Building Deformation Prediction Based on Ground Surface Settlements of Metro-Station Deep Excavation

Building deformations are not only closely related to the distance from the building to metro-station excavation but also related to the relative positions of the building and metro-station excavation. Building deformations can be predicted using ground surface settlement profiles. Based on typical geological parameters of Nanjing metro-station excavation, ground surface settlements were numerically simulated by auxiliary planes perpendicular and parallel to the excavation and by angled auxiliary planes at the excavation corner. Results show that the ground surface settlement profiles in auxiliary planes are closely related to the relative positions of the auxiliary planes and the metro-station excavation. Partitioning of ground surface settlements was proposed according to the three types of ground surface settlement profiles; furthermore, bending deformation and torsional deformation regularities of surrounding buildings were analyzed, and an estimation method for building settlements was developed. Finally, field-monitored settlement data of 21 buildings in different zones were compared with the estimated settlement data, and the application of the settlement estimation method to different types of foundations was analyzed. *e results of this study can serve as reference for metro-station deep excavation construction and protection of surrounding buildings.


Introduction
Metro-station deep excavations are generally located in bustling areas of a city.e excavation design should meet not only the strength and stability requirements of the support structure but also the deformation-control requirements of the surrounding environment [1].Soil-mass displacements around station excavations have complex three-dimensional (3D) characteristics.However, previous studies mainly focused on wall deflection and involved limited considerations for ground surface settlements [2][3][4][5][6][7][8].Ground surface settlements can be studied through auxiliary planes perpendicular and parallel to the excavation, as well as through angled auxiliary planes at the excavation corner (Figure 1).
Ground surface settlements in the perpendicular auxiliary plane have been studied by many scholars but mainly in the case of two-dimensional (2D) plane-strain states.For example, researchers have proposed triangular and troughshaped ground surface settlement profiles in perpendicular auxiliary planes [9,10].However, few studies have investigated ground surface settlements in the case of 3D states, especially ground surface settlements in angled auxiliary planes and in parallel auxiliary planes.
Building deformation around metro-station excavation involves geotechnical-structural interaction, making it a cross-disciplinary geotechnical engineering problem.Son and Cording [11] studied the phenomenon of building failure due to excavation in scaled models of 1 : 10 and found that cracks in buildings can be classified as "shear + tension," "convex + stretch," and "concave + stretch."e different deformation forms are closely related to the ground surface settlement profile; that is, the relative position relationship between the building and excavation determines the deformation form of the building.
ese conclusions are consistent with the numerical simulation results reported by Zheng and Li [12][13][14].In addition, Bryson and Zapata-Medina [15] and Sabzi and Fakher [16] studied building deformations around excavations through field monitoring, theoretical analysis, and numerical simulation.
Li et al. [17] studied ground surface settlement profiles by analyzing field-monitoring data of 30 station excavations in the construction of Nanjing Metro Line 3, Line 10, and Line S8.In the present study, the modified Cam-clay model was adopted with typical geological parameters in the Nanjing region, and the 3D characteristics of ground surface settlements resulting from station excavation were numerically analyzed using FLAC3D.e numerical simulation in the present paper is a supplementary study to the report by Li et al. [17].Li et al. [17] reported that three types of ground surface settlement profiles suitable for different zones (zones A, B, and C) around the excavation were obtained in the construction of Nanjing Metro Line 3, Line 10, and Line S8.
e present study conducted further research on building deformations.Partitioning of ground surface settlements was proposed according to the three types of ground surface settlement profiles; then, a prediction method for the type of building deformation and an estimation method for building settlements were developed.Finally, field-monitored data and estimated settlement values of building settlements were compared, and the application of the settlement estimation method to different types of foundations was discussed.
It should be noted that the three surface settlement profiles reported by Li et al. [17] were based on the greenfield ground settlement.us, the greenfield ground settlement was used to assess the building deformation, and there was no consideration of the excavation-building interaction.

Preparation of Numerical Analysis
2.1.Modeling of Soil Mass.According to Xu et al. [18] and Ding et al. [19], the settlement influence range of excavation is generally within 4 times the excavation depth.For soft-soil areas with poor engineering properties, the settlement influence range will not exceed 5 times the excavation depth.Zheng and Jiao [1] showed that the influence range of bottom uplift of deep excavation is generally 2 times the excavation depth.Furthermore, the choice of the soil constitutive model is very important in numerical analysis.According to analyses of different constitutive models by Ou et al. [20], Potts [21], António et al. [22], and Anthony et al. [23], the modified Cam-clay model is preferred for deepexcavation analysis.To improve the calculation efficiency, symmetry can be considered in rectangular excavation, and only one-half or one-quarter model can be used for the analysis.Boundary conditions were generally set up such that the ground surface boundary was a free boundary, the displacements of lateral boundaries were constrained in the horizontal direction, and the displacement of the bottom boundary was constrained in the vertical direction.e initial stress equilibrium was achieved by applying a gravitational field.
In general, the width and depth of the deep excavations of Nanjing metro stations were approximately 20 m, while the length was approximately 200 m [17].To improve the calculation efficiency, the middle part of the deep excavation was considered to be in a 2D plane-strain state; therefore, appropriate size reduction in the length direction of the model could meet the analysis requirements.Taking the size of the station excavation as 120 m × 20 m × 20 m, the onehalf model was established with dimensions of 200 m × 150 m × 90 m, as shown in Figure 2.
e soil mass was modeled using 8-node 6-faceted elements.
Nanjing is located in the lower reaches of the Chang Jiang river, belonging to the Yangtze depression fold belt in geotectonic geology.Marine strata, continental strata, and marinecontinental strata of different eras have been alternately deposited here since the Sinian period.
e ground surface consists mostly of Quaternary alluvial clay overlying Cretaceous sandstones.Table 1 presents the clay soil parameters used in numerical analysis, which is typical for Nanjing.

Modeling of Support Structure.
e support structure of station excavation is a combination of diaphragm walls and strutting levels.
e diaphragm walls had a reinforced concrete structure with a thickness of 0.8 m, the insertion ratio of the diaphragm walls was 0.5 (the excavation depth is 20 m, so the diaphragm wall depth is 30 m, 10 m of which is under the excavation bottom, as shown in Figure 3), and a liner lining element was used in the simulation.e excavation was carried out in 5 steps of 4 m each, and 5 layers of horizontal support were built.A structure element beam was adopted in the simulation.e 1 st layer of strutting levels was a reinforced concrete beam with a cross section of 0.6 m × 0.8 m set at the surface; the 2 nd to 5 th layers of strutting levels were steel pipe beams of ϕ609, with layer spacings of 4 m each (Figure 3).
For each layer of strutting levels in the middle of the station excavation, the beams were supported in parallel with a spacing of 4 m between them.In the corner of the station excavation, the beams were in the form of bracing, and the spacing between the supporting points was 4 m.e parameters of diaphragm walls and strutting levels are listed in Table 2.

Ground Surface Settlements around the Excavation
ere are two types of ground surface settlement profiles: triangular and trough-shaped [10].For the cantilever support structure without strutting levels, the ground surface   Advances in Civil Engineering settlement profile is generally triangular, while for the support structure with strutting levels, the ground surface settlement profile is generally trough-shaped.e study of ground surface settlements mainly focuses on important parameters such as the maximum settlement value, maximum settlement position, and influence range of settlement.e ground surface settlements can be analyzed through the perpendicular auxiliary plane, parallel auxiliary plane, and angled auxiliary plane around the station excavation (Figure 1).   4. In the figure, l represents the distance from the perpendicular auxiliary plane to the excavation corner, and the corner 30 °direction auxiliary plane indicates that the plane at the corner is at an angle of 30 °with respect to the perpendicular auxiliary plane l � 0 m.A similar definition applies to the corner 45 °direction auxiliary plane.Figure 4(a) shows the variation regularities of the ground surface settlements at different positions on the short side.It can be observed that the settlements decrease continuously from the short-side center perpendicular auxiliary plane to the corner 45 °direction auxiliary plane; however, the positions of the maximum ground surface settlements gradually shift away from the diaphragm wall.
Figure 4(b) shows the variation regularities of the ground surface settlements at different positions on the long side.It can be observed that when l > 28 m, the ground surface settlement curves coincide, indicating that this region is in the 2D plane-strain state.In the process of transition from l � 28 m to l � 0 m, the ground surface settlements decrease while the positions of the maximum surface settlement move closer to the diaphragm wall to a certain extent owing to 3D effects.In the process of transition from l � 0 m to the corner 45 °direction, the ground surface settlements decrease further, but the positions of the maximum settlements moved farther away from the diaphragm wall, which is essentially the same as that of the long-side center perpendicular auxiliary plane without 3D effects.
e variation regularities of vertical settlements at different positions were consistent with the results reported by Li et al. [17].

Partitioning of Ground Surface Settlements
Based on the numerical analysis of ground surface settlements and according to the three settlement profiles in the three types of zones (zone A, B, and C) around the station excavation [17], partitioning of ground surface settlements was proposed, as shown in Figure 6.ere are three critical positions of settlements outside the diaphragm wall: the maximum settlement line, settlement turning line, and settlement boundary line.e area within the settlement boundary line is referred to as the main influence area.In this region, the influence of surface settlements is significant, and the buildings are subject to significant differential settlements.e area outside the settlement boundary line is referred to as the secondary influence area.In this region, the statistical values of surface settlements are generally distributed within 0-3 mm, and the surface settlements have little influences on the buildings.For a deep metro-station excavation, buildings in the main influence area should be monitored and protected.Minor settlements may also occur in the secondary influence area, but the settlement hazard in this area is negligible.
It can be observed from Figure 6 that there are three types of zones around the station excavation, namely, zones A, B, and C, and each zone has three critical settlement lines: the maximum settlement line, settlement turning line, and settlement boundary line.e variation regularities are as follows:

Prediction of Building Deformations
ere are mainly two methods to predict building deformations due to excavation: the finite element method (FEM) and simplified analysis method (SAM).e process of FEM is complex and not easily performed by engineers.SAM is used to predict building deformations through ground surface settlements.is method is simple and easily applied in practice [24][25][26].
Buildings located around the station excavation will inevitably cross the critical settlement lines.
e relative position relationship between the building and excavation will directly affect the building deformations.
Buildings are generally composed of longitudinal walls, inner longitudinal walls, transverse walls, and inner transverse walls.e deformation regularities of buildings can be analyzed from two aspects, as shown in Figure 7: "bending deformation of wall" and "torsional deformation of building."

Bending Deformation of Wall.
Consider the building in zone A. When the building is perpendicular to the  Advances in Civil Engineering excavation (α � 90°), the longitudinal walls of the building will exhibit bending deformation.Because the transverse wall is parallel to the diaphragm wall without differential settlement, there will be no bending deformation.Similarly, when the building is parallel to the excavation (α � 0°), only the transverse walls will exhibit bending deformation.When the building and the excavation are at angles in the range of 0°< α < 90°in zone A, or when the building is located in zones B or C with 3D effects, longitudinal and transverse walls will cross the critical settlement lines; these longitudinal and transverse walls will exhibit bending deformation simultaneously.
(1) As shown in Figure 8, when the building crosses the maximum settlement line, it will be affected by concave-bending deformation.Under this condition, the main tensile strain on the longitudinal wall is trough-shaped.Assuming that the building is perpendicular to the diaphragm wall, bending deformation occurs on the longitudinal wall only.(2) As the distance from the building to the diaphragm wall d increases, when a part of the building crosses the maximum settlement line and another part crosses the settlement turning line, the building will be affected by both concave-bending deformation and convex-bending deformation.e main tensile strain on the longitudinal wall will be trough-shaped near the excavation and crest-shaped away from the excavation.It can be observed from Figure 8 that although the building exhibits both concave and convex bending deformations simultaneously, the deflections of the concave and convex deformations are small; therefore, the main tensile strains on the wall are not significant.(3) As the distance from the building to the diaphragm wall d increases further, the building mainly crosses the settlement turning line.Under this condition, the main tensile strain on the longitudinal wall shows a crest-shaped distribution.(4) If the distance from the building to the diaphragm wall d increases further, the main tensile strain on the longitudinal wall will be significantly weakened owing to the rapid decrease in the surface settlements.When the building is located outside the surface settlement boundary line, it is no longer affected by bending deformation.

Torsional Deformation of Building.
When the building and the excavation are in the range of 0°< α < 90°, the two parallel longitudinal walls will simultaneously cross the critical surface settlement lines.Owing to the positions of settlements, the critical lines crossing the two walls are different; therefore, in addition to the bending deformation of each wall, the building also exhibits torsional deformation.
(1) As shown in Figure 9, when the building crosses the maximum settlement line, the maximum settlement point of the back longitudinal wall is located closer to the front transverse wall than that of the front longitudinal wall.Consequently, the building will 6 Advances in Civil Engineering exhibit torsional deformation.e direction of the torsional deformation of the front longitudinal wall is clockwise, while that of the back longitudinal wall is Because the left side of the front transverse wall is closer to the maximum settlement line than the right side, the front transverse wall exhibits counterclockwise rotation.In contrast, the back transverse wall exhibits clockwise rotation since the right side of the back transverse wall is closer to the maximum settlement line than the left side.Note that the clockwise direction, counterclockwise direction, left side, and right side in this context are the relative position relationships when the observer faces the facade.(2) As shown in Figure 10, when the building crosses the settlement turning line, the settlement turning point of the back longitudinal wall is located closer to the front transverse wall than that of the front longitudinal wall.Consequently, the building will exhibit torsional deformation.e direction of torsional deformation of the front longitudinal wall is counterclockwise, while that of the back longitudinal wall is clockwise.Because the left side of the front transverse wall is closer to the settlement turning line than the right side, the front transverse wall exhibits clockwise rotation.In contrast, the back transverse wall exhibits counterclockwise rotation since the right side of the back transverse wall is closer to the settlement turning line than the left side.
(3) Similar analysis can be carried out for the arc-shaped critical settlement lines in zone C, as shown in Figure 11.It can be concluded that the front longitudinal wall exhibits counterclockwise rotation, the back longitudinal wall exhibits clockwise rotation, the front transverse wall exhibits clockwise rotation, and the back transverse wall exhibits counterclockwise rotation.
e above analysis of the longitudinal and transverse walls can be carried out for the inner longitudinal and transverse walls.
e analysis above indicates that when α � 0°, 90°or the center symmetrical line of the building in zone C passes through the excavation corner, the positions of the critical settlement line through the parallel walls are the same.Consequently, the walls only exhibit bending deformation and do not exhibit torsional deformation.

Estimation of Building Settlements
According to Li et al. [17], the maximum surface settlements δ Vm can be directly estimated from the excavation depth H; Advances in Civil Engineering then, the ground surface settlements at different zones can be estimated through the ground surface settlement profiles.
e ground surface settlements in different zones are regarded as the settlements of the building foundation.erefore, the building settlements at different zones around the metro-station excavation can be estimated.
However, the ground surface settlements and building settlements may not be completely consistent with each other.
e relationship between building settlements and ground surface settlements should be further investigated.
In this section, 21 buildings around the station excavations were selected for field monitoring.e surroundings of the station excavation were divided into three different zones, namely, zones A, B, and C, and there were seven buildings in each zone.e building structures include the commonly used brick-concrete structure and the frame structure, and the type of foundations mostly includes the strip foundation, raft foundation, and pile foundation.e measured settlement values of the building foundations were compared with the estimated free surface settlement values, as shown in Figures 12-14.
e regularities between the actual foundation settlements and the estimated ground surface settlements are summarized as follows: (1) For strip foundations, it can be observed from It should be noted that because the strip foundation itself has a certain resistance capacity to deformation, the actual settlement profile of the building foundation at the maximum settlement position of the surface settlement profile will not indicate a sharp angle but will rather be relatively smooth at the maximum settlement.(2) e raft foundation has greater integral rigidity than the strip foundation, which is helpful to adjust the uneven settlement of the foundation.It can be observed from Figures 12(g), 13(g), and 14(g) that the actual settlement values of the raft foundations are generally smaller than the estimated ground surface settlements, and it is a conservative estimation to consider the ground surface settlements as the building foundation settlements.(3) Pile foundation is a type of deep foundation commonly used in high-rise buildings.e main objective of using a pile is to utilize its own stiffness much more than that of the soil and to transfer the upper structure load to the hard soil or rock around the pile to reduce structure settlements.erefore, settlements of deep soil mass at the pile bottom can directly affect the pile foundation, while the influence of ground surface settlements on the pile foundation is relatively small.is can be verified as shown in Figures 12(e   Advances in Civil Engineering show the differences between the actual settlements of pile foundations and the estimated ground surface settlements are large.
e above analysis indicates a specific relationship between the actual settlements of building foundation and the estimated ground surface settlements, and the estimated ground surface settlements can be regarded as the building settlements.However, this estimation method is more reliable in strip foundations because raft foundations are conservative.For pile foundations, the ground surface settlements are not appropriate for the prediction of settlements of pile foundations.

Conclusions
Based on the numerical simulation and analysis of surrounding building deformation presented in this paper, the following conclusions may be drawn.
(1) For the ground surface settlements, the surface settlement profiles in the perpendicular auxiliary plane are all trough-shaped at the short-side center, long-side center, and corner 45 °direction.e maximum settlement position of the short side is closer to the diaphragm wall than that of the long side and the corner 45 °direction, and the maximum settlement positions of the long side and the corner 45 °direction are essentially the same.When the distance of the parallel auxiliary plane to the diaphragm wall is within 0.5H (approximately 10 m), the ground surface settlements in the parallel auxiliary plane increase when they cross the excavation corner, and the settlement profile is trough-shaped.When the distance of the parallel auxiliary plane to the diaphragm wall is greater than 0.5H, the ground surface settlements continue to decrease when they cross the excavation corner; however, the rates of decrease were lower, and the settlement profile was triangular.e surface settlement phenomenon in the parallel plane is related to the surface settlement profiles in the perpendicular auxiliary plane at different zones around the station excavation.Advances in Civil Engineering line was proposed according to the three types of surface settlement profiles at different zones, and the surrounding area of station excavation was divided into two parts, namely, the main influence area and the secondary influence area.us, bending deformation and torsional deformation of the surrounding buildings can be easily predicted.
(3) Settlement data of 21 buildings and the estimated ground surface settlements were compared.It was shown that settlements for a strip foundation were consistent with the estimated ground surface settlements, while settlements with raft foundations or pile foundations were different from the estimated free surface settlements.(4) It is possible to estimate the ground surface settlements at different zones around the station excavation according to the excavation depth H in order to determine the settlements of the strip foundation structure.e main processes are as follows.First, the maximum settlement value δ Vm of ground surface settlements is estimated from the excavation depth H according to the ratios H/δ Vm .Second, the greenfield-condition settlements at different zones around the station excavation are determined according to H, δ Vm , and three surface settlement profiles.ird, the ground surface settlements are regarded as the settlements of the building foundation, and the settlement values of the building are then determined.
p e n d ic u la r a u x il ia r y p la n e P ar al le l au xi lia ry pl an e Su pp or t st ru ct ur e St at io n ex ca va ti on

( 1 )
Parallel Auxiliary Plane. Figure 5 shows the variations of ground surface settlements in the parallel auxiliary planes around the station excavation, where l represents the distance from the parallel auxiliary plane to the diaphragm wall.e position d � 0 m is the midpoint of the diaphragm wall, while positions d � 10 m and d � 60 m in Figures 5(a) and 5(b), respectively, correspond to the excavation corner.Consider the parallel auxiliary planes outside the shortside support structure.It can be observed from Figure 5(a) that the ground surface settlements in the parallel auxiliary planes at different distances l outside the diaphragm wall exhibit the following characteristics: During the transition from d � 0 m to 10 m, the ground surface settlement values δ v gradually decrease.(2) When the parallel auxiliary planes are close to the diaphragm wall (l � 2 m, 6 m, and 10 m), the ground surface settlement values δ v increase for d > 10 m (position d � 10 m is the excavation corner), and the ground surface settlement profiles take the troughshaped form.e maximum settlement values and the positions of the maximum settlement values of the trough-shaped settlement both decrease with increase in l. (3) When the parallel auxiliary planes are far from the diaphragm wall (l > 10 m), the ground surface settlement values δ v do not increase when d > 10 m but instead continue to decrease; the rate of decrease slows down, and the ground surface settlement profiles take the triangular form.

Figure 5 (
Figure 5(b) shows the variations of ground surface settlements in the parallel auxiliary planes outside the long-side support structure at different distances from the diaphragm wall, where the position d � 60 m is the excavation corner.On the two sides of the demarcation plane l � 10 m, when d > 10 m, the ground surface settlements show two types of profiles: trough-shaped and triangular.e settlement trend in the parallel auxiliary planes is related to that in the perpendicular auxiliary planes around the station excavation.

( 1 )
Compared to zone A and zone C, the critical settlement lines of zone B are considerably short.(2) e distances in zone C from the critical settlement lines to the excavation corner are the same as those in zone A; however, the critical settlement lines of zone C are circular arcs with the excavation corner as the center.(3) e critical settlement lines of zone B are not the settlement contour lines, and the settlement values decrease from zone A to zone C. e critical 4 Advances in Civil Engineering settlement lines of other zones can be regarded as settlement contours.

-Figure 4 :Figure 5 :
Figure 4: Ground surface settlements at different positions: (a) short side and (b) long side.

Figure 7 :
Figure Bending deformation of a wall.
Figures 12(a)-12(d), 13(a)-13(f), and 14(a)-14(d) that, although there are deviations between the measured settlement values of the strip foundation and the estimated values of the ground surface settlements, the trend is essentially the same.

Figure 9 :Figure 10 :Figure 11 :Figure 12 :
Figure 9: Torsional deformation of a building across the maximum settlement line.

( 2 )
Partitioning of ground surface settlements related to the maximum settlement line and settlement turning Distance to excavation is 13.0 m, 5 floors, frame structure, and ra foundation.

Figure 14 :
Figure 14: Building foundation settlements in zone C: (a) Xinzhuang Uptown Station: Building of Nanjing Forestry University; (b) Fenghuangshan Park Station: Commercial Building of Liuhe District; (c) Fenghuangshan Park Station: Residential Building of Water Conservancy Bureau of Liuhe District; (d) Fenghuangshan Park Station: Residential Building of No. 2 Nanjing Lock Factory; (e) Daxinggong Square Station: Chang'an International Building; (f ) Longhua Road Station: Residential Building of Agricultural Bank; (g) Longhua Road Station: Dormitory of Tobacco Company.

Table 1 :
Parameters of the clay soil.

Table 2 :
Parameters of the support structure.