of the pile shaft with respect to D values and the fitted curve are plotted in Figure 9a, it can be observed that the slope of the fitted curve gradually increases with the increase in floors. It can be inferred that the increment of the maximum displacement of the building’s piles increases with the increase in floors, and, when D = 3.0 H, the maximum displacement of the pile remains nearly the same. It can be inferred that when D > 3.0 H, foundation pit excavation has little impact on the building. The normalized pile head displacement values for different floors with respect to the distance from the edge of the excavation are plotted along with the fitting curve in Figure 9b. By comparing the pile head displacement values for different floors at the same distance, it is observed that, as the number of floors increases, the pile head displacement first increases and then decreases (five floors > seven floors > nine floors > three floors). This phenomenon is a result of the combined effects of the increased weight of the building and the increased horizontal stiffness of the structure with increasing floors.

By comparing the bending moment variation curves of pile 1 at different distances from the excavation, as shown in Figure 10, it is observed that the bending moments of both the pile shaft and the pile head gradually increase with the increase in the number of floors. Additionally, the increase in the bending moment at the pile head is larger than that of the pile shaft. Here, the positive and negative signs of the pile bending moments only indicate the different sides of tension in the pile, not their magnitudes. By comparing the bending moments of the pile at different distances, it is observed that the bending moments of both the pile shaft and the pile head gradually decrease with the increase in D value. When D is from 0.1 H to 2.0 H, the maximum bending moment occurs at the pile head position, while, when D > 2.0 H, the maximum bending moment occurs at the pile shaft position. Moreover, with the decrease in the D value, the maximum position of the positive bending moment of the pile (the bending moment value of the pile when the side of the pile closer to the excavation experiences tension) gradually becomes deeper and tends to approach the maximum position of the displacement of the retaining structure.

The relationship between the maximum bending moment of the pile and D values for different floor levels is plotted in Figure 11a. It is observed that the maximum variation in the pile bending moment occurs when D is from 0.1 H to 1.0 H. When D is from 1.0 H to 3.0 H, the variation in the pile bending moment is relatively small. The reason is that during this range (0.1 H ≤ D ≤ 1.0 H) the majority of the building is located within the main settlement influence zone of the soil behind the wall. When D is from 1.0 H to 3.0 H, the majority of the building is located within the minor settlement influence zone of the soil behind the wall. When D = 3.0 H, regardless of the floor height, the difference in the pile bending moment values is relatively small. This also confirms the conclusion obtained in Section 4.2 that when D ≥ 3.0 H, the impact of building floor height on the response of the pile bending moment to excavation is relatively small.

The relationship between pile head bending moment values and D values for different floor levels is depicted in Figure 11b. It can be observed that with the increase in D values, the pile head bending moment values gradually decrease, then gradually increase, and eventually converge to a consistent value. Moreover, the side of the pile head under tension changes from the side farther from the excavation to the side closer to the excavation.

4.3. Settlement Characteristics of Longitudinal Walls for Different Floored Buildings and Potential Failure Surfaces of Soil behind the Wall

The longitudinal wall settlement variation of the building with $\theta$ = 90${}^{\circ }$ as the distance from the excavation edge changes is shown in Figure 12. By comparing the longitudinal wall settlement curves with the variation in distance from the excavation edge, it can be observed that with the increase in the D value, the settlement curves of the wall gradually become flatter and approach the settlement of the ground behind the wall. This is due to the relatively large overall stiffness of the pile foundation structure and the fact that the piles can provide substantial support to the building. Therefore, the settlement of the building’s longitudinal wall is less than that of the ground without the building, and no significant settlement trough has been observed. By comparing the settlement curves of longitudinal walls at different floors, it can be observed that as the number of floors increases, the self-weight of the building gradually increases, and the magnitude of settlement increase in the longitudinal walls also gradually increases. Moreover, the settlement range also gradually increases. That is, the higher the floors, the greater the impact of excavation on the building. However, when D = 3.0 H, the settlement of the longitudinal walls is almost equal to that of the ground behind the walls, indicating that the building is minimally affected by the excavation.

The settlement variation curves of the ground behind the walls at different distances from the retaining structure for the nine-floor building are compared in Figure 13. The monitoring section is shown in Figure 2b. It can be observed that when D < 2.0 H, which is the boundary between the major and minor influence zones crossed by the building, the presence of the building has a significant impact on the settlement of the ground behind the walls, and the increase in ground settlement amplitude is also considerable when D ≥ 2.0 H, which means the building is located in the minor influence zone. The settlement of the ground behind the walls is minimally affected by the presence of the building, and the increase in ground settlement amplitude is also small.

The estimation of shear bands and potential failure surfaces is based on the maximum shear strain increments in the soil. In this study, the influence of building height (9 floors) and orientation ($\theta$ = 90${}^{\circ }$) on the soil strain increments with varying D values is investigated, as shown in Figure 14. Due to the presence of piles, the displacement of the soil behind the wall is effectively prevented. Therefore, when the building is located closer to the edge of the excavation, when D is from 0.1 H to 0.5 H, no apparent potential failure surface is observed in the soil on the building side, when D = 1.0 H, a relatively noticeable potential failure surface begins to appear in the soil behind the wall, when D ≥ 2.0 H, that is, when the entire building is located in the secondary influence zone of the soil settlement behind the wall, the positions of potential failure surfaces in the soil behind the wall relative to the distance between the building and the excavation edge become less significant. Moreover, the potential failure surfaces of the soil on both sides of the excavation are almost symmetrically related. By comparing the displacement vector plots of the soil, this rule can also be observed, which contradicts the findings of Maddah et al. [22], who reported that the positions of potential failure surfaces in the soil are not significantly related to the location of the buildings, this discrepancy is attributed to the consideration of the presence of piles in this study, which significantly enhances the overall stiffness of the soil behind the wall. Moreover, the piles can effectively transfer the upper loads to deeper soil layers, leading to the inconsistency between the two sets of results.

4.4. Characteristics of Longitudinal Wall Settlement of Nine-Floor Building

The longitudinal wall settlement curves for the nine-floor building at various positions (including angle and distance) from the excavation edge are analyzed and shown in Figure 15. By comparing the longitudinal wall settlement curves for buildings at different angles, it can be observed that, as the $\theta$ value increases, the influence range of building settlement gradually decreases. This is due to the adjusting effect that buildings have on wall settlements. When $\theta$ = 0${}^{\circ }$, the adjustment effect of buildings on wall settlements is minimal, and the settlement range is the largest. Conversely, when $\theta$ = 90${}^{\circ }$, the adjustment effect of buildings on wall settlements is maximal, and the settlement range is the smallest. This indicates that with an increase in the length of the building perpendicular to the direction of the excavation boundary, the adjusting effect of the building on wall settlements becomes more significant. By comparing the longitudinal wall settlements at different distances from the excavation boundary, it can be concluded that when the building is at 3.0 H from the excavation edge, the building is minimally affected by the excavation.

From Figure 15, it can be seen that when the building is 0.1 H away from the edge of the foundation pit, the excavation of the foundation pit has the greatest impact on adjacent buildings. Therefore, a building displacement contour of 0.1 H from the edge of the foundation pit is selected for comparison, as shown in Figure 16. It was found that when $\theta$ = 0${}^{\circ }$, 30${}^{\circ }$, 45${}^{\circ }$, 60${}^{\circ }$, and 90${}^{\circ }$, the maximum displacement of the building was 11.53 mm, 12.17 mm, 11.77 mm, 10.42 mm, and 9.93 mm, respectively. The numerical pattern gradually decreased, but the difference between the maximum and minimum displacement of the building was 7.16 mm, 9.44 mm, 9.71 mm, 8.55 mm, and 7.81 mm, respectively. The trend of the change first increases and then decreases, with the maximum difference when $\theta$ = 45${}^{\circ }$. Therefore, it can be inferred that when $\theta$ = 45${}^{\circ }$, the uneven deformation of buildings is the largest, so special attention should be paid to protecting buildings within this angle range.

4.5. The Displacement and Moment Characteristics of Building Pile 0 at Different Distances from the Excavation

As the building is not perpendicular to the excavation, the displacement and moment curves of pile 0, which is closest to the excavation edge, for the nine-floor building are compared. The comparisons are shown in Figure 17 and Figure 18. Due to space constraints, only the displacement and moment variation curves of pile 0 for buildings with D = 0.1 H and D = 3.0 H are presented in Figure 17 and Figure 18, respectively. The displacement variation curves for other values of D are similar. From Figure 17, it can be observed that when the value of D is kept constant, the pile displacement variation with respect to $\theta$ is similar with only slight differences, and the overall trend remains consistent. From Figure 17, it can be observed that when the value of D is kept constant, the pile bending moment variation is quite similar with only minor differences, and the overall trend remains consistent. By comparing the displacement and bending moment curves of pile 0 with D = 0.1 H and $\theta$ = 0${}^{\circ }$ from Figure 18a and Pile 1 with $\theta$ = 0${}^{\circ }$ and D = 0.1 H from Figure 10d, it can be observed that the maximum displacement and bending moment values of pile 0 are greater than those of pile 1. This is because, although the building is not affected by the spatial effect of the excavation, the interaction between the building and the surrounding soil creates a spatial effect within the building itself.

4.6. The Settlement Difference between the Front and Back Facades of the Building

When a certain angle is formed between the building’s walls and the edge of the excavation, uneven settlement occurs in the building. In this study, a comparison is made by analyzing the settlement difference between the front and back facades of the building, at the same distance and different angles, in order to understand the distribution characteristics of building settlement under various conditions. The relative position relationship between the settlement trough of the soil behind the wall and the building is shown in Figure 19. When D = 0.1 H, both ends of the building are not positioned at the locations where the maximum settlement for the soil behind the wall occurs, but the entire building is situated within the primary influence zone of settlement for the soil behind the wall. When D = 0.5 H, the building is positioned closer to one end of the excavation and is located at the location where the maximum settlement for the soil behind the wall occurs. Furthermore, the entire building is situated within the main influence zone of settlement for the soil behind the wall. When D = 1.0 H, one end of the building is positioned closer to one end of the excavation within the main influence zone of settlement for the soil behind the wall, while the other end is within the secondary influence zone of settlement for the soil behind the wall. Moreover, a significant portion of the building is situated within the main influence zone. When D = 1.5 H, although one end of the building is positioned closer to one end of the excavation within the main influence zone of settlement for the soil behind the wall, the other end is within the secondary influence zone of settlement for the soil behind the wall. However, a significant portion of the building is situated within the secondary influence zone. When D ≥ 2.0 H, the building is entirely within the secondary influence zone of settlement for the soil behind the wall.

With the building’s corner point ‘O’ as the origin of coordinates, the distance along the vertical wall direction is taken as the horizontal axis, and the settlement difference between the front and back facades of the wall is taken as the vertical axis, as shown in Figure 4. When comparing Figure 20b–e, it can be observed that when the angle $\theta$ between the building and the excavation remains constant, larger values of D result in smaller disparities in building settlement. Taking 0.1 H as an example, when $\theta$ = 30${}^{\circ }$, 45${}^{\circ }$, and 60${}^{\circ }$, the differences between the maximum and minimum values of longitudinal wall settlement are 0.087$\delta$${}_{vm}$, 0.102$\delta$${}_{vm}$, and 0.092$\delta$${}_{vm}$. Therefore, when $\theta$ = 45${}^{\circ }$, the building exhibits the largest degree of uneven settlement along the longitudinal wall with the maximum disparity in longitudinal wall settlement occurring at a distance of approximately 1 H from the excavation pit edge. As uneven settlement of the building to a certain extent reflects the degree of torsion, the torsional deformation of the building is also maximized at this point.

When D from 0.1 H to 1.0 H, most of the building is situated within the main influence zone of settlement for the soil behind the wall. The wall exhibits a settlement pattern with both ‘concave interval’ (closer to the excavation) and ‘upper convex interval’ (farther from the excavation) effects, as shown in Figure 20 for D = 0.5 H. This deformation phenomenon becomes more pronounced with an increase in θ, making the building’s deformation characteristics more complex, the building experiences the greatest influence from the excavation at locations closer to the excavation. Therefore, when the building is located within this range, it should be given special attention for protection. When D from 1.0 H to 3.0 H, meaning that most of the building is within the minor influence zone of settlement for the soil behind the wall, the wall exhibits ‘upper convex interval’ settlement pattern. And when D = 3.0 H, the settlement difference for the building is nearly zero, indicating that the excavation has no impact on the building.

5. Conclusions

The research in this paper analyzed the influence of excavation on the pile deformation and internal forces of pile-supported buildings located at different floors, distances, and angles behind the retaining wall while ensuring reasonable horizontal and settlement displacements of the soil outside the excavation. The study also included an investigation of the settlement characteristics of the buildings. The main conclusions are as follows:

1.

The moment values of the piles increase with the number of floors. Specifically, the increase in the bending moment at the pile shaft for pile 1 is 62.63 kN·m, and the increase in the bending moment at the pile head is 224.72 kN·m. The increase in the bending moment at the pile head is 3.59 times that of it at the pile shaft. When D ≤ 1.0 H, there is a substantial variation in the bending moment of the pile shaft. As D ≥ 1.0 H, the magnitude of change in the pile shaft’s bending moment diminishes. When D ≥ 3 H, the excavation of the foundation pit has almost no effect on the internal forces of the pile shaft. Therefore, for pile foundation structures within a range of 1 H, particular attention should be paid to the variation in the pile head bending moment.

2.

When $\theta$ = 45${}^{\circ }$, the uneven settlement of the building is maximized. Additionally, when the building spans an area mainly located in the main influence area of surface settlement, that is when D ≤ 1.0 H, and the wall exhibits a settlement characteristic of ‘concave’ and ‘upper convex’ combined action. When most of the building is located in the secondary impact area of surface settlement, that is when D ≥ 1.0 H, and the wall exhibits an ‘upper convex’ settlement difference characteristic. When D ≥ 3.0 H, the settlement difference of the longitudinal walls is almost 0, indicating that foundation pit excavation has almost no impact on the settlement of buildings in this range.

The research and analysis in this paper primarily focus on a specific form of retaining the structure deformation and pile length. Therefore, in future studies, the team will emphasize conducting in-depth research on the deformation effects of different forms of retaining the structure deformation and pile lengths on buildings.