Displacement Analyses of Main Structure of Parallel Pit Excavation and Analysis of Countermeasures

Abstract

To solve the impact on the pre-existing main structure due to the need for early traffic restoration of urban roads within the cross-hub and the difficulty of co-ordinating a construction plan among groups of pits, a construction method combining TD and BU was proposed. By establishing a three-dimensional finite difference method (FDM) of parallel pit excavation considering the small strain constitutive model of the strata, the influence of four different excavation schemes on the pre-existing main structs is studied. The results of the study show that: (1) the asynchronous excavation of the pit on both sides of the cover excavation area causes additional deformation of the steel pipe structs; sequential excavation produces the greatest additional deformation of the steel tube columns, followed by staggered excavation and the least simultaneous excavation; (2) the middle 1 slab enhances the overall stiffness of the main structure in the cover excavation area, reducing the additional deformation caused by the unsynchronized excavation of the pit, with the maximum horizontal deformation of 5.8 mm, a reduction of 61%; (3) the greater the depth of excavation and the closer the distance from the pit, the more obvious the deformation of the steel pipe column; and (4) the function relationship between δ_hm/H and the relative stiffness coefficient R_d was obtained by fitting, and the maximum controlled mis-step spacing of the foundation excavation on both sides was 4.3 m when the middle 1 floor slab was cast.

1. Introduction

Urban transportation hubs are integrated with comprehensive development projects combining transportation, commercial, office, and entertainment development, which can intensively utilize underground space resources and facilitate passengers’ access to stations and interchanges. The various underground facilities in the transportation hubs are characterized by a three-dimensional arrangement and centralized arrangement, resulting in large-scale hub projects, a deep excavation depth, a complex surrounding environment, numerous individual units, and different duration requirements for each unit. Due to the difficulty of co-ordinating the construction schedule of the pit group, the designers and contractors were not only faced with the pressure of not interfering with ground traffic but also with the difficulties of the tight construction schedule and mutual interference between excavations of parallel pits. Therefore, it is very necessary to choose a reasonable construction method and support structure [1,2,3,4,5,6].

Due to the simple construction, short construction period, and low cost, most of the excavation of foundation pits with less strict deformation control use the bottom-up (BU) excavation method. During excavation, it is necessary to temporarily close the municipal road crossing the pit, which affects traffic passage; given this, in order to reduce the impact of pit excavation on traffic, the pit below the urban road is usually excavated by the top-down (TD) excavation method. Compared with the BU excavation method [7,8], the TD method has the following advantages: (1) the excavation of the pit occupies the city road for a short period, and the road traffic can be resumed after the top slab is completed; (2) the main structural system is stiff, and the slab, steel pipe structs, and pile together form a stiffer structural system, which can reduce the impact of additional stress on the structure caused by the different excavation progress between the pit groups; and (3) there are fewer temporary supports to avoid waste. In addition, the TD method also faces the following disadvantages: (1) the limited construction space under the roof slab and slow excavation progress of the soil; (2) strict requirements for the accuracy of the steel pipe structs—the deviation of the verticality of the steel pipe structs during construction cannot exceed L/500 (L is the length of the steel pipe column); and (3) the additional deformation of the existing steel pipe structs caused by the construction of the adjacent foundation pit, which affects the performance of the main structure. It can be seen that the structural stiffness is greater when excavating by the TD method, while the construction is simple and the excavation efficiency is higher when using the BU method.

At present, most of the excavations only use the BU method or TD method to study the deformation characteristics of the support structure caused by the excavation of the foundation pit. Dai et al. [9] proposed eight types of foundation support and reinforcement schemes in order to reduce the impact of shield tunneling on the supporting system in the foundation pits with the BU method, and studied the deformation characteristics of the supporting system during the shield underpass process. Tan [7,10] proposed an innovative deep foundation excavation method using a semi-cover excavation method for problems such as a complex environment around the foundation pit. Li et al. [11] used numerical simulation and field monitoring to study the effect of excavation on the supporting system in four pits with the BU method. Zhou et al. [12] studied the deformation characteristics of a multi-stage supporting system during the excavation of multi-stage foundation pits with the BU method. In contrast, the aforementioned studied cases only focus on the influence of different excavation schemes on the supporting system under one construction method. In addition, there are a few cases of parallel foundation pit excavation with a combination of the TD method and open excavation method. In addition, besides the need to choose a reasonable construction method during the foundation pit construction, the influence of the construction sequence on the pre-existing structures should not be ignored [13].

In the face of the increasingly complex surrounding environment, the design concept of the supporting system based on a deformation-based design philosophy is adopted for the excavation of the foundation pit in the city. Therefore, a reasonable stiffness of the supporting system is essential to control the deformation and cost of the support structure. Many scholars [14,15,16,17,18] have studied the factors affecting structural deformation and surface settlement. Clough et al. [17] proposed an expression for the stiffness coefficient of the support structs for the foundation excavation to assess its effect on structural deformation. Ou et al. [19] established an expression that can evaluate the degree of influence of the foundation excavation on the structure by analyzing a large amount of data on the deformation of the surrounding environment caused by the foundation excavation. Bryson et al. [18] proposed a more suitable stiffness ratio of the support structure to evaluate the deep foundation excavation for the characteristics of the large depth of excavation and complex spatial relationship of the support structure. Dai et al. [9] proposed a stiffness ratio formula that can respond to the depth of overburden and the diameter of the tunnel, which can better reflect the effect of the shield underpass on the existing pit structure. The above research cases of structural system stiffness mainly focus on the complex soil–structure interaction problem, but the influence of key factors such as staggered spacing and distance from the pit edge on the main structural system during parallel pit excavation is not fully reflected.

The deep foundation pit project of the Tongzhou City Sub-center Transportation Hub in Beijing is composed of several parallel pits, which makes it difficult to co-ordinate the construction schedule and mutual interference between the pit groups; and the city road above the underground transportation hub needs to be connected as soon as possible. Therefore, the excavation of the foundation pit group cannot adopt the traditional and single construction method, and no similar foundation pit case has been found in Beijing for reference. Based on the above engineering characteristics, the advantages of the TD method and the BU method are fully absorbed; the TD method is proposed for the foundation pits below the road, and the BU method is adopted for the foundation pits on both sides of the road. By analyzing the different excavation schemes of the pits on both sides of the road and studying the deformation characteristics of the pre-existing structure in the cover excavation area, the optimal excavation scheme suitable for the project is derived. A relative stiffness coefficient R_d that can consider the excavation depth and distance from the pit edge is proposed, and a nonlinear curve that can consider the lateral wall displacement δ_hm/H and the stiffness of the main structural system R_d is fitted. The results of this study can help to provide a reference for the design of supporting structs based on deformation control in Beijing.

2. Project Overview

2.1. Project Background

The Beijing City Vice Center Comprehensive Transportation Hub is a project that is located on Yangtuo Street, Tongzhou District, Beijing. It is a sizable transportation hub that integrates buses, private automobiles, urban railways, suburban railroads, and multi-level transportation. It is entirely underground. This thesis is based on Project 04 Section 02B Area. The excavation depth is 20.2–33.6 m below the ground surface (BGS), the pit length is approximately 234.66 m, and the width is about 136.16 mm. Since Yangtuo 1 Street above the transportation hub is an important traffic artery of the sub-center, it is necessary to complete the widening and transformation of the original Yangtuo 1 Street as soon as possible and form a traffic network with the surrounding roads, as shown in Figure 1.

According to the above characteristics of the surrounding environment of the pit group, the pit (02B area and 03A area) is divided into three parallel pits, which are the 03A area pit with the BU method, the 02B area pit below the road with the TD method, and the remaining 02B area pit with the open excavation of the multi-stage slope, as shown in Figure 2.

2.2. Site Condition

The proposed site is situated in the middle of the eastern alluvial fan of the Yongding River and in the middle and lower part of the alluvial fan of the Chaobai River, which is an alluvial and flood plain landform. The stratum within 90 m BGS is an artificial fill layer, recent sediment layer, and Quaternary alluvium layer. The physical parameters of the strata are shown in

Table 1. Physical and mechanical parameters of the strata.

Soil	Depth (m)	γ (kN/m3)	Cohesion/c (kPa)	Friction Angle/φ (°)	${\mathit{E}}_0^{\mathit{r}\mathit{e}\mathit{f}}$	${\mathit{E}}_{50}^{\mathit{r}\mathit{e}\mathit{f}}$	${\mathit{E}}_{\mathit{o}\mathit{e}\mathit{d}}^{\mathit{r}\mathit{e}\mathit{f}}$	${\mathit{E}}_{\mathit{u}\mathit{r}}^{\mathit{r}\mathit{e}\mathit{f}}$
					(MPa)	(MPa)	(MPa)	(MPa)
Fill	0–3	1950	8	15	180	15	10	62
Silty clay	3–9	1760	15	27	185	20.8	15.8	61
Fine medium sand	9–24	1900	5	28	390	30	25	130
Silty clay	24–30	1870	35	15	330	25	18	110
Fine medium sand	30–36	1960	5	32	480	39	35	160
Silty clay	36–39	1960	33	15	450	28	22	150
Fine medium sand	39–48	1980	6	31	750	55	45	255
Silty clay	48–54	1930	36	15	420	31	28	140
Fine medium sand	54–60	2020	5	34	990	70	65	330
Silty clay	60–63	2020	47	17	420	31	28	145
Fine medium sand	63–90	2020	6	5	1350	99	90	450

Notes: $E_0^{ref}$ = initial stiffness; $E_{50}^{ref}$ = secant stiffness; $E_{oed}^{ref}$ = tangent stiffness; $E_{ur}^{ref}$ = unloading–reloading stiffness; γ_0.7 = shear strain.

, which can obtain information through ground investigation and indoor testing. The site featured fill (layer 1) above 3 m BGS, follow by silty clay (layer 2) to a depth of 9 m BGS. The next layer was fine medium sand (layer 3) extending to a depth of 25 m BGS, underlain by silty clay (layer 4) to a depth of 31 m BGS. Beneath the silty clay, there is fine medium sand (layer 5) to a depth of 37 m BGS. The next layer was silty clay (layer 6) to a depth of 40 m BGS, followed by fine medium sand (layer 7) to a depth of 49 m BGS. Below the fine medium sand, there is silty clay (layer 8) to a depth of 55 m BGS, followed by fine medium sand (layer 9) at 55–60 m BGS. The next layer was silty clay (layer 10) to a depth of 63 m BGS, followed by fine medium sand (layer 11) to the termination depth of field exploration at 90 m BGS. The long-term phreatic water level was 9.4~13.2 m BGS, in which layer 3 dives.

Considering the municipal road crossing the pit needs to resume traffic in advance, and the potential advantages of the TD method in controlling the deformation caused by the pit and the convenience of earth excavation, in this project, the pit under the road crossing the 02B area is constructed by the TD method, as with Area B in Figure 3; the 03A area is constructed by the BU method, as with Area A in Figure 3; and the remaining 02B area pit is constructed by BU method with multi-level slope excavation, as with Area C in Figure 3. The section of the foundation pit group location relationship is shown in Figure 3.

The physical and mechanical parameters of the pre-stressing anchor cable are shown in

Table 2. Physical and mechanical parameters of structures.

Name	Structure	Young’s Modulus	Poisson’s Ratio	Diameter	Length	Design Tension	Length of the Free
		(GPa)		(m)	(m)	(kN)	(m)
First pre-stressed anchor	Cable element	200	0.25	0.2	24	230	10
Second pre-stressed anchor	Cable element	200	0.25	0.2	24	400	9
Third pre-stressed anchor	Cable element	200	0.25	0.2	25	640	8
Fourth pre-stressed anchor	Cable element	200	0.25	0.2	28	660	7
Soil nail	Cable element	200	0.25	0.022	10/9/8/7	/	/
Pore pile	Pile element	31.5	0.2	1/2	/	/	/
beam	Beam element	31.5	0.2	/	/	/	/
The retaining wall	Plate element	31.5	0.2	/	/	/	/

. The reinforced concrete diaphragm walls (D-walls) were 1 m thick, with a depth of 18.7 BGS; the pull-out resistant piles were 1 m in diameter and 28 m in length to prevent excessive heave deformation at the bottom of the pit during excavation. The thickness of the roof slab was 400 mm. The thickness of the middle slab 1 was 400 mm. The bored retaining piles, cast in situ, are 2 m in diameter and 43~48 m in length; the steel pipe structs are 1~1.1 m in diameter, 9 m in spacing, 0.02~0.04 m in wall thickness, and 18.75 m~27.847 m in length; and the beams are of the “well”-type structure, the cross-sectional size of the main beam is 0.9 × 1.6 m, and the size of the secondary beam is 0.4 × 1.4 m; see Figure 4. Among them, Areas A and B share the reinforced concrete diaphragm walls (D-walls), and Area C is excavated by the multi-stage slope. The physical and mechanical parameters of the soil nails are shown in Table 2.

The cover excavation area is an underground three-story structure. According to the construction schedule, the construction of the steel pipe column and top slab will be completed in May 2022, and the road in the cover excavation area will be restored. After that, the earthwork excavation of Area A and C will be carried out from June to August of the same year, and the earthwork will be excavated to 13.5 m BGS. In addition, only the top slab was applied in the cover excavation area, and only the top of the steel pipe column was restrained. Therefore, the impact of the excavation below 13.5 m BGS in Area A and Area C on the steel pipe structs is unknown, which aggravates the safety risk of the steel pipe structs.

2.3. Monitoring Results and Discussion

In order to obtain the excavation-induced deformation data of the steel pipe structs in time, we master the deformation characteristics of the steel pipe column. Twenty surface (DB) vertical deformation monitoring points were firstly selected in the road surface of Area B, as shown in Figure 5, numbered as DB157–DB176. The steel pipe column in Area B is the main vertical bearing structure, and it has strict requirements for horizontal deformation as an axially pressurized structure. Excessive differential deformation results in the additional bending moment or eccentric load on the steel pile structs. According to the relevant specification of the “Technical specification for the retaining and protecting of building foundation excavation” (DB11/489-2016), the safety level of the pit side wall in this area is level 1. The structural deformation should meet the following provisions: the maximum horizontal displacement control value of the support structure is 0.1% H; the specified value of the vertical deformation of the steel pipe column structure is 10 mm; the vertical differential settlement is 10 mm; and the maximum horizontal deformation allowed is 8 mm.

Figure 6 shows the vertical displacement of the pavement monitoring points in Area B during the excavation of soil above 13.5 m BGS in Areas A and C. The surface deformation trends of the south and north sides of Area B are the same, both showing a typical bulging-type profile. The maximum vertical deformation of 16 mm on the south side and 20 mm on the north side is mainly due to the rebound of the excavation, and excavation in Area C is faster than in Area A. In addition, it can also be seen that the east side of the B area’s vertical deformation is much larger than the west side, mainly because the steel pipe structs of the west side arrangement is regular, with a spacing of only 9 m, and the steel pipe structs of the east side spacing is larger, about 18 m; the steel pipe column arrangement shape is irregular; the steel pipe structs’ spacing is different so that the excavation-induced stress release on the steel pipe structs’ impact of the east side is larger than the west side.

From the above, it can be seen that the unsynchronized excavation of the soil in Area A and Area C makes the steel pipe structs produce differential deformation. In addition, the differential deformation of the steel pipe structs may cause cracking at the nodes of the beam, column, and slab, which affects the service performance of the main structure in the cover excavation area. Therefore, based on the spatial effect of the pit excavation, it is necessary to study the effect of different excavation schemes of the pit in Area A and Area C on the deformation of the steel pipe structs in Area B through a three-dimensional numerical simulation model to select the most optimal excavation scheme.

3. Parallel Pit Excavation Scheme

The excavation plan of the parallel pit group faced the following problems: (1) the deformation control standard of the steel pipe structs in Area B is strict, while the impact of the excavation of pits in Area A and C on the main structure of Area B is unknown; (2) the steel pipe structs below the top slab has no restraining effect, whether the deformation of the steel pipe structs can be controlled more effectively by applying the middle floor slab; and (3) the construction progress of Area A and C is difficult to co-ordinate, causing additional deformation of the pre-existing steel pipe structs exceeding the specified value.

In order to solve the problems, four different excavation schemes were proposed to study the excavation-induced deformations on the steel pipe structs, as shown in Figure 7, Figure 8, Figure 9 and Figure 10. Combined with the location of the anchor cables in the D-walls in Area A, excavation was carried out in four layers with excavation elevations of 13.0 m, 10.5 m, 8.0 m, and 5.5 m, as shown in Figure 3.

Case 1: The top slab of Area B was applied, and Area A and C were excavated simultaneously, as shown in Figure 7; Area A and C are excavated simultaneously to 13.5 mBGS, 10.5 m BGS, 8 m BGS, and 5.5 m BGS.

Case 2: The top slab of Area B was applied, and Area A and C were excavated sequentially, as in Figure 8; Area A was excavated to the bottom of the pit first, and then Area C was excavated to the bottom of the pit.

Case 3: The top slab of Area B was applied, and Area A and C were excavated in staggered steps, as shown in Figure 9. Area A was excavated to 10.5 m BGS first, then Area A and C were excavated in staggered steps to 8.0 m BGS and 10.5 m BGS, respectively, and excavated in staggered steps until completion.

Case 4: The middle 1 slab of Area B was applied, and the excavation of Area A and C was staggered, as shown in Figure 10; Area A and C were excavated to 10.5 m BGS first, and the middle 1 slab in Zone B cast; then, Area A and C were excavated to 8.0 m BGS and 10.5 m BGS, respectively, and the excavation was staggered until completion.

4. FDM Model and Results Discussion

4.1. Numerical Model

In order to study the influence of the construction of Area A and C on the steel pipe structs in Area B, this paper uses the FLAC3D finite difference method (FDM) to simulate the construction process. Based on the actual size of the structure and in order to avoid the boundary effects of the computational model, the model size is 430 m (X-direction) × 322 m (Y-direction) × 90 m (Z-direction), with total zones of 406,874. The soil is simulated with the zone; the support structures such as beams, columns, and pile supports are simulated with the beam; and the D-walls are simulated with the plate. The concrete structure is simulated with elastic, and the soil is simulated with the Plastic-Hardening (PH) constitutive model, as shown in Figure 11.

To consider the shear-hardening and compression-hardening properties of the soil and to reflect the properties of the soil in the range of small strains [20,21] where the shear modulus decreases with increasing shear strain, the Plastic-Hardening (PH) model is a shear- and volumetric-hardening constitutive model for the simulation of soil behavior. Schanz [22] proposed the basis of Duncan’s [23] framework of hardening plasticity. The main features of the PH model are (1) plastic strain in mobilizing friction; (2) plastic strain in main compression; and (3) elastic unloading/reloading compared to virgin loading.

The model can be immediately calibrated through lab testing or field tests. It is effective in numerous applications, including excavation, settlement studies, and issues involving soil and structure interaction. Due to the soil stiffness modulus being strain-dependent, which decreases nonlinearly with the increase in shear strain, the excavation process of the foundation pit shows the opposite deformation trend of pit bottom uplift and surface settlement, using the plastic-hardening model with small-strain stiffness to simulate the unloading–reloading paths [24]. The other two parameters need to be defined: stiffness-0-reference ($E_0^{ref}$) and strain-70 (γ₇₀). Defined at the reference pressure, the following relationships between the initial stiffness modulus and reference pressure ($E_0^{ref}$) and the shear stiffness modulus (G₀) are shown in Equations (1) and (2):

$$E_0=E_0{}^{ref}{Z}^m$$

(1)

$$G_0=\frac{E_0}{2\left(1+\nu \right)}$$

(2)

where Z, m, and ν are defined in the standard Plastic-Hardening model. The value of $E_0^{ref}$ is taken as 3$E_{ur}^{ref}$.

The reference shear strain (γ₇₀) is selected as the value at which the secant shear stiffness modulus is about 70% [25]. The value of γ₇₀ varies between 1 × 10⁻⁴ and 4 × 10⁻⁴, γ₇₀ = 2 × 10⁻⁴.

Once G₀ and γ₇₀ are known, the small-strain secant stiffness modulus G_s is calculated using Equation (3):

$$G_s=\frac{G_0}{1+\frac{0.385\gamma }{{\gamma }_{70}}}$$

(3)

This thesis did not consider additional elements; it examined just the impact of pit excavation on the structure. In this model, the following presumptions were made: (1) Since the precipitation had been completed before the foundation pit excavation, this paper does not study the groundwater effect during the excavation. (2) Since the excavation area is a fine sand formation with high permeability, the consolidation process was not considered.

4.2. Retaining Wall Deformation

4.2.1. The Diaphragm Wall Deformation

Figure 12 shows the relationship between the maximum disturbance δ_hm of the D-walls and the excavation depth H under different cases. Among them, the maximum lateral deformation of the D-walls in Cases 1, 2, 3, and 4 are 17.8 mm, 12.2 mm, 11.8 mm, and 8.5 mm, and the maximum deformation values are less than the control values. Because the construction of the anchor needs to be completed after the excavation of each layer of the foundation pit, the D-walls are in an unsupported condition; thus, the cantilever deformation occurs on the top of the D-walls [14,26]; The stress redistribution caused by soil unloading causes the deformation of the diaphragm wall above the pit bottom towards the excavation side. The maximum horizontal deformation of the D-walls occurred near the bottom of the pit, which is consistent with the results of Li [27]. At the same time, it shows that this constitutive model can better reflect the complex soil–structure interaction during the excavation of the pit.

4.2.2. The Steel Pipe Structs’ Vertical Deformation

The spatial effect of the pit excavation causes different deformation at the bottom of the pit, which leads to different vertical deformation of the structure at different locations. Figure 13 shows the maximum vertical deformation of the steel pile structs in Area B. The vertical deformation of the steel pile structs in Area B (east–west direction) shows a “convex” trend of the large in the middle and small on both sides; it is mainly because the vertical deformation of the soil around the pit is much smaller than that in the pit, due to the mutual restraint effect of the soil around the pit. The vertical deformation of the steel pile structs shows that South 1, North 1 > South 2, North 2, with the maximum value of 6.7 mm, and the vertical deformation of the steel pipe column meets the design requirements; the unloading of soil in Areas A and C causes the rebound of the pit bottom, and the vertical deformation of the steel pipe column adjacent to the excavation side increases due to the mutual friction of the soil−structure interaction.

4.2.3. The Steel Pipe Structs’ Horizontal Deformation

Because of this paper’s length constraint, only the middle column of the steel pipe in Area B is selected as the object of analysis (see Figure 5).

(1)

Under Case 1 conditions

The horizontal deformation of the steel pipe structs is mainly caused by the redistribution of soil stress caused by the excavation of the foundation pit. Figure 14 shows the horizontal deformation of the steel pipe structs under the condition of Case 1. The deformation trends of the steel pipe structs (Struct 1, Struct 2, and Struct 4) immediately adjacent to the excavation side are the same, and they show a convex deformation to the excavation side, respectively; and Struct 1, Struct 2, and Struct 3 show deformation to the south side, while Struct 4 shows deformation to the north side. The maximum horizontal deformation values of the steel pipe Struct 1 and Struct 4 are 8.25 mm and 5.8 mm, respectively. The main reason is that the distance of the steel pipe structs from the pit edge is different. Struct 1, Struct 2, and Struct 3 are 3 m, 12 m, and 21 m from the common D-walls, while Struct 3 and Struct 4 are 24 m and 15 m from the pit in Area C. The excavation of Area C is using the slope-cut method, and the soil behind the slope limits the horizontal deformation of Struct 4. In addition, the distance of Struct 3 from the pit edge is larger, and the soil-stress redistribution has less influence on Struct 3. It can be seen that the excavation of the pit on both sides has a more obvious influence on the steel pipe structs on the adjacent excavation side, and the distance from the pit edge is the key factor affecting the deformation of the structure.

(2)

Under Case 2 conditions

a. Under Case 2 conditions, after excavation in Area A was complete, the lateral displacement of the steel pipe struct is shown in Figure 15.

As can be seen from Figure 16, Struct 1 after the excavation of Area A is completed, the steel pipe structs as a whole move to Area A. The closer they are to Area A, the greater the horizontal deformation of the structure, in the order of Struct 1 > Struct 2 > Struct 3 > Struct 4. The maximum lateral deformation of Struct 1 and Struct 4 is 14.86 mm and 11.06 mm, respectively.

Struct 1 and Struct 2 show a convex deformation, while Struct 3 and Struct 4 show a cantilever-type deformation. The main reason is that only the top slab is applied in Area B; the top and bottom of the steel pipe structs are restrained, while the middle part is relatively free. Struct 1 and Struct 2 near Area A are most obviously influenced by the asymmetric lateral soil pressure, which makes the steel pipe structs present the deformation of the large in the middle and small on both sides. Struct 3 and Struct 4, which are far away from the pit, are less affected by the soil pressure but are “pulled” by the steel pipe structs (Struct 1 and Struct 2), which makes Struct 3 and Struct 4 show a larger deformation at the top.

The above can be seen, that the steel pile structs is not only affected by the redistribution of stress in the soil on the side of the adjacent excavation, but also by the superposition of the differential deformation of the steel pile structs.

b. Under the condition of Case 2, with the excavation in Area C completed, the lateral deformation of the steel pipe structs is shown in Figure 16.

As can be seen from Figure 16, after the completion of excavation in Area C, the overall horizontal deformation of the steel pipe structs decreases; the deformation direction of the steel pipe column Struct 1 and Struct 4 is opposite, and the deformation trend of the steel pipe structs is similar to that of Case 1; the structure of the adjacent excavation side (Struct 1 and Struct 4) is deformed to Area A and C, respectively; and the maximum deformation of steel pipe structs is 10.2 mm. After the completion of excavation in Area C, the soil pressure in Area B was distributed to Area A and C, respectively, which caused the deformation of the steel pipe structs to the excavation side, respectively; in addition, the deformation of the steel pipe structs in the opposite direction produced the mutual restraint effect. Compared with only the excavation in Area A, the maximum deformation of the steel pipe structs was reduced by 31%. Although the deformation of the structure is reduced after the excavation is completed in Area A and C, it still exceeds the design value by 25%. Therefore, such a construction plan should be avoided during the construction process.

(3)

Under Case 3 conditions

Controlling the staggered spacing of the pit excavation can significantly reduce the asymmetric external stresses acting on the steel pile structs by the asymmetric excavation. Figure 17 gives the horizontal deformation curves of the steel pile structs under Case 3. The deformation trends of the steel pipe structs is similar between Cases 3 and 1, which show the deformation of Struct 1, Struct 2, and Struct 3 to the excavation side of Area A, with the deformation of Struct 4 to the excavation side of the north side. The staggered spacing of the excavation in the A area and C area is controlled within 3 m, and the staggered spacing is small, and the additional stresses acting on the steel pipe structs are not obvious. It shows that a reasonable staggered spacing can reduce the influence of the asymmetric earth pressure on the structure. The smaller the staggered spacing, the smaller the asymmetric additional earth pressure and the smaller the horizontal deformation of the structure.

(4)

Under Case 4 conditions

As shown in Figure 18, the deformation of the steel pipe structs above the middle 1 slab in Area B is consistent and approximately a straight line after the middle 1 slab cast. In addition, the horizontal deformation of the steel pipe structs is only 3 mm; this indicates that the bottom plate, top plate, beam, and steel pipe column form a “frame”, which effectively increases the overall stiffness of the main structure of Area B and resists the influence of additional external loading. The horizontal deformation of the steel pipe structs below the middle 1 slab is significantly reduced, with a maximum value of 5.8 mm; the trend of horizontal deformation of the steel pipe structs is similar in Cases 4 and 3, but the horizontal deformation of the structure is reduced by 30% compared with Case 3. Therefore, the early closure of the structure in Area B can effectively resist the additional stresses generated by the asymmetric excavation of the foundation pit, and the additional impact on the steel pipe column structure is minimal. Case 4 should be adopted as much as possible in the actual construction process.

4.3. Discussion

4.3.1. The Additional Deformation Rate

In short, the closer the distance from the excavation side, the greater the horizontal deformation of the steel pipe column. The asymmetric stress distribution caused by the unsynchronized excavation makes the steel pipe column structure produce additional deformation. To evaluate the degree of impact of the different excavation schemes on the steel pipe structs, the additional deformation rate η was introduced to quantify the additional deformation generated by the asymmetric excavation on the structure. The maximum horizontal deformation of the D-walls and steel pipe structs during asymmetric excavation is δ_qh, and δ_sh is the maximum horizontal deformation of the D-walls and steel pipe structs during synchronous excavation. Equation (4) is as follows:

$$\eta =\frac{{\delta }_{qh}}{{\delta }_{sh}}$$

(4)

According to the above Equation (4), the additional deformation rate of the structure for different excavation cases is as shown in

Table 3. Additional deformation rates for different excavation schemes.

Excavation Schemes	Additional Deformation Rates
	The Retaining Walls	Struct 1	Struct 2	Struct 3	Struct 4
Case 2—Area A finished	1.5	1.7	2.67	5.75	1.96
Case 2—Area C finished	1.1	1.1	1.4	3.45	0.64
Case 3	1	1	1	1	0.87
Case 4	0.72	0.68	0.95	1.35	0.58

:

Combining the data in the Table 3, it can be concluded that:

(1)

In Case 2, after the excavation of Area A is completed, the value η of the D-walls is 1.5; with the completion of the excavation of Area C in Case 2, the lateral soil pressure decreases, and the value η of the D-walls decreases to 1.1. For Case 3, the excavation of the Areas A and C is staggered, and the staggered distance is only 3 m, and the value η of the D-walls is similar to that of simultaneous excavation, which is 1.02. In Case 4, compared with the above options, after the middle 1 slab cast, the horizontal direction of the steel pipe column is constrained by the top slab and the middle slab, and the value of η of the D-wall is much smaller than that of the synchronous excavation, at only 0.72.

(2)

The additional deformation rate of the steel pipe structs in Case 2 > Case 3 > Case 4, which is more similar to the deformation trend of the steel pipe structs for the different excavation options. Different from the above deformation is the fact that the additional deformation rate of Struct 2 and Struct 3 is much larger than that of Struct 1 and Struct 4, mainly because the soil unloading caused less disturbance to Struct 2 and Struct 3, which causes the synchronous excavation to have a smaller δ_sh, as the value η of the steel pipe structs gets larger.

(3)

The value η in Case 3 is more consistent with Case 1, and the smaller excavation spacing in Areas A and C has no obvious effect on the steel pipe structs. The value η in Case 4 is less than 1. The greater the stiffness of the main structure in Area B, the smaller the additional deformation.

According to the above analysis, the additional deformation rate of the steel pipe column is mainly related to the pit excavation’s staggered spacing and the overall stiffness of the main structure. The spacing between Areas A and C is controlled at about 3 m, so the impact of the asymmetric additional stress on the steel pipe column is limited; by applying a middle 1 slab, the overall stiffness of the main structure in the cover excavation area is increased, which effectively reduces the additional deformation rate generated by the asymmetric excavation of the pit.

4.3.2. Relative Stiffness Coefficient of the Main Structure

The relative stiffness ratio of the retaining system proposed by Clough [17] and Bryson [18] was used to evaluate the maximum disturbance of the diagram wall during excavation. The above study of the stiffness coefficient of the supporting structs focuses on the relative strength ratio of the soil−structure interaction and the relative stiffness ratio of the support to the retaining structure. Combined with the above simulation results, it can be seen that the stability of the main structure is also related to the distance from the pit edge and excavation depth. Therefore, based on this paper, the relative stiffness coefficient of the main structural system in the cover excavation area is proposed, which can comprehensively respond to the relative stiffness of the soil−structure interaction, the overall stiffness of the main structure, and the influence of factors such as the excavation depth and distance from the pit edge on the permanent structure system. Three dimensionless groups are used to express the relationship between the variables, among which: the relative stiffness resistance ratio, E_s/E, indicates the interaction between the soil and structure; the relative flexural bearing capacity ratio, SvS_hH/I, indicates the ratio between the vertical support structure of the steel pipe column and the horizontal support structure of the beam and slab; and the depth distance ratio, D/L, reflects the ratio between the excavation depth of the foundation pit and the distance of the vertical structure from the edge of the foundation pit. The relative stiffness coefficient of the main structure is shown in Equation (5):

$$R_d=\frac{E_s}{E}•\frac{S_h{S}_{v}H}{I}•\frac{D}{L}$$

(5)

R_d is the relative stiffness coefficient of the main structure; E is Young’s modulus of the supporting structure; I is the moment of inertia of the structure per unit length; E_s is the average Young’s modulus of the soil; H is the total height of the supporting structure; D is the excavation depth; S_v is the average horizontal spacing of the main structure; S_h is the average vertical spacing of the main structure; and L is the distance of the vertical structure from the edge of the pit. The greater the excavation depth or the closer to the edge of the pit, and the more significant the impact of the adjacent pit excavation on the structure, the larger the value of R_d.

According to the physical parameters, spatial location relationship, and excavation depth of the main structure in the cover excavation area in the above four excavation cases,

Table 4. Relative stiffness coefficient of the main structure.

Excavation Schemes	Relative Stiffness Coefficient
	Struct 1	Struct 2	Struct 3	Struct 4
Case 1	21	7	1	10
Case 2 (03A finished)	65	50	43	36
Case 2 (02B finished)	30	15	4	2
Case 3	23	8	2	8
Case 4	13	7	3	1

calculates the relative stiffness of the main structure R_d.

It can be seen that the changing trend of the relative stiffness coefficient of the steel pile structs is consistent with the trend of horizontal deformation. The greater the stiffness of the main structural system, the smaller the relative stiffness coefficient.

The value of E_s can be calculated by the following equation, Equation (6):

$$E_s=\frac{{\displaystyle \sum H_i{E}_{si}}}{H}$$

(6)

where H_i = thickness of each layer of soil within the enclosure; and E_si = modulus of elasticity of each layer of soil.

Figure 19 shows the relationship between the maximum lateral deformation δ_hm/H_e and the relative stiffness coefficient R_d according to the above four excavation cases, where the maximum lateral deformation δ_hm is normalized to the excavation depth H_e, in order to value the relative stiffness magnitude required for the structure through the maximum control deformation, and thus to carry out a more reasonable structural design. Fitting δ_hm/H_e with R_d, the optimal stiffness required for the main structure is calculated through the structural deformation values specified in the design code, which can provide a reference for the designer in the design of the supporting structs.

The fitting formula is the following Equation (7):

$$\raisebox{1ex}{${\delta }_{hm}$}\!\left/ \!\raisebox{-1ex}{$H_e$}\right.(\%)=0.011\times R_d{}^{0.51} R^2=0.9824$$

(7)

The goodness of fit (R²) is 0.9824. It shows that δ_hm/H_e fits well with R_d. It can be seen that δ_hm/H_e and R_d are positively correlated, and the larger the relative stiffness coefficient R_d of the main structure, the larger the maximum lateral deformation δ_hm.

Combined with the steel pipe struct deformation provisions in the project design instructions, the maximum horizontal deformation of the steel pipe structs should not exceed 8 mm; according to the fitting curve of δ_hm/H_e and R_d, the physical and mechanical parameters of the steel pipe column and soil body are brought into the above Formula (8) to find out the maximum control value of R_d when the top slab cast and the middle 1 slab cast are close to 22 and 11.34 respectively.

Combined with the above research results, the closer the distance from the excavation side of the pit, the greater the influence of the horizontal deformation of the steel pipe structs. Struct 1 is the most affected by the excavation of the pit; therefore, the steel pipe structs from the pit side with the distance L = 3 m have the most unfavorable working conditions. In order to guide the excavation of the pit, when the middle 1 slab was cast, the R_d of 11.34 is brought into Formula (6), and the maximum distance between the excavation of the pit is 4.3 m. The above research results can guide the excavation of such parallel pits.

4.4. Program Validation

According to the above simulation results, the parallel pit excavation is constructed by Case 4, and the pit on both sides of the middle 1 slab cast and the Areas A and C are excavated in staggered steps. The following monitoring data reflect the horizontal deformation curve of the steel pipe structs above the middle 1 slab when the construction of Case 4 is adopted, as shown in Figure 20.

With the excavation of the pit on both sides of the cover excavation area, the horizontal deformation of the steel pipe structs gradually increases, and the maximum horizontal deformation is 3.5 mm, and the deformation trend is more similar. The numerical simulation results are in good agreement with the monitoring data, which verifies the feasibility of Case 4.

5. Conclusions

This paper presents a parallel foundation pit project with a combination of the BU and TD methods. The site-monitoring results of the surface settlement in the cover excavation area are analyzed; a 3D finite element model of the parallel foundation excavation considering the small strain model of the soil is established, and the effects of four different excavation cases on steel pipe structs are studied, and a construction case suitable for this project is proposed:

(1)

The unsynchronized excavation of the pits on both sides of the cover excavation area causes additional deformation of the steel pipe column. The horizontal deformation of the steel pipe column caused by synchronous excavation, and staggered excavation is similar, and the steel pipe column is deformed to the excavation side, respectively. The maximum deformation value is only 8.25 mm, and the maximum additional deformation rate is 1.02; while the sequential excavation makes the steel pipe column as a whole first produce, to the excavation side, a “side-down” deformation; when both sides of the pit excavation is completed, the steel pipe column produces, respectively, the maximum deformation value of only 14.86 mm, with the maximum additional deformation rate of 5.75. Therefore, controlling the excavation spacing of the foundation pit can effectively reduce the excavation-induced additional deformation.

(2)

The middle 1 slab cast can effectively control the horizontal deformation of the steel pipe structs and enhance the overall stiffness of the main structure in the cover excavation area. The deformation trend of the steel pipe column above the middle 1 slab is the same, and the steel pipe column below the middle 1 slab is deformed to the excavation side, respectively. The maximum horizontal deformation is only 5.8 mm, which is reduced by 41% compared with the simultaneous excavation of the top slab only. Therefore, the middle 1 slab should be applied as early as possible during the construction process.

(3)

The soil–structure’s physical and mechanical parameters, the spatial location relationship, and excavation depth can be reflected by the relative stiffness coefficient; the greater the excavation depth or the closer to the edge of the pit, the more susceptible the structure is to the impact of excavation in the adjacent pit.

(4)

The function relationship between the δ_hm/H of the structure and the relative stiffness coefficient R_d was obtained by fitting, which showed a non-linear growth trend, when the middle 1 slab cast and the maximum control mis-step spacing of the foundation pit excavation on both sides was 4.3 m.