ISSN 1062-7391, Journal of Mining Science, 2016, Vol. 52, No. 3, pp. 461–472. © Pleiades Publishing, Ltd., 2016.

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Twin Tunnel Behavior under Static and Dynamic Loads of , Iran1 R. Shirinabadi and E. Moosavi* Islamic Azad University, South Tehran Branch, Tehran, *e-mail: [email protected] Received February 14, 2016

Abstract—Safety during construction and long-term stability of tunnels is among important factors in the design and implementation of underground spaces. Since tunnels and underground spaces are under dynamic loads such as earthquakes and explosions during construction and operation stages, dynamic stability analysis of such structures is of great importance. In this study, the twin tunnels of Shiraz subway were numerically modeled under static and dynamic loads with the help of Universal Distinct Element Code (UDEC). This is a finite element method (FEM) software, is any of a family of numerical methods. Unbalanced forces increase after tunnel excavation and applying static and dynamic loads. Although the increase in unbalanced forces was higher under dynamic loads, under static loads, velocity and displacement changes in the ceiling of the tunnel were higher than the rest of the tunnel. To apply a dynamic load, a sine wave was applied to the lower boundary of the model. After applying the dynamic load, velocity and displacement changes of the tunnel floor were higher than the rest of the tunnel. According to modeling results, the twin tunnels are quite unstable under static and dynamic loads and need a support system. Keywords: Static and dynamic loads, finite element method, universal distinct element code software, twin tunnel of Shiraz metro, earthquake. DOI: 10.1134/S1062739116030669

INTRODUCTION According to recorded data, underground structures are safer than surface structures against dynamic waves, because surface structures are only connected to the ground from the lower surface and vibrate freely; but, underground structures are completely connected to the surrounding environment and thus are more resistant to vibration. However, there are reports of damage to such structures due to dynamic waves. This implies that underground structures are not absolutely immune against dynamic waves and are prone to damages. Thus, relative strength of underground structures against seismic waves does not guarantee an adequate resistance to dynamic loads, especially earthquakes. Accordingly, there is a crucial need for fundamental and continuous research on wave propagation in rock and soil environments. Most urban underground structures are constructed in shallow and soft grounds and thus are prone to seismic disturbances. Such structures, depending on their use, are of great importance in terms of long-term safety. If the construction site of large underground structures such as public transport tunnels is very soft or loose, their seismic behavior should be estimated. In the past decades, many studies were concentrated on the consequence of single tunnel excavation in terms of surface and subsurface movements [1–4]. On the other hand, the case of twin tunnels nowadays very common in many metro-line projects around the world because twin tunneling is particularly favored when developing underground transportation systems all over the world [5–13]. Interactions between closely-spaced tunnels were studied in the past using a variety of approaches: physical model tests [14–19], numerical modeling [20–27], empirical and analytical

1The article is published in the original. 461 462 SHIRINABADI, MOOSAVI methods [28–33]. The physical modeling to predict, as well possible different construction settings adopted during the second excavation, generally alters the expected ground movements due to the construction of a new one, often leading to a non-symmetric final settlement trough. Numerical methods demonstrate a valuable tool to analyze this class of problems, overcoming the limitations related to the empirical methods. In several cases, a detailed investigation can only be fulfilled adopting a three-dimensional (3D) solution, which permits to calculate for any construction scheme, including the case of twin tunnels, for any kind of surface structure and its relative position with respect to the tunnels’ axes. However, the validity of such methods is strongly affected by different factors [34], the correct simulation of the tunnel excavation sequence [35] and the detail of the structural modeling [36]. Extensive surveys of the papers submitted for the session on numerical and physical modeling of tunnels were provided by Jacobsz [37]. Do et al. [38] induced that due to the interaction of twin tunnels, an increase in the surface settlement can be expected compared to that induced above a single tunnel. A full 3-D finite element of tunnel–structure problem was performed [39] in which the weight and stiffness of a surface skeletal structure were considered. In that parametric study, the tunnel construction parameters and real structure stiffness were not properly considered. The interaction between the ground and tunnel lining during earthquake excitation studied by Pakbaz and Yareevand [40], they concluded effect of earthquake on tunnel–ground interaction depend on various parameters including peak acceleration, intensity and duration of earthquake and the relative rigidity between tunnel and ground. Liu and song [41] found that the increase in buried depth improved the safety of the underground structure against earthquake damage. Park et al. [42] simulated tunnel response under spatially varying ground motion, they found that the spatially variable ground motion causes longitudinal bending of the tunnel and can induce substantial axial stress on the tunnel lining. A new model study on the effects of input motion on the seismic behavior of tunnels via Cilingir and Gopal [43], they found that the magnitude of the maximum input acceleration plays a crucial role on the maximum and residual lining forces, which the tunnel experiences. Shong-loong and Meen-wah [44] ended that the deeper the location of the tunnel, the less the tunnel lining is affected by the effect of earthquake. Sahoo and Kumar [45] investigated seismic stability of a long unsupported circular tunnel and concluded that the failure zones around the periphery of the tunnel becomes always asymmetrical with an inclusion of horizontal seismic body forces. Gomes [46] examined the effect of stress disturbance induced by construction on the seismic response of shallow bored tunnels, he found that stress disturbance due to tunnel construction may significantly increase lining forces induced by earthquake loading. Sahoo and Kumar [47] concluded that an increase in the magnitude of the earthquake acceleration leads to a significant increment in the magnitude of internal compressive pressure. However, the above mentioned studies improved the knowledge of tunnel–structure interaction and the effects of operation parameters on the settlement, the interactions of twin tunnel construction parameters and adjacent structures were not considered simultaneously. In this paper, the interaction between twin tunnels from static and dynamic loads has been studied using numerical finite element method. The main purpose of this study was to provide a numerical model which would allow the behavior of the interaction of mechanized twin tunnels to be evaluated, in terms of structural forces induced in the ceiling and floor of the tunnel and ground displacement surrounding the two tunnels. The content of this paper is organized as follows. In Section 1, the effect of dynamic loading on twin tunnels discussed in sufficient detail. The problem statement is studied in section 2. In Section 3, at

JOURNAL OF MINING SCIENCE Vol. 52 No. 3 2016 TWIN TUNNEL BEHAVIOR UNDER STATIC AND DYNAMIC LOADS OF SHIRAZ METRO, IRAN 463 first the numerical modeling of construction parameters effects on the speed and direction of loading applied on the tunnel was studied. In section 4, a full analysis of the interaction between tunnels and the static and dynamic forces, considering unbalanced force and bending moment variations in all structural members, was performed. Finally, the conclusions are given in section 5.

1. EFFECTS OF DYNAMIC LOADING ON TWIN TUNNELS Understanding the behavior of underground structures during earthquake events is one of the most interesting challenges in geotechnical engineering. While tunnels generally enforced better than above ground structures during earthquakes, damage to some of these important structures during previous earthquake events, that is, the 1995 Kobe, Japan earthquake, the 1999 Chi Chi, Taiwan earthquake, the 1999 Bolu, Turkey earthquake, the 2004 Baladeh, Iran earthquake, the 2008 Sichuan, China earthquake, the 2014 Valparaiso, Chile earthquake, and recently the 2015 Illapel, Chile earthquake, highlights the need to account for seismic loading in the design of underground structures. Earthquake effects on underground structures leads into two groups: (1) ground shaking, and (2) ground failures such as liquefaction, fault displacement, and slope instabilities [48]. Ground shaking implies to the vibration of the ground induced by seismic waves that propagate through the earth’s crust. Fig.1 shows the ground response due to the various types of seismic waves: (i) Body waves travel within the earth’s material (P waves and S waves), (ii) Surface waves travel along the earth’s surface (Rayleigh waves or Love waves, see Fig. 1) [28]. Owen and Scholl [49] asserted that the behavior of an underground structure during seismic event can be approximated to that of an elastic beam subject to deformations imposed by the surrounding ground. Three types of deformations express the response of underground structures to seismic motions (see Fig. 2): • Axial compression/extension, • Longitudinal bending, • Ovaling/racking. Axial and curvature deformations in horizontal or near horizontal tunnel occur because of wave propagation parallel or at an angle to the axis of tunnel (Fig. 2- A, B). On the other hand, Ovaling or racking deformations are due to wave propagating perpendicular or near perpendicular to the axis of tunnel (Figs. 2c and 2d) [49].

Fig. 1. Ground response to seismic waves [28].

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Fig. 2. Type of tunnel deformations during a seismic event: (a) is the axial deformation along tunnel; (b) is the Bending (curvature) deformation along tunnel; (c) is the Ovaling deformation of a circular tunnel; (d) is the Racking deformation of a rectangular tunnel [49]. 2. THE NEW SHIRAZ METRO-: DESCRIPTION OF THE CASE-HISTORY Shiraz, the center of Fars province and third largest city in Iran is located in southwestern Iran. Geologically, Shiraz is a part of the Zagros fold-thrust zone in Alpine-Himalayan orogenic belt. These structures are associated with structural abnormalities formed by rupture mechanisms and main faults. Numerous earthquakes have occurred in Shiraz. The soil of Shiraz is very loose and prone to failure by strong earthquakes. Thus, the seismic analysis of such an important structure is inevitable. Over 555 earthquakes have been recorded in Fars province in 2013 in The Geophysics Institute of Tehran University. According to literature, Shiraz and some areas of Fars province are located on a fault line. Shiraz region is a semi-active seismic zone as compared to other regions of Zagros and many low to moderate earthquakes occur in this region, but the probability of large earthquakes is very weak. Shiraz subway includes six lines with an overall length of 90 km. The case study of this paper is a part of Line One of Shiraz metro lines, which the line with a 24.5 km long includes two tunnels with an approximate length of 15 km, shown Table 1. The line is routed through the downtown of a major metropolitan area and has been tunneling under Modares freeway, historical places (Arge Karimkhan, Pars monument and Vakil Bazaar), beneath the crowded city streets and adjacent to heavy structures (Qadir bridge, Zand underpass) as shown in Fig. 3. Because of the high water level in the East Shiraz (from Gole-Sorkh-Allah Square Station to Namazi Square), mechanized drilling method was used to excavate the tunnels. Excavation was performed by Tunnel Boring Machine (TBM) of Earth Pressure Balance (EPB) type with an excavation diameter of 6.88 and a useful diameter of 6 m. The tunnels are permanently supported by prefabricated concrete blocks with 1+2+2+1 arrangement. The rest of the line was drilled by new Austrian tunneling and cut-and-cover methods. Table 1. Tunneling methods for Shiraz metro-line 1

Method Path length, m The twin tunnels through Tunnel Boring Machine (TBM) 12.5 New Austrian Tunneling Method (NATM) 1.5 Cut and Cover 8 Surface 2.5 Total 24.5

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Fig. 3. Shiraz metro-line system. 2.1. Geotechnical Properties of Twin Tunnel—Shiraz Metro The geological conditions of the site were almost uniform. It is primarily comprised of lean clay (CL) with alternate layers of gravel and silty sand. The ground water table was approximately at a depth of 6-9 m. Fig. 4 presents a geological profile at a location along the course of twin tunnels. It is evident from the geological profile that the predominant soil type at the site was clay. The physical properties of the clay soil are stated in Table 2. The numerical analyses were conducted using these soil properties. Also, it was presumed to behave as an isotropic and homogeneous material. The details regarding the numerical simulation are presented later.

Fig. 4. Geological profile of site for Shiraz metro-line 1. γ Table 2. The estimated subsurface geotechnical parameters of case study: E—Elastic modulus, d —dry unit weight, γ ϕ s —saturated unit weight, C—soil cohesion, —the internal angle of friction, ν—Poisson’s ratio, σc—compressive strength, n—degree of porosity γ γ Layers E, d , s , C, ϕ ν σc, n -2 -2 KN.m KN.m-3 KN.m-3 KN.m KPa Lean clay 22500 17 20.8 25 29 0.25 85 0.15 Silty sand 15000 17 20 10 34 0.25 37 0.2 Gravel 50000 17 19 0 33 0.3 - 0.3

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Fig. 5. Numerical model of the twin tunnels and layers. 3. NUMERICAL ANALYSIS PROCEDURE Shiraz subway tunnels, between Zand and Imam Hossein Square stations, have been constructed with a circular cross section with a diameter of 8.6, wall to wall distance of 8 m and an overburden of 8.5 m on a fine sand layer. A model with a length of 80 m and a width of 40 m was constructed. The section has three layers of sand, silt and clay from top to bottom. The same layers were included in the numerical model. Fig. 5 shows the numerical model of the twin tunnels and layers. After creating the tunnel structure, the tunnel was modeled under gravity loads (before and after excavated tunnel), dead (static) loads and dynamic loads (seismic waves). The model was solved under static loads. Figs. 6 and 7 show unbalanced forces and velocity (along y-axis) converged to zero before and after excavated tunnel. As can be seen in Fig. 7, the ceiling of the tunnel has the highest velocity along the y-axis. The velocity decreases with increasing distance from the ceiling of the tunnel so that the ground surface has the lowest velocity.

Fig. 6. Unbalanced forces before and after excavated tunnel.

Fig. 7. The y-axis speed of the tunnel roof to ground.

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Fig. 8. Displacement in the direction of y-axis of the tunnel roof to ground.

Fig. 9. Displacement floor tunnel in the direction of the y-axis. Figure 8 shows displacement along y-axis before and after excavated tunnel. As shown, a maximum displacement of 2.1 m occurs in the tunnel roof. Displacement decreases with increasing distance from the tunnel roof so that the ground surface is displaced only 1.3 m. Figure 9 shows displacement of tunnel floor along y-axis indicating 15 cm upward displacement of the tunnel floor after excavation. Figure 10 shows displacement of two points of the left wall of tunnel along x-axis. As can be seen, the wall closer to the adjacent tunnel (the right wall) is displaced 1.2 m into after the excavation of the tunnel. However, the opposite wall is displaced 80 cm. In other words, the right wall (the wall close to the adjacent tunnel) is more displaced into the tunnel. Since both tunnels are symmetric with equal stress, velocity and displacement levels, the diagrams are only presented for the left tunnel.

Fig. 10. Displacement the left and right walls.

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Fig. 11. The stresses in tunnel roof and various parts to ground of the tunnel.

Figure 11 shows σyy diagrams for the tunnel roof and different points to the ground surface. As can be seen, stress decreases from the tunnel roof to the ground surface. According to Figs. 8 to 10, the twin tunnels are quite unstable under static loads and necessarily need a support system. 4. APPLYING DYNAMIC LOAD To solve dynamic problems at wave boundaries, the waves are usually expressed by stress history input (SHI) or velocity history input (VHI) methods [50]. In VHI method, the data can be easily entered, but in SHI method, the equivalent stress history is calculated from velocity history using Eqs. (1) and (2): δ = ρ n 2.( .C p ).vn , (1) where σn is the applied normal stress; is the mass density; CP is the speed of p-wave propagation through medium; vn is the input normal particle velocity. VHI was used in this study. To apply a dynamic wave on the lower boundary, a wave with a velocity of 2 m/s along x-axis and 3 m/s along y-axis with a frequency of 4 Hz was applied to the model for 1 second. Figure 12 shows unbalanced force changes before and after applying the dynamic load. As can be seen, dynamic unbalanced forces are higher than static unbalanced forces. Figure 13 shows displacement curves of five different points from the tunnel roof to the ground surface along y-axis. After applying the dynamic load, the upward displacements of the tunnel roof and ground surface are 5 cm and 8 cm, respectively. Figure 14 shows displacement of the tunnel floor along the y-axis. After applying the dynamic load, the tunnel floor experienced an upward displacement of 60 cm. Figure 15 shows displacement curves for the left and right walls of the tunnel along the x-axis. After applying the dynamic load, the walls were displaced about 15 cm into the tunnel.

Fig. 12. Unbalanced force before and after applying the dynamic load.

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Fig. 13. Displacement in the direction of y-axis (the roof of the tunnel to ground).

Fig. 14. Displacement floor tunnel y-axis before and after applying the dynamic load.

Fig. 15. Displacement left and right walls of the tunnel before and after applying the dynamic load.

Fig. 16. Speed variations in the direction of y-axis of the tunnel roof to ground.

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Fig. 17. Speed variations in the direction of the y-axis of tunnel floor.

CONCLUSIONS It is well known that the interaction between mechanized twin tunnels excavated in soft ground is complex. In this paper, the interaction between twin tunnels from static and dynamic loads has been studied using numerical finite element method. Urban tunnels are of great importance because they are usually bored in shallow and loose grounds. Thus, dynamic stability analysis of such structures is essential. Considering the constituent materials of the study area and model results, the twin tunnels are quite unstable under static and dynamic loads and need a support system. After excavating in the underground space, stress distribution is changed and induced stresses are developed. However, shear stress at excavation boundary is zero and the tangential stress increases. It is possible to draw the following conclusions, (i) After boring the tunnel and applying static and dynamic loads, unbalanced force increases, but the increase in the unbalanced force is higher under dynamic load. (ii) Under static loads, displacement and velocity variations in the tunnel roof are more than the rest of the tunnel. (iii) To apply a dynamic load, a sine wave was applied to the lower boundary of the model. After applying the dynamic load, displacement and velocity variations of the tunnel floor were more than the rest of the tunnel.

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