Numerical Model for Rectangular Pedestrian Underpass Excavations with Pipe-Roof Preconstruction Method: A Case Study

Abstract

Under weak geological conditions, soil deformation and surface settlement are the key factors affecting the success of shallow-buried rectangular excavation. To investigate this issue, an underpass of Zhongxiao East Road in Taipei City was used as a case study. The surface settlement and lateral deformation of an underground diaphragm wall caused by the excavation of a rectangular pedestrian underpass using the pipe-roof preconstruction method (PPM) were investigated by 3D finite element analysis. The numerical analysis results showed that the constructed numerical analysis model had considerable accuracy. The use of PPM combined with a box culvert structure to form a pedestrian underpass could effectively control the surface displacement above the box culvert. Under the condition of the same sectional area, the smaller the width of the pipe-roof structure, the more the impact on the ground surface was reduced. The maximum positive bending moment and maximum negative bending moment on the pipe roof produced by excavation at each stage were roughly inversely related to the height per the width of the cross-section of the pipe diaphragm structure. The results showed that the pipe-roof structure was suitable for underground excavation with shallow-buried depth in the soft soil of the Taipei Basin. Moreover, the shallow-buried box culvert was more sensitive to the subsidence caused by construction than the deep-buried box culvert.

1. Introduction

Pedestrian underpasses are often set up in modern metropolitan areas for pedestrians to pass through in order to minimize vehicle–pedestrian conflicts at the ground level. After the comprehensive consideration of cost, drainage, and other factors, a shallow pedestrian underpass is usually constructed by the cut-and-cover method. However, this method interferes with the convenience of transportation above the underpass and often causes settlement of the surrounding ground surface. Therefore, in the construction of shallow underpasses, the pipe-roof preconstruction method (PPM) is now often chosen to reduce the impact on traffic and avoid affecting the normal use of surrounding buildings during construction [1,2,3,4].

In general, the PPM jacks relatively rigid large-diameter steel pipes along the contour of the underground structure to serve as the enclosure structure of the underground passage and pre-provide space for the construction of the underground structure [5,6,7]. In this method, the steel pipes are gradually jacked into the design position by a pipe jacking machine, and then the adjacent pipes are supported, cut, and welded so that all the pipes form a closed steel pipe roof; at the same time, steel mesh is laid and concrete is poured inside the steel pipe roof to form a supporting structure. Once the structural strength and rigidity of the steel pipe roof meet the requirements, the soil inside the steel pipe roof is excavated to form an underground passage or a tunnel space. The PPM is a trenchless pre-reinforcement technique applied before shallow underground excavation, which can be carried out on sensitive ground with various facilities nearby, importantly without affecting ground traffic [8]. Therefore, the PPM has now become an auxiliary method widely used in the trenchless construction of underground structures for the protection of soft soil foundation areas in various countries [6,9,10,11,12,13,14,15,16,17,18,19].

Many researchers have carried out extensive research on the application and support ability of the PPM and put forward numerous technical improvement schemes [5,9,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Yang et al. [5] presented a case study of ground and tunnel deformations caused by the excavation of a pipe-roof pre-construction tunnel. He et al. [9] conducted a field measurement on the interaction between socketed pipes during pipe-roof jacking in soft ground and the corresponding surface settlement. Bae et al. [20] proposed a mathematical framework based on the homogenization technique to simulate a grouted pipe-roofing reinforcement method used in the construction of tunnels passing through soft ground, considering the influence of the main design parameters on the elastic and elastoplastic analyses. Park et al. [21] proposed the pressure-induced inflatable pipe method. This method utilized the concept of cavity expansion to strengthen the tunnel by forming an umbrella arch on the roof of the tunnel. The reinforcing effect of this new concept was verified through a pilot-scale chamber test, numerical analysis, and trapdoor test. Zhang et al. [22] proposed a double-parameter elastic foundation beam model with variable subgrade coefficients to simulate the pipe umbrella support mechanism in disturbed shallow-buried tunnel sections. Through the finite difference formula, the deflection and internal force of the pipe umbrella system during excavation were analyzed. Xie et al. [23] proposed a stability model for rectangular large excavations reinforced by pipe roofing, suggesting that it be used for underground passages in crowded urban spaces. In this model, the elastic foundation beam was used to simulate the mechanical action of the pipe roof, and the lower bound solution was obtained. In addition, the proposed model was used together with the finite element software ABAQUS for the analysis of a roof-box jacking excavation on Tianlin Road in Shanghai. The results of the model were close to those of finite element analysis, which proved that the model could be used in engineering practice. Based on the Winkler elastic foundation beam model, Heng et al. [24] established a calculation model for ultra-shallow-buried pipe roof and steel bracing and proposed a new method of ultra-shallow-buried excavation under interactive effects. The accuracy of the calculation method of the interaction effect was verified by the measured data of the example. Lu et al. [25] proposed the steel support cutting pipe method and studied its failure mode and mechanical behavior through laboratory experiments. Yang et al. [26] used MIDAS/GTS to explore pipe cutting and support in the PPM. The measured data were consistent with the numerical simulation results, which verified the reliability of the numerical simulation results. Li et al. [27] proposed a theoretical analysis of the effectiveness of pipe roofs in shallow tunnels. Through a comparative analysis with the measured results, it was proven that the calculation model for surrounding rock pressure and the calculation model for the stress and deformation of the pipe roof were reasonable. Xu et al. [28] proposed a unified mechanical model of the elastic foundation beam for pipe-roof. The calculation formulas for deflection and internal force in the model were derived. In addition, combined with actual engineering cases, the model was compared and analyzed. Bai et al. [29] presented a case study of Shifu Road station in Shenyang by the construction of a subway station using the small pipe roof-beam method. Hong et al. [30] proposed a mathematical model of the temperature field and its analytical solution for the freeze-sealing pipe-roof method induced by the radial offset of adjacent jacking pipes. Mei et al. [31] proposed a study on the whole-process application of advanced grouting pipe shed support under urban complex stratum conditions. Morovatdar et al. [32] evaluated the influence of pipe characteristics in the umbrella arch method on controlling tunneling-induced settlements in soft ground. Oggeri and Oreste [33] present a global approach to back-analysis in a probabilistic context to evaluate tunnel static behavior.

The use of PPM as an auxiliary construction method has been widely accepted by the engineering community, and there are many successful examples in public works. However, there are few studies on shallow-buried rectangular excavations reinforced by a pipe roof [34,35]. The formations in the Taipei Basin are mostly composed of weak clay layers, which are highly sensitive, causing the formations to be easily disturbed and the undrained shear strength to be greatly reduced. Soil deformation and ground surface settlement are key issues for the success of the project, especially when applying the PPM to a shallow-buried underground passage project with weak geology in the Taipei Basin. For this reason, this paper uses the new construction of a pedestrian underpass on Zhongxiao East Road in Taipei City as a case study. In other words, the novelty of this paper is the application of the PPM to underground passage projects that were shallowly buried and located in a weak formation. The structure of this paper is divided into the following major sections: project overview of the case study, numerical simulation modeling, numerical simulation results analysis, and conclusions. This study was conducted by using the finite element software PLAXIS 3D CE to simulate and analyze the entire construction process and to consider various overburden depths (i.e., 0.7, 1.7, 2.7, and 3.7 m) and aspect ratios (i.e., 0.30, 0.36, 0.40, and 0.45), defined as the height per the width of the cross-section of the pipe diaphragm structure, and then to investigate the trend of surface subsidence above the pipe diaphragm. Since PLAXIS 3D CE has no appropriate elements that can be directly applied to the pipe-roof structure, this study used the tunnel designer-plate element to simulate the steel pipe and filled concrete of the pipe-roof structure. Another focus of the analysis was the lateral displacement of the diaphragm wall caused by the excavation of the launching shaft and receiving shaft and the ground surface settlement outside the excavation area. This case study can serve as a design and construction reference for the industry to better control the jacking accuracy and ground disturbance of the PPM in the future.

2. Project Overview of the Case Study

2.1. Project Location and Scope

The project was located in Taipei City. On the south side of the site was the Sun Yat-Sen Memorial Hall, and the north side was adjacent to the fourth section of Zhongxiao East Road, as shown in Figure 1. The underground structure on the north side of the site was the tunnel of the Bannan Line of the Taipei Metro, and the aboveground structure was the Taipei Dome Park. Located directly below Zhongxiao East Road and above the Bannan Line of the Taipei Metro, there was already a box culvert that was created when the Sun Yat-Sen Memorial Hall Station of the Taipei Metro was originally built. Therefore, this project mainly used the PPM to build a new box culvert structure and construct a six-meter-long pedestrian underpass to connect the existing box culvert. In this way, the Sun Yat-Sen Memorial Hall and the Taipei Dome Park were connected, making the flow of people to and from both sides more convenient. In addition, this project also included the construction of the diaphragm wall of the launching shaft, the driving of the steel sheet piles of the receiving shaft, and the placement of related electromechanical facilities. Since the scope of this project covered a total of eight melaleuca and camphor trees of a certain age, the common cut and cover method was not used for construction. Instead, deep excavation was carried out on the north and south sides of those trees first, and then the pedestrian underground passage was excavated under the trees with the PPM to prevent excessive ground subsidence from causing damage to the above plants.

2.2. Geology and Groundwater Level Overview of the Construction Site

The project carried out geological drilling on the construction site. A total of five holes were drilled, each drilling depth was 30 m, and the total drilling depth was 150 m. Within the survey depth, the site strata were roughly divided into three layers; from top to bottom were the backfill layer, the silty clay layer (brownish yellow), and the silty clay layer (gray), as shown in Figure 2.

Forcellini [36] pointed out the importance of considering the water level of buildings on shallow foundations in terms of settlement, base shear forces, and floor displacement. According to the groundwater level observation results during the geological survey, the groundwater level at the construction site was about 2.8 to 3.1 m below the surface, which would have been the normal water level above the thick clay layer. Considering that the groundwater level will change with the seasons, the design constant water level for foundation analysis and retaining structure analysis was 2.0 m below the ground surface. In addition, considering the impact of short-term water level rise during heavy rain, the highest water level in the short-term design was the ground surface.

2.3. Specifications of Steel Pipes Used in PPM

The specifications of the steel pipe used in this project are shown in

Table 1. Specifications of the steel pipes.

Outer Diameter (mm)	Inner Diameter (mm)	Center Distance between Adjacent Steel Pipes (mm)	Unit Weight (kg/m)
812.8	787.4	910	250.6

. The steel pipe was designed with mortise and tenon, the position of the tenon was on the outside of the steel pipe, and the position of the mortise was on the inside of the steel pipe, as shown in Figure 3. The arrangement of steel pipes is shown in Figure 4. The mortise and tenon can make the pipes fix tightly to each other and can achieve a similar function to the plate so as to withstand the surrounding soil and achieve the effect of stabilizing the excavation.

2.4. Monitoring System

This project was a construction of a shallow-buried pipe roof. Above the pedestrian underpass were melaleuca and camphor trees with relatively little economic value, so they were not monitored. The main monitoring effort was focused on the subsidence points of the diaphragm wall and the Bannan Line of the Taipei Metro, so as to monitor the inclination of the diaphragm wall and the vertical displacement of the lane of the Bannan Line to avoid damage during excavation.

The monitoring items included the lateral deformation of the retaining structure, the inclination of the building, the subsidence of the ground surface and the building, the uplift of the bottom of the excavation surface, the floating of the middle column, etc. The instruments used to monitor displacement in this project included subsidence observation points, inclinometer casing in the soil, tiltmeters, inclinometer casing in the walls, and heave indicators. Subsidence observation points were set up around the construction site and above the lanes of the Bannan Line of the Taipei Metro for observation, so as to observe whether there was obvious vertical displacement during construction. Tiltmeters were installed on the Bannan Line of the Taipei Metro and the Sun Yat-Sen Memorial Hall to observe their horizontal displacement. Before the deep excavation of the base, the initial value should be established first. As the project progressed, regular observations and records were made. By comparing with the initial value, the measured displacement of the soil layer was obtained, and the size, speed, direction and position of the maximum displacement was analyzed. A plane configuration diagram of the monitoring instruments is shown in Figure 5. The monitoring frequency and control standard values of the monitoring instruments are shown in

Table 2. Monitoring frequency and control standard values of the monitoring instruments.

Monitoring Instrument	Monitoring Frequency	Warning Value	Action Value
Subsidence observation point	Once a day during excavation and twice a week after the structure is complete	40 mm	50 mm
Inclinometer casing in soil		40 mm	50 mm
Observation well	Once a day during pumping, twice a week	Install initial value ±1.0 m	Install initial value ±2.0 m
Transducer piezometer		40 mm	50 mm
Strain gauges for strut	Once a day during excavation and twice a week after the structure is complete	90% of the design support load	125% of the design support load
Tiltmeter		1/940	1/750
Inclinometer casing in wall		30 mm	50 mm
Diaphragm steel bar strain gauge		0.75fy	0.9 fy
Heave indicator		30 mm	50 mm

.

3. Numerical Simulation Modeling

PLAXIS launched the first 3D software in 2010, which was a finite element analysis software dedicated to soil and rock [37]. Thereafter, its functions have been continuously updated, with PLAXIS 3D CE being released in 2021. This software is capable of simulating most geotechnical cases and is very easy to use, having a user-friendly interface. Therefore, this study used PLAXIS 3D CONNECT Edition V21 to simulate the excavation process and analysis.

3.1. Numerical Analysis Process

Figure 6 shows a flow chart of the steps for applying PLAXIS 3D CE to simulate and analyze the entire construction process, including the geometric boundary setting for analysis, model building, material models and parameter setting, pedestrian underpass structure setting, mesh generation, numerical calculation, analysis result output, etc.

3.2. Model Building Phase

For this study, the influence of adjacent building structures had to be taken into account in the simulation. The east–west (X-axis) width extended five times the excavation depth from the east and west sides of the launching shaft, and the north–south (Y-axis) extended five times the excavation depth from the diaphragm wall on the south side of the launching shaft and the steel sheet pile on the north side of the receiving shaft. For the depth of the model soil, the Z-axis extended to 50 m below the surface, as per the geological drilling report. Therefore, the outer geometric dimensions of the model were X_max = 92.5 m, X_min = −92.5 m, Y_max = 78.5 m, Y_min = −78.5 m, Z_max = 0 m, and Z_min = −50 m, as shown in Figure 7. In the constructed model, the Encastre boundary condition was used at the bottom, which restricted the displacement and rotation in all directions. The side boundary of the model was set as roler, which allowed displacement.

3.3. Material Models

The structure of this project included the diaphragm wall of the launching shaft, the steel sheet pile of the receiving shaft, the cross wall, axial support, fence, pipe-roof structure, and box culvert excavation support, as shown in Figure 8 and Figure 9. The schematic diagram of the support profile of the diaphragm wall and the steel sheet pile during excavation is shown in Figure 10. The model used plate elements to simulate diaphragm walls, steel sheet piles, cross walls, box culvert structures, and pipe-roof structures; the axial support of the launching and receiving shafts was simulated by node-to-node anchors; the base’s fence of launching and receiving shafts was simulated by beam element; the temporary support of the box culvert excavation was simulated by line load.

Under load, soil and rock tend to behave highly nonlinearly. PLAXIS 3D CE provides different models to simulate this nonlinear stress–strain behavior, which can be modeled according to the level of sophistication required. In this study, the Hardening Soil model was selected in the PLAXIS 3D program, which can simulate the behaviors of sand and gravel as well as softer soil types. This model adopts the Mohr–Coulomb failure criterion and uses plasticity theory, and its stress–strain behavior is more consistent with the response of real soil than the traditional Mohr–Coulomb model.

3.4. Material Parameters

When applying PLAXIS 3D analysis, the parameters required for the Hardening Soil mode are as follows:

• c: Cohesion [kN/m²];
• $\phi$: Angle of friction [°];
• ψ: Angle of dilatancy [°], the default value is ψ = $\phi -30°$, when φ > 30°; the default value is ψ = 0, when φ < 30°;
• $E_{50}^{ref}$: Secant stiffness in standard drained triaxial test [kN/m²];
• $E_{oed}^{ref}$: Tangent stiffness for primary oedometer loading [kN/m²], the default value is $E_{oed}^{ref}=0.7E_{50}^{ref}$, in this study, $E_{oed}^{ref}=0.7E_{50}^{ref}$;
• $E_{ur}^{ref}$: Unloading/reloading stiffness, the default value is $E_{ur}^{ref}=3E_{50}^{ref}$;
• m: Power for stress-level dependency of stiffness, its value is between 0.5 and 1.0;
• $v_{ur}$: Poisson’s ratio for unloading–reloading, the default value is 0.2;
• $p^{ref}$: Reference stress for stiffnesses, the default value is 100 kN/m²;
• $K_0^{nc}$: K₀ value for normal consolidation, the default value is $K_0^{nc}=1-\sin \phi$;
• $R_f$: Failure ratio, the default value is 0.9;
• ${\sigma }_{tension}$: The allowable tensile strength, the default value is 0 kPa.

The drilling depth of the drilling report for this research case was 30 m. After referring to the drilling reports of surrounding cases, the depth of this model was extended to 50 m below the ground to provide the response depth required for program analysis. Therefore, the soil layer of the model was divided into four layers, which included the backfill layer (SF)—its depth was from the ground level to 1 m underground; the silty clay layer (CL1)—its depth was 1 m to 3 m underground; the soil clay layer (CL2)—its depth was 3 m to 35 m underground; and the rock layer (RL)—its depth was 35 m to 50 m underground. The parameters of the Hardening Soil model are shown in

Table 3. Material parameters of the Hardening Soil model.

Layers	Depth (m)		${\gamma }_{unsat}$ (kN/m3)	${\gamma }_{sat}$ (kN/m3)	$E_{50}^{ref}$ (kN/m2)	$E_{oed}^{ref}$ (kN/m2)	$E_{ur}^{ref}$ (kN/m2)	$c_{ref}^{\prime }$ (kN/m2)	${\phi }^{\prime }$ (°)	ψ (°)	m
	Top	Bottom
SF	0	−1.0	18.6	19.1	22,000	22,000	66,000	0.5	30	0	0.5
CL1	−1.0	−3.0	18.0	18.3	22,300	18,000	66,900	1	29	0	1.0
CL2	−3.0	−35.0	18.3	18.8	29,000	23,000	87,000	1	28	0	1.0
RL	−35.0	−50.0	21.5	21.8	90,000	90,000	27,000	80	34	4	0.5
AFI	0	−15.0	22	22.5	70,000	70,000	21,000	1	34	4	0.5

Notes: ${\gamma }_{unsat}$ = unsaturated unit weight; ${\gamma }_{sat}$ = saturated unit weight; $c_{ref}^{\prime }$ = effective cohesion; ${\phi }^{\prime }$ = effective friction angle; AFI = after geological improvement.

.

As mentioned above, the pipe roof was arranged in such a way that the steel pipes were connected with one another using mortise and tenon joints and embedded in the soil horizontally. The backfill grouting was carried out after the construction of each pipe roof. Then, each row of pipes was like a large impermeable plate structure. Both ends of the steel pipe were closely connected to the wall of the concrete and the wall of the steel sheet pile. In order to make the simulation of the software closer to the real project, this study used the tunnel designer-plate element to simulate the steel pipe and filled concrete of the pipe-roof structure. In addition, interfacial properties were added around plate elements to simulate water permeability properties. In the simulation analysis, the pipe-roof structure was regarded as a composite material composed of steel pipe and concrete. Assuming that the section of the pipe roof was a square section, the calculated cross-sectional area of a single pipe roof was 0.519 m². After the equivalent transformation of the sectional area, the plate thickness of the pipe-roof structure was set to 0.72 m for simulation analysis. The elastic modulus $E_{Pr}$ and unit weight ${\gamma }_{Pr}$ of the composite material composed of steel pipe and concrete were calculated by using the transformed section in material mechanics, as shown in Equations (1) and (2), respectively.

$$E_{Pr}=\frac{E_s{A}_s+E_c{A}_c}{A_{total}},$$

(1)

$${\gamma }_{Pr}=\frac{{\gamma }_s{v}_s+{\gamma }_c{v}_c}{v_{total}},$$

(2)

where $E_s$ = elastic modulus of steel pipe; $E_c$ = modulus of elasticity of concrete; $A_s$ = cross-sectional area occupied by the steel pipe in a single composite material; $A_c$ = cross-sectional area occupied by concrete in a single composite; $A_{total}$ = cross-sectional area of a single composite material; ${\gamma }_s$ = unit weight of steel pipe; ${\gamma }_c$ = unit weight of concrete; $v_s$ = the volume occupied by the steel pipe in a single composite material; $v_c$ = the volume occupied by concrete in a single composite; $v_{total}$ = the volume of a single composite material.

Diaphragm walls, cross walls, and foundations are all reinforced concrete structures, and their concrete materials were simulated in elastic mode. According to the information of the actual project in this case, the thickness of the diaphragm wall was 0.8 m and its depth was 21.5 m; the thickness of the steel sheet pile was 0.08 m, the penetration depth of the north side was 13 m, and the penetration depth of the other side was 18 m; the thickness of the cross wall was 0.8 m, and its depth was 12.15 to 21.5 m below the surface; the thickness of the foundation was 0.6 m and its depth was 12.15 m below the surface. The foundation of the launching shaft with a thickness of 0.6 m was to facilitate the construction of the pipe roof and provided a certain degree of stiffness. The material parameters of the above structures are shown in

Table 4. Material parameters of the structures.

Item	Code Name	Thickness (m)	Unit Weight (kN/m3)	${\mathit{f}}_{\mathit{c}}^{\prime }$ (kgf/cm2)	Modulus of Elasticity (kN/m2)	Poisson’s Ratio
Diaphragm wall	DW	0.8	24	280	$1.76\times {10}^7$	0.17
Cross wall	CW	0.8	24	280	$1.76\times {10}^7$	0.17
Foundation	FS	0.6	24	210	$1.52\times {10}^7$	0.17
Steel sheet pile	SP	0.08	78.5	-	$1.68\times {10}^8$	0.28
Box culvert	BC	1.0	24	210	$1.52\times {10}^7$.	0.17
Pipe roof	PR	0.72	26	210	$2.3\times {10}^7$	0.23

Notes: $f_c^{\prime }$ = 28-day compressive strength of concrete.

. On the other hand, under the same underpass cross-sectional area, four different aspect ratios (0.30, 0.36, 0.40, and 0.45) were designed in this study, as shown in Figure 11.

This case was divided into two deep excavation areas, namely the diaphragm wall excavation area and the steel sheet pile excavation area. Both areas adopted five-stage excavation and four-stage support. The support system used H-shape steel sections as temporary support, most of which were used in the early stage of the project. When the structure reached a certain strength, the support system was dismantled. In this study, the node-to-node anchor was used to simulate the axial support and the beam element was used to simulate the base’s fence. The support system consisted of three different types of H-shape steel, which were H 350 × 350 × 12 × 19, H 400 × 400 × 13 × 21, and H 414 × 400 × 18 × 28. The relevant parameters of the support materials for the diaphragm wall and the steel sheet pile are shown in

Table 5. Parameters of the support materials for the diaphragm wall.

Type of H-Shape Steel	Cross-Sectional Area (m2)	Modulus of Elasticity (kN/m2)	Reduction Coefficient	Effective Stiffness (kN)
$\mathrm{H} 350\times 350\times 12\times 19$	0.0172	$2.1\times {10}^8$	0.75	$2.71\times {10}^6$
$\mathrm{H} 400\times 400\times 13\times 21$	0.0219	$2.1\times {10}^8$	0.75	$3.45\times {10}^6$
$\mathrm{H} 414\times 400\times 18\times 28$	0.0295	$2.1\times {10}^8$	0.75	$4.65\times {10}^6$

and

Table 6. Parameters of the support materials for the steel sheet pile.

Type of H-Shape Steel	Modulus of Elasticity (kN/m2)	Unit Weight (KN/m2)	Cross-Sectional Area (m2)	I2 (m4)	I3 (m4)
$\mathrm{H} 350\times 350\times 12\times 19$	$2.1\times {10}^8$	78.5	0.0172	$9.87\times {10}^{-5}$	$9.87\times {10}^{-5}$
$\mathrm{H} 400\times 400\times 13\times 21$	$2.1\times {10}^8$	78.5	0.0219	$1.63\times {10}^{-4}$	$1.63\times {10}^{-4}$

, respectively. In addition, the axial forces of the supports at individual stages are shown in

Table 7. Axial preload of the supports.

Construction Stage	Preload of Diaphragm Wall End (kN)	Preload of Steel Sheet Pile End (kN)
The first stage	60	50
The second stage	140	130
The third stage	220	180
The fourth stage	320	350

.

The excavation of the underground underpass adopted three rounds of excavation, and each round was two meters long. During the excavation process, temporary supports were used to resist the surrounding earth pressure. In the numerical simulation, “line load” was used to simulate the temporary supports of the underpass, as shown in Figure 12. The parameter values of the temporary supports are shown in

Table 8. Numerical value of the temporary supports for the underground underpass.

Cross-Sectional Aspect Ratio	Support Force on the Upperside of the Underpass ${\mathit{\sigma }}_{\mathit{z}}$ (KN/m)	Support Force on the Lateral Side of the Underpass ${\mathit{\sigma }}_{\mathit{x}}$ (KN/m)	Support Force on the Underside of the Underpass ${\mathit{\sigma }}_{\mathit{z}}$ (KN/m)	Excavation Face Load ${\mathit{\sigma }}_{\mathit{y}}$ (KN/m)
0.30	36	60	87	60
0.36	36	64	94	64
0.40	36	66	98	66
0.45	36	69	103	69

.

This site was surrounded by Sun Yat-Sen Memorial Hall, Taipei Dome, existing underground box culverts, and roads, as shown in Figure 13. In order to ensure the safety of the project construction, the impact of the above-mentioned adjacent structure load and road load on the excavation process was analyzed. According to the field survey, the length and width of the surrounding structures, the length and width of the road, and the relative distance between the diaphragm wall of the excavation base and the adjacent buildings were measured. The coordinates of the floor plan of the structures around the construction site and load point are shown in Figure 14. The parameters related to adjacent structures and road loads are shown in

Table 9. Parameters related to the adjacent structures and road loads.

Item	Floor Number (Above Ground/Underground)	Load per Unit Area (kN/m${}^2$)
Taipei Dome	$5\mathrm{F}/2\mathrm{F}$	74
Existing structure under the dome	$0\mathrm{F}/1\mathrm{F}$	12
Existing structure of the underground crossing	$0\mathrm{F}/4\mathrm{F}$	48
Zhongxiao East Road	-	10
Tree Belt of Melaleuca and Camphor	-	5
Sun Yat-Sen Memorial Hall	$+3\mathrm{F}/-2\mathrm{F}$	54

.

3.5. Mesh Generation

After defining the geometric conditions of the model and assigning the material properties of the individual soil layer parameters and the structural object, the program divided the geometric model into several independent finite elements according to the five built-in options and whether to refine the mesh. In this case, based on the limitations of the program and the consideration of the length of analysis time, the “medium + dense grid” was used for the mesh setting. The grids for the soil and structures are shown in Figure 15 and Figure 16, respectively.

3.6. Construction and Calculation Phase

PLAXIS 3D was used to simulate the on-site construction steps, and the construction was divided into 18 phases (as shown in

Table 10. Steps in the staged construction.

Steps	Launching Shaft	Receiving Shaft	Remark
Initial state	Establish initial soil stress
Phase 1	Construction of diaphragm wall and underground wall	Construction of steel sheet piles	Reset displacement to zero
Phase 2	Excavation to GL −2.8 m	Excavation to GL −2.5 m	Lower water level to −3.8 m
Phase 3	Erection support at GL −1.8 m Apply a preload of 60 kN	Erection support at GL −1.5 m Apply a preload of 50 kN
Phase 4	Excavation to GL −5.75	Excavation to GL −5.6 m	Lower water level to −6.75 m
Phase 5	Erection support at GL −4.75 m Apply a preload of 130 kN	Erection support at GL −4.6 m Apply a preload of 140 kN
Phase 6	Excavation to GL −8.75 m	Excavation to GL −8.1 m	Lower water level to −9.75 m
Phase 7	Erection support at GL −7.75 m Apply a preload of 220 kN	Erection support at GL −7.1 m Apply a preload of 180 kN
Phase 8	Excavation to GL −11.5 m	Excavation to GL −10.6 m	Lower water level to −12.5 m
Phase 9	Erection support at GL −10.5 m Apply a preload of 320 kN	Erection support at GL −9.6 m Apply a preload of 350 kN
Phase 10	Excavation to GL −12.15 m	Excavation to GL −12 m	Lower water level to −14 m
Phase 11	Build the bottom floor
Phase 12	Remove part of the support (pipe roof application range)
Phase 13	Construction of the top row of pipe roof
Phase 14	Construction of the left row and right row of pipe roof
Phase 15	Construction of the bottom row of pipe roof
Phase 16	The first round of excavation and box culvert construction
Phase 17	The second round of excavation and box culvert construction
Phase 18	Completion of underpass construction

) to investigate the lateral displacement of the diaphragm wall, surface subsidence, and the force on the pipe roof caused by excavation. In addition, the differences between the analysis results and the numerical values stipulated in the specification were also compared to verify the correctness of the constructed model and related parameters. The initial state activated the soil, and Phase 1 activated the existing structures, tree belts, diaphragm wall, steel sheet pile, cross wall, site improvement, etc., and reset the initial displacement to zero. Phases 2 to 11 were the earthwork excavations and support erections in the first to fifth stages, and the water level of the excavation surface was lowered in conjunction with the excavation stage. Phase 12 was to remove the support in the pipe power range according to the local conditions. Phases 13 to 15 were sequentially applying the top row of pipe roof, the left and right rows of pipe roof, and the bottom row of pipe roof. The length of the underground passage was six meters, and its simulated excavation was divided into three rounds. That is, the length of each round was two meters. Therefore, from Phases 16 to 18, the excavation was divided into three rounds in conjunction with the construction of the box culvert structure.

4. Numerical Simulation Results Analysis

4.1. Impact of Excavation at Individual Stages on the Retaining Wall

4.1.1. Surface Subsidence in the Excavation Area

The formations in the Taipei Basin are mostly composed of soft clay layers. Most of the soft clay soils have a natural moisture content equal to or greater than the liquid limit of the soil, with an SPT-N value between about 1 and 4, and have characteristics such as extremely soft to weak consistency. In this case, subsidence observation points were set up to monitor the amount of surface subsidence caused by excavation in each stage at each observation point. For the south side and north side of the diaphragm wall, the surface subsidence analysis values and the monitoring values were compared after the completion of each stage of construction. The results are shown in

Table 11. Comparison of the numerical analysis and actual values of surface subsidence on the south side of the diaphragm wall.

South Side/Location	After the Completion of Pipe Roof			After the Completion of Underpass
	Analysis Value (mm)	Actual Value (mm)	Difference (mm)	Analysis Value (mm)	Actual Value (mm)
One meter away from the diaphragm wall	−6.68	−5.90	0.78	−7.06	-
Five meters away from the diaphragm wall	−10.02	−9.64	0.38	−10.78	-
Sixteen meters away from the diaphragm wall	−1.05	−0.75	0.30	−1.46	-

and

Table 12. Comparison of the numerical analysis and actual values of surface subsidence on the north side of the diaphragm wall.

North Side/Location	After the Completion of Pipe Roof			After the Completion of Underpass
	Analysis Value (mm)	Actual Value (mm)	Difference (mm)	Analysis Value (mm)	Actual Value (mm)
2.5 m away from the diaphragm wall	−4.68	−5.28	0.60	−6.01	-
6.0 m away from the diaphragm wall	−6.05	−6.82	0.77	−7.36	-
13.5 m away from the diaphragm wall	−3.82	−3.13	0.42	−5.04	-

, respectively. The surface subsidence was successfully controlled within 10.78 mm, which did not affect the traffic above and the normal use of buildings at ground level. Moreover, the errors between the analyzed values and the monitored values were between 0.3 and 0.78 mm. The results showed that the constructed numerical analysis model had considerable accuracy.

On the other hand, in order to verify the validity of the numerical model, the cumulative values of surface subsidence obtained from the numerical simulation and field measurement in each construction stage were further compared. In order to analyze the surface subsidence caused by the excavation of the diaphragm wall, a section A-A was selected on the south side of the diaphragm wall, and a section B-B was selected on the north side of the diaphragm wall, as shown in Figure 17. The surface subsidence curves for the south and north sides of the diaphragm wall after the completion of each stage are shown in Figure 18 and Figure 19, respectively. From the analysis results, it can be seen that the surface subsidence curves on both sides of the diaphragm wall were groove-shaped curves, which were consistent with the research results of most of the deep excavation cases collected by Ou et al. [39]. Further observation of Figure 18 shows that the figure could be divided into two regions, with a distance of 15 m from the diaphragm wall as the boundary. The surface subsidence curve of the first area (0–15 m) had a concave shape, which was presumed to be mainly affected by the excavation of the arrival well. The surface subsidence curve of the second area (15–35 m) was also in the shape of a depression. It was speculated that it was mainly affected by the excavation support of steel sheet piles. The excavation area was small, but caused a large amount of soil deformation.

4.1.2. Lateral Deformation of the Diaphragm Wall

In this case, three inclinometer casings in the wall (the configuration points are shown in Figure 20) were set up to measure the wall displacement in each excavation stage. Figure 21, Figure 22 and Figure 23 show the numerical analysis results of the lateral displacements of the diaphragm wall at different excavation stages. In addition, the comparisons between the wall deformation curves and the standard warning value (30 mm) after the completion of the pedestrian crossing are also presented in Figure 21, Figure 22 and Figure 23. The maximum lateral displacement of the wall obtained in the analysis mode of monitoring point 1 was 4.82 mm, and its depth was at GL −8.78 m, which was 25 mm different from the warning value. The maximum lateral displacement of the wall at monitoring point 2 in the analysis mode was 27.95 mm, and its depth was at GL −6.75 m, which was only 2 mm away from the warning value. The maximum lateral displacement of the wall obtained in the analysis mode of monitoring point 3 was 5.42 mm, and its depth was at GL −8.42 m, which was 24 mm different from the warning value. It can be seen from Figure 21, Figure 22 and Figure 23 that the lateral displacement of monitoring point 2 was much larger than the values of monitoring point 1 and monitoring point 3. It was assumed that the main reason for this was that part of the lateral support in the launching shaft was removed for the convenience of personnel operations and the space requirements for equipment placement before the construction of the pipe roof. In this area, only the supports of the first stage and the foundation plate were left to resist the lateral soil pressure outside the diaphragm wall, which in turn affected the lateral displacement of the diaphragm wall.

4.2. Impact of Excavation in Individual Stages on the Surface Subsidence above the Pipe-Roof Structure

The whole project was roughly divided into three stages. The first stage was the completion of the working well (and the impact caused by deep excavation), the second stage was the completion of the construction of the pipe roof, and the third stage was the completion of the excavation of the underpass (and the impact caused by the box culvert excavation). There were many factors affecting the deformation around the base due to deep excavation and box culvert excavation in the project; for example, the geological conditions, excavation methods, support types, construction methods, etc., were highly correlated with the size and distribution of deformation. In the general PPM construction process, there is a complex interaction between the inner connection pipes, which in turn affects the closure of the pipe roof and surface settlement [9]. The pipes used in this project were designed with mortise and tenon joints, which allows the pipes to be tightly fixed to each other, thus resisting the surrounding soil and reducing ground subsidence.

There are several geometrical cross-section design options for box culvert constructions of rectangular cross-section. Under the condition of the same sectional area, the influence of different aspect ratios on ground surface subsidence is uncertain, and there is a lack of past cases for reference. Therefore, although the actual section aspect ratio used in this case was 0.36, three other different aspect ratios (0.30, 0.40, and 0.45) of the box culvert were used to compare their effects on the surface settlement.

Table 13. The surface subsidence values above the pipe-roof structure during excavation in individual stages.

Aspect Ratio	Stage	Maximum Subsidence (mm)	Increase in Stages (mm)	Proportion of Total Subsidence (%)
0.30	Completion of working well	−6.656	−6.656	35.78
	Completion of pipe roof construction	−10.470	−3.814	20.50
	Completion of underpass excavation	−18.602	−8.132	43.27
0.36	Completion of working well	−7.674	−7.674	49.32
	Completion of pipe roof construction	−8.769	−1.095	7.10
	Completion of underpass excavation	−15.402	−6.630	43.26
0.40	Completion of working well	−5.406	−5.406	45.56
	Completion of pipe roof construction	−8.076	−2.670	22.50
	Completion of underpass excavation	−11.865	−3.789	31.93
0.45	Completion of working well	−3.945	−3.945	39.27
	Completion of pipe roof construction	−5.386	−1.441	14.35
	Completion of underpass excavation	−10.045	−4.659	46.38

shows the surface subsidence values above the pipe-roof structure with four different aspect ratios during excavation in individual stages. The maximum surface subsidence caused by the construction of the working well accounted for about 35–40% of the total subsidence. The maximum surface subsidence caused by the completion of the pipe-roof construction accounted for about 10–20% of the overall total subsidence. Compared with other stages, the amount of subsidence caused by this stage was mainly due to the filling of concrete and backfill grouting immediately after the construction of the pipework on site, so as to avoid the occurrence of large surface subsidence due to the rapid drop of the upper water level and soil loss in this stage. In software analysis, the surface of the pipe-roof structure was provided with interface properties, just like the pavement of an impermeable layer. The maximum surface subsidence caused by the construction of the underpass accounted for 30–50% of the total subsidence. The surface subsidence in this stage was caused by the excavation of the box culvert. Before the excavation of the box culvert, the interior of the soil was in a state of original stress. After excavation, this stress state was broken, the surrounding soil deformed towards the inside of the box culvert, the original stress of the surrounding soil gradually decreased, and the box culvert and the stratum deformed to a certain extent. After the support was applied, the interaction between the surrounding soil and the support reached a state of deformation harmony, and the internal stress also reached a state of equilibrium, resulting in the final amount of surface subsidence. The analysis results showed that the pipe-roof structure was suitable for underground excavation with shallow-buried depth in the soft soil of the Taipei Basin.

On the other hand, the subsidence curves of the ground above the box culverts with different aspect ratios excavated in different stages are shown in Figure 24, Figure 25, Figure 26 and Figure 27. These curves showed that the surface deformation pattern caused by the earthwork excavation of the closed pipe-roof preconstruction structure still conformed to the Peck model [40]. In other words, the surface subsidence was the largest at the symmetrical axis of the pipe roof, and the surface subsidence gradually decreased with the increase in the distance from the symmetrical axis of the pipe roof. These results are consistent with those in the literature [5,9,31]. The overall subsidence data after the completion of the underpass construction were compared to explore the influence of the height-to-width ratio of the underpass section, as shown in Figure 28. When the aspect ratio was 0.30, the final surface subsidence was −18.602 mm, which was the aspect ratio with the largest subsidence. Conversely, when the aspect ratio was 0.45, the final surface subsidence was −10.045 mm, which was the aspect ratio with the minimum subsidence. From this point of view, with the increase in the aspect ratio, the excavation impact on the surface subsidence above the underpass would gradually decrease. In other words, under the condition of the same sectional area, the smaller the width of the pipe-roof structure, the more the impact on the ground surface was reduced.

4.3. Analysis of the Force on the Pipe-Roof Structure by Excavation of Pedestrian Underpass

Generally speaking, the failure of structures is usually located at the point of maximum stress. Abdellah et al. [41] pointed out that a shallow-buried rectangular tunnel produced a stress concentration at the top and bottom of the tunnel. This phenomenon will cause a large bending moment on the structural slab, and the upper slab of the pipe roof is a place to which special attention must be paid during tunnel construction. Therefore, this study used the bending moment distribution of each construction stage to analyze the situation of the force received by the pipe roof, so as to investigate the bending moment change and safety of the upper pipe wall during the excavation of the box culvert.

Table 14. Maximum positive and negative bending moments on the upper row of the pipe roof generated by box culvert excavation in each stage.

Aspect Ratio	Maximum Positive Bending Moment (kN·m/m)			Maximum Negative Bending Moment (kN·m/m)
	First Round of Excavation	Second Round of Excavation	Third Round of Excavation	First Round of Excavation	Second round of Excavation	Third Round of Excavation
0.30	152.1	173.6	209.8	−154.9	−184.5	−220.1
0.36	147.9	163.7	152.9	−146.4	−166.5	−176.8
0.40	149.5	163.0	151.2	−149.3	−164.1	−157.1
0.45	130.3	137.9	137.6	−132.5	−141.3	−166.5

shows the maximum positive and negative bending moments on the upper row of the pipe roof generated by the box culvert excavation in each stage. It can be seen from the data in the table that when the aspect ratio was 0.30, the maximum positive bending moment value and maximum negative bending moment value of the pipe roof were the largest. As the aspect ratio increased, the maximum positive bending moment and the maximum negative bending moment gradually decreased. The results showed that the maximum positive bending moment and the maximum negative bending moment on the pipe roof produced by excavation at each stage were roughly inversely related to the aspect ratio and presented a non-linear decrease.

Comparing the analysis results for different box culvert sections, it can be seen that the absolute values of the maximum negative bending moment and maximum positive bending moment on the pipe roof during the excavation of the underpass were basically the same. When the underpass was completed, the maximum positive bending moment and the maximum negative bending moment of the tube power were the largest in the three stages. Therefore, special attention must be paid during the excavation of an underpass to avoid damage to the pipe-roof structure. In addition, when the underpass was excavated, the maximum positive bending moment occurred on both sides of the upper row of the pipe roof, and the maximum negative bending moment occurred in the center of the upper row of the pipe roof, as shown in Figure 29, Figure 30, Figure 31 and Figure 32. The results of this analysis were the same as those observed in experiments conducted by scholars in the past [4,8,14,23,41].

4.4. Influence of Overburden Depth of Underpass on Surface Subsidence and Culvert Deformation

In this section, having assumed that the soil parameters and box culvert parameters remained unchanged, the impacts of the shallow-buried pipe-roof box culvert on the surface subsidence and culvert deformation were examined for different overburden depths above the pedestrian underpass. Therefore, although the actual overburden depth of the underpass in the original project was 2.7 m, three other different overburden depths (i.e., 0.7, 1.7, and 3.7 m) were used to compare their effects on the surface subsidence and culvert deformation. The selected analysis points were a point on the ground above the symmetry axis of the box culvert, and points on the top and bottom of the box culvert, as shown in Figure 33.

Under different soil depths, the analysis values for the vertical displacement of the G1 analysis point in each stage are shown in Figure 34. It can be seen from Figure 34 that when the launching and receiving shafts were completed, the surface subsidence of the observation point was about 10 mm. Later, the surface subsidence increased to about 14 mm due to the removal of the lateral supports. During the box culvert excavation stage, the shallow box culvert was affected by the buoyancy of groundwater. With the excavation of the box culvert, the overall weight of the box culvert decreased, and the amount of surface subsidence tended to decrease. Among the different soil depths, when the overburden depth was 3.7 m, the impact was the greatest, and when the overburden depth was 0.7 m, it was the least affected. In the steel sheet pile removal stage, the support of the steel sheet pile was lost under the top pipe roof, and the amount of surface subsidence at this stage tended to increase. The subsidence amount was the largest when the overburden depth was 0.7 m, and the subsidence amount was the smallest when the overburden depth was 3.7 m. According to the results, it was inferred that the shallow-buried box culvert was more sensitive to the subsidence caused by construction than the deep-buried box culvert. Nevertheless, the analysis results showed that for the shallow-buried depth underground passage, the effect of pipe-roof structure on the reduction of excavation face load is significant. This showed that the pipe-roof structure was suitable for underground excavation with shallow-buried depth in soft soil. This is consistent with the results of Xie et al. [23].

After the excavation of the earthwork, the closed structure of the box culvert deformed under the action of external loads [5]. The deformations of the top and bottom of the box culvert are important indicators of the safety of the underground passage and ground buildings. According to the test results of Hisatake and Ohno [14], the surface subsidence caused by the PPM during tunnel excavation was maximum at the position closest to the tunnel excavation face. Therefore, in this study, the center line of the box culvert roof 10 cm away from the excavation face of the box culvert was taken as the T1 analysis point, and the center line of the bottom plate 10 cm away from the excavation face was taken as the B1 analysis point to observe the vertical displacements of the top and bottom of the box culvert. The deformed height of the center of the box culvert was calculated by the displacements of these two points, and then the vertical deformation rates of the center of the box culvert were obtained by dividing the obtained height by the original height of the box culvert.

Under different overburden depths, the analysis values of the vertical displacements of the T1 and B1 analysis points in each stage are shown in Figure 35 and Figure 36, respectively. It can be seen from Figure 35 that during the excavation stage of the box culvert, the displacement trend of the top of the box culvert first increased and then decreased. During the first excavation, due to the knockout of the diaphragm wall, the support of the diaphragm wall was lost under the top pipe roof. Therefore, vertical displacement tended to increase at this stage, and then there was a slight decrease (about 3 mm) at the top of the box culvert due to buoyancy. In other words, on the one hand, the shallow-buried box culvert was affected by the buoyancy of groundwater, and on the other hand, the overall weight of the culvert decreased with the excavation, so the vertical displacement of the observation points tended to decrease. In addition, during the steel sheet pile removal stage, since the T1 point was far away from the steel sheet piles, its vertical displacement did not change significantly. It can be seen from Figure 36 that during the excavation stage of the box culvert, the displacement trend of the bottom of the box culvert continued to decrease until it became flat. During the first excavation, due to the knockout of the continuous wall, the bundle of the diaphragm wall was lost above the bottom pipe roof. Therefore, the vertical displacement in this stage tended to decrease significantly compared with other stages. Similarly, in the steel sheet pile removal stage, since the B1 point was far away from the steel sheet pile, its vertical displacement did not change significantly.

5. Conclusions

In this paper, the ground surface settlement and lateral deformation of a diaphragm wall induced by rectangular pedestrian underpass excavations with the PPM were investigated using 3D finite element analysis. According to the analysis results, the following conclusions were reached:

(1)

For the south and north sides of the diaphragm wall, the errors between the analysis values and the monitoring values of the surface settlement after the construction of each stage were between 0.3 and 0.78 mm. The results showed that the constructed numerical analysis model had considerable accuracy.

(2)

The lateral displacement of monitoring point 2 was much larger than the values of monitoring point 1 and monitoring point 3. It was assumed that the main reason for this was that part of the lateral support in the launching shaft was removed for the convenience of personnel operations and the space requirements for equipment placement before the construction of the pipe roof. In this area, only the supports of the first stage and the foundation plate were left to resist the lateral soil pressure outside the diaphragm wall, which in turn affected the lateral displacement of the diaphragm wall.

(3)

Numerical analysis results showed that the use of the pipe-roof preconstruction method combined with a box culvert structure to form the pedestrian underpass could effectively control the surface displacement above the box culvert. For the four different aspect ratios, the final subsidence of the ground surface was within 2 cm, which was in line with past construction experience.

(4)

With the increase in the aspect ratio, the excavation would cause the surface subsidence above the underpass to gradually decrease. In other words, under the condition of the same sectional area, the smaller the width of the pipe-roof structure, the more the impact on the ground surface was reduced.

(5)

As the aspect ratio increased, the maximum positive bending moment and the maximum negative bending moment gradually decreased. The results showed that the maximum positive bending moment and the maximum negative bending moment on the pipe roof produced by excavation in each stage were roughly inversely related to the aspect ratio.

(6)

The shallow-buried box culvert was more sensitive to the subsidence caused by construction than the deep-buried box culvert.

(7)

The shallow-buried box culvert was affected by the buoyancy of groundwater, and on the other hand, the overall weight of the culvert decreased with the excavation, so the vertical displacements of the observation points tended to decrease.

(8)

The simulation analysis showed that under different overburden depths, the vertical displacement trends of the shallow-buried box culvert at the observation point on the top or bottom in each excavation stage were roughly the same.

According to the analysis results, the maximum lateral displacement of the diaphragm wall caused by the excavation of the launching well was 27.95 mm, which was caused by the removal of part supports, and its value was very close to the design warning value (30 mm). Therefore, it is suggested that in actual engineering, more attention should be paid to the lateral displacement of the diaphragm wall caused by the removal of part supports for the convenience of personnel operations or the space requirements for equipment placement before the construction of the pipe roof. In addition, for the surface subsidence around the excavation area, the maximum subsidence value on the north side and south side was about −7 mm and −10 mm, respectively, the difference from the on-site monitoring data was within 1 mm, and the subsidence influence range was about three times the excavation depth. From this point of view, the model boundary was set to 5 times the excavation depth, which was sufficient to cover the impact of excavation in each stage on surface subsidence.