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Interaction between an underground parking and twin tunnels – Case of the Shiraz subway line
Tunnelling and Underground Space Technology 95 (2020) 103150
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Interaction between an underground parking and twin tunnels – Case of the Shiraz subway line Mojtaba Nematollahia, Daniel Diasb,c,
T
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a
Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, China c Antea Group, Antony, France b
A R T I C LE I N FO
A B S T R A C T
Keywords: Three-dimensional simulation Soil-structure interaction Segmental lining Shielded Mechanized tunneling Shiraz metro line 2 CYsoil model
Three-dimensional numerical analyses were developed to study the interaction between twin tunnels and underground parking in an urban area. The mechanized tunneling procedure and segmental lining were accurately simulated using a finite difference code and a nonlinear perfectly plastic constitutive model (CYsoil). In this paper, the interaction between tunneling in clay and an underground parking was performed using two scenarios: construction of the underground parking above the existing tunnels and excavating the twin tunnels under the existing parking. The soil/structure interaction is investigated in terms of soil movements, structural forces induced in the tunnel lining and displacements of the parking structure. On the base of the numerical results, the construction sequence of underground structures, which are located nearby to each other, have a considerable effect on the soil and structures behavior.
1. Introduction Shiraz, the cultural capital city of Iran, has a high need for an extensive subway network and transportation infrastructure to avoid urban congestion. The excavation of new underground space changes the soil stress distribution and then causes ground movements. Sometimes, two different underground structures (parking or tunnel for example) have to pass closely. It can induce a considerable effect on the nearby existing underground structures. In this case, it is necessary to investigate the soil-structure interaction effect and to ensure the safety of both underground structures at a long time. Many researchers (Afifipour et al., 2011; Do et al., 2014, 2016; Hasanpour et al., 2012; Li et al., 2010; Mahmutoğlu, 2011; Ng et al., 2004, Nematollahi et al., 2018) have conducted researches to highlight the influence of a new tunnel excavation on an existing one. They found that the tunnels spacing has a significant impact on the ground movements and induced structural forces. Also, some studies have focused on the influence of excavating a crossing tunnel on an existing tunnel like (Liu et al., 2009; Chakeri et al., 2011; Li and Yuan, 2012; Ng et al., 2013; Fang et al., 2015; Ng et al., 2018). All of them showed that the excavation of a new tunnel would induce more displacements in the soil surrounding the previous tunnel as well as surface settlements. Huang et al. (2012) and Li et al. (2014) performed a series of centrifuge tests to study the effect of the tunnel excavation above two
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existing metro tunnels. The upheaval of the existing tunnel was observed, and it was reported that the back-fill grouting has a significant influence on the heave reduction. Sharma et al. (2001) investigate the impact of a large excavation close to tunnels using field monitoring data and the finite element method. They found that twin tunnels can bear the deformations and displacements due to the soil stress release. The tunnel lining stiffness has a considerable impact on the tunnel's displacements and distortions. Zhang et al., 2013 used a semi-analytical method to assess the heave of the underlying tunnel close to a deep excavation by field measurements. The interaction between the tunnel and the excavation was studied to highlight the effect of different factors like the excavation area, relative clearance and construction procedure. The results showed that the tunnel displacements increase with increasing the area ratio (defined as R = B/D where B is the excavation's width and D the tunnel's diameter) and decrease quickly with increasing the relative distance (defined as d, the horizontal distance between the excavation center and the cross-sectional center of the tunnel). Nevertheless, no research has considered the interaction effect between a tunnel and an underground parking. This paper provides a thorough numerical analysis related to the interaction of twin tunnels and an underground parking which is of major interest in urban areas. The second line of Shiraz subway project meets the underground parking in Azadi Park and is considered as the case study in this paper.
Corresponding author at: School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, China. E-mail address: [email protected] (D. Dias).
https://doi.org/10.1016/j.tust.2019.103150 Received 9 March 2019; Received in revised form 25 August 2019; Accepted 14 October 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 95 (2020) 103150
M. Nematollahi and D. Dias
Using a full 3D numerical model with a nonlinear strain hardening perfectly plastic constitutive model (Cap-Yield model named CYsoil) to model the soil behavior, a study is presented to specify the potential hazards in the construction procedures. The main excavation using an EPB-TBM (Earth Pressure Balance–Tunnel Boring Machine) are performed within a three-dimensional numerical model to simulate the conical shield, TBM selfweight and its trailer, face pressure, jacking force, tail void grouting and its consolidation. Furthermore, the concrete segmental lining of the tunnels was modeled using structural element, named liner which is qualified to model the segmental lining as well as longitudinal (segment) and circumferential (ring) joints (Do et al., 2013). This paper aims to propose to evaluate the interaction between twin tunnels and underground parking. For this purpose, two different scenarios are studied. In the first one, the twin tunnels are excavated before the parking setup. In the second scenario, the twin tunnels are excavated after the parking. Full three-dimensional numerical models considering the soil/structure interaction are developed to highlight the impact of these two scenarios. The results of both scenarios are presented and discussed. The construction of the parking causes a heave of the parking bottom level, while tunneling causes a downward movement above the twin tunnels.
Table 1 Lining parameters corresponding to the Shiraz metro line 2 (Tose-e, 2014). Parameter
Value
Young's modulus (GPa) Poisson's ratio Concrete lining density (kg/m3) Lining thickness (m) External diameter (m) Length of the lining ring (m)
31.2 0.22 2647 0.3 6.88 1.4
Table 2 Underground parking structure characteristics (Tose-e, 2014). Parameter
Value
Elastic modulus (GPa) Poisson's ratio Concrete density (kg/m3) Wall thickness (m) Wall height (m) Raft Thickness (m) Column height (m) Column section (m × m)
30 0.2 2650 0.5 10 0.4 2.8 0.5 × 0.5
2. Study case of the second line of the Shiraz subway
3. Constitutive model
In 2014, two EPB-TBMs started to excavate the twin tunnels of the Shiraz subway line 2, from the Southern station, Shekoofeh, to the Kolbehsa'di station in the North of the city consists of two tunnel tubes of 6.88 m diameter and 15 km long. A total of 13 underground stations were also part of this project. The tunnels pass mainly through marly lean clays with gypsum and the main tunnel length is in saturated clays (Tose-e, 2014). In the middle of this route, the twin tunnels underpass an underground parking in the Azadi park. A typical view of the transverse section where the twin tunnels and the underground parking are located is presented in Fig. 1. In this project, every lining ring consists of 6 segments, four trapezoidal and two parallelograms. They have different sizes, and the smaller one is called the key segment. Furthermore, the prefabricated segments made of reinforced concrete has a 1.4 m length and 30 cm thickness. The underground parking comprises four diaphragm walls and is a three-storey structure with a 30 m length in the Y direction (perpendicular to Fig. 1) and 26 m width. Two inclinometers (I_L and I_R) where setup near the parking walls and are shown in Fig. 1. The segmental lining and underground parking properties of this project are respectively provided in Tables 1 and 2.
The Cap-Yield (CYsoil) model is a strain-hardening constitutive model that provides a general description of the nonlinearity of soils. This constitutive model permits to consider the loading/unloading response of soils (Itasca Group, 2012). The input parameters corresponding to CYsoil model for Shiraz subway are summarized in Table 3 from geotechnical investigations (on-site and laboratory). They were presented in the work of Nematollahi and Dias (2019). The deviatoric stress-axial strain diagrams obtained from experimental data of Consolidated Drained (CD) tests are considered to back analyze the input parameters for soils. These data are obtained from Kankavan (2013). Three confining pressures 50, 100 and 150 kPa were considered during the triaxial tests for both clay soils. Only the case of the marly lean clay soil is presented in Fig. 2. To confirm the considered initial values, numerical simulations of these triaxial compression tests are done firstly using Flac3D using the CYsoil constitutive model. Then a comparison with the obtained data from the experimental triaxial tests has permitted the parameters to be back analyzed. It can be seen in Fig. 2 that for the lower confining pressure (50 kPa), the numerical and experimental diagrams are in good accordance with each other.
Table 3 Soil layer's parameters corresponding to the CYsoil constitutive model (Nematollahi and Dias, 2019).
Fig. 1. Cross section view of the problem. 2
CYsoil Model
Clay
Saturated clay
Marly lean clay
Young modulus E (MPa) Poisson's ratio ν Angle of internal friction ϕ (degree) Dilation angle ψ (degree) Cohesion C (kPa) Bulk modulus (reference) (MPa) Shear modulus (reference) (MPa) Calibration factor β Failure ratio Rf Reference effective pressure Pa (kPa) Earth pressure coefficient K0 Density (kg/m3)
78.75 0.35 28.7 0 11 87.5 29.17 1 0.9 100 0.5 1670
71.06 0.35 25.8 0 5 78.96 26.32 1 0.9 100 0.5 2042
173.73 0.35 29.6 0 17 193.03 64.34 1 0.9 100 0.5 2058
Tunnelling and Underground Space Technology 95 (2020) 103150
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Fig. 2. Deviatoric stress vs axial strain curves with loading–unloading phases.
Fig. 3. The schematic view of the generated model −2nd line of Shiraz subway.
4. Three-dimensional numerical model
Where H is depth of the tunnel center and D is the excavation diameter of the tunnel. A parametric study was done to be sure that no boundary effects are present due to the parking dimensions. The considered model size is enough to avoid them in this case study. A full three-dimensional layout of the underground parking and the twin tunnels of the second line of the Shiraz metro with a height of 50 m, width of 116 m, and length of 70 m was developed using Flac3D. It should be noted that this model consists of around 914,100 zones and 971,750 grid points. A perspective view of the numerical model is shown in Fig. 3. All the nodes on the bottom model are blocked in the vertical direction, whereas the model sides boundaries were restricted in their normal directions. As can be seen in Fig. 3, the grid density decreases by getting away from the underground structures to the model boundaries, which is quite effective to increase the calculations speed and accuracy.
4.1. Geometry, boundary and initial conditions In this study, numerical simulations were executed through a finite difference program, Flac3D, which permits to do three-dimensional analysis and consider non-linear soil-structure interaction problems. To avoid boundary effects in numerical simulations, the model boundaries were set at an optimal distance from the subterranean structures. For this purpose, the model dimensions were assumed larger than the proposed values by Rodriguez (2000).
• (H + 4D), for the model height, • (H + 3D), for the model length, • 3H, for the model width (for half of the model). 3
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Fig. 4. 3D layout of the mechanized tunneling process in second line of Shiraz subway. Table 4 Mechanical parameters of the modeled shield of Shiraz metro line 2 (Nematollahi and Dias, 2019). Parameter
Elastic modulus (MPa) Poisson's ratio Shield Thickness (mm) Shield Density (kg/m3)
Front Shield
Middle Shield
Rear Shield
P1
P2
P3
P4
P5
P6
20 0.15 50 7800
200 0.15 50 7800
2e3 0.15 50 7800
2e4 0.15 50 7800
2e5 0.15 50 7800
2e5 0.15 50 7800
(Farashar, 2010). This is due to permeabilities which are higher than 10−5 m/s in all the layers. Therefore, the evolution of pore pressures with time is not considered in the numerical calculations. Fig. 5. Schematic vision of the proposed conical shield in the numerical model.
4.2. Numerical simulation of the shielded mechanized tunneling phases
Furthermore, the mesh density around the underground parking walls is increased locally. All the models are run in drained conditions, because of the rapid dispersion of the observed in situ pore pressures
Mechanized tunneling is a successive procedure of excavation and simultaneous installation of the lining segments. In order to simulate an
Fig. 6. Tunnel crown vertical displacement versus the distance to the tunnel face (Nematollahi and Dias, 2019). 4
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Fig. 7. Springs of the joints; (a) segment's joint, (b) ring's joint.
Table 5 Parameters of the lining joints (Nematollahi et al., 2018). Parameter
Value
Axial Stiffness Kaxi and KRaxi (MN/m) Radial Stiffness Krad and KRrad (MN/m) Rotational Stiffness Krot and KRrot (MN m/rad/m) Maximum bending moment at segment joint Myield (kN.m/m)
550 3960 80 115
Fig. 10. Schematic view of the twin tunnels and underground parking.
EPB-TBM tunneling process accurately, various elements must be taken into consideration. In this study, the TBM advancement in the ground is simulated considering the components and actions that could happen in real tunneling. The simulation of the mechanized tunneling components for the Shiraz subway line 2 is summarized below. A schematic view of the EPB-TBM tunneling is provided in Fig. 4. In this paper, the face pressure is simulated by exerting horizontal stress with a trapezoidal distribution at the tunnel face (Kasper and Meschke, 2004, 2006; Do et al., 2014, 2015). The mean value of the face pressure, exerted at the tunnel center, is set equal to 0.15 MPa with a vertical gradient due to the slurry weight (1494 kg/m3) which is given by the monitoring data. The trapezoidal distribution of applied face pressure is presented in Fig. 4. In this study, to model the conical shape of the shield, a simplified method is utilized by using shell elements. This method has already used by the same authors (Nematollahi and Dias, 2019). In this method, the shield consists of smaller parts with length equal to the advance step, 1.4 m, and each section has a different stiffness. Thus, six pieces with a total length of 8.4 m make the taper shield. The schematic configuration of the proposed shield is shown in Figs. 4 and 5. Without shield elements, the vertical displacement of the tunnel crown during the TBM progress can reach 30 cm, as can be seen in Fig. 6. Whereas, in the real project, the gap between the tunnel boundary and the shield's outer surface in the middle part is equal to
Fig. 8. Lining pattern: (a) Common pattern (b) Oblique joints (Used in this work) (Nematollahi et al., 2018).
Fig. 9. Design steps of the underground parking construction.
Table 6 Parameters of the diaphragm wall - soil interface. Parameter
Retaining wall - Clay
Diaphragm wall – Saturated clay
Diaphragm wall – Marly lean clay
Normal Stiffness Kn (MN/m) Shear Stiffness Ks (MN/m) Friction Angle (degree) Cohesion (kPa)
5.06e4 5.06e4 19.1 0
4.56e4 4.56e4 17.2 0
1.12e5 1.12e5 19.7 0
5
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Fig. 11. The horizontal displacement profile in (a) Right side (I_R), (b) Left side (I_L) of the tunnels.
Fig. 12. The vertical displacement of the parking bottom (A-A profile).
Fig. 13. Axial displacements induced in the right tunnel lining (Ring 26).
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Fig. 14. Normal displacements induced in the right tunnel lining (Ring 26).
Fig. 15. Contour of vertical displacement before and after the underground parking excavation (A-A section).
Fig. 16. Axial force induced in the right tunnel lining (Ring 26).
Fig. 17. Contour of the Max. principal stress before and after the underground parking excavation (A-A section).
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Fig. 18. Bending moment induced in the right tunnel lining (Ring 26).
Fig. 19. Longitudinal displacement induced in the right tunnel lining (Ring 26).
Fig. 20. Longitudinal force induced in the right tunnel lining (Ring 26).
vertical gradient due to the grout weight is applied to a thin layer in the existing gap between the lining and the ground. Zone elements which permit to highlight the interaction of the grout-lining and grout-soil interface are presented in Fig. 4. The average grout injection pressure applied at the tunnel center level is set equal to 238 kPa, which is obtained from the monitoring sensors located on the grouting nozzles (Fater, 2016). A hard grout is simulated by a linear elastic model in the prior works of Mollon (2010), Mollon et al. (2013), Phienwej et al. (2006), Dias and Kastner (2013). To simplify the transition from fresh to hard grout, the physical characteristics of the consolidated grout (i.e., Ecg = 173.73 MPa and νcg = 0.22 where Ecg is Young's modulus and νcg is the Poisson's ratio of the consolidated grout) is assigned to the fresh grout zones after two excavation steps. On average, every excavation step takes more less 1.5 h. Based on the experiments performed on the grout, its properties after 3 h (two excavation steps) can be assumed the ones of the hardened grout. The fresh and hard grout are shown in Fig. 4.
7.5 cm. Nematollahi and Dias (2019) suggest using the following method to simulate a conical shield. The Young's modulus of the front shield (P1) should be lower than the elastic modulus of the tunnel surrounding soil. Then the Young's modulus of the other parts rises gradually. In Table 4, the assigned parameters according to the shield portions of this project are shown. By using this method, the tunnel crown movement is controlled from the middle shield (P3), which illustrates the capability of the proposed approach to numerically simulate a conical shield (Fig. 6). By thrust jacks, a force is applied on the last installed ring. It permits then to the TBM to go ahead. To simulate the jacking forces, all the nodes in the end section of the segment are exposed to the concentrated forces (Fig. 4). Furthermore, the average value of the real forces is defined from the monitoring data and taken equal to 7.1 MN (Fater, 2016). The tail void grout injection and its hardening process is a significant parameter in mechanized tunneling simulations. Like the method used by Nematollahi et al. (2018), a normal pressure with a 8
Tunnelling and Underground Space Technology 95 (2020) 103150
M. Nematollahi and D. Dias
Fig. 21. Vertical displacement of the underground parking bottom (A-A profile).
Fig. 22. Horizontal displacement in (a) Right side (I1), (b) Left side (I2) of the twin tunnels.
A downward load distribution acting on the tunnel floor over the shield length with a direction of 90 degrees is considered to simulate the TBM's self-weight (Do et al., 2014; Hasanpour, 2014; Nematollahi et al., 2018). In this work, the Shiraz TBM weight is equal to 3846 kN (Fater, 2016). Despite of the work done by Do et al. (2014), where the back-up train weight is modeled by exerting downward forces on the bottom sector of the tunnel lining over the train length, the trailer weight modeling is developed by applying vertical forces on two parallel lines with a transverse distance of 3 m in the lining invert in this project (Nematollahi et al., 2018; Nematollahi and Dias, 2019). The TBM and back-up weight simulation is presented in Fig. 4.
introduced a tunnel lining model using a structural element, named liner, that is qualified to simulate the segments and joints directly. The liner element is a proper choice for generating a node to node and a node to zone link to model segment-segment and grout-segment interactions respectively because it provides two links for each node. Furthermore, the influence of the grout-lining interaction has been considered using the normal spring stiffness (Kn) and the shear spring stiffness (Ks), respectively. Kn and Ks are calculated about one hundred times the stiffness of the attached zone (Itasca Group, 2012). The apparent stiffness of an attached zone is computed as the maximum value
⎡ (K + G ) ⎤ of ⎢ ΔZ 3 ⎥ relation where K and G are the bulk and shear moduli min ⎣ ⎦ respectively. ΔZmin is the shortest normal distance of the grout attached zone. A node to node link with six degrees of freedom that are indicated by six springs is provided to simulate the segmental joint. For a segmental joint, three springs should be taken into accounts such as an 4
4.3. Segmental lining The simulation method of the segmental lining and the joints is crucial in mechanized tunneling models. Do et al. (2013) has 9
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and Dias, 2019), an oblique geometry was developed to model the segmental joints which is in good agreement with the real condition and is used in the present model (see Fig. 8b). However, Ding et al. (2004), Do et al. (2013), Do et al. (2014), Do et al. (2015), Do et al. (2016), assumed the segmental joints parallel to the tunnel axis (see Fig. 8a). A 3D layout of both kinds of lining patterns is illustrated in Fig. 8. 4.4. Numerical simulation of the underground parking For the underground parking, a diaphragm wall (D-wall) was chosen due to the water table level. A 0.5 m thickness diaphragm wall is used for the excavation down to 10 m below the ground surface. The excavation is performed while the trench is filled with a bentonite slurry (fluid support) to provide lateral stability to the trench walls. Then, the diaphragm walls are created by placing the rebar cage and pouring concrete into the excavated trench (Pakbaz et al., 2013). The design steps of the underground parking in the numerical modeling are the following ones which are shown in Fig. 9: 1. Diaphragm walls construction considering a bentonite slurry volumic weight of 12 kN/m3, 2. Setting up the first roof, 3. Excavation of the first level (Level-1) to the depth of 3.6 m, 4. Setting up the second roof, 5. Installation of columns for the first level, 6. Repeat the top five stages to the 3rd level (Level-3) down to the final depth of 10 m. Fig. 23. A schematic view of the considered profiles on underground parking's structure.
In this study, the D-wall is simulated by liner elements which behave as a linear elastic material. The liner element integrates an interface that allows gaps to form and slip to happen (Itasca Group, 2012). The normal and shear springs stiffness related to the interface between the retaining wall and the soil are calculated as in Section 4.3 and are given in Table 6.
axial spring (Kaxi), a radial spring (Krad) and a rotational spring (Krot) (Fig. 7a). The axial spring has a linear behavior which is represented by a constant coefficient; While both radial and rotational springs' stiffness are determined by the stiffness modulus and yield limit parameters (Cavalaro and Aguado, 2012). In this project, no packer in the joints of the concrete segments is considered, so a linear behavior is supposed for the radial springs. Besides, all the other springs are set to be rigid. In order to determine the stiffness of the springs, Thienert and Pulsfort (2011) and Do et al. (2013) developed a simplified way which is employed in this study. The circumferential joints (joints between two successive rings) are modeled like the segmental joints with three springs (axial spring (KRaxi), radial spring (KRrad) and rotational spring (KRrot)) with the same stiffness coefficients similar to the segmental joints as shown in Fig. 7b. The parameters of the segmental and ring joints are shown in Table 5. In work by the same authors (Nematollahi et al., 2018; Nematollahi
4.5. Soil/structure interaction: Underground parking construction To investigate the effect of the excavation of two subterranean tunnels in a close distance in urban environments, the following scenarios for a twin tunnel and underground parking are considered: 1) Twin tunnels excavation before the underground parking construction, 2) Twin tunnels excavation after the underground parking construction.
Fig. 24. Vertical displacement of the underground parking invert (M-M profile). 10
Tunnelling and Underground Space Technology 95 (2020) 103150
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Fig. 25. Horizontal displacement induced in the (a) left, (b) right wall of underground parking.
Fig. 26. Horizontal displacement induced in the (a) Front, (b) back wall of underground parking.
5. Numerical results and discussion
In both scenarios, the twin tunnels excavation is simulated simultaneously to ensure that the effect of the lagging distance between the two tunnels faces around the tunnels is not considered (Nematollahi et al., 2018). In the first scenario, the excavation of the twin tunnels is performed before the construction of the underground parking. It is necessary to mention that this scenario shows the actual status in the Shiraz subway which will be done in the future. Whereas in the second scenario, the twin tunnels excavation is completed after the parking construction. A 3D view of the twin tunnels and underground parking as well as the two inclinometers position are presented in Fig. 10.
In this chapter, the obtained results from the first scenario are presented first. It permits to relate the excavation steps impact of threefloor underground parking on the existing twin tunnels. Then, the results of the second scenario, are considered to highlight the influence of the twin tunnel's excavation on the existing underground parking. 5.1. Influence of the underground parking construction on existing twin tunnels With regards to the two inclinometers installation around the 11
Tunnelling and Underground Space Technology 95 (2020) 103150
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Fig. 27. Contour of the horizontal displacements before and after the twin tunnels excavation (F-B section).
Fig. 28. Vertical displacement profile of the underground parking bottom for both scenarios (A-A line).
parking excavation. In the final step, the maximum vertical displacement increases of about 73% compared to the parking pre-excavation time. At the final excavation level (Level-3), an upward movement of the soil in the parking center can be observed and reaches 22 mm. Then, the vertical displacement's profile of the soil at the "Final" state is similar to the one of the "level-3" profile with an insignificant increase of about 2 mm (see Fig. 12). To investigate the impact of the underground parking construction above the excavated twin tunnels on the tunnel lining behavior, the 26th ring of the right tube which is located under the parking center (Y = 35 m) is selected to extract the lining displacements and induced structural forces (Fig. 10). For this purpose, the numerical modeling data before and after the parking construction are highlighted. As can be seen in Figs. 13 and 14, the axial and normal displacements in the right tunnel lining prior to the parking construction are lower than the corresponding values after the parking execution. The axial and normal displacements distribution in the tunnel lining for the "With Parking" case illustrates an upward movement of the full lining about 1 mm (see Figs. 13 & 14). This phenomenon can be attributed to the elevation of the parking floor, which has led to this soil upward displacement around the tunnels (Fig. 15). The soil vertical displacement contour (AA cross-section) due to the underground spaces excavation is presented in Fig. 15. The segmental joints position is illustrated near the horizontal axis.
tunnels and underground parking, the horizontal displacements occurring during the tunnel excavation were monitored and used to validate the numerical modeling (see Fig. 11). After tunneling, both inclinometers showed lateral displacements due to the excavation of the tunnels. By constructing the underground parking above the existing twin tunnels, an additional horizontal movement occurred named "With Parking" in Fig. 11. The maximum lateral displacement happens at the ground surface (about 7.6 mm in I_R) at the right side of the underground parking. It is worth noting that the retaining wall toes play a significant role in preventing the soil from horizontal movement in the parking bottom. A good agreement between the monitoring data and the numerical was found which permits to validate the numerical modeling in terms of horizontal movements. In order to study the effect of an underground parking construction on existing twin tunnels, the vertical displacement profile of the soil is plotted at the parking floor level (see Fig. 12, A-A line) for the "Without Parking" case and during the construction of the underground parking case. This last case is named "With Parking". The results are presented in Fig. 12. For the "Without Parking" case, the maximum soil vertical displacement at the parking bottom level is close to 10 mm and occurs above the tunnel's vertical axis. The excavation steps of the parking induce a vertical displacement upward which increases all along the
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displacements and forces induced in the 26th ring of the right tunnel lining. After the underground parking construction, the longitudinal displacement values in the upper lining part decreases compared to the "Without parking" case. This phenomenon could be related to the upward soil movements above the tunnel due to the parking excavation process. The longitudinal forces induced in the tunnel lining in Fig. 20 also confirm that the ground movements above the tunnels cause a lateral stress release after the parking construction. 5.2. Influence of the twin tunnels excavation on existing underground parking In the second scenario, the underground parking was constructed before the twin tunnels excavation. To highlight the effect of the construction sequence of these two underground structures on the ground, the soil behavior is investigated before tunneling and is compared numerically with the results after the tunnels' excavation. Fig. 21 presents the vertical ground displacement profile due to the underground parking and twin tunnels construction. Before tunneling, the ground heave is due to the parking construction, which is shown as "Without Tunnel" in Fig. 21. During the tunnel excavation, the soil around the right and left retaining walls showed an additional downward movement. It causes a ground displacement of 3.2 mm ("With Tunnel" in Fig. 21). This phenomenon could be related to the fact that the parking walls are situated in the soil's disturbance zone of the twin tunnels. Moreover, It could be seen in Fig. 21 that the happened heave due to the excavation of the underground parking slightly decreases above the two tunnels (after tunneling). This is related to the soil's downward movement in this area. In general, the twin tunnels excavation downcrossing the existing underground parking has no significant effect on the surrounding ground under the parking bottom. In Fig. 22, the horizontal displacement profile related to the right (I_R) and left (I_L) sides of the underground structures are shown for the second scenario. Based on numerical simulation results, after the parking construction, there is a constant soil lateral displacement increase of about 1 mm towards the underground structures which can be attributed to the twin tunnels excavation (see Fig. 22). It should be noted that the maximum movement happens near the ground surface. By approaching the bottom level of the underground parking, the lateral displacement is reduced and presents its lower value. For instance, for the "With Tunnel" profile for I_R, the maximum horizontal displacement at the surface is equal to 4.8 mm. It decreases to 1.4 mm at the parking bottom level and then raises to more than 3 mm at the −10 m level under the centerline of the tunnels. To further examine the tunnel digging effect down-crossing existing underground parking on the parking structure, Fig. 23 shows the position of the considered sections on the walls and floor of the parking. As can be seen in Fig. 24, the underground parking invert vertical displacement (M-M line) is presented before and after tunneling. In the "Without Tunnel" case, a heave occurs and is in the range of 19 to
Fig. 29. Horizontal displacement in Right side (I_R) of the underground spaces.
The influence of the underground parking excavation above the existing twin tunnels on the lining's axial forces is shown in Fig. 16. Prior to the parking excavation, the maximum axial forces are equal to 640 kN at the right wall of the tunnel lining. For the "With Parking" case, a significant effect of the underground parking construction on the axial forces can be seen in Fig. 16. The axial forces for the right tunnel lining show a reduction of about 37.5% compared to the "Without Parking" case (see Fig. 16). A considerable decrease in the lining axial forces is observed in the "With Parking" case. It is due to the stress release around the tunnels, which is shown in Fig. 17. The maximum stress contour related to the A-A section is provided in Fig. 17, which permits to validate the axial force reduction induced in the tunnel lining due to the underground parking excavation. Fig. 18 shows the bending moments variation induced in the right tunnel lining. Due to the underground parking impact, the maximum bending moments for the case of "With Parking" are at the tunnel crown lower of 78% than the corresponding "Without parking" ones. Figs. 19 and 20 illustrate the distribution of the longitudinal
Fig. 30. Axial force induced in the right tunnel lining for both scenarios (Ring 26). 13
Tunnelling and Underground Space Technology 95 (2020) 103150
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Fig. 31. Max. principal stress contour for both excavation scenarios (a) First, (b) Second scenario (A-A section).
Fig. 32. Horizontal displacement induced in the (a) Right, (b) Front wall of underground parking for two scenarios.
tunneling direction (Fig. 23), the front wall experienced a considerable movement of about 6 mm outward the underground parking during the tunnels' excavation. It could be attributed to the soil downward movements due to the tunneling. On the other hand, the back wall kept moving in the opposite direction of the tunnel excavation and a final horizontal displacement of 7 mm at the wall base (Fig. 26b) is observed. To better understand the movement of the front and rear walls of Fig. 26, the longitudinal cross-section (F-B section) of the horizontal displacement contour before and after the twin tunnels excavation is provided in Fig. 27. It illustrates the soil lateral deformation around the tunnel route. As can be seen in Fig. 27b, the soil behind the front wall shows a horizontal movement toward the right direction. It is due to the large displacement under the front wall. On the other side and around the back wall, tunneling causes higher soil movements toward the wall.
28.5 mm. The highest value is located at the center of the parking invert whereas by excavating the twin tunnels ("With Tunnel" status), the parking floor reaches 1.4 mm during a downward movement near the retaining walls. The parking center movement remains unchanged (see Fig. 24). The horizontal displacement values in the underground parking side walls are shown in Fig. 25. For both walls, the inward movement which increases from the walls' top to bottom happens after the parking completion ("Without Tunnel" case). This phenomenon is in accordance with the lateral stress distribution around the subterranean parking. In the "With Tunnel" profiles in Fig. 25 extracted after the tunnels excavation, the right and left walls continue to move toward the underground parking and increase from 3.7 to 4.2 mm in the walls toes. This is due to the additional displacements related to the twin tunnels excavation. The impact of excavating the twin tunnels under existing underground parking on the front and back walls that are placed perpendicular to the tunneling direction are illustrated in Fig. 26. Before the tunnels' construction, both front and rear walls have the same lateral displacement toward the parking space. It reaches respectively 2.9 and 2 mm from the bottom to the top of the walls. With regards to the
5.3. Comparison of the first and second scenarios In previous sections, the effect of the underground space's excavation sequence was studied. In this part, the results obtained from the two considered scenarios are compared to highlight the differences of each case. First, the final vertical displacement at the underground 14
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3. In the meantime, by comparing both scenarios in terms of soil behavior and structures analysis, the maximum heave in the central part of the parking is observed in the 2nd scenario. Whereas the downward movement of the soil under the walls in the second scenario is lower than the first one. Also, Performing the 2nd scenario induces lower axial forces in some parts of the tunnel lining, which is due to the smaller stress distribution around the tunnels in this state. Regarding the horizontal soil displacement around the walls of the underground parking, the side walls experience higher deformations in the first scenario, while the front and back walls move in a different direction in both scenarios due to the distinct soil behavior surrounding the underground structures. 4. Consequently, the obtained numerical results prove that performing the second scenario is preferable in terms of soil displacement and induced forces and deformations in the parking walls and tunnel linings.
parking bottom level is shown in Fig. 28. The maximum heave observed in the center part of the profile for the 1st scenario is 8 mm lower than the corresponding value for the 2nd one, while the vertical movement under the walls in the first scenario is lower of 5 mm compared to the second one. Moreover, the horizontal soil movement on the right side of the underground spaces (I_R) is investigated for both scenarios in Fig. 29. Near the ground surface, the maximum lateral displacement of the first state is equal to 7.4 mm, around 2.6 mm higher than for the 2nd scenario. By moving from the surface to the tunnels spring line, the difference between the two scenarios decreases and remains smaller than 0.5 mm at lower depths (Fig. 29). To illustrate the influence of the underground parking - twin tunnels interaction on the tunnel lining structural forces, the axial forces obtained from the 26th ring of the right tunnel for the two scenarios are shown in Fig. 30. There is a slight difference in the induced axial forces in the upper and the lower right tunnel lining part. It could be attributed to the distinct stress distribution around the tunnels for these two scenarios (see Fig. 31). The maximum principal stress distribution around the twin tunnels and underground parking are shown in Fig. 31. The horizontal displacement values induced in both right and front walls of the underground parking for the two executed cases are shown in Fig. 32. It could be seen that the right wall in the first scenario experiences more lateral displacements compared to the 2nd scenario one (Fig. 32a). It is in good accordance with the horizontal soil movements around the right side of the parking (see Fig. 29). The highest lateral displacement, of about 7.2 mm, happens on the upper part of the right wall in the first scenario. It is higher of about 58% than the second scenario one. In the front wall diagram (Fig. 32b), the horizontal displacement values in the wall are in the same range for both scenarios. Nevertheless, they are different in terms of movements direction. On the other word, the wall moves toward the underground parking in the first case, while it moves to the opposite side for the 2nd scenario (see Fig. 32b).
Further numerical analysis should be made to investigate the influence of the distance between the underground parking and tunnels and of the lagging distance between the twin tunnels. References Afifipour, M., Sharifzadeh, M., Shahriar, K., Jamshidi, H., 2011. Interaction of twin tunnels and shallow foundation at Zand underpass, Shiraz metro Iran. Tunn. Undergr. Space Technol. 26, 356–363. Cavalaro, S., Aguado, A., 2012. Packer behavior under simple and coupled stresses. Tunn. Undergr. Space Technol. 28, 159–173. Chakeri, H., Hasanpour, R., Hindistan, M.A., Ünver, B., 2011. Analysis of interaction between tunnels in soft ground by 3D numerical modeling. Bull. Eng. Geol. Environ. 70, 439–448. Dias, D., Kastner, R., 2013. Movements caused by the excavation of tunnels using face pressurized shields-analysis of monitoring and numerical modeling results. Eng. Geol. 152 (1), 17–25. Ding, W., Yue, Z., Tham, L., Zhu, H., Lee, C., Hashimoto, T., 2004. Analysis of shield tunnel. Int. J. Numer. Anal. Meth. Geomech. 28 (1), 57–91. Do, N.A., Dias, D., Oreste, P.P., Djeran-Maigre, I., 2013. 3D modelling for mechanized tunneling in soft ground-Inflence of the constitutive model. Am. J. Appl. Sci. 10 (8), 863–875. Do, N.A., Dias, D., Oreste, P., 2015. 3D numerical investigation on the interaction between mechanized twin tunnels in soft ground. Environ. Earth Sci. 73 (5), 2101–2113. Do, N.A., Dias, D., Oreste, P., 2016. 3D numerical investigation of mechanized twin tunnels in soft ground–Influence of lagging distance between two tunnel faces. Eng. Struct. 109, 117–125. Do, N.A., Dias, D., Oreste, P., Djeran-Maigre, I., 2014. Three-dimensional numerical simulation of a mechanized twin tunnels in soft ground. Tunn. Undergr. Space Technol. 42, 40–51. Fang, Q., Zhang, D., Li, Q., Wong, L.N.Y., 2015. Effects of twin tunnels construction beneath existing shield-driven twin tunnels. Tunn. Undergr. Space Technol. 45, 128–137. Farashar Asia Consulting Engineer, 2010. Geotechnical report of Amirkabir ring road project - Edalat overpass. Fater Construction Company, 2016. TBM1 monitoring report from 3+000 km to 4+000 km of Shiraz subway line 2. Hasanpour, R., 2014. Advance numerical simulation of tunneling by using a double shield TBM. Comput. Geotech. 57, 37–52. Hasanpour, R., Chakeri, H., Ozcelik, Y., Denek, H., 2012. Evaluation of surface settlements in the Istanbul metro in terms of analytical, numerical and direct measurements. Bull. Eng. Geol. Environ. 71, 499–510. Huang, D.-Z., Ma, X.F., Wang, J.S., Li, X.Y., Yu, L., 2012. Centrifuge modelling of effects of shield tunnels on existing tunnels in soft clay. Chinese J. Geotech. Eng. 34 (3), 520–527 (in Chinese). Itasca Group, 2012. FLAC fast Lagrangian analysis of continua, User’s manual (Version 5.0). Kankavan Consulting Engineers, 2013. Field and Laboratory tests Report of Shiraz Metro Line2. Kasper, T., Meschke, G., 2004. A 3D finite element simulation model for TBM tunnelling in soft ground. Int. J. Numer. Anal. Meth. Geomech. 28 (14), 1441–1460. Kasper, T., Meschke, G., 2006. A numerical study of the effect of soil and grout material properties and cover depth in shield tunneling. Comput. Geotech. 33 (4–5), 234–247. Li, X., Du, S., Zhang, D., 2010. Numerical simulation of the interaction between two parallel shield tunnels. In: Proceeding of ICPTT 2012: Better Pipeline Infrastructure for a Better, Life, pp. 1521–1533. Li, X.G., Yuan, D.J., 2012. Responses of a double-decked metro tunnel to shield driving of twin closely under-crossing tunnels. Tunn. Undergr. Space Technol. 28, 18–30. Liu, H.Y., Small, J.C., Carter, J.P., Williams, D.J., 2009. Effects of tunneling on existing support systems of perpendicularly crossing tunnels. Comput. Geotech. 36 (5), 880–894.
6. Conclusions This study illustrates a fully three-dimensional numerical model of mechanized tunneling provided by a finite difference code. It highlights underground parking-soil-twin tunnels interaction. In order to investigate the interaction of the tunnel-underground parking on each other, two scenarios were discussed. About the results of the numerical analysis, the following conclusions can be drawn: 1. In the scenario of constructing the underground parking above the existing twin tunnels, the numerical simulation results illustrate the increase in horizontal displacements behind the retaining walls by constructing the parking which is due to the inward movement of walls. Also, the underground parking installation caused considerable heave in the parking bottom and downward movement under the walls. On the other hand, building subterranean parking induces the upward movement of the tunnel lining, while it causes a reduction in axial forces and bending moments induced in the tunnel lining, 2. In the case of twin tunnels excavation under the underground parking, it can be observed that the tunneling has a slight effect on the central heave of parking bottom but causes considerable downward subsidence under the retaining walls which are attributed to the downward displacement of the soil above the tunnels. Moreover, crossing the twin tunnels under the underground parking brings additional downward displacement beneath the parking level that causes an increase in inward movement of the soils behind the walls. About the front and back walls, tunneling direction makes a significant lateral displacement in soils around the parking walls inclined to the tunnel advancement which leads to the walls' permanent deformation, 15
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modeling of the interaction between perpendicularly crossing tunnels. Can. Geotech. J. 50 (9), 935–946. Pakbaz, M.S., Imanzadeh, S., Bagherinia, K.H., 2013. Characteristics of diaphragm wall lateral deformations and ground surface settlements: case study in Iran-Ahwaz metro. Tunn. Undergr. Space Technol. 35, 109–121. Phienwej, N., Hong, C.P., Sirivachiraporn, A., 2006. Evaluation of ground movements in EPB-shield tunnelling for Bangkok MRT by 3D-numerical analysis. Tunn. Undergr. Space Technol. 21 (3–4), 273. Rodriguez, L.E.M., 2000. Estudio de los movimientos originados por la excavación de túneles con escudos de presión de tierras en lossue los tosquizos de Madrid. PhD Thesis. University of La Coruña, spain. Sharma, J.S., Hefny, A.M., Zhao, J., Chan, C.W., 2001. Effect of large excavation on deformation of adjacent MRT tunnels. Tunn. Undergr. Space Technol. 16 (2), 93–98. Thienert, C., Pulsfort, M., 2011. Segment design under consideration of the material used to fill the annular gap. Geomechanics Tunneling 4, 665–680. Tose-e Consulting Engineers, 2014. Geotechnical engineering services report of Shiraz Metro Line 2. Zhang, J.F., Chen, J.J., Wang, J.H., Zhu, Y.F., 2013. Prediction of tunnel displacement induced by adjacent excavation in soft soil. Tunn. Undergr. Space Technol. 36, 24–33.
Mahmutoğlu, Y., 2011. Surface subsidence induced by twin subway tunneling in soft ground conditions in Istanbul. Bull. Eng. Geol. Environ. 70, 115–131. Mollon, G. 2010. Etude déterministe probabiliste du comportement des tunnels. Lyon, France. Mollon, G., Dias, D., Soubra, A.-H., 2013. Probabilistic analyses of tunneling-induced ground movements. Acta Geotech. 8 (2), 181–199. Nematollahi, M., Dias, D., 2019. Three-dimensional numerical simulation of pile-twin tunnels interaction–Case of the Shiraz subway line. Tunn. Undergr. Space Technol. 86, 75–88. Nematollahi, M., Molladavoodi, H., Dias, D., 2018. Three-dimensional numerical simulation of the Shiraz subway second line-influence of the segmental joints geometry and of the lagging distance between twin tunnels’ faces. Eur. J. Environ. Civil Eng. 1–17. https://doi.org/10.1080/19648189.2018.1476270. Ng, C.W.W., Fong, K.Y., Liu, H.L., 2018. The effects of existing horseshoe-shaped tunnel sizes on circular crossing tunnel interactions: three-dimensional numerical analyses. Tunn. Undergr. Space Technol. 77, 68–79. Ng, C.W.W., Lee, K.M., Tang, D.K.W., 2004. Three-dimensional numerical investigations of new Austrian tunneling method (NATM) twin tunnel interactions. Can. Geotech. J. 41, 523–539. Ng, C.W.W., Boonyarak, T., Mašín, D., 2013. Three-dimensional centrifuge and numerical
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Interaction between an underground parking and twin tunnels – Case of the Shiraz subway line Mojtaba Nematollahia, Daniel Diasb,c,
T
⁎
a
Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, China c Antea Group, Antony, France b
A R T I C LE I N FO
A B S T R A C T
Keywords: Three-dimensional simulation Soil-structure interaction Segmental lining Shielded Mechanized tunneling Shiraz metro line 2 CYsoil model
Three-dimensional numerical analyses were developed to study the interaction between twin tunnels and underground parking in an urban area. The mechanized tunneling procedure and segmental lining were accurately simulated using a finite difference code and a nonlinear perfectly plastic constitutive model (CYsoil). In this paper, the interaction between tunneling in clay and an underground parking was performed using two scenarios: construction of the underground parking above the existing tunnels and excavating the twin tunnels under the existing parking. The soil/structure interaction is investigated in terms of soil movements, structural forces induced in the tunnel lining and displacements of the parking structure. On the base of the numerical results, the construction sequence of underground structures, which are located nearby to each other, have a considerable effect on the soil and structures behavior.
1. Introduction Shiraz, the cultural capital city of Iran, has a high need for an extensive subway network and transportation infrastructure to avoid urban congestion. The excavation of new underground space changes the soil stress distribution and then causes ground movements. Sometimes, two different underground structures (parking or tunnel for example) have to pass closely. It can induce a considerable effect on the nearby existing underground structures. In this case, it is necessary to investigate the soil-structure interaction effect and to ensure the safety of both underground structures at a long time. Many researchers (Afifipour et al., 2011; Do et al., 2014, 2016; Hasanpour et al., 2012; Li et al., 2010; Mahmutoğlu, 2011; Ng et al., 2004, Nematollahi et al., 2018) have conducted researches to highlight the influence of a new tunnel excavation on an existing one. They found that the tunnels spacing has a significant impact on the ground movements and induced structural forces. Also, some studies have focused on the influence of excavating a crossing tunnel on an existing tunnel like (Liu et al., 2009; Chakeri et al., 2011; Li and Yuan, 2012; Ng et al., 2013; Fang et al., 2015; Ng et al., 2018). All of them showed that the excavation of a new tunnel would induce more displacements in the soil surrounding the previous tunnel as well as surface settlements. Huang et al. (2012) and Li et al. (2014) performed a series of centrifuge tests to study the effect of the tunnel excavation above two
⁎
existing metro tunnels. The upheaval of the existing tunnel was observed, and it was reported that the back-fill grouting has a significant influence on the heave reduction. Sharma et al. (2001) investigate the impact of a large excavation close to tunnels using field monitoring data and the finite element method. They found that twin tunnels can bear the deformations and displacements due to the soil stress release. The tunnel lining stiffness has a considerable impact on the tunnel's displacements and distortions. Zhang et al., 2013 used a semi-analytical method to assess the heave of the underlying tunnel close to a deep excavation by field measurements. The interaction between the tunnel and the excavation was studied to highlight the effect of different factors like the excavation area, relative clearance and construction procedure. The results showed that the tunnel displacements increase with increasing the area ratio (defined as R = B/D where B is the excavation's width and D the tunnel's diameter) and decrease quickly with increasing the relative distance (defined as d, the horizontal distance between the excavation center and the cross-sectional center of the tunnel). Nevertheless, no research has considered the interaction effect between a tunnel and an underground parking. This paper provides a thorough numerical analysis related to the interaction of twin tunnels and an underground parking which is of major interest in urban areas. The second line of Shiraz subway project meets the underground parking in Azadi Park and is considered as the case study in this paper.
Corresponding author at: School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, China. E-mail address: [email protected] (D. Dias).
https://doi.org/10.1016/j.tust.2019.103150 Received 9 March 2019; Received in revised form 25 August 2019; Accepted 14 October 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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Using a full 3D numerical model with a nonlinear strain hardening perfectly plastic constitutive model (Cap-Yield model named CYsoil) to model the soil behavior, a study is presented to specify the potential hazards in the construction procedures. The main excavation using an EPB-TBM (Earth Pressure Balance–Tunnel Boring Machine) are performed within a three-dimensional numerical model to simulate the conical shield, TBM selfweight and its trailer, face pressure, jacking force, tail void grouting and its consolidation. Furthermore, the concrete segmental lining of the tunnels was modeled using structural element, named liner which is qualified to model the segmental lining as well as longitudinal (segment) and circumferential (ring) joints (Do et al., 2013). This paper aims to propose to evaluate the interaction between twin tunnels and underground parking. For this purpose, two different scenarios are studied. In the first one, the twin tunnels are excavated before the parking setup. In the second scenario, the twin tunnels are excavated after the parking. Full three-dimensional numerical models considering the soil/structure interaction are developed to highlight the impact of these two scenarios. The results of both scenarios are presented and discussed. The construction of the parking causes a heave of the parking bottom level, while tunneling causes a downward movement above the twin tunnels.
Table 1 Lining parameters corresponding to the Shiraz metro line 2 (Tose-e, 2014). Parameter
Value
Young's modulus (GPa) Poisson's ratio Concrete lining density (kg/m3) Lining thickness (m) External diameter (m) Length of the lining ring (m)
31.2 0.22 2647 0.3 6.88 1.4
Table 2 Underground parking structure characteristics (Tose-e, 2014). Parameter
Value
Elastic modulus (GPa) Poisson's ratio Concrete density (kg/m3) Wall thickness (m) Wall height (m) Raft Thickness (m) Column height (m) Column section (m × m)
30 0.2 2650 0.5 10 0.4 2.8 0.5 × 0.5
2. Study case of the second line of the Shiraz subway
3. Constitutive model
In 2014, two EPB-TBMs started to excavate the twin tunnels of the Shiraz subway line 2, from the Southern station, Shekoofeh, to the Kolbehsa'di station in the North of the city consists of two tunnel tubes of 6.88 m diameter and 15 km long. A total of 13 underground stations were also part of this project. The tunnels pass mainly through marly lean clays with gypsum and the main tunnel length is in saturated clays (Tose-e, 2014). In the middle of this route, the twin tunnels underpass an underground parking in the Azadi park. A typical view of the transverse section where the twin tunnels and the underground parking are located is presented in Fig. 1. In this project, every lining ring consists of 6 segments, four trapezoidal and two parallelograms. They have different sizes, and the smaller one is called the key segment. Furthermore, the prefabricated segments made of reinforced concrete has a 1.4 m length and 30 cm thickness. The underground parking comprises four diaphragm walls and is a three-storey structure with a 30 m length in the Y direction (perpendicular to Fig. 1) and 26 m width. Two inclinometers (I_L and I_R) where setup near the parking walls and are shown in Fig. 1. The segmental lining and underground parking properties of this project are respectively provided in Tables 1 and 2.
The Cap-Yield (CYsoil) model is a strain-hardening constitutive model that provides a general description of the nonlinearity of soils. This constitutive model permits to consider the loading/unloading response of soils (Itasca Group, 2012). The input parameters corresponding to CYsoil model for Shiraz subway are summarized in Table 3 from geotechnical investigations (on-site and laboratory). They were presented in the work of Nematollahi and Dias (2019). The deviatoric stress-axial strain diagrams obtained from experimental data of Consolidated Drained (CD) tests are considered to back analyze the input parameters for soils. These data are obtained from Kankavan (2013). Three confining pressures 50, 100 and 150 kPa were considered during the triaxial tests for both clay soils. Only the case of the marly lean clay soil is presented in Fig. 2. To confirm the considered initial values, numerical simulations of these triaxial compression tests are done firstly using Flac3D using the CYsoil constitutive model. Then a comparison with the obtained data from the experimental triaxial tests has permitted the parameters to be back analyzed. It can be seen in Fig. 2 that for the lower confining pressure (50 kPa), the numerical and experimental diagrams are in good accordance with each other.
Table 3 Soil layer's parameters corresponding to the CYsoil constitutive model (Nematollahi and Dias, 2019).
Fig. 1. Cross section view of the problem. 2
CYsoil Model
Clay
Saturated clay
Marly lean clay
Young modulus E (MPa) Poisson's ratio ν Angle of internal friction ϕ (degree) Dilation angle ψ (degree) Cohesion C (kPa) Bulk modulus (reference) (MPa) Shear modulus (reference) (MPa) Calibration factor β Failure ratio Rf Reference effective pressure Pa (kPa) Earth pressure coefficient K0 Density (kg/m3)
78.75 0.35 28.7 0 11 87.5 29.17 1 0.9 100 0.5 1670
71.06 0.35 25.8 0 5 78.96 26.32 1 0.9 100 0.5 2042
173.73 0.35 29.6 0 17 193.03 64.34 1 0.9 100 0.5 2058
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Fig. 2. Deviatoric stress vs axial strain curves with loading–unloading phases.
Fig. 3. The schematic view of the generated model −2nd line of Shiraz subway.
4. Three-dimensional numerical model
Where H is depth of the tunnel center and D is the excavation diameter of the tunnel. A parametric study was done to be sure that no boundary effects are present due to the parking dimensions. The considered model size is enough to avoid them in this case study. A full three-dimensional layout of the underground parking and the twin tunnels of the second line of the Shiraz metro with a height of 50 m, width of 116 m, and length of 70 m was developed using Flac3D. It should be noted that this model consists of around 914,100 zones and 971,750 grid points. A perspective view of the numerical model is shown in Fig. 3. All the nodes on the bottom model are blocked in the vertical direction, whereas the model sides boundaries were restricted in their normal directions. As can be seen in Fig. 3, the grid density decreases by getting away from the underground structures to the model boundaries, which is quite effective to increase the calculations speed and accuracy.
4.1. Geometry, boundary and initial conditions In this study, numerical simulations were executed through a finite difference program, Flac3D, which permits to do three-dimensional analysis and consider non-linear soil-structure interaction problems. To avoid boundary effects in numerical simulations, the model boundaries were set at an optimal distance from the subterranean structures. For this purpose, the model dimensions were assumed larger than the proposed values by Rodriguez (2000).
• (H + 4D), for the model height, • (H + 3D), for the model length, • 3H, for the model width (for half of the model). 3
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Fig. 4. 3D layout of the mechanized tunneling process in second line of Shiraz subway. Table 4 Mechanical parameters of the modeled shield of Shiraz metro line 2 (Nematollahi and Dias, 2019). Parameter
Elastic modulus (MPa) Poisson's ratio Shield Thickness (mm) Shield Density (kg/m3)
Front Shield
Middle Shield
Rear Shield
P1
P2
P3
P4
P5
P6
20 0.15 50 7800
200 0.15 50 7800
2e3 0.15 50 7800
2e4 0.15 50 7800
2e5 0.15 50 7800
2e5 0.15 50 7800
(Farashar, 2010). This is due to permeabilities which are higher than 10−5 m/s in all the layers. Therefore, the evolution of pore pressures with time is not considered in the numerical calculations. Fig. 5. Schematic vision of the proposed conical shield in the numerical model.
4.2. Numerical simulation of the shielded mechanized tunneling phases
Furthermore, the mesh density around the underground parking walls is increased locally. All the models are run in drained conditions, because of the rapid dispersion of the observed in situ pore pressures
Mechanized tunneling is a successive procedure of excavation and simultaneous installation of the lining segments. In order to simulate an
Fig. 6. Tunnel crown vertical displacement versus the distance to the tunnel face (Nematollahi and Dias, 2019). 4
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Fig. 7. Springs of the joints; (a) segment's joint, (b) ring's joint.
Table 5 Parameters of the lining joints (Nematollahi et al., 2018). Parameter
Value
Axial Stiffness Kaxi and KRaxi (MN/m) Radial Stiffness Krad and KRrad (MN/m) Rotational Stiffness Krot and KRrot (MN m/rad/m) Maximum bending moment at segment joint Myield (kN.m/m)
550 3960 80 115
Fig. 10. Schematic view of the twin tunnels and underground parking.
EPB-TBM tunneling process accurately, various elements must be taken into consideration. In this study, the TBM advancement in the ground is simulated considering the components and actions that could happen in real tunneling. The simulation of the mechanized tunneling components for the Shiraz subway line 2 is summarized below. A schematic view of the EPB-TBM tunneling is provided in Fig. 4. In this paper, the face pressure is simulated by exerting horizontal stress with a trapezoidal distribution at the tunnel face (Kasper and Meschke, 2004, 2006; Do et al., 2014, 2015). The mean value of the face pressure, exerted at the tunnel center, is set equal to 0.15 MPa with a vertical gradient due to the slurry weight (1494 kg/m3) which is given by the monitoring data. The trapezoidal distribution of applied face pressure is presented in Fig. 4. In this study, to model the conical shape of the shield, a simplified method is utilized by using shell elements. This method has already used by the same authors (Nematollahi and Dias, 2019). In this method, the shield consists of smaller parts with length equal to the advance step, 1.4 m, and each section has a different stiffness. Thus, six pieces with a total length of 8.4 m make the taper shield. The schematic configuration of the proposed shield is shown in Figs. 4 and 5. Without shield elements, the vertical displacement of the tunnel crown during the TBM progress can reach 30 cm, as can be seen in Fig. 6. Whereas, in the real project, the gap between the tunnel boundary and the shield's outer surface in the middle part is equal to
Fig. 8. Lining pattern: (a) Common pattern (b) Oblique joints (Used in this work) (Nematollahi et al., 2018).
Fig. 9. Design steps of the underground parking construction.
Table 6 Parameters of the diaphragm wall - soil interface. Parameter
Retaining wall - Clay
Diaphragm wall – Saturated clay
Diaphragm wall – Marly lean clay
Normal Stiffness Kn (MN/m) Shear Stiffness Ks (MN/m) Friction Angle (degree) Cohesion (kPa)
5.06e4 5.06e4 19.1 0
4.56e4 4.56e4 17.2 0
1.12e5 1.12e5 19.7 0
5
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Fig. 11. The horizontal displacement profile in (a) Right side (I_R), (b) Left side (I_L) of the tunnels.
Fig. 12. The vertical displacement of the parking bottom (A-A profile).
Fig. 13. Axial displacements induced in the right tunnel lining (Ring 26).
6
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Fig. 14. Normal displacements induced in the right tunnel lining (Ring 26).
Fig. 15. Contour of vertical displacement before and after the underground parking excavation (A-A section).
Fig. 16. Axial force induced in the right tunnel lining (Ring 26).
Fig. 17. Contour of the Max. principal stress before and after the underground parking excavation (A-A section).
7
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Fig. 18. Bending moment induced in the right tunnel lining (Ring 26).
Fig. 19. Longitudinal displacement induced in the right tunnel lining (Ring 26).
Fig. 20. Longitudinal force induced in the right tunnel lining (Ring 26).
vertical gradient due to the grout weight is applied to a thin layer in the existing gap between the lining and the ground. Zone elements which permit to highlight the interaction of the grout-lining and grout-soil interface are presented in Fig. 4. The average grout injection pressure applied at the tunnel center level is set equal to 238 kPa, which is obtained from the monitoring sensors located on the grouting nozzles (Fater, 2016). A hard grout is simulated by a linear elastic model in the prior works of Mollon (2010), Mollon et al. (2013), Phienwej et al. (2006), Dias and Kastner (2013). To simplify the transition from fresh to hard grout, the physical characteristics of the consolidated grout (i.e., Ecg = 173.73 MPa and νcg = 0.22 where Ecg is Young's modulus and νcg is the Poisson's ratio of the consolidated grout) is assigned to the fresh grout zones after two excavation steps. On average, every excavation step takes more less 1.5 h. Based on the experiments performed on the grout, its properties after 3 h (two excavation steps) can be assumed the ones of the hardened grout. The fresh and hard grout are shown in Fig. 4.
7.5 cm. Nematollahi and Dias (2019) suggest using the following method to simulate a conical shield. The Young's modulus of the front shield (P1) should be lower than the elastic modulus of the tunnel surrounding soil. Then the Young's modulus of the other parts rises gradually. In Table 4, the assigned parameters according to the shield portions of this project are shown. By using this method, the tunnel crown movement is controlled from the middle shield (P3), which illustrates the capability of the proposed approach to numerically simulate a conical shield (Fig. 6). By thrust jacks, a force is applied on the last installed ring. It permits then to the TBM to go ahead. To simulate the jacking forces, all the nodes in the end section of the segment are exposed to the concentrated forces (Fig. 4). Furthermore, the average value of the real forces is defined from the monitoring data and taken equal to 7.1 MN (Fater, 2016). The tail void grout injection and its hardening process is a significant parameter in mechanized tunneling simulations. Like the method used by Nematollahi et al. (2018), a normal pressure with a 8
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Fig. 21. Vertical displacement of the underground parking bottom (A-A profile).
Fig. 22. Horizontal displacement in (a) Right side (I1), (b) Left side (I2) of the twin tunnels.
A downward load distribution acting on the tunnel floor over the shield length with a direction of 90 degrees is considered to simulate the TBM's self-weight (Do et al., 2014; Hasanpour, 2014; Nematollahi et al., 2018). In this work, the Shiraz TBM weight is equal to 3846 kN (Fater, 2016). Despite of the work done by Do et al. (2014), where the back-up train weight is modeled by exerting downward forces on the bottom sector of the tunnel lining over the train length, the trailer weight modeling is developed by applying vertical forces on two parallel lines with a transverse distance of 3 m in the lining invert in this project (Nematollahi et al., 2018; Nematollahi and Dias, 2019). The TBM and back-up weight simulation is presented in Fig. 4.
introduced a tunnel lining model using a structural element, named liner, that is qualified to simulate the segments and joints directly. The liner element is a proper choice for generating a node to node and a node to zone link to model segment-segment and grout-segment interactions respectively because it provides two links for each node. Furthermore, the influence of the grout-lining interaction has been considered using the normal spring stiffness (Kn) and the shear spring stiffness (Ks), respectively. Kn and Ks are calculated about one hundred times the stiffness of the attached zone (Itasca Group, 2012). The apparent stiffness of an attached zone is computed as the maximum value
⎡ (K + G ) ⎤ of ⎢ ΔZ 3 ⎥ relation where K and G are the bulk and shear moduli min ⎣ ⎦ respectively. ΔZmin is the shortest normal distance of the grout attached zone. A node to node link with six degrees of freedom that are indicated by six springs is provided to simulate the segmental joint. For a segmental joint, three springs should be taken into accounts such as an 4
4.3. Segmental lining The simulation method of the segmental lining and the joints is crucial in mechanized tunneling models. Do et al. (2013) has 9
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and Dias, 2019), an oblique geometry was developed to model the segmental joints which is in good agreement with the real condition and is used in the present model (see Fig. 8b). However, Ding et al. (2004), Do et al. (2013), Do et al. (2014), Do et al. (2015), Do et al. (2016), assumed the segmental joints parallel to the tunnel axis (see Fig. 8a). A 3D layout of both kinds of lining patterns is illustrated in Fig. 8. 4.4. Numerical simulation of the underground parking For the underground parking, a diaphragm wall (D-wall) was chosen due to the water table level. A 0.5 m thickness diaphragm wall is used for the excavation down to 10 m below the ground surface. The excavation is performed while the trench is filled with a bentonite slurry (fluid support) to provide lateral stability to the trench walls. Then, the diaphragm walls are created by placing the rebar cage and pouring concrete into the excavated trench (Pakbaz et al., 2013). The design steps of the underground parking in the numerical modeling are the following ones which are shown in Fig. 9: 1. Diaphragm walls construction considering a bentonite slurry volumic weight of 12 kN/m3, 2. Setting up the first roof, 3. Excavation of the first level (Level-1) to the depth of 3.6 m, 4. Setting up the second roof, 5. Installation of columns for the first level, 6. Repeat the top five stages to the 3rd level (Level-3) down to the final depth of 10 m. Fig. 23. A schematic view of the considered profiles on underground parking's structure.
In this study, the D-wall is simulated by liner elements which behave as a linear elastic material. The liner element integrates an interface that allows gaps to form and slip to happen (Itasca Group, 2012). The normal and shear springs stiffness related to the interface between the retaining wall and the soil are calculated as in Section 4.3 and are given in Table 6.
axial spring (Kaxi), a radial spring (Krad) and a rotational spring (Krot) (Fig. 7a). The axial spring has a linear behavior which is represented by a constant coefficient; While both radial and rotational springs' stiffness are determined by the stiffness modulus and yield limit parameters (Cavalaro and Aguado, 2012). In this project, no packer in the joints of the concrete segments is considered, so a linear behavior is supposed for the radial springs. Besides, all the other springs are set to be rigid. In order to determine the stiffness of the springs, Thienert and Pulsfort (2011) and Do et al. (2013) developed a simplified way which is employed in this study. The circumferential joints (joints between two successive rings) are modeled like the segmental joints with three springs (axial spring (KRaxi), radial spring (KRrad) and rotational spring (KRrot)) with the same stiffness coefficients similar to the segmental joints as shown in Fig. 7b. The parameters of the segmental and ring joints are shown in Table 5. In work by the same authors (Nematollahi et al., 2018; Nematollahi
4.5. Soil/structure interaction: Underground parking construction To investigate the effect of the excavation of two subterranean tunnels in a close distance in urban environments, the following scenarios for a twin tunnel and underground parking are considered: 1) Twin tunnels excavation before the underground parking construction, 2) Twin tunnels excavation after the underground parking construction.
Fig. 24. Vertical displacement of the underground parking invert (M-M profile). 10
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Fig. 25. Horizontal displacement induced in the (a) left, (b) right wall of underground parking.
Fig. 26. Horizontal displacement induced in the (a) Front, (b) back wall of underground parking.
5. Numerical results and discussion
In both scenarios, the twin tunnels excavation is simulated simultaneously to ensure that the effect of the lagging distance between the two tunnels faces around the tunnels is not considered (Nematollahi et al., 2018). In the first scenario, the excavation of the twin tunnels is performed before the construction of the underground parking. It is necessary to mention that this scenario shows the actual status in the Shiraz subway which will be done in the future. Whereas in the second scenario, the twin tunnels excavation is completed after the parking construction. A 3D view of the twin tunnels and underground parking as well as the two inclinometers position are presented in Fig. 10.
In this chapter, the obtained results from the first scenario are presented first. It permits to relate the excavation steps impact of threefloor underground parking on the existing twin tunnels. Then, the results of the second scenario, are considered to highlight the influence of the twin tunnel's excavation on the existing underground parking. 5.1. Influence of the underground parking construction on existing twin tunnels With regards to the two inclinometers installation around the 11
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Fig. 27. Contour of the horizontal displacements before and after the twin tunnels excavation (F-B section).
Fig. 28. Vertical displacement profile of the underground parking bottom for both scenarios (A-A line).
parking excavation. In the final step, the maximum vertical displacement increases of about 73% compared to the parking pre-excavation time. At the final excavation level (Level-3), an upward movement of the soil in the parking center can be observed and reaches 22 mm. Then, the vertical displacement's profile of the soil at the "Final" state is similar to the one of the "level-3" profile with an insignificant increase of about 2 mm (see Fig. 12). To investigate the impact of the underground parking construction above the excavated twin tunnels on the tunnel lining behavior, the 26th ring of the right tube which is located under the parking center (Y = 35 m) is selected to extract the lining displacements and induced structural forces (Fig. 10). For this purpose, the numerical modeling data before and after the parking construction are highlighted. As can be seen in Figs. 13 and 14, the axial and normal displacements in the right tunnel lining prior to the parking construction are lower than the corresponding values after the parking execution. The axial and normal displacements distribution in the tunnel lining for the "With Parking" case illustrates an upward movement of the full lining about 1 mm (see Figs. 13 & 14). This phenomenon can be attributed to the elevation of the parking floor, which has led to this soil upward displacement around the tunnels (Fig. 15). The soil vertical displacement contour (AA cross-section) due to the underground spaces excavation is presented in Fig. 15. The segmental joints position is illustrated near the horizontal axis.
tunnels and underground parking, the horizontal displacements occurring during the tunnel excavation were monitored and used to validate the numerical modeling (see Fig. 11). After tunneling, both inclinometers showed lateral displacements due to the excavation of the tunnels. By constructing the underground parking above the existing twin tunnels, an additional horizontal movement occurred named "With Parking" in Fig. 11. The maximum lateral displacement happens at the ground surface (about 7.6 mm in I_R) at the right side of the underground parking. It is worth noting that the retaining wall toes play a significant role in preventing the soil from horizontal movement in the parking bottom. A good agreement between the monitoring data and the numerical was found which permits to validate the numerical modeling in terms of horizontal movements. In order to study the effect of an underground parking construction on existing twin tunnels, the vertical displacement profile of the soil is plotted at the parking floor level (see Fig. 12, A-A line) for the "Without Parking" case and during the construction of the underground parking case. This last case is named "With Parking". The results are presented in Fig. 12. For the "Without Parking" case, the maximum soil vertical displacement at the parking bottom level is close to 10 mm and occurs above the tunnel's vertical axis. The excavation steps of the parking induce a vertical displacement upward which increases all along the
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displacements and forces induced in the 26th ring of the right tunnel lining. After the underground parking construction, the longitudinal displacement values in the upper lining part decreases compared to the "Without parking" case. This phenomenon could be related to the upward soil movements above the tunnel due to the parking excavation process. The longitudinal forces induced in the tunnel lining in Fig. 20 also confirm that the ground movements above the tunnels cause a lateral stress release after the parking construction. 5.2. Influence of the twin tunnels excavation on existing underground parking In the second scenario, the underground parking was constructed before the twin tunnels excavation. To highlight the effect of the construction sequence of these two underground structures on the ground, the soil behavior is investigated before tunneling and is compared numerically with the results after the tunnels' excavation. Fig. 21 presents the vertical ground displacement profile due to the underground parking and twin tunnels construction. Before tunneling, the ground heave is due to the parking construction, which is shown as "Without Tunnel" in Fig. 21. During the tunnel excavation, the soil around the right and left retaining walls showed an additional downward movement. It causes a ground displacement of 3.2 mm ("With Tunnel" in Fig. 21). This phenomenon could be related to the fact that the parking walls are situated in the soil's disturbance zone of the twin tunnels. Moreover, It could be seen in Fig. 21 that the happened heave due to the excavation of the underground parking slightly decreases above the two tunnels (after tunneling). This is related to the soil's downward movement in this area. In general, the twin tunnels excavation downcrossing the existing underground parking has no significant effect on the surrounding ground under the parking bottom. In Fig. 22, the horizontal displacement profile related to the right (I_R) and left (I_L) sides of the underground structures are shown for the second scenario. Based on numerical simulation results, after the parking construction, there is a constant soil lateral displacement increase of about 1 mm towards the underground structures which can be attributed to the twin tunnels excavation (see Fig. 22). It should be noted that the maximum movement happens near the ground surface. By approaching the bottom level of the underground parking, the lateral displacement is reduced and presents its lower value. For instance, for the "With Tunnel" profile for I_R, the maximum horizontal displacement at the surface is equal to 4.8 mm. It decreases to 1.4 mm at the parking bottom level and then raises to more than 3 mm at the −10 m level under the centerline of the tunnels. To further examine the tunnel digging effect down-crossing existing underground parking on the parking structure, Fig. 23 shows the position of the considered sections on the walls and floor of the parking. As can be seen in Fig. 24, the underground parking invert vertical displacement (M-M line) is presented before and after tunneling. In the "Without Tunnel" case, a heave occurs and is in the range of 19 to
Fig. 29. Horizontal displacement in Right side (I_R) of the underground spaces.
The influence of the underground parking excavation above the existing twin tunnels on the lining's axial forces is shown in Fig. 16. Prior to the parking excavation, the maximum axial forces are equal to 640 kN at the right wall of the tunnel lining. For the "With Parking" case, a significant effect of the underground parking construction on the axial forces can be seen in Fig. 16. The axial forces for the right tunnel lining show a reduction of about 37.5% compared to the "Without Parking" case (see Fig. 16). A considerable decrease in the lining axial forces is observed in the "With Parking" case. It is due to the stress release around the tunnels, which is shown in Fig. 17. The maximum stress contour related to the A-A section is provided in Fig. 17, which permits to validate the axial force reduction induced in the tunnel lining due to the underground parking excavation. Fig. 18 shows the bending moments variation induced in the right tunnel lining. Due to the underground parking impact, the maximum bending moments for the case of "With Parking" are at the tunnel crown lower of 78% than the corresponding "Without parking" ones. Figs. 19 and 20 illustrate the distribution of the longitudinal
Fig. 30. Axial force induced in the right tunnel lining for both scenarios (Ring 26). 13
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Fig. 31. Max. principal stress contour for both excavation scenarios (a) First, (b) Second scenario (A-A section).
Fig. 32. Horizontal displacement induced in the (a) Right, (b) Front wall of underground parking for two scenarios.
tunneling direction (Fig. 23), the front wall experienced a considerable movement of about 6 mm outward the underground parking during the tunnels' excavation. It could be attributed to the soil downward movements due to the tunneling. On the other hand, the back wall kept moving in the opposite direction of the tunnel excavation and a final horizontal displacement of 7 mm at the wall base (Fig. 26b) is observed. To better understand the movement of the front and rear walls of Fig. 26, the longitudinal cross-section (F-B section) of the horizontal displacement contour before and after the twin tunnels excavation is provided in Fig. 27. It illustrates the soil lateral deformation around the tunnel route. As can be seen in Fig. 27b, the soil behind the front wall shows a horizontal movement toward the right direction. It is due to the large displacement under the front wall. On the other side and around the back wall, tunneling causes higher soil movements toward the wall.
28.5 mm. The highest value is located at the center of the parking invert whereas by excavating the twin tunnels ("With Tunnel" status), the parking floor reaches 1.4 mm during a downward movement near the retaining walls. The parking center movement remains unchanged (see Fig. 24). The horizontal displacement values in the underground parking side walls are shown in Fig. 25. For both walls, the inward movement which increases from the walls' top to bottom happens after the parking completion ("Without Tunnel" case). This phenomenon is in accordance with the lateral stress distribution around the subterranean parking. In the "With Tunnel" profiles in Fig. 25 extracted after the tunnels excavation, the right and left walls continue to move toward the underground parking and increase from 3.7 to 4.2 mm in the walls toes. This is due to the additional displacements related to the twin tunnels excavation. The impact of excavating the twin tunnels under existing underground parking on the front and back walls that are placed perpendicular to the tunneling direction are illustrated in Fig. 26. Before the tunnels' construction, both front and rear walls have the same lateral displacement toward the parking space. It reaches respectively 2.9 and 2 mm from the bottom to the top of the walls. With regards to the
5.3. Comparison of the first and second scenarios In previous sections, the effect of the underground space's excavation sequence was studied. In this part, the results obtained from the two considered scenarios are compared to highlight the differences of each case. First, the final vertical displacement at the underground 14
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3. In the meantime, by comparing both scenarios in terms of soil behavior and structures analysis, the maximum heave in the central part of the parking is observed in the 2nd scenario. Whereas the downward movement of the soil under the walls in the second scenario is lower than the first one. Also, Performing the 2nd scenario induces lower axial forces in some parts of the tunnel lining, which is due to the smaller stress distribution around the tunnels in this state. Regarding the horizontal soil displacement around the walls of the underground parking, the side walls experience higher deformations in the first scenario, while the front and back walls move in a different direction in both scenarios due to the distinct soil behavior surrounding the underground structures. 4. Consequently, the obtained numerical results prove that performing the second scenario is preferable in terms of soil displacement and induced forces and deformations in the parking walls and tunnel linings.
parking bottom level is shown in Fig. 28. The maximum heave observed in the center part of the profile for the 1st scenario is 8 mm lower than the corresponding value for the 2nd one, while the vertical movement under the walls in the first scenario is lower of 5 mm compared to the second one. Moreover, the horizontal soil movement on the right side of the underground spaces (I_R) is investigated for both scenarios in Fig. 29. Near the ground surface, the maximum lateral displacement of the first state is equal to 7.4 mm, around 2.6 mm higher than for the 2nd scenario. By moving from the surface to the tunnels spring line, the difference between the two scenarios decreases and remains smaller than 0.5 mm at lower depths (Fig. 29). To illustrate the influence of the underground parking - twin tunnels interaction on the tunnel lining structural forces, the axial forces obtained from the 26th ring of the right tunnel for the two scenarios are shown in Fig. 30. There is a slight difference in the induced axial forces in the upper and the lower right tunnel lining part. It could be attributed to the distinct stress distribution around the tunnels for these two scenarios (see Fig. 31). The maximum principal stress distribution around the twin tunnels and underground parking are shown in Fig. 31. The horizontal displacement values induced in both right and front walls of the underground parking for the two executed cases are shown in Fig. 32. It could be seen that the right wall in the first scenario experiences more lateral displacements compared to the 2nd scenario one (Fig. 32a). It is in good accordance with the horizontal soil movements around the right side of the parking (see Fig. 29). The highest lateral displacement, of about 7.2 mm, happens on the upper part of the right wall in the first scenario. It is higher of about 58% than the second scenario one. In the front wall diagram (Fig. 32b), the horizontal displacement values in the wall are in the same range for both scenarios. Nevertheless, they are different in terms of movements direction. On the other word, the wall moves toward the underground parking in the first case, while it moves to the opposite side for the 2nd scenario (see Fig. 32b).
Further numerical analysis should be made to investigate the influence of the distance between the underground parking and tunnels and of the lagging distance between the twin tunnels. References Afifipour, M., Sharifzadeh, M., Shahriar, K., Jamshidi, H., 2011. Interaction of twin tunnels and shallow foundation at Zand underpass, Shiraz metro Iran. Tunn. Undergr. Space Technol. 26, 356–363. Cavalaro, S., Aguado, A., 2012. Packer behavior under simple and coupled stresses. Tunn. Undergr. Space Technol. 28, 159–173. Chakeri, H., Hasanpour, R., Hindistan, M.A., Ünver, B., 2011. Analysis of interaction between tunnels in soft ground by 3D numerical modeling. Bull. Eng. Geol. Environ. 70, 439–448. Dias, D., Kastner, R., 2013. Movements caused by the excavation of tunnels using face pressurized shields-analysis of monitoring and numerical modeling results. Eng. Geol. 152 (1), 17–25. Ding, W., Yue, Z., Tham, L., Zhu, H., Lee, C., Hashimoto, T., 2004. Analysis of shield tunnel. Int. J. Numer. Anal. Meth. Geomech. 28 (1), 57–91. Do, N.A., Dias, D., Oreste, P.P., Djeran-Maigre, I., 2013. 3D modelling for mechanized tunneling in soft ground-Inflence of the constitutive model. Am. J. Appl. Sci. 10 (8), 863–875. Do, N.A., Dias, D., Oreste, P., 2015. 3D numerical investigation on the interaction between mechanized twin tunnels in soft ground. Environ. Earth Sci. 73 (5), 2101–2113. Do, N.A., Dias, D., Oreste, P., 2016. 3D numerical investigation of mechanized twin tunnels in soft ground–Influence of lagging distance between two tunnel faces. Eng. Struct. 109, 117–125. Do, N.A., Dias, D., Oreste, P., Djeran-Maigre, I., 2014. Three-dimensional numerical simulation of a mechanized twin tunnels in soft ground. Tunn. Undergr. Space Technol. 42, 40–51. Fang, Q., Zhang, D., Li, Q., Wong, L.N.Y., 2015. Effects of twin tunnels construction beneath existing shield-driven twin tunnels. Tunn. Undergr. Space Technol. 45, 128–137. Farashar Asia Consulting Engineer, 2010. Geotechnical report of Amirkabir ring road project - Edalat overpass. Fater Construction Company, 2016. TBM1 monitoring report from 3+000 km to 4+000 km of Shiraz subway line 2. Hasanpour, R., 2014. Advance numerical simulation of tunneling by using a double shield TBM. Comput. Geotech. 57, 37–52. Hasanpour, R., Chakeri, H., Ozcelik, Y., Denek, H., 2012. Evaluation of surface settlements in the Istanbul metro in terms of analytical, numerical and direct measurements. Bull. Eng. Geol. Environ. 71, 499–510. Huang, D.-Z., Ma, X.F., Wang, J.S., Li, X.Y., Yu, L., 2012. Centrifuge modelling of effects of shield tunnels on existing tunnels in soft clay. Chinese J. Geotech. Eng. 34 (3), 520–527 (in Chinese). Itasca Group, 2012. FLAC fast Lagrangian analysis of continua, User’s manual (Version 5.0). Kankavan Consulting Engineers, 2013. Field and Laboratory tests Report of Shiraz Metro Line2. Kasper, T., Meschke, G., 2004. A 3D finite element simulation model for TBM tunnelling in soft ground. Int. J. Numer. Anal. Meth. Geomech. 28 (14), 1441–1460. Kasper, T., Meschke, G., 2006. A numerical study of the effect of soil and grout material properties and cover depth in shield tunneling. Comput. Geotech. 33 (4–5), 234–247. Li, X., Du, S., Zhang, D., 2010. Numerical simulation of the interaction between two parallel shield tunnels. In: Proceeding of ICPTT 2012: Better Pipeline Infrastructure for a Better, Life, pp. 1521–1533. Li, X.G., Yuan, D.J., 2012. Responses of a double-decked metro tunnel to shield driving of twin closely under-crossing tunnels. Tunn. Undergr. Space Technol. 28, 18–30. Liu, H.Y., Small, J.C., Carter, J.P., Williams, D.J., 2009. Effects of tunneling on existing support systems of perpendicularly crossing tunnels. Comput. Geotech. 36 (5), 880–894.
6. Conclusions This study illustrates a fully three-dimensional numerical model of mechanized tunneling provided by a finite difference code. It highlights underground parking-soil-twin tunnels interaction. In order to investigate the interaction of the tunnel-underground parking on each other, two scenarios were discussed. About the results of the numerical analysis, the following conclusions can be drawn: 1. In the scenario of constructing the underground parking above the existing twin tunnels, the numerical simulation results illustrate the increase in horizontal displacements behind the retaining walls by constructing the parking which is due to the inward movement of walls. Also, the underground parking installation caused considerable heave in the parking bottom and downward movement under the walls. On the other hand, building subterranean parking induces the upward movement of the tunnel lining, while it causes a reduction in axial forces and bending moments induced in the tunnel lining, 2. In the case of twin tunnels excavation under the underground parking, it can be observed that the tunneling has a slight effect on the central heave of parking bottom but causes considerable downward subsidence under the retaining walls which are attributed to the downward displacement of the soil above the tunnels. Moreover, crossing the twin tunnels under the underground parking brings additional downward displacement beneath the parking level that causes an increase in inward movement of the soils behind the walls. About the front and back walls, tunneling direction makes a significant lateral displacement in soils around the parking walls inclined to the tunnel advancement which leads to the walls' permanent deformation, 15
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modeling of the interaction between perpendicularly crossing tunnels. Can. Geotech. J. 50 (9), 935–946. Pakbaz, M.S., Imanzadeh, S., Bagherinia, K.H., 2013. Characteristics of diaphragm wall lateral deformations and ground surface settlements: case study in Iran-Ahwaz metro. Tunn. Undergr. Space Technol. 35, 109–121. Phienwej, N., Hong, C.P., Sirivachiraporn, A., 2006. Evaluation of ground movements in EPB-shield tunnelling for Bangkok MRT by 3D-numerical analysis. Tunn. Undergr. Space Technol. 21 (3–4), 273. Rodriguez, L.E.M., 2000. Estudio de los movimientos originados por la excavación de túneles con escudos de presión de tierras en lossue los tosquizos de Madrid. PhD Thesis. University of La Coruña, spain. Sharma, J.S., Hefny, A.M., Zhao, J., Chan, C.W., 2001. Effect of large excavation on deformation of adjacent MRT tunnels. Tunn. Undergr. Space Technol. 16 (2), 93–98. Thienert, C., Pulsfort, M., 2011. Segment design under consideration of the material used to fill the annular gap. Geomechanics Tunneling 4, 665–680. Tose-e Consulting Engineers, 2014. Geotechnical engineering services report of Shiraz Metro Line 2. Zhang, J.F., Chen, J.J., Wang, J.H., Zhu, Y.F., 2013. Prediction of tunnel displacement induced by adjacent excavation in soft soil. Tunn. Undergr. Space Technol. 36, 24–33.
Mahmutoğlu, Y., 2011. Surface subsidence induced by twin subway tunneling in soft ground conditions in Istanbul. Bull. Eng. Geol. Environ. 70, 115–131. Mollon, G. 2010. Etude déterministe probabiliste du comportement des tunnels. Lyon, France. Mollon, G., Dias, D., Soubra, A.-H., 2013. Probabilistic analyses of tunneling-induced ground movements. Acta Geotech. 8 (2), 181–199. Nematollahi, M., Dias, D., 2019. Three-dimensional numerical simulation of pile-twin tunnels interaction–Case of the Shiraz subway line. Tunn. Undergr. Space Technol. 86, 75–88. Nematollahi, M., Molladavoodi, H., Dias, D., 2018. Three-dimensional numerical simulation of the Shiraz subway second line-influence of the segmental joints geometry and of the lagging distance between twin tunnels’ faces. Eur. J. Environ. Civil Eng. 1–17. https://doi.org/10.1080/19648189.2018.1476270. Ng, C.W.W., Fong, K.Y., Liu, H.L., 2018. The effects of existing horseshoe-shaped tunnel sizes on circular crossing tunnel interactions: three-dimensional numerical analyses. Tunn. Undergr. Space Technol. 77, 68–79. Ng, C.W.W., Lee, K.M., Tang, D.K.W., 2004. Three-dimensional numerical investigations of new Austrian tunneling method (NATM) twin tunnel interactions. Can. Geotech. J. 41, 523–539. Ng, C.W.W., Boonyarak, T., Mašín, D., 2013. Three-dimensional centrifuge and numerical
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