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Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking

Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking applied sciences Article Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking Ahsan Naseem * , Muhammad Kashif, Nouman Iqbal, Ken Schotte and Hans De Backer Department of Civil Engineering, Ghent University, Technologiepark 60, B-9052 Zwijnaarde, Belgium; muhammad.kashif@ugent.be (M.K.); nouman.iqbal@ugent.be (N.I.); ken.schotte@ugent.be (K.S.); hans.debacker@ugent.be (H.D.B.) * Correspondence: ahsan.naseem@ugent.be Received: 8 December 2019; Accepted: 30 December 2019; Published: 2 January 2020 Abstract: Combining multiple tunnels into a single tunnel complex while keeping the surrounding area compact is a complicated procedure. The condition becomes more complex when soft soil is present and the area is prone to seismic activity. Seismic vibrations produce sudden ground shaking, which causes a sharp decrease in the shear strength and bearing capacity of the soil. This results in larger ground displacements and deformation of structures located at the surface and within the soil mass. The deformations are more pronounced at shallower depths and near the ground surface. Tunnels located in that area are also a ected and can undergo excessive distortions and uplift. The condition becomes worse if the tunnel area is larger, and, thus, the respective tunnel complex needs to be properly evaluated. In this research, a novel triple tunnel complex formed by combining three closely spaced tunnels is numerically analyzed using Plaxis 2D software under variable dynamic loadings. The e ect of variations in lining thickness, the inner supporting structure, embedment depth on the produced ground displacements, tunnel deformations, resisting bending moments, and the developed thrusts are studied in detail. The triple tunnel complex is also compared with the rectangular and equivalent horizontal twin tunnel complexes in terms of generated thrusts and resisted seismic-induced bending moments. From the results, it is concluded that increased thickness of the lining, inner structure, and greater embedment depth results in decreased ground displacements, tunnel deformations, and increased resistance to seismic-induced bending moments. The comparison of shapes revealed that the triple tunnel complex has better resistance against moments with the least amount of thrust and surface heave produced. Keywords: triple tunnel complex; soft soil; seismic response; finite element analysis 1. Introduction Tunnels are one of the important means of underground transportation. They are useful in the build-up area where further surface construction in order to accommodate large trac infrastructure is not possible. Second, they also provide fast, uninterrupted flow from one point to the other. Many densely populated cities in the world are now planning to provide metro lines through an underground tunnel system. Although it has many useful purposes, at the same time, it is vulnerable to excessive damage if present in an earthquake-prone area. The condition becomes more critical when multiple tunnels lie in closer proximity. Previously, it was believed that the underground structures are less prone to damage in comparison with the on-surface constructions, but major earthquakes in the recent past like Kobe (1995), Coyote (1979), Kocaeli (1999), Chi-Chi (1999), etc. have proved these to be equally vulnerable. The damage su ered by the tunnels depends upon the type of surrounding soil, embedment depth, the amplitude of the earthquake, and the groundwater table (GWT) conditions. The type of soil plays a very important role in the overall behavior of tunnels under seismic activity. Appl. Sci. 2020, 10, 334; doi:10.3390/app10010334 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 334 2 of 22 Tunnels constructed in soft soil are far vulnerable to severe damage than in dense rock. Similarly, the more shallow tunnels su er more distortions in comparison to the deeper ones [1]. Researchers now focus on the dynamic behavior of tunnels in di erent types of rocks and soils. Wang [2], Penzien [3], and Bobet [4] developed closed-form solutions to estimate the seismically-induced moments and thrust in rectangular and circular tunnels causing racking and ovaling, respectively. Hashash and Hook et al. [5] and Hashash and Park et al. [6] conducted an extensive review of the available methods used to determine seismic induced forces that aid in the seismic design of di erent tunnels. Liu and Song [7] and Azadi and Hosseini [8] studied the seismic behavior of shallow tunnels subjected to horizontal and vertical shaking in the liquefiable sands in order to assess the distortions occurring in the tunnel lining and its uplift due to excess pore pressure generation. Unutmaz [9] investigated the liquefaction possibilities of soil surrounding the tunnels using 3D finite element modeling (FEM) and studied the acceleration variations and the power spectra developed under the seismic vibrations for various tunnel embedment depths. Lanzano and Bilotta et al. [10] studied the behavior of circular tunnels, both using a centrifuge and analytical modeling in order to determine the hoop forces and the distortions produced in the tunnel lining and concluded that both techniques produce results in good agreement. Cilinger and Madabhushi performed centrifuge tests to study the e ect of embedment depth and behavior of circular and rectangular tunnels in dry sand subjected to di erent intensity seismic vibrations [11–13]. Qiu and Xie et al. [14] conducted centrifuge testing to study the e ect of ground movements and the interaction between twin tunnels in loess and concluded on the optimized spacing and the interval between the tunnels. Shahrour and Khoshnoudian et al. [15] numerically studied the seismically-induced bending moments and soil dilatancy around tunnels in soft soils. Patil and Choudhury et al. [16] performed FEM on circular tunnels and studied the lining distortions, bending moments under variable ground vibrations, and di erent embedment depth and tunnel lining thickness to develop better understanding of tunnel behavior in soft soils. Tsinidis [17] conducted FEM to study response characteristics of rectangular tunnels under seismic shaking varying the tunnel-soil interface properties and input motion characteristics embedment depths and concluded in the development of racking-flexibility (RF) relations for rectangular tunnels in soft soils. Apart from this, the response of underground tunnels subjected to seismic ground shaking have been studied experimentally (Chian and Madabhushi [18], Graziani and Boldini [19], Chian and Madabhushi [20], Abuhajar and Naggar et al. [21]), analytically (Power et al. [1], Chian and Tokimatsu [22], Bobet and Fernandez et al. [23]) and numerically (Chou and Yang et al. [24], Amorosi and Boldini [25], Baziar and Moghadam et al. [26], Huo and Bobet et al. [27], Nguyen and Lee et al. [28]). However, all literature considers the conventional circular, rectangular or horseshoe shapes. None of them has studied the behavior of multiple tunnels that have been combined to form a single tunnel complex of an unconventional shape. This research includes the dynamic response of a new, unconventional tunnel shape, which is proposed to be constructed in Brussels, which is the capital of Belgium, and has never been used earlier. The literature also lacks analytical solutions for it. This shape has resulted from the combination of three closely spaced tunnels into a triplet complex that would carry multiple train tracks for the underground trac movement and has been discussed with respect to construction arrangements by Naseem and Schotte et al. [29]. This unconventional triplet complex in soft soil has been numerically studied in detail using the dynamic module of FEM software Plaxis 2D under variable seismic vibrations and embedment depths in order to determine the tunnel distortions, which results in ground settlements, seismically-induced bending moments and axial forces, and make the comparison with the conventional rectangular complex and the equivalent horizontal twin tunnel complex. This study would help determine the optimized tunnel parameters and to understand the dynamic behavior of this unique tunnel shape in a better way. Appl. Sci. 2020, 10, 334 3 of 22 2. Stages of Analysis The research is comprised of static and dynamic analyses. First, the tunnel system is analyzed Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 21 statically. Since it is a long-term response, drained conditions are considered. After the equilibrium conditions are established, the dynamic analyses are performed, which include rapid ground shaking. conditions are established, the dynamic analyses are performed, which include rapid ground Therefore, undrained conditions are considered at that stage. shaking. Therefore, undrained conditions are considered at that stage. 3. Reference Model 3. Reference Model This research focuses on the parametric study of an unconventional shape and a unique triple This research focuses on the parametric study of an unconventional shape and a unique triple tunnel complex under seismic shaking in order to evaluate deformations in tunnel lining, moments, tunnel complex under seismic shaking in order to evaluate deformations in tunnel lining, moments, and thr and thrust devel ust developed. oped. As studi As studied ed f for or the the f first irst ti time, me, it it la lacks cks th the e ana analytical lytical solsolutions. utions. HencHence, e, it is it is compared with a reference model. The reference model considered in this case is taken from the compared with a reference model. The reference model considered in this case is taken from the research of Milind and Choudhury et al. [16]. It comprises of a circular tunnel with a diameter of 6 m research of Milind and Choudhury et al. [16]. It comprises of a circular tunnel with a diameter of 6 analyzed using FEM software Plaxis 2D under different seismic vibrations. The Mohr-Coulomb m analyzed using FEM software Plaxis 2D under di erent seismic vibrations. The Mohr-Coulomb constitutive model was used in the research and the results of the developed thrusts and moments constitutive model was used in the research and the results of the developed thrusts and moments were were compared with the analytical solutions of Wang [2], Penizen [3], and Bobet [4] as shown in compared with the analytical solutions of Wang [2], Penizen [3], and Bobet [4] as shown in Figure 1. Figure 1. The results obtained were in close agreement except from one anomalous result of thrust in The results obtained were in close agreement except from one anomalous result of thrust in case of case of Penizen [3], which indicates their accuracy. Penizen [3], which indicates their accuracy. In this research, the seismic shaking of a triple tunnel complex is analyzed using the same FEM In this research, the seismic shaking of a triple tunnel complex is analyzed using the same FEM suite with the same layered soil system and the constitutive model so that the obtained results have suiteth with e con the fidesame nce of layer accured acysoil . system and the constitutive model so that the obtained results have the confidence of accuracy. Thrust, T (kN/m) Wang (1993) Penizen (2000) Bobet (2010) 0 200 400 600 800 Numerical analysis (a) Bending Moment, M (kN-m/m) Wang (1993) Penizen (2000) Bobet (2010) 0 250 500 750 1000 Numerical analysis (b) Figure 1. Comparison between numerical and analytical solutions: (a) thrust and (b) bending moment Figure 1. Comparison between numerical and analytical solutions: (a) thrust and (b) bending [16]. moment [16]. Analytical solution Analytical solution Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 21 Appl. Sci. 2020, 10, 334 4 of 22 4. Details of the Finite Element Analysis 4. Details of the Finite Element Analysis 4.1. Software and Soil Parameters 4.1. Software and Soil Parameters In this study, the FEM program Plaxis 2D is used, which offers a wide range of constitutive models and different modules to numerically analyze both the linear and non-linear behavior of the In this study, the FEM program Plaxis 2D is used, which o ers a wide range of constitutive soil and tunnel structure. A layered soil system is considered to have a soft silty clay layer underlain models and di erent modules to numerically analyze both the linear and non-linear behavior of the by silty clay, very soft silty clay, clay, and silty clay with silty sand, respectively, as used by Hu and soil and tunnel structure. A layered soil system is considered to have a soft silty clay layer underlain Yue et al. [30] along with Milind and Choudhury et al. [16]. The soil media is taken as fully saturated by silty clay, very soft silty clay, clay, and silty clay with silty sand, respectively, as used by Hu and with the GWT considered to be at the ground level. The triple tunnel complex is provided in the soil Yue et al. [30] along with Milind and Choudhury et al. [16]. The soil media is taken as fully saturated system keeping the embedment depth (C) and tunnel complex width (H) as a variable. The triple with the GWT considered to be at the ground level. The triple tunnel complex is provided in the soil tunnel complex along with the layered soil system is shown by Figure 2a–c while the detailed soil system keeping the embedment depth (C) and tunnel complex width (H) as a variable. The triple properties used in the study are tabulated in Table 1. This layered soil system is categorized as soft tunnel complex along with the layered soil system is shown by Figure 2a–c while the detailed soil soil with soil type D, according to Euro code (EC 8) [31] based on its shear wave profile given in properties used in the study are tabulated in Table 1. This layered soil system is categorized as soft soil Figure 2d. with soil type D, according to Euro code (EC 8) [31] based on its shear wave profile given in Figure 2d. (a) (b) (c) Figure 2. Cont. Appl. Appl. Sci. Sci. 2020 2020,, 10 10,, x FO 334 R PEER REVIEW 5 of 5 of 21 22 110 140 170 200 Shear wave velocity (m/s) (d) Figure 2. (a–c) Soil-Tunnel geometry: (a) Soil layers with the embedded triple tunnel complex. (b) Soil Figure 2. (a–c) Soil-Tunnel geometry: (a) Soil layers with the embedded triple tunnel complex. (b) Soil column w.r.t depth and type. (c) Enlarged triple tunnel complex section, also showing the truncated column w.r.t depth and type. (c) Enlarged triple tunnel complex section, also showing the truncated parts (units in ‘m’). (d) Shear wave velocity profile w.r.t depth. parts (units in ‘m’). (d). Shear wave velocity profile w.r.t depth. Table 1. Soil properties used in the study. Table 1. Soil properties used in the study. Permeability (m/s) Rayleigh Coecients Saturated Shear Rayleigh Soil Type Unit Weight Permeability (m/s) No. Strength Coefficients Saturated Unit3 Shear Strength Horizontal Vertical (kN/m ) (kPa) 3 No. Soil Type ( 10 ) Weight (kN/m ) (kPa) β 7 9 Horizontal Vertical α 1 Silty clay 18.4 29.9 5.5  10 2.50  10 9.660 0.776 −3 (×10 ) 6 8 2 Very soft silty clay 17.5 27.4 3.5  10 1.70  10 3.893 1.926 −7 −9 1 Silty clay 18.4 29.9 5.5 × 10 2.50 × 10 9.660 0.776 8 9 3 Very soft clay 16.9 19.8 5.13  10 1.91  10 1.771 4.238 Very soft 6 8 4 Clay 18 26.3 3.40  10 3.51  10 1.744 4.301 −6 −8 2 17.5 27.4 3.5 × 10 1.70 × 10 3.893 1.926 5 6 silty clay 5 Silty clay-silty sand 18.1 30 2.13  10 2.67  10 1.706 4.397 Very soft −8 −9 3 16.9 19.8 5.13 × 10 1.91 × 10 1.771 4.238 clay 4.2. Constitutive Model and Boundary Conditions −6 −8 4 Clay 18 26.3 3.40 × 10 3.51 × 10 1.744 4.301 TheSilty soil clay tunnel - system is modeled using Plaxis 2D, considering the Mohr-Coulomb constitutive −5 −6 5 18.1 30 2.13 × 10 2.67 × 10 1.706 4.397 silty sand model for the soils used by many other researchers [16,30,32]. In order to use for the dynamic analysis, Plaxis 2D makes use of the modified Mohr-Coulomb constitutive model. The shear, elastic moduli and other parameters in this model are dependent on the primary input of the shear wave velocity 4.2. Constitutive Model and Boundary Conditions of the soil medium and, thus, are calculated accordingly. Apart from this, shear and elastic moduli The soil tunnel system is modeled using Plaxis 2D, considering the Mohr-Coulomb constitutive variation w.r.t depth and confining stresses are also taken into account. The equations can be given by model for the soils used by many other researchers [16,30,32]. In order to use for the dynamic analysis, the equation below. Plaxis 2D makes use of the modified Mohr-Coulomb constitutive model. The shear, elastic moduli G = V (1) and other parameters in this model are dependent on the primary input of the shear wave velocity of the soil medium and, thus, are calculated accordingly. Apart from this, shear and elastic moduli ( ) E = 2G 1 +  (2) variation w.r.t depth and confining stresses are also taken into account. The equations can be given E(y) = E + y y E (3) re f re f inc by the equation below. where G is the shear modulus, V is the shear wave velocity, E is the elastic modulus,  is the s s (1) 𝐺= 𝛾𝑉 soil’s Poisson’s ratio, y is the depth in the vertical direction, E is the value of elastic modulus at ref 𝐸= 2𝐺(1 + 𝜐 ) (2) reference point, y is the depth of the reference point, and E is the increment in value of the elastic ref inc modulus [33,34]. 𝐸 (𝑦 ) =𝐸 +𝑦 −𝑦𝐸 (3) The seismic ground shaking produces cyclic stresses in the soil, which generates a hysteresis loop where G is the shear modulus, Vs is the shear wave velocity, E is the elastic modulus, υs is the soil’s with the dissipation of energy and damping. The Mohr-Coulomb soil model is an elastic-perfectly Poisson’s ratio, y is the depth in the vertical direction, Eref is the value of elastic modulus at reference plastic soil model and cannot capture this phenomenon. To cater this limitation, the Rayleigh viscous point, yref is the depth of the reference point, and Einc is the increment in value of the elastic modulus [33,34]. Depth (m) Appl. Sci. 2020, 10, 334 6 of 22 damping coecients are introduced through a frequency-dependent formulation, which is given by the equation below. !  !  !  ! 2 2 2 2 1 1 1 1 = 2! ! , = 2 (4) 1 2 2 2 2 2 ! ! ! ! 1 2 1 2 While ! (rad/s) = 2 f , ! (rad/s) = 2 f (5) 1 1 2 2 V 3V s s f (Hz) = , f (Hz) = (6) 1 2 4h 4h where and are the Rayleigh viscous damping coecients, ! is the angular frequency, h is the thickness of the soil layer, f and f are the first and second target frequencies, and  and  are the 1 2 1 2 respective damping ratios. The damping ratio is taken as 10% for all of the soil layers that attributes to the soft soil [35]. The damping coecients are calculated individually for each of the soil layers incorporated into the constitutive model definition. The tunnel lining and inner supporting structure are modeled using linear elastic plate elements as used by many other researchers in the past [8,9,16,17]. The Elastic modulus is taken as 37 MPa while the unit weight of concrete and the Poisson’s ratio are taken as 25 kN/m and 0.2, respectively. The lateral boundaries are kept far apart at a distance of 400 m based on the sensitivity analysis so that they do not interfere with the passage of earthquake waves. The tied degree of freedom condition is assigned to the lateral boundaries so that the left and right nodes move together while absorbing the lateral waves. This condition is used to simulate the free-field phenomenon of the soil. The base of the model is taken as rigid, which ensures that the waves do not escape and are reflected back into the model. The base is kept at a depth of 75 m and the earthquake signals are applied at the base of the model. The schematic diagram of the defined model geometry can be seen in Figure 2a. The model is discretized using 15-noded triangular elements with the mesh size selected based on Equation (7) given by Kuhlemeyer and Lysmer [36]. Dl = to (7) 10 8 And = (8) where Dl is the length of the finite elements and  is the wavelength, f is the frequency, and V is the least shear wave velocity among all the soil layers. The time-step also plays an important role in the overall accuracy of the results and, hence, is selected by the equation below. t = (9) m  n where t is the time step, t is the total time duration of the seismic vibration. In addition, m and n are the maximum number of steps and the number of sub-steps, respectively. This ensures that the waves do not pass more than one element at each time step. 4.3. Input Ground Motion Characteristics In order to evaluate the seismic performance of any structure, the major devastating earthquakes of higher magnitudes in history like Kobe (Japan, 1995), Loma Prieta (USA, 1989), Chi-Chi (Taiwan, 1999), and Coyote (USA, 1979) are used, which can be seen from the literature. In this study, two major earthquakes acceleration-time histories are used to analyze the dynamic behavior of the triple tunnel complex. The ground motions used are of the Coyote earthquake (USA, 1979) and the Kocaeli earthquake (Turkey, 1999). The acceleration-time histories, their Fourier response spectra, and spectral accelerations are shown in Figure 3a,b while their details are tabulated in Table 2. In order to use in the Appl. Sci. 2020, 10, 334 7 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 21 research, all of them are scaled to 0.4 g unless otherwise stated and named as input motion (IM) 1 and with the EC8 site class A and their average normalized curve compares well with the design 2, respectively. The spectral accelerations of the input motions are also compared with the EC8 site spectrum, which can be seen in Figure 3c. class A and their average normalized curve compares well with the design spectrum, which can be seen in Figure 3c. 0.15 Coyote Earthquake (1979) 0.1 0.05 -0.05 -0.1 -0.15 0 5 10 15 20 25 Dynamic time (s) 0.1 0.08 0.06 0.04 0.02 0 5 10 15 20 25 Frequency (Hz) 0.4 0.3 0.2 0.1 0.01 0.1 1 10 Period (s) (a) Figure 3. Cont. Fourier amplitude (g-s) Spectral acceleration (g) Acceleration (g) Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 21 Appl. Sci. 2020, 10, 334 8 of 22 0.2 Kocaeli earthquake (1999) 0.15 0.1 0.05 -0.05 -0.1 -0.15 -0.2 -0.25 0 5 10 15 20 25 30 Dynamic time (s) 0.1 0.08 0.06 0.04 0.02 0 5 10 15 20 25 Frequency (Hz) 0.8 0.6 0.4 0.2 0.01 0.1 1 10 Period (s) (b) Figure 3. Cont. Acceleration (g) Spectral acceleration (g) Fourier amplitude (g-s) Appl. Sci. 2020, 10, 334 9 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 21 3.5 Site class A (EC 8) 2.5 Coyote 1.5 Kocaeli Average 0.5 0 123 4 Time (s) (c) Figure 3. (a–c) Acceleration-Time history, the Fourier amplitude, and the spectral acceleration of (a) Figure 3. (a–c) Acceleration-Time history, the Fourier amplitude, and the spectral acceleration of Coyote earthquake (1979), (b) Kocaeli earthquake (1999), and (c) comparison of the normalized (a) Coyote earthquake (1979), (b) Kocaeli earthquake (1999), and (c) comparison of the normalized spectral accelerations with the design spectrum of site class A (Eurocode 8 or EC8). spectral accelerations with the design spectrum of site class A (EC8). Table 2. Input motion records. Table 2. Input motion records. Peak Epicenter Peak Ground Peak Ground Epicenter Peak Ground Magnitude Magnitude Ground No. Earthquake Station Year Distance Acceleration Velocity PGV No. Earthquake Station Year Distance Acceleration (Mw) (Mw) Velocity (Km) (Km) PGA (g PGA ) (g) (m/s) PGV (m/s) San Juan 1 Coyote, USA 1979 5.7 17.2 0.124 0.176 San Juan Bautista 1 Coyote, USA 1979 5.7 17.2 0.124 0.176 Bautista 2 Kocaeli, Turkey Arcelik 1999 7.4 17 0.218 0.177 2 Kocaeli, Turkey Arcelik 1999 7.4 17 0.218 0.177 5. Parametric Study 5. Parametric Study This research is focused on the dynamic analysis of a novel triple tunnel complex, which requires This research is focused on the dynamic analysis of a novel triple tunnel complex, which requires an exhaustive study. In order to better understand its behavior, a detailed parametric study is an exhaustive study. In order to better understand its behavior, a detailed parametric study is conducted conducted by varying the thickness of lining, inner supporting structures, and changing the by varying the thickness of lining, inner supporting structures, and changing the embedment depth to embedment depth to a tunnel complex width (C/H) ratio under the effect of variable amplitudes of a tunnel complex width (C/H) ratio under the e ect of variable amplitudes of seismic vibrations to seismic vibrations to determine the effect of each of the parameters on the overall tunnel deformations determine the e ect of each of the parameters on the overall tunnel deformations and the resulting and the resulting surface displacements. Apart from the parametric study, two other tunnel shapes surface displacements. Apart from the parametric study, two other tunnel shapes named a rectangular named a rectangular complex and the equivalent horizontal twin complex are also analyzed for the complex and the equivalent horizontal twin complex are also analyzed for the seismic-induced bending seismic-induced bending moments and thrusts. The obtained results are compared with the triple moments and thrusts. The obtained results are compared with the triple tunnel complex to evaluate its tunnel complex to evaluate its performance. On the basis of the results obtained, the conclusions are performance. On the basis of the results obtained, the conclusions are then drawn. then drawn. 5.1. E ect of the Variation in Lining Thickness 5.1. Effect of the Variation in Lining Thickness In order to study the e ect of tunnel lining thickness, the tunnel lining thickness is kept variable In order to study the effect of tunnel lining thickness, the tunnel lining thickness is kept variable from 0.4 m to 0.8 m, which constitutes 1.63% to 3.26% of the total tunnel width. All the other factors, from 0.4 m to 0.8 m, which constitutes 1.63% to 3.26% of the total tunnel width. All the other factors, i.e., inner structure’s thickness, the amplitude of the IM and the C/H ratio are kept constant and the i.e., inner structure’s thickness, the amplitude of the IM and the C/H ratio are kept constant and the overall surface displacements are calculated. Apart from this, the normalized tunnel deformations overall surface displacements are calculated. Apart from this, the normalized tunnel deformations and the bending moments are also computed. Normalized tunnel deformation is defined as the ratio and the bending moments are also computed. Normalized tunnel deformation is defined as the ratio of distortions between the top and bottom parts of the tunnel complex to the distortions at the same of distortions between the top and bottom parts of the tunnel complex to the distortions at the same points in the free-field. This parameter is important in determining the flexibility of the tunnel lining. points in the free-field. This parameter is important in determining the flexibility of the tunnel lining. From the results shown in Figure 4b, it can be depicted that the normalized tunnel deformations are From the results shown in Figure 4b, it can be depicted that the normalized tunnel deformations are almost equal to 1 when the lining thickness is 1 m. It means that the lining thickness greater than 1 m almost equal to 1 when the lining thickness is 1 m. It means that the lining thickness greater than 1 m would behave as rigid while a lesser thickness would act as flexible. The increased lining thickness would behave as rigid while a lesser thickness would act as flexible. The increased lining thickness causes a reduction in the flexibility of the tunnel and resistance to deformations increases. It also causes a reduction in the flexibility of the tunnel and resistance to deformations increases. It also results in the reduced surface heave with increased resistance to seismic-induced bending moments, Normalized Spectral Acceleration (g) Appl. Sci. 2020, 10, 334 10 of 22 results in the reduced surface heave with increased resistance to seismic-induced bending moments, which can be seen in Figure 4a–d. The results show a similar trend obtained in the reference study [16] and by Azadi and Hosseini [8]. From the figures, it is evident that the tunnel complex with thicker lining has greater resistance to the seismic-induced uplift, distortions, and bending moments. From the study, it was also noted that reduction in lining thickness from 0.4 m to 0.3 m made the tunnel Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 22 complex very fragile and resulted in the collapse of the structure. 0.09 Inner structure thickness = 0.4m 0.07 C/H = 0.5 0.05 IM 2 0.03 0.4 m 0.01 0.5 m 0.6 m -0.01 0.7 m 0.8 m -0.03 -200 -100 0 100 200 Distance from the Axis (m) (a) Inner structure thickness = 0.4m C/H = 0.5 IM 2 Rigid Flexible 00.5 11.522.5 Lining thickness (m) (b) Inner structure thickness = 0.4m C/H = 0.5 IM 2 00.5 1 1.522.5 Lining thickness (m) (c) Figure 4. Cont. Normalised tunnel deformation Bending Moment (kN-m/m) Surface displacements (m) (Δ /Δ ) str soil Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 22 0.12 Inner structure Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 22 Appl. Sci. 2020, 10, 334 11 of 22 thickness = 0.4m 0.1 C/H = 0.5 0.08 0.12 Inner structure IM 2 thickness = 0.4m 0.1 0.06 C/H = 0.5 0.08 0.04 IM 2 0.06 0.02 0.04 8000 9000 10000 11000 12000 13000 0.02 Bending Moment (kN-m/m) 8000 9000 10000 11000 12000 13000 (d) Bending Moment (kN-m/m) Figure 4. (a–d) Effect of variation in the lining thickness on (a) surface settlements, (b) normalized (d) tunnel deformations, (c) resisted bending moments, and (d) surface displacements vs. bending moments. Figure 4. (a–d) Effect of variation in the lining thickness on (a) surface settlements, (b) normalized Figure 4. (a–d) E ect of variation in the lining thickness on (a) surface settlements, (b) normalized tunnel tunnel deformations, (c) resisted bending moments, and (d) surface displacements vs. bending deformations, (c) resisted bending moments, and (d) surface displacements vs. bending moments. moments. 5.2. Effect of Variation in the Inner Structure 5.2. E ect of Variation in the Inner Structure The triple tunnel complex is formed by truncating some of the portions of the three closely 5.2. Effect of Variation in the Inner Structure The triple tunnel complex is formed by truncating some of the portions of the three closely spaced spaced tunnels and joining them with the slab and the concrete walls in between, as shown in Figure The triple tunnel complex is formed by truncating some of the portions of the three closely tunnels 2c [29]. Th and joining is inner st them ruct with ure p thela slab ys an i andm the port concr ant rol eteewalls in thin e ov between, erall dyn asashown mic behav in Figur ior oef t 2c he t [29r]. iple spaced tunnels and joining them with the slab and the concrete walls in between, as shown in Figure This tuinner nnel compl structur ex and e plays , hence an ,important is studied rin ole th in is re the sea overall rch. The t dynamic hicknebehavior ss is varie of d fr the om 0. triple 3 m t tunnel o 0.7 m 2c [29]. This inner structure plays an important role in the overall dynamic behavior of the triple complex while and, keepin hence, g all t ishstudied e other par in this amet resear ers, i ch. .e., The lining thickness thickness is ,varied C/H, and fromamp 0.3 m litud to e of t 0.7 mh while e IM as tunnel complex and, hence, is studied in this research. The thickness is varied from 0.3 m to 0.7 m keeping constant. Fro all the other m Figure parameters, 5, it can be seen that, i.e., lining thickness, asC the thi /H, andckness of amplitude the i of the nner supporti IM as constant. ng structure From while keeping all the other parameters, i.e., lining thickness, C/H, and amplitude of the IM as Figur incre econstant. Fro 5a , ses it can , the be sur m seen Figure face that, heave 5, asit can be seen that, decre the thickness ases. Even t of the haough t s the thi inner hsupporting ec reduct kness of ion i the i str s minima uctur nner supporti e incr l in co eases, n mparison g structure the surface to when heave the lin incre decr ing a eases. ses th , tic he kness Even surface i though s v he aave ried the decre byr t eduction h ase e s s. Ev ame en t amo is h minimal ough t unt, it he c in reduct an be comparison ion i infes rred minima to thwhen atl t in co he t the mparison hick lining er inn tthickness o e r when support ising the lining thickness is varied by the same amount, it can be inferred that the thicker inner supporting varied structure wo by the same uld amount, add to th ite enhanced can be inferr re ed sist that ance of t the thicker he triple t inner unn supporting el complex. structur From t e would he stud add y, itto was structure would add to the enhanced resistance of the triple tunnel complex. From the study, it was thea enhanced lso noted tha resistance t, when the t of the h triple ickness wa tunnels complex. further re Fr duced to 0.2 m, t om the study, ith was e tunnel compl also noted that, ex was una when the ble to also noted that, when the thickness was further reduced to 0.2 m, the tunnel complex was unable to thickness bear thwas e seifurther smic vib reduced rations an to d re 0.2 m, sult the ed in t tunnel he col complex lapse. was unable to bear the seismic vibrations bear the seismic vibrations and resulted in the collapse. and resulted in the collapse. 0.1 0.1 Lining thickness Lining thickness = 0.5 m = 0.5 m 0.08 0.08 C/H = 0.5 0.06 C/H = 0.5 0.06 0.04 IM 2 0.04 IM 2 0.3 m 0.3 m 0.02 0.02 0.4 m 0.4 m 0.5 m 0.5 m -0.02 0.6 m -0.02 0.6 m 0.7 m -0.04 0.7 m -0.04 -200 -100 0 100 200 -200 -100 0 100 200 Distance from the Axis (m) Distance from the Axis (m) Figure Figure 5. 5. E ect Effe ofct variation of variation in the in the thick thickness ness of ofthe the internal internal structure on structure on the surface the surface settlem settlements. ents. Figure 5. Effect of variation in the thickness of the internal structure on the surface settlements. 5.3. E ect of the Variation in the Amplitude of the Input Motion To study this e ect, the IM 1 is scaled up and down in order to have a range varying from 0.1 g to 0.5 g. Keeping all other parameters, i.e., tunnel thickness, inner structure thickness, C/H as a constant, Surface displacements (m) Surface displacements (m) Surface Displacments (m) Surface Displacments (m) Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 22 5.3. Effect of the Variation in the Amplitude of the Input Motion To study this effect, the IM 1 is scaled up and down in order to have a range varying from 0.1 g Appl. Sci. 2020, 10, 334 12 of 22 to 0.5 g. Keeping all other parameters, i.e., tunnel thickness, inner structure thickness, C/H as a constant, the IM is applied in order to compute the surface displacements and the corresponding the IM is applied in order to compute the surface displacements and the corresponding tunnel uplift. tunnel uplift. From Figure 6a and Figure 6b, it can be seen that, as the amplitude of the IM increases From Figure 6a,b, it can be seen that, as the amplitude of the IM increases from 0.1 g to 0.5 g, the surface from 0.1 g to 0.5 g, the surface heave increases from 0.011 m to 0.105 m. The increase in the amplitude heave increases from 0.011 m to 0.105 m. The increase in the amplitude of IM results in a greater of IM results in a greater tunnel uplift as compared to the surface heave, which is minimal at the tunnel uplift as compared to the surface heave, which is minimal at the lower amplitudes but more lower amplitudes but more pronounced at the higher amplitudes. This trend also follows a similar pronounced at the higher amplitudes. This trend also follows a similar pattern as obtained by Azadi pattern as obtained by Azadi and Hosseini [8]. and Hosseini [8]. 0.11 Lining thickness = 0.5m 0.09 Inner structuture thickness = 0.4m 0.07 C/H = 0.5 0.05 IM 1 0.03 0.5g 0.01 0.4g 0.3g -0.01 0.2g -0.03 0.1g -200 -100 0 100 200 Distance from the Axis (m) (a) 0.12 Lining thickness = 0.5 m Inner structure 0.09 thickness = 0.4 m C/H = 0.5 0.06 IM 1 Ground surface Tunnel 0.03 0 0.2 0.4 0.6 Acceleration (g) (b) Figure 6. (a, b) Effect of variation in the amplitude of input motion on (a) surface settlements and (b) Figure 6. (a,b) E ect of variation in the amplitude of input motion on (a) surface settlements and tunnel uplift in comparison to the surface heave. (b) tunnel uplift in comparison to the surface heave. 5.4. E ect of Variation in the Embedment Depth 5.4. Effect of Variation in the Embedment Depth To study the e ect of embedment depth on the dynamic behavior of the triple tunnel complex, To study the effect of embedment depth on the dynamic behavior of the triple tunnel complex, a tunnel with constant lining thickness and inner structure embedded at di erent C/H ratios was a tunnel with constant lining thickness and inner structure embedded at different C/H ratios was analyzed using a constant amplitude IM 2. Figure 7a,b are showing the detailed plots of the obtained analyzed using a constant amplitude IM 2. Figure 7a and Figure 7b are showing the detailed plots of settlements and normalized tunnel deformations. From Figure 7a, it is evident that, as the embedment depth increases, the amount of surface heave decreases while the plot in Figure 7b shows that the Displacements (m) Surface displacements (m) Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 22 the obtained settlements and normalized tunnel deformations. From Figure 7a, it is evident that, as Appl. Sci. 2020, 10, 334 13 of 22 the embedment depth increases, the amount of surface heave decreases while the plot in Figure 7b shows that the increased embedment depth causes the normalized tunnel deformations to decrease. It mea increased ns tha embedment t the triple tunnel depth causes complthe ex embedded normalizedde tunnel eper would h deformations ave more r to decr esistance to the ease. It means that linin the g di triple stortitunnel ons thacomplex n the sha embedded llower tunne deeper l complex. In would have othe mor r word e resistance s, a deeper embed to the lining ded tunn distortions el co than mplex the would shallower behav tunnel e as rcomplex. igid in comparison In other wor to ds, the same a deeper tunembedded nel complex tunnel embedded sh complex a would llowerbehave . as rigid in comparison to the same tunnel complex embedded shallower. 0.14 Lining thickness = 0.5 m 0.11 Inner structure thickness = 0.4 m 0.08 IM 2 0.05 C/H = 0.25 C/H = 0.5 0.02 C/H = 1 -0.01 C/H = 1.5 C/H = 2 -0.04 -200 -100 0 100 200 Distance from the Axis (m) (a) Inner structure thickness = 0.4m IM 2 C/H = 0.25 C/H = 0.5 C/H = 0.75 00.5 11.5 22.5 Lining thickness (m) (b) Figure 7. (a, b) Effect of variation in the embedment depth on: (a) surface settlements and (b) Figure 7. (a,b) E ect of variation in the embedment depth on: (a) surface settlements and (b) normalized normalized tunnel deformations. tunnel deformations. 5.5. E ect of Variation in the Shape of the Tunnel Complex 5.5. Effect of Variation in the Shape of the Tunnel Complex To study the e ect of shape on the dynamic behavior of the tunnel complex, two other shapes To study the effect of shape on the dynamic behavior of the tunnel complex, two other shapes named rectangular and an equivalent horizontal twin tunnel complex [29], which are shown in named rectangular and an equivalent horizontal twin tunnel complex [29], which are shown in Figure Figure 8a,b, respectively, are also analyzed. Keeping all other parameters, i.e., tunnel lining, inner 8a,b, respectively, are also analyzed. Keeping all other parameters, i.e., tunnel lining, inner structure, structure, embedment depth, and amplitude of the IM as constant, the thrusts and moments are embedment depth, and amplitude of the IM as constant, the thrusts and moments are computed for computed for the previously mentioned shapes and a comparison is made. Figure 9a–c are showing the previously mentioned shapes and a comparison is made. Figure 9a–c are showing the seismic- the seismic-induced bending moments and thrusts in the triple tunnel complex, rectangular tunnel induced bending moments and thrusts in the triple tunnel complex, rectangular tunnel complex, and complex, and equivalent horizontal twin tunnel complex, respectively. In order to compare the dynamic equivalent horizontal twin tunnel complex, respectively. In order to compare the dynamic performance, the surface displacements produced in the presence of each of the individual tunnel performance, the surface displacements produced in the presence of each of the individual tunnel complexes and the variation of moments and thrusts are plotted along the normalized tunnel perimeter, complexes and the variation of moments and thrusts are plotted along the normalized tunnel which can be seen in Figure 10a–d. From Figure 10a, it is clear that the surface heave developed in the Displacements above the Crown (m) Normalised tunnel deformation (Δ /Δ ) str soil Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 22 perimeter, which can be seen in Figure 10a–d. From Figure 10a, it is clear that the surface heave Appl. Sci. 2020, 10, 334 14 of 22 developed in the presence of a triple tunnel complex is the minimum among all, equaling 0.082 m, followed by 0.113 m by a rectangular tunnel complex while the maximum is produced by the presence of a triple tunnel complex is the minimum among all, equaling 0.082 m, followed by 0.113 m equivalent horizontal twin tunnel complex, which is 0.135 m, i.e., almost 36.44% and 63.85% more, by a rectangular tunnel complex while the maximum is produced by the equivalent horizontal twin respectively. From Figure 10b and Figure 10c, it can be noted that the resisted seismic-induced tunnel complex, which is 0.135 m, i.e., almost 36.44% and 63.85% more, respectively. From Figure 10b,c, bending moments along the normalized perimeter of about 0.375, 0.5, and 0.625, the resisted moments it can be noted that the resisted seismic-induced bending moments along the normalized perimeter in case of the triple tunnel complex are about 79.86% more than the rectangular tunnel complex. The of about 0.375, 0.5, and 0.625, the resisted moments in case of the triple tunnel complex are about maximum resisted moments compared to the equivalent horizontal twin complex are almost 6.55% 79.86% more than the rectangular tunnel complex. The maximum resisted moments compared to the more. equivalent horizontal twin complex are almost 6.55% more. (a) (b) Figure 8. (a,b) Tunnel complex with dimensions: (a) Rectangular. (b) Equivalent horizontal twin, also Figure 8. (a, b) Tunnel complex with dimensions: (a) Rectangular. (b) Equivalent horizontal twin, also showing the truncated parts (units in ‘m’). showing the truncated parts (units in ‘m’). Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 22 Appl. Sci. 2020, 10, 334 15 of 22 (a) Figure 9. Cont. Appl. Sci. 2020, 10, 334 16 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 22 (b) Figure 9. Cont. Appl. Sci. 2020, 10, 334 17 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 21 (c) (c) Figure 9. (a–c) Seismic-induced bending moments and thrusts in: (a) triple tunnel complex, (b) Figure 9. (a–c) Seismic-induced bending moments and thrusts in: (a) triple tunnel complex, (b) Figure 9. (a–c) Seismic-induced bending moments and thrusts in: (a) triple tunnel complex, equivalent twin tunnel complex, and (c) rectangular tunnel complex. rectangular tunnel complex, and (c) equivalent twin tunnel complex. (b) rectangular tunnel complex, and (c) equivalent twin tunnel complex. 0.14 Lining thickness = 0.5 m 0.14 Lining thickness = 0.5 m 0.11 Inner structure 0.11 thickness = 0.4 m Inner structure 0.08 thickness = 0.4 m C/H = 0.5 0.08 0.05 C/H = 0.5 IM 2 0.05 0.02 IM 2 Triple tunnel complex Triple tunnel 0.02 -0.01 Rectangular tunnel complex complex Rectangular tunnel -0.01 Equivalent twin -0.04 complex tunnel complex -200 -100 0 100 200 Equivalent twin -0.04 tunnel complex Distance from the Axis (m) -200 -100 0 100 200 Distance from the Axis (m) (a) Figure 10. Cont. (a) Surface displacements (m) Surface displacements (m) Appl. Sci. 2020, 10, 334 18 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 22 (b) Lining thickness = 0.5 m Inner structure thickness = 0.4 m C/H = 0.5 IM 2 Triple complex Rectangular complex -5000 Twin complex -10000 0 0.25 0.5 0.75 1 Normalized tunnel perimeter (c) Figure 10. Cont. Maximum moment (kN-m/m) Appl. Sci. 2020, 10, 334 19 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 22 -4500 Lining thickness = 0.5 m Inner structure -3500 thickness = 0.4 m C/H = 0.5 -2500 IM 2 Triple complex -1500 Rectangular complex Twin complex -500 0 0.25 0.5 0.75 1 Normalized tunnel perimeter (d) Figure 10. (a–d) Comparison among triple tunnel complex, equivalent twin tunnel complex, and Figure 10. (a–d) Comparison among triple tunnel complex, equivalent twin tunnel complex, and rectangular tunnel complex in terms of: (a) surface displacements, (b) normalized tunnel perimeter, rectangular tunnel complex in terms of: (a) surface displacements, (b) normalized tunnel perimeter, (c) maximum moments, and (d) maximum thrust generated along the perimeter. (c) maximum moments, and (d) maximum thrust generated along the perimeter. 6. Conclusions This research has been carried out to study the dynamic behavior of a triple tunnel complex in 6. Conclusions soft soil and the e ect of di erent parameters on the overall behavior in case of transversal shaking by an earthquake. From the detailed study conducted, the following conclusions are drawn. This research has been carried out to study the dynamic behavior of a triple tunnel complex in soft soil and the effect of different parameters on the overall behavior in case of transversal shaking (1) The increase in the lining thickness from 0.4 m to 0.8 m decreases the surface displacements from by an earthquake. From the detailed study conducted, the following conclusions are drawn. 0.088 m to 0.045 m, reduces the normalized tunnel deformations from 6.37 to 1.12, and the resisted seismic-induced bending moments increase from 8698.27 kN-m/m to 9568.54 kN-m/m, respectively. (1). The increase in the lining thickness from 0.4 m to 0.8 m decreases the surface displacements from (2) The increase in the thickness of the inner structure from 0.3 m to 0.7 m decreases the surface heave 0.088 m to 0.045 m, reduces the normalized tunnel deformations from 6.37 to 1.12, and the from 0.088 m to 0.069 m, respectively. resisted seismic-induced bending moments increase from 8698.27 kN-m/m to 9568.54 kN-m/m, (3) respectively. When the amplitude of the IM increases from 0.1 g to 0.5 g, the surface heave increases from (2). The incre 0.088 m to ase 0.106 in th m e t while hicknthe ess o tunnel f the uplift inner st incr ruct eases ure fr from om 0. 0.013 3 mm to to 0. 0.116 7 m decre m. ases the surface heave from 0.088 m to 0.069 m, respectively. (4) The change in embedment depth of the tunnel from 0.25 to 2 decreases the surface heave from (3). When the amplitude of the IM increases from 0.1 g to 0.5 g, the surface heave increases from 0.120 m to 0.051 m while the normalized tunnel deformations are also reduced. In other words, 0.088 m to 0.106 m while the tunnel uplift increases from 0.013 m to 0.116 m. the deeper embedded tunnel would act more rigid in comparison to the shallower embedded (4). The change in embedment depth of the tunnel from 0.25 to 2 decreases the surface heave from tunnel with the same lining thickness. 0.120 m to 0.051 m while the normalized tunnel deformations are also reduced. In other words, (5) The shape of the tunnel complex also plays an important role in its seismic behavior. The triple the deeper embedded tunnel would act more rigid in comparison to the shallower embedded tunnel complex results in a surface heave of 0.083 m as compared to 0.113 m and 0.136 m, which tunnel with the same lining thickness. are 36.44% and 63.85% more in the presence of a rectangular tunnel complex and the equivalent (5). The shape of the tunnel complex also plays an important role in its seismic behavior. The triple horizontal twin tunnel complex, respectively. tunnel complex results in a surface heave of 0.083 m as compared to 0.113 m and 0.136 m, which (6) The maximum resisted seismic-induced bending moments by the triple tunnel complex are are 36.44% and 63.85% more in the presence of a rectangular tunnel complex and the equivalent 33.37% less than that of the rectangular tunnel complex while 6.55% more than the equivalent horizontal twin tunnel complex, respectively. horizontal twin tunnel complex at the tunnel invert. Looking to the resisted seismic-induced (6). The maximum resisted seismic-induced bending moments by the triple tunnel complex are bending moments along the tunnel perimeter, it can be noted that, at the normalized perimeter of 33.37% less than that of the rectangular tunnel complex while 6.55% more than the equivalent about 0.375, 0.5, and 0.625, the resisted moments in case of the triple tunnel complex are about horizontal twin tunnel complex at the tunnel invert. Looking to the resisted seismic-induced 30.20% more while, at the crown level, about 79.86% more than at the rectangular tunnel complex. bending moments along the tunnel perimeter, it can be noted that, at the normalized perimeter From the conclusions drawn, it is evident that the triple tunnel complex resists more of about 0.375, 0.5, and 0.625, the resisted moments in case of the triple tunnel complex are about seismic-induced bending moments than that of the equivalent horizontal twin tunnel complex 30.20% more while, at the crown level, about 79.86% more than at the rectangular tunnel and the rectangular tunnel complex. The produced surface heaves are the least among the three complex. shapes as well. This highlights the performance of a triple tunnel complex against the transversal From the conclusions drawn, it is evident that the triple tunnel complex resists more seismic- seismic vibrations. induced bending moments than that of the equivalent horizontal twin tunnel complex and the rectangular tunnel complex. The produced surface heaves are the least among the three shapes as Maximum thrust (kN/m) Appl. Sci. 2020, 10, 334 20 of 22 7. Limitations Since this study comprises of a new, unconventional shape that lacks analytical solutions, the reliability of results is based on the comparison of seismic-induced bending moments and thrusts results with the analytical solutions of the reference model. For more authenticity, analytical solutions addressing this particular shape are needed to develop. Apart from this, experimentation using centrifuge must be conducted in order to validate and compare the results. Currently, the literature lacks research regarding this unique shape. Hence, on the basis of the reference model, the Mohr-Coulomb model modified for incorporating the e ect of cyclic stresses using viscous damping and moduli increment is used in order to compare the results. Since the earthquake also results in the shear modulus degradation with the development of shear strains, advanced models like the Hardening strain with small strain sti ness (HS ) or the soft soil model should also be used. The results should small be compared and more refined. 8. Future Work This research is focused on the detailed parametric study of the triplet tunnel complex and its comparison with the other tunnel shapes numerically. In this research, continuous tunnel lining is used with the minimal internal structure thickness for the analyses. Therefore, the conclusions are valid for that condition. It is recommended that the e ect of segmental lining and fortification of the tunnel complex using a thicker internal structure should also be evaluated. 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Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking

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applied sciences Article Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking Ahsan Naseem * , Muhammad Kashif, Nouman Iqbal, Ken Schotte and Hans De Backer Department of Civil Engineering, Ghent University, Technologiepark 60, B-9052 Zwijnaarde, Belgium; muhammad.kashif@ugent.be (M.K.); nouman.iqbal@ugent.be (N.I.); ken.schotte@ugent.be (K.S.); hans.debacker@ugent.be (H.D.B.) * Correspondence: ahsan.naseem@ugent.be Received: 8 December 2019; Accepted: 30 December 2019; Published: 2 January 2020 Abstract: Combining multiple tunnels into a single tunnel complex while keeping the surrounding area compact is a complicated procedure. The condition becomes more complex when soft soil is present and the area is prone to seismic activity. Seismic vibrations produce sudden ground shaking, which causes a sharp decrease in the shear strength and bearing capacity of the soil. This results in larger ground displacements and deformation of structures located at the surface and within the soil mass. The deformations are more pronounced at shallower depths and near the ground surface. Tunnels located in that area are also a ected and can undergo excessive distortions and uplift. The condition becomes worse if the tunnel area is larger, and, thus, the respective tunnel complex needs to be properly evaluated. In this research, a novel triple tunnel complex formed by combining three closely spaced tunnels is numerically analyzed using Plaxis 2D software under variable dynamic loadings. The e ect of variations in lining thickness, the inner supporting structure, embedment depth on the produced ground displacements, tunnel deformations, resisting bending moments, and the developed thrusts are studied in detail. The triple tunnel complex is also compared with the rectangular and equivalent horizontal twin tunnel complexes in terms of generated thrusts and resisted seismic-induced bending moments. From the results, it is concluded that increased thickness of the lining, inner structure, and greater embedment depth results in decreased ground displacements, tunnel deformations, and increased resistance to seismic-induced bending moments. The comparison of shapes revealed that the triple tunnel complex has better resistance against moments with the least amount of thrust and surface heave produced. Keywords: triple tunnel complex; soft soil; seismic response; finite element analysis 1. Introduction Tunnels are one of the important means of underground transportation. They are useful in the build-up area where further surface construction in order to accommodate large trac infrastructure is not possible. Second, they also provide fast, uninterrupted flow from one point to the other. Many densely populated cities in the world are now planning to provide metro lines through an underground tunnel system. Although it has many useful purposes, at the same time, it is vulnerable to excessive damage if present in an earthquake-prone area. The condition becomes more critical when multiple tunnels lie in closer proximity. Previously, it was believed that the underground structures are less prone to damage in comparison with the on-surface constructions, but major earthquakes in the recent past like Kobe (1995), Coyote (1979), Kocaeli (1999), Chi-Chi (1999), etc. have proved these to be equally vulnerable. The damage su ered by the tunnels depends upon the type of surrounding soil, embedment depth, the amplitude of the earthquake, and the groundwater table (GWT) conditions. The type of soil plays a very important role in the overall behavior of tunnels under seismic activity. Appl. Sci. 2020, 10, 334; doi:10.3390/app10010334 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 334 2 of 22 Tunnels constructed in soft soil are far vulnerable to severe damage than in dense rock. Similarly, the more shallow tunnels su er more distortions in comparison to the deeper ones [1]. Researchers now focus on the dynamic behavior of tunnels in di erent types of rocks and soils. Wang [2], Penzien [3], and Bobet [4] developed closed-form solutions to estimate the seismically-induced moments and thrust in rectangular and circular tunnels causing racking and ovaling, respectively. Hashash and Hook et al. [5] and Hashash and Park et al. [6] conducted an extensive review of the available methods used to determine seismic induced forces that aid in the seismic design of di erent tunnels. Liu and Song [7] and Azadi and Hosseini [8] studied the seismic behavior of shallow tunnels subjected to horizontal and vertical shaking in the liquefiable sands in order to assess the distortions occurring in the tunnel lining and its uplift due to excess pore pressure generation. Unutmaz [9] investigated the liquefaction possibilities of soil surrounding the tunnels using 3D finite element modeling (FEM) and studied the acceleration variations and the power spectra developed under the seismic vibrations for various tunnel embedment depths. Lanzano and Bilotta et al. [10] studied the behavior of circular tunnels, both using a centrifuge and analytical modeling in order to determine the hoop forces and the distortions produced in the tunnel lining and concluded that both techniques produce results in good agreement. Cilinger and Madabhushi performed centrifuge tests to study the e ect of embedment depth and behavior of circular and rectangular tunnels in dry sand subjected to di erent intensity seismic vibrations [11–13]. Qiu and Xie et al. [14] conducted centrifuge testing to study the e ect of ground movements and the interaction between twin tunnels in loess and concluded on the optimized spacing and the interval between the tunnels. Shahrour and Khoshnoudian et al. [15] numerically studied the seismically-induced bending moments and soil dilatancy around tunnels in soft soils. Patil and Choudhury et al. [16] performed FEM on circular tunnels and studied the lining distortions, bending moments under variable ground vibrations, and di erent embedment depth and tunnel lining thickness to develop better understanding of tunnel behavior in soft soils. Tsinidis [17] conducted FEM to study response characteristics of rectangular tunnels under seismic shaking varying the tunnel-soil interface properties and input motion characteristics embedment depths and concluded in the development of racking-flexibility (RF) relations for rectangular tunnels in soft soils. Apart from this, the response of underground tunnels subjected to seismic ground shaking have been studied experimentally (Chian and Madabhushi [18], Graziani and Boldini [19], Chian and Madabhushi [20], Abuhajar and Naggar et al. [21]), analytically (Power et al. [1], Chian and Tokimatsu [22], Bobet and Fernandez et al. [23]) and numerically (Chou and Yang et al. [24], Amorosi and Boldini [25], Baziar and Moghadam et al. [26], Huo and Bobet et al. [27], Nguyen and Lee et al. [28]). However, all literature considers the conventional circular, rectangular or horseshoe shapes. None of them has studied the behavior of multiple tunnels that have been combined to form a single tunnel complex of an unconventional shape. This research includes the dynamic response of a new, unconventional tunnel shape, which is proposed to be constructed in Brussels, which is the capital of Belgium, and has never been used earlier. The literature also lacks analytical solutions for it. This shape has resulted from the combination of three closely spaced tunnels into a triplet complex that would carry multiple train tracks for the underground trac movement and has been discussed with respect to construction arrangements by Naseem and Schotte et al. [29]. This unconventional triplet complex in soft soil has been numerically studied in detail using the dynamic module of FEM software Plaxis 2D under variable seismic vibrations and embedment depths in order to determine the tunnel distortions, which results in ground settlements, seismically-induced bending moments and axial forces, and make the comparison with the conventional rectangular complex and the equivalent horizontal twin tunnel complex. This study would help determine the optimized tunnel parameters and to understand the dynamic behavior of this unique tunnel shape in a better way. Appl. Sci. 2020, 10, 334 3 of 22 2. Stages of Analysis The research is comprised of static and dynamic analyses. First, the tunnel system is analyzed Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 21 statically. Since it is a long-term response, drained conditions are considered. After the equilibrium conditions are established, the dynamic analyses are performed, which include rapid ground shaking. conditions are established, the dynamic analyses are performed, which include rapid ground Therefore, undrained conditions are considered at that stage. shaking. Therefore, undrained conditions are considered at that stage. 3. Reference Model 3. Reference Model This research focuses on the parametric study of an unconventional shape and a unique triple This research focuses on the parametric study of an unconventional shape and a unique triple tunnel complex under seismic shaking in order to evaluate deformations in tunnel lining, moments, tunnel complex under seismic shaking in order to evaluate deformations in tunnel lining, moments, and thr and thrust devel ust developed. oped. As studi As studied ed f for or the the f first irst ti time, me, it it la lacks cks th the e ana analytical lytical solsolutions. utions. HencHence, e, it is it is compared with a reference model. The reference model considered in this case is taken from the compared with a reference model. The reference model considered in this case is taken from the research of Milind and Choudhury et al. [16]. It comprises of a circular tunnel with a diameter of 6 m research of Milind and Choudhury et al. [16]. It comprises of a circular tunnel with a diameter of 6 analyzed using FEM software Plaxis 2D under different seismic vibrations. The Mohr-Coulomb m analyzed using FEM software Plaxis 2D under di erent seismic vibrations. The Mohr-Coulomb constitutive model was used in the research and the results of the developed thrusts and moments constitutive model was used in the research and the results of the developed thrusts and moments were were compared with the analytical solutions of Wang [2], Penizen [3], and Bobet [4] as shown in compared with the analytical solutions of Wang [2], Penizen [3], and Bobet [4] as shown in Figure 1. Figure 1. The results obtained were in close agreement except from one anomalous result of thrust in The results obtained were in close agreement except from one anomalous result of thrust in case of case of Penizen [3], which indicates their accuracy. Penizen [3], which indicates their accuracy. In this research, the seismic shaking of a triple tunnel complex is analyzed using the same FEM In this research, the seismic shaking of a triple tunnel complex is analyzed using the same FEM suite with the same layered soil system and the constitutive model so that the obtained results have suiteth with e con the fidesame nce of layer accured acysoil . system and the constitutive model so that the obtained results have the confidence of accuracy. Thrust, T (kN/m) Wang (1993) Penizen (2000) Bobet (2010) 0 200 400 600 800 Numerical analysis (a) Bending Moment, M (kN-m/m) Wang (1993) Penizen (2000) Bobet (2010) 0 250 500 750 1000 Numerical analysis (b) Figure 1. Comparison between numerical and analytical solutions: (a) thrust and (b) bending moment Figure 1. Comparison between numerical and analytical solutions: (a) thrust and (b) bending [16]. moment [16]. Analytical solution Analytical solution Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 21 Appl. Sci. 2020, 10, 334 4 of 22 4. Details of the Finite Element Analysis 4. Details of the Finite Element Analysis 4.1. Software and Soil Parameters 4.1. Software and Soil Parameters In this study, the FEM program Plaxis 2D is used, which offers a wide range of constitutive models and different modules to numerically analyze both the linear and non-linear behavior of the In this study, the FEM program Plaxis 2D is used, which o ers a wide range of constitutive soil and tunnel structure. A layered soil system is considered to have a soft silty clay layer underlain models and di erent modules to numerically analyze both the linear and non-linear behavior of the by silty clay, very soft silty clay, clay, and silty clay with silty sand, respectively, as used by Hu and soil and tunnel structure. A layered soil system is considered to have a soft silty clay layer underlain Yue et al. [30] along with Milind and Choudhury et al. [16]. The soil media is taken as fully saturated by silty clay, very soft silty clay, clay, and silty clay with silty sand, respectively, as used by Hu and with the GWT considered to be at the ground level. The triple tunnel complex is provided in the soil Yue et al. [30] along with Milind and Choudhury et al. [16]. The soil media is taken as fully saturated system keeping the embedment depth (C) and tunnel complex width (H) as a variable. The triple with the GWT considered to be at the ground level. The triple tunnel complex is provided in the soil tunnel complex along with the layered soil system is shown by Figure 2a–c while the detailed soil system keeping the embedment depth (C) and tunnel complex width (H) as a variable. The triple properties used in the study are tabulated in Table 1. This layered soil system is categorized as soft tunnel complex along with the layered soil system is shown by Figure 2a–c while the detailed soil soil with soil type D, according to Euro code (EC 8) [31] based on its shear wave profile given in properties used in the study are tabulated in Table 1. This layered soil system is categorized as soft soil Figure 2d. with soil type D, according to Euro code (EC 8) [31] based on its shear wave profile given in Figure 2d. (a) (b) (c) Figure 2. Cont. Appl. Appl. Sci. Sci. 2020 2020,, 10 10,, x FO 334 R PEER REVIEW 5 of 5 of 21 22 110 140 170 200 Shear wave velocity (m/s) (d) Figure 2. (a–c) Soil-Tunnel geometry: (a) Soil layers with the embedded triple tunnel complex. (b) Soil Figure 2. (a–c) Soil-Tunnel geometry: (a) Soil layers with the embedded triple tunnel complex. (b) Soil column w.r.t depth and type. (c) Enlarged triple tunnel complex section, also showing the truncated column w.r.t depth and type. (c) Enlarged triple tunnel complex section, also showing the truncated parts (units in ‘m’). (d) Shear wave velocity profile w.r.t depth. parts (units in ‘m’). (d). Shear wave velocity profile w.r.t depth. Table 1. Soil properties used in the study. Table 1. Soil properties used in the study. Permeability (m/s) Rayleigh Coecients Saturated Shear Rayleigh Soil Type Unit Weight Permeability (m/s) No. Strength Coefficients Saturated Unit3 Shear Strength Horizontal Vertical (kN/m ) (kPa) 3 No. Soil Type ( 10 ) Weight (kN/m ) (kPa) β 7 9 Horizontal Vertical α 1 Silty clay 18.4 29.9 5.5  10 2.50  10 9.660 0.776 −3 (×10 ) 6 8 2 Very soft silty clay 17.5 27.4 3.5  10 1.70  10 3.893 1.926 −7 −9 1 Silty clay 18.4 29.9 5.5 × 10 2.50 × 10 9.660 0.776 8 9 3 Very soft clay 16.9 19.8 5.13  10 1.91  10 1.771 4.238 Very soft 6 8 4 Clay 18 26.3 3.40  10 3.51  10 1.744 4.301 −6 −8 2 17.5 27.4 3.5 × 10 1.70 × 10 3.893 1.926 5 6 silty clay 5 Silty clay-silty sand 18.1 30 2.13  10 2.67  10 1.706 4.397 Very soft −8 −9 3 16.9 19.8 5.13 × 10 1.91 × 10 1.771 4.238 clay 4.2. Constitutive Model and Boundary Conditions −6 −8 4 Clay 18 26.3 3.40 × 10 3.51 × 10 1.744 4.301 TheSilty soil clay tunnel - system is modeled using Plaxis 2D, considering the Mohr-Coulomb constitutive −5 −6 5 18.1 30 2.13 × 10 2.67 × 10 1.706 4.397 silty sand model for the soils used by many other researchers [16,30,32]. In order to use for the dynamic analysis, Plaxis 2D makes use of the modified Mohr-Coulomb constitutive model. The shear, elastic moduli and other parameters in this model are dependent on the primary input of the shear wave velocity 4.2. Constitutive Model and Boundary Conditions of the soil medium and, thus, are calculated accordingly. Apart from this, shear and elastic moduli The soil tunnel system is modeled using Plaxis 2D, considering the Mohr-Coulomb constitutive variation w.r.t depth and confining stresses are also taken into account. The equations can be given by model for the soils used by many other researchers [16,30,32]. In order to use for the dynamic analysis, the equation below. Plaxis 2D makes use of the modified Mohr-Coulomb constitutive model. The shear, elastic moduli G = V (1) and other parameters in this model are dependent on the primary input of the shear wave velocity of the soil medium and, thus, are calculated accordingly. Apart from this, shear and elastic moduli ( ) E = 2G 1 +  (2) variation w.r.t depth and confining stresses are also taken into account. The equations can be given E(y) = E + y y E (3) re f re f inc by the equation below. where G is the shear modulus, V is the shear wave velocity, E is the elastic modulus,  is the s s (1) 𝐺= 𝛾𝑉 soil’s Poisson’s ratio, y is the depth in the vertical direction, E is the value of elastic modulus at ref 𝐸= 2𝐺(1 + 𝜐 ) (2) reference point, y is the depth of the reference point, and E is the increment in value of the elastic ref inc modulus [33,34]. 𝐸 (𝑦 ) =𝐸 +𝑦 −𝑦𝐸 (3) The seismic ground shaking produces cyclic stresses in the soil, which generates a hysteresis loop where G is the shear modulus, Vs is the shear wave velocity, E is the elastic modulus, υs is the soil’s with the dissipation of energy and damping. The Mohr-Coulomb soil model is an elastic-perfectly Poisson’s ratio, y is the depth in the vertical direction, Eref is the value of elastic modulus at reference plastic soil model and cannot capture this phenomenon. To cater this limitation, the Rayleigh viscous point, yref is the depth of the reference point, and Einc is the increment in value of the elastic modulus [33,34]. Depth (m) Appl. Sci. 2020, 10, 334 6 of 22 damping coecients are introduced through a frequency-dependent formulation, which is given by the equation below. !  !  !  ! 2 2 2 2 1 1 1 1 = 2! ! , = 2 (4) 1 2 2 2 2 2 ! ! ! ! 1 2 1 2 While ! (rad/s) = 2 f , ! (rad/s) = 2 f (5) 1 1 2 2 V 3V s s f (Hz) = , f (Hz) = (6) 1 2 4h 4h where and are the Rayleigh viscous damping coecients, ! is the angular frequency, h is the thickness of the soil layer, f and f are the first and second target frequencies, and  and  are the 1 2 1 2 respective damping ratios. The damping ratio is taken as 10% for all of the soil layers that attributes to the soft soil [35]. The damping coecients are calculated individually for each of the soil layers incorporated into the constitutive model definition. The tunnel lining and inner supporting structure are modeled using linear elastic plate elements as used by many other researchers in the past [8,9,16,17]. The Elastic modulus is taken as 37 MPa while the unit weight of concrete and the Poisson’s ratio are taken as 25 kN/m and 0.2, respectively. The lateral boundaries are kept far apart at a distance of 400 m based on the sensitivity analysis so that they do not interfere with the passage of earthquake waves. The tied degree of freedom condition is assigned to the lateral boundaries so that the left and right nodes move together while absorbing the lateral waves. This condition is used to simulate the free-field phenomenon of the soil. The base of the model is taken as rigid, which ensures that the waves do not escape and are reflected back into the model. The base is kept at a depth of 75 m and the earthquake signals are applied at the base of the model. The schematic diagram of the defined model geometry can be seen in Figure 2a. The model is discretized using 15-noded triangular elements with the mesh size selected based on Equation (7) given by Kuhlemeyer and Lysmer [36]. Dl = to (7) 10 8 And = (8) where Dl is the length of the finite elements and  is the wavelength, f is the frequency, and V is the least shear wave velocity among all the soil layers. The time-step also plays an important role in the overall accuracy of the results and, hence, is selected by the equation below. t = (9) m  n where t is the time step, t is the total time duration of the seismic vibration. In addition, m and n are the maximum number of steps and the number of sub-steps, respectively. This ensures that the waves do not pass more than one element at each time step. 4.3. Input Ground Motion Characteristics In order to evaluate the seismic performance of any structure, the major devastating earthquakes of higher magnitudes in history like Kobe (Japan, 1995), Loma Prieta (USA, 1989), Chi-Chi (Taiwan, 1999), and Coyote (USA, 1979) are used, which can be seen from the literature. In this study, two major earthquakes acceleration-time histories are used to analyze the dynamic behavior of the triple tunnel complex. The ground motions used are of the Coyote earthquake (USA, 1979) and the Kocaeli earthquake (Turkey, 1999). The acceleration-time histories, their Fourier response spectra, and spectral accelerations are shown in Figure 3a,b while their details are tabulated in Table 2. In order to use in the Appl. Sci. 2020, 10, 334 7 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 21 research, all of them are scaled to 0.4 g unless otherwise stated and named as input motion (IM) 1 and with the EC8 site class A and their average normalized curve compares well with the design 2, respectively. The spectral accelerations of the input motions are also compared with the EC8 site spectrum, which can be seen in Figure 3c. class A and their average normalized curve compares well with the design spectrum, which can be seen in Figure 3c. 0.15 Coyote Earthquake (1979) 0.1 0.05 -0.05 -0.1 -0.15 0 5 10 15 20 25 Dynamic time (s) 0.1 0.08 0.06 0.04 0.02 0 5 10 15 20 25 Frequency (Hz) 0.4 0.3 0.2 0.1 0.01 0.1 1 10 Period (s) (a) Figure 3. Cont. Fourier amplitude (g-s) Spectral acceleration (g) Acceleration (g) Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 21 Appl. Sci. 2020, 10, 334 8 of 22 0.2 Kocaeli earthquake (1999) 0.15 0.1 0.05 -0.05 -0.1 -0.15 -0.2 -0.25 0 5 10 15 20 25 30 Dynamic time (s) 0.1 0.08 0.06 0.04 0.02 0 5 10 15 20 25 Frequency (Hz) 0.8 0.6 0.4 0.2 0.01 0.1 1 10 Period (s) (b) Figure 3. Cont. Acceleration (g) Spectral acceleration (g) Fourier amplitude (g-s) Appl. Sci. 2020, 10, 334 9 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 21 3.5 Site class A (EC 8) 2.5 Coyote 1.5 Kocaeli Average 0.5 0 123 4 Time (s) (c) Figure 3. (a–c) Acceleration-Time history, the Fourier amplitude, and the spectral acceleration of (a) Figure 3. (a–c) Acceleration-Time history, the Fourier amplitude, and the spectral acceleration of Coyote earthquake (1979), (b) Kocaeli earthquake (1999), and (c) comparison of the normalized (a) Coyote earthquake (1979), (b) Kocaeli earthquake (1999), and (c) comparison of the normalized spectral accelerations with the design spectrum of site class A (Eurocode 8 or EC8). spectral accelerations with the design spectrum of site class A (EC8). Table 2. Input motion records. Table 2. Input motion records. Peak Epicenter Peak Ground Peak Ground Epicenter Peak Ground Magnitude Magnitude Ground No. Earthquake Station Year Distance Acceleration Velocity PGV No. Earthquake Station Year Distance Acceleration (Mw) (Mw) Velocity (Km) (Km) PGA (g PGA ) (g) (m/s) PGV (m/s) San Juan 1 Coyote, USA 1979 5.7 17.2 0.124 0.176 San Juan Bautista 1 Coyote, USA 1979 5.7 17.2 0.124 0.176 Bautista 2 Kocaeli, Turkey Arcelik 1999 7.4 17 0.218 0.177 2 Kocaeli, Turkey Arcelik 1999 7.4 17 0.218 0.177 5. Parametric Study 5. Parametric Study This research is focused on the dynamic analysis of a novel triple tunnel complex, which requires This research is focused on the dynamic analysis of a novel triple tunnel complex, which requires an exhaustive study. In order to better understand its behavior, a detailed parametric study is an exhaustive study. In order to better understand its behavior, a detailed parametric study is conducted conducted by varying the thickness of lining, inner supporting structures, and changing the by varying the thickness of lining, inner supporting structures, and changing the embedment depth to embedment depth to a tunnel complex width (C/H) ratio under the effect of variable amplitudes of a tunnel complex width (C/H) ratio under the e ect of variable amplitudes of seismic vibrations to seismic vibrations to determine the effect of each of the parameters on the overall tunnel deformations determine the e ect of each of the parameters on the overall tunnel deformations and the resulting and the resulting surface displacements. Apart from the parametric study, two other tunnel shapes surface displacements. Apart from the parametric study, two other tunnel shapes named a rectangular named a rectangular complex and the equivalent horizontal twin complex are also analyzed for the complex and the equivalent horizontal twin complex are also analyzed for the seismic-induced bending seismic-induced bending moments and thrusts. The obtained results are compared with the triple moments and thrusts. The obtained results are compared with the triple tunnel complex to evaluate its tunnel complex to evaluate its performance. On the basis of the results obtained, the conclusions are performance. On the basis of the results obtained, the conclusions are then drawn. then drawn. 5.1. E ect of the Variation in Lining Thickness 5.1. Effect of the Variation in Lining Thickness In order to study the e ect of tunnel lining thickness, the tunnel lining thickness is kept variable In order to study the effect of tunnel lining thickness, the tunnel lining thickness is kept variable from 0.4 m to 0.8 m, which constitutes 1.63% to 3.26% of the total tunnel width. All the other factors, from 0.4 m to 0.8 m, which constitutes 1.63% to 3.26% of the total tunnel width. All the other factors, i.e., inner structure’s thickness, the amplitude of the IM and the C/H ratio are kept constant and the i.e., inner structure’s thickness, the amplitude of the IM and the C/H ratio are kept constant and the overall surface displacements are calculated. Apart from this, the normalized tunnel deformations overall surface displacements are calculated. Apart from this, the normalized tunnel deformations and the bending moments are also computed. Normalized tunnel deformation is defined as the ratio and the bending moments are also computed. Normalized tunnel deformation is defined as the ratio of distortions between the top and bottom parts of the tunnel complex to the distortions at the same of distortions between the top and bottom parts of the tunnel complex to the distortions at the same points in the free-field. This parameter is important in determining the flexibility of the tunnel lining. points in the free-field. This parameter is important in determining the flexibility of the tunnel lining. From the results shown in Figure 4b, it can be depicted that the normalized tunnel deformations are From the results shown in Figure 4b, it can be depicted that the normalized tunnel deformations are almost equal to 1 when the lining thickness is 1 m. It means that the lining thickness greater than 1 m almost equal to 1 when the lining thickness is 1 m. It means that the lining thickness greater than 1 m would behave as rigid while a lesser thickness would act as flexible. The increased lining thickness would behave as rigid while a lesser thickness would act as flexible. The increased lining thickness causes a reduction in the flexibility of the tunnel and resistance to deformations increases. It also causes a reduction in the flexibility of the tunnel and resistance to deformations increases. It also results in the reduced surface heave with increased resistance to seismic-induced bending moments, Normalized Spectral Acceleration (g) Appl. Sci. 2020, 10, 334 10 of 22 results in the reduced surface heave with increased resistance to seismic-induced bending moments, which can be seen in Figure 4a–d. The results show a similar trend obtained in the reference study [16] and by Azadi and Hosseini [8]. From the figures, it is evident that the tunnel complex with thicker lining has greater resistance to the seismic-induced uplift, distortions, and bending moments. From the study, it was also noted that reduction in lining thickness from 0.4 m to 0.3 m made the tunnel Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 22 complex very fragile and resulted in the collapse of the structure. 0.09 Inner structure thickness = 0.4m 0.07 C/H = 0.5 0.05 IM 2 0.03 0.4 m 0.01 0.5 m 0.6 m -0.01 0.7 m 0.8 m -0.03 -200 -100 0 100 200 Distance from the Axis (m) (a) Inner structure thickness = 0.4m C/H = 0.5 IM 2 Rigid Flexible 00.5 11.522.5 Lining thickness (m) (b) Inner structure thickness = 0.4m C/H = 0.5 IM 2 00.5 1 1.522.5 Lining thickness (m) (c) Figure 4. Cont. Normalised tunnel deformation Bending Moment (kN-m/m) Surface displacements (m) (Δ /Δ ) str soil Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 22 0.12 Inner structure Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 22 Appl. Sci. 2020, 10, 334 11 of 22 thickness = 0.4m 0.1 C/H = 0.5 0.08 0.12 Inner structure IM 2 thickness = 0.4m 0.1 0.06 C/H = 0.5 0.08 0.04 IM 2 0.06 0.02 0.04 8000 9000 10000 11000 12000 13000 0.02 Bending Moment (kN-m/m) 8000 9000 10000 11000 12000 13000 (d) Bending Moment (kN-m/m) Figure 4. (a–d) Effect of variation in the lining thickness on (a) surface settlements, (b) normalized (d) tunnel deformations, (c) resisted bending moments, and (d) surface displacements vs. bending moments. Figure 4. (a–d) Effect of variation in the lining thickness on (a) surface settlements, (b) normalized Figure 4. (a–d) E ect of variation in the lining thickness on (a) surface settlements, (b) normalized tunnel tunnel deformations, (c) resisted bending moments, and (d) surface displacements vs. bending deformations, (c) resisted bending moments, and (d) surface displacements vs. bending moments. moments. 5.2. Effect of Variation in the Inner Structure 5.2. E ect of Variation in the Inner Structure The triple tunnel complex is formed by truncating some of the portions of the three closely 5.2. Effect of Variation in the Inner Structure The triple tunnel complex is formed by truncating some of the portions of the three closely spaced spaced tunnels and joining them with the slab and the concrete walls in between, as shown in Figure The triple tunnel complex is formed by truncating some of the portions of the three closely tunnels 2c [29]. Th and joining is inner st them ruct with ure p thela slab ys an i andm the port concr ant rol eteewalls in thin e ov between, erall dyn asashown mic behav in Figur ior oef t 2c he t [29r]. iple spaced tunnels and joining them with the slab and the concrete walls in between, as shown in Figure This tuinner nnel compl structur ex and e plays , hence an ,important is studied rin ole th in is re the sea overall rch. The t dynamic hicknebehavior ss is varie of d fr the om 0. triple 3 m t tunnel o 0.7 m 2c [29]. This inner structure plays an important role in the overall dynamic behavior of the triple complex while and, keepin hence, g all t ishstudied e other par in this amet resear ers, i ch. .e., The lining thickness thickness is ,varied C/H, and fromamp 0.3 m litud to e of t 0.7 mh while e IM as tunnel complex and, hence, is studied in this research. The thickness is varied from 0.3 m to 0.7 m keeping constant. Fro all the other m Figure parameters, 5, it can be seen that, i.e., lining thickness, asC the thi /H, andckness of amplitude the i of the nner supporti IM as constant. ng structure From while keeping all the other parameters, i.e., lining thickness, C/H, and amplitude of the IM as Figur incre econstant. Fro 5a , ses it can , the be sur m seen Figure face that, heave 5, asit can be seen that, decre the thickness ases. Even t of the haough t s the thi inner hsupporting ec reduct kness of ion i the i str s minima uctur nner supporti e incr l in co eases, n mparison g structure the surface to when heave the lin incre decr ing a eases. ses th , tic he kness Even surface i though s v he aave ried the decre byr t eduction h ase e s s. Ev ame en t amo is h minimal ough t unt, it he c in reduct an be comparison ion i infes rred minima to thwhen atl t in co he t the mparison hick lining er inn tthickness o e r when support ising the lining thickness is varied by the same amount, it can be inferred that the thicker inner supporting varied structure wo by the same uld amount, add to th ite enhanced can be inferr re ed sist that ance of t the thicker he triple t inner unn supporting el complex. structur From t e would he stud add y, itto was structure would add to the enhanced resistance of the triple tunnel complex. From the study, it was thea enhanced lso noted tha resistance t, when the t of the h triple ickness wa tunnels complex. further re Fr duced to 0.2 m, t om the study, ith was e tunnel compl also noted that, ex was una when the ble to also noted that, when the thickness was further reduced to 0.2 m, the tunnel complex was unable to thickness bear thwas e seifurther smic vib reduced rations an to d re 0.2 m, sult the ed in t tunnel he col complex lapse. was unable to bear the seismic vibrations bear the seismic vibrations and resulted in the collapse. and resulted in the collapse. 0.1 0.1 Lining thickness Lining thickness = 0.5 m = 0.5 m 0.08 0.08 C/H = 0.5 0.06 C/H = 0.5 0.06 0.04 IM 2 0.04 IM 2 0.3 m 0.3 m 0.02 0.02 0.4 m 0.4 m 0.5 m 0.5 m -0.02 0.6 m -0.02 0.6 m 0.7 m -0.04 0.7 m -0.04 -200 -100 0 100 200 -200 -100 0 100 200 Distance from the Axis (m) Distance from the Axis (m) Figure Figure 5. 5. E ect Effe ofct variation of variation in the in the thick thickness ness of ofthe the internal internal structure on structure on the surface the surface settlem settlements. ents. Figure 5. Effect of variation in the thickness of the internal structure on the surface settlements. 5.3. E ect of the Variation in the Amplitude of the Input Motion To study this e ect, the IM 1 is scaled up and down in order to have a range varying from 0.1 g to 0.5 g. Keeping all other parameters, i.e., tunnel thickness, inner structure thickness, C/H as a constant, Surface displacements (m) Surface displacements (m) Surface Displacments (m) Surface Displacments (m) Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 22 5.3. Effect of the Variation in the Amplitude of the Input Motion To study this effect, the IM 1 is scaled up and down in order to have a range varying from 0.1 g Appl. Sci. 2020, 10, 334 12 of 22 to 0.5 g. Keeping all other parameters, i.e., tunnel thickness, inner structure thickness, C/H as a constant, the IM is applied in order to compute the surface displacements and the corresponding the IM is applied in order to compute the surface displacements and the corresponding tunnel uplift. tunnel uplift. From Figure 6a and Figure 6b, it can be seen that, as the amplitude of the IM increases From Figure 6a,b, it can be seen that, as the amplitude of the IM increases from 0.1 g to 0.5 g, the surface from 0.1 g to 0.5 g, the surface heave increases from 0.011 m to 0.105 m. The increase in the amplitude heave increases from 0.011 m to 0.105 m. The increase in the amplitude of IM results in a greater of IM results in a greater tunnel uplift as compared to the surface heave, which is minimal at the tunnel uplift as compared to the surface heave, which is minimal at the lower amplitudes but more lower amplitudes but more pronounced at the higher amplitudes. This trend also follows a similar pronounced at the higher amplitudes. This trend also follows a similar pattern as obtained by Azadi pattern as obtained by Azadi and Hosseini [8]. and Hosseini [8]. 0.11 Lining thickness = 0.5m 0.09 Inner structuture thickness = 0.4m 0.07 C/H = 0.5 0.05 IM 1 0.03 0.5g 0.01 0.4g 0.3g -0.01 0.2g -0.03 0.1g -200 -100 0 100 200 Distance from the Axis (m) (a) 0.12 Lining thickness = 0.5 m Inner structure 0.09 thickness = 0.4 m C/H = 0.5 0.06 IM 1 Ground surface Tunnel 0.03 0 0.2 0.4 0.6 Acceleration (g) (b) Figure 6. (a, b) Effect of variation in the amplitude of input motion on (a) surface settlements and (b) Figure 6. (a,b) E ect of variation in the amplitude of input motion on (a) surface settlements and tunnel uplift in comparison to the surface heave. (b) tunnel uplift in comparison to the surface heave. 5.4. E ect of Variation in the Embedment Depth 5.4. Effect of Variation in the Embedment Depth To study the e ect of embedment depth on the dynamic behavior of the triple tunnel complex, To study the effect of embedment depth on the dynamic behavior of the triple tunnel complex, a tunnel with constant lining thickness and inner structure embedded at di erent C/H ratios was a tunnel with constant lining thickness and inner structure embedded at different C/H ratios was analyzed using a constant amplitude IM 2. Figure 7a,b are showing the detailed plots of the obtained analyzed using a constant amplitude IM 2. Figure 7a and Figure 7b are showing the detailed plots of settlements and normalized tunnel deformations. From Figure 7a, it is evident that, as the embedment depth increases, the amount of surface heave decreases while the plot in Figure 7b shows that the Displacements (m) Surface displacements (m) Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 22 the obtained settlements and normalized tunnel deformations. From Figure 7a, it is evident that, as Appl. Sci. 2020, 10, 334 13 of 22 the embedment depth increases, the amount of surface heave decreases while the plot in Figure 7b shows that the increased embedment depth causes the normalized tunnel deformations to decrease. It mea increased ns tha embedment t the triple tunnel depth causes complthe ex embedded normalizedde tunnel eper would h deformations ave more r to decr esistance to the ease. It means that linin the g di triple stortitunnel ons thacomplex n the sha embedded llower tunne deeper l complex. In would have othe mor r word e resistance s, a deeper embed to the lining ded tunn distortions el co than mplex the would shallower behav tunnel e as rcomplex. igid in comparison In other wor to ds, the same a deeper tunembedded nel complex tunnel embedded sh complex a would llowerbehave . as rigid in comparison to the same tunnel complex embedded shallower. 0.14 Lining thickness = 0.5 m 0.11 Inner structure thickness = 0.4 m 0.08 IM 2 0.05 C/H = 0.25 C/H = 0.5 0.02 C/H = 1 -0.01 C/H = 1.5 C/H = 2 -0.04 -200 -100 0 100 200 Distance from the Axis (m) (a) Inner structure thickness = 0.4m IM 2 C/H = 0.25 C/H = 0.5 C/H = 0.75 00.5 11.5 22.5 Lining thickness (m) (b) Figure 7. (a, b) Effect of variation in the embedment depth on: (a) surface settlements and (b) Figure 7. (a,b) E ect of variation in the embedment depth on: (a) surface settlements and (b) normalized normalized tunnel deformations. tunnel deformations. 5.5. E ect of Variation in the Shape of the Tunnel Complex 5.5. Effect of Variation in the Shape of the Tunnel Complex To study the e ect of shape on the dynamic behavior of the tunnel complex, two other shapes To study the effect of shape on the dynamic behavior of the tunnel complex, two other shapes named rectangular and an equivalent horizontal twin tunnel complex [29], which are shown in named rectangular and an equivalent horizontal twin tunnel complex [29], which are shown in Figure Figure 8a,b, respectively, are also analyzed. Keeping all other parameters, i.e., tunnel lining, inner 8a,b, respectively, are also analyzed. Keeping all other parameters, i.e., tunnel lining, inner structure, structure, embedment depth, and amplitude of the IM as constant, the thrusts and moments are embedment depth, and amplitude of the IM as constant, the thrusts and moments are computed for computed for the previously mentioned shapes and a comparison is made. Figure 9a–c are showing the previously mentioned shapes and a comparison is made. Figure 9a–c are showing the seismic- the seismic-induced bending moments and thrusts in the triple tunnel complex, rectangular tunnel induced bending moments and thrusts in the triple tunnel complex, rectangular tunnel complex, and complex, and equivalent horizontal twin tunnel complex, respectively. In order to compare the dynamic equivalent horizontal twin tunnel complex, respectively. In order to compare the dynamic performance, the surface displacements produced in the presence of each of the individual tunnel performance, the surface displacements produced in the presence of each of the individual tunnel complexes and the variation of moments and thrusts are plotted along the normalized tunnel perimeter, complexes and the variation of moments and thrusts are plotted along the normalized tunnel which can be seen in Figure 10a–d. From Figure 10a, it is clear that the surface heave developed in the Displacements above the Crown (m) Normalised tunnel deformation (Δ /Δ ) str soil Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 22 perimeter, which can be seen in Figure 10a–d. From Figure 10a, it is clear that the surface heave Appl. Sci. 2020, 10, 334 14 of 22 developed in the presence of a triple tunnel complex is the minimum among all, equaling 0.082 m, followed by 0.113 m by a rectangular tunnel complex while the maximum is produced by the presence of a triple tunnel complex is the minimum among all, equaling 0.082 m, followed by 0.113 m equivalent horizontal twin tunnel complex, which is 0.135 m, i.e., almost 36.44% and 63.85% more, by a rectangular tunnel complex while the maximum is produced by the equivalent horizontal twin respectively. From Figure 10b and Figure 10c, it can be noted that the resisted seismic-induced tunnel complex, which is 0.135 m, i.e., almost 36.44% and 63.85% more, respectively. From Figure 10b,c, bending moments along the normalized perimeter of about 0.375, 0.5, and 0.625, the resisted moments it can be noted that the resisted seismic-induced bending moments along the normalized perimeter in case of the triple tunnel complex are about 79.86% more than the rectangular tunnel complex. The of about 0.375, 0.5, and 0.625, the resisted moments in case of the triple tunnel complex are about maximum resisted moments compared to the equivalent horizontal twin complex are almost 6.55% 79.86% more than the rectangular tunnel complex. The maximum resisted moments compared to the more. equivalent horizontal twin complex are almost 6.55% more. (a) (b) Figure 8. (a,b) Tunnel complex with dimensions: (a) Rectangular. (b) Equivalent horizontal twin, also Figure 8. (a, b) Tunnel complex with dimensions: (a) Rectangular. (b) Equivalent horizontal twin, also showing the truncated parts (units in ‘m’). showing the truncated parts (units in ‘m’). Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 22 Appl. Sci. 2020, 10, 334 15 of 22 (a) Figure 9. Cont. Appl. Sci. 2020, 10, 334 16 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 22 (b) Figure 9. Cont. Appl. Sci. 2020, 10, 334 17 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 21 (c) (c) Figure 9. (a–c) Seismic-induced bending moments and thrusts in: (a) triple tunnel complex, (b) Figure 9. (a–c) Seismic-induced bending moments and thrusts in: (a) triple tunnel complex, (b) Figure 9. (a–c) Seismic-induced bending moments and thrusts in: (a) triple tunnel complex, equivalent twin tunnel complex, and (c) rectangular tunnel complex. rectangular tunnel complex, and (c) equivalent twin tunnel complex. (b) rectangular tunnel complex, and (c) equivalent twin tunnel complex. 0.14 Lining thickness = 0.5 m 0.14 Lining thickness = 0.5 m 0.11 Inner structure 0.11 thickness = 0.4 m Inner structure 0.08 thickness = 0.4 m C/H = 0.5 0.08 0.05 C/H = 0.5 IM 2 0.05 0.02 IM 2 Triple tunnel complex Triple tunnel 0.02 -0.01 Rectangular tunnel complex complex Rectangular tunnel -0.01 Equivalent twin -0.04 complex tunnel complex -200 -100 0 100 200 Equivalent twin -0.04 tunnel complex Distance from the Axis (m) -200 -100 0 100 200 Distance from the Axis (m) (a) Figure 10. Cont. (a) Surface displacements (m) Surface displacements (m) Appl. Sci. 2020, 10, 334 18 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 22 (b) Lining thickness = 0.5 m Inner structure thickness = 0.4 m C/H = 0.5 IM 2 Triple complex Rectangular complex -5000 Twin complex -10000 0 0.25 0.5 0.75 1 Normalized tunnel perimeter (c) Figure 10. Cont. Maximum moment (kN-m/m) Appl. Sci. 2020, 10, 334 19 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 22 -4500 Lining thickness = 0.5 m Inner structure -3500 thickness = 0.4 m C/H = 0.5 -2500 IM 2 Triple complex -1500 Rectangular complex Twin complex -500 0 0.25 0.5 0.75 1 Normalized tunnel perimeter (d) Figure 10. (a–d) Comparison among triple tunnel complex, equivalent twin tunnel complex, and Figure 10. (a–d) Comparison among triple tunnel complex, equivalent twin tunnel complex, and rectangular tunnel complex in terms of: (a) surface displacements, (b) normalized tunnel perimeter, rectangular tunnel complex in terms of: (a) surface displacements, (b) normalized tunnel perimeter, (c) maximum moments, and (d) maximum thrust generated along the perimeter. (c) maximum moments, and (d) maximum thrust generated along the perimeter. 6. Conclusions This research has been carried out to study the dynamic behavior of a triple tunnel complex in 6. Conclusions soft soil and the e ect of di erent parameters on the overall behavior in case of transversal shaking by an earthquake. From the detailed study conducted, the following conclusions are drawn. This research has been carried out to study the dynamic behavior of a triple tunnel complex in soft soil and the effect of different parameters on the overall behavior in case of transversal shaking (1) The increase in the lining thickness from 0.4 m to 0.8 m decreases the surface displacements from by an earthquake. From the detailed study conducted, the following conclusions are drawn. 0.088 m to 0.045 m, reduces the normalized tunnel deformations from 6.37 to 1.12, and the resisted seismic-induced bending moments increase from 8698.27 kN-m/m to 9568.54 kN-m/m, respectively. (1). The increase in the lining thickness from 0.4 m to 0.8 m decreases the surface displacements from (2) The increase in the thickness of the inner structure from 0.3 m to 0.7 m decreases the surface heave 0.088 m to 0.045 m, reduces the normalized tunnel deformations from 6.37 to 1.12, and the from 0.088 m to 0.069 m, respectively. resisted seismic-induced bending moments increase from 8698.27 kN-m/m to 9568.54 kN-m/m, (3) respectively. When the amplitude of the IM increases from 0.1 g to 0.5 g, the surface heave increases from (2). The incre 0.088 m to ase 0.106 in th m e t while hicknthe ess o tunnel f the uplift inner st incr ruct eases ure fr from om 0. 0.013 3 mm to to 0. 0.116 7 m decre m. ases the surface heave from 0.088 m to 0.069 m, respectively. (4) The change in embedment depth of the tunnel from 0.25 to 2 decreases the surface heave from (3). When the amplitude of the IM increases from 0.1 g to 0.5 g, the surface heave increases from 0.120 m to 0.051 m while the normalized tunnel deformations are also reduced. In other words, 0.088 m to 0.106 m while the tunnel uplift increases from 0.013 m to 0.116 m. the deeper embedded tunnel would act more rigid in comparison to the shallower embedded (4). The change in embedment depth of the tunnel from 0.25 to 2 decreases the surface heave from tunnel with the same lining thickness. 0.120 m to 0.051 m while the normalized tunnel deformations are also reduced. In other words, (5) The shape of the tunnel complex also plays an important role in its seismic behavior. The triple the deeper embedded tunnel would act more rigid in comparison to the shallower embedded tunnel complex results in a surface heave of 0.083 m as compared to 0.113 m and 0.136 m, which tunnel with the same lining thickness. are 36.44% and 63.85% more in the presence of a rectangular tunnel complex and the equivalent (5). The shape of the tunnel complex also plays an important role in its seismic behavior. The triple horizontal twin tunnel complex, respectively. tunnel complex results in a surface heave of 0.083 m as compared to 0.113 m and 0.136 m, which (6) The maximum resisted seismic-induced bending moments by the triple tunnel complex are are 36.44% and 63.85% more in the presence of a rectangular tunnel complex and the equivalent 33.37% less than that of the rectangular tunnel complex while 6.55% more than the equivalent horizontal twin tunnel complex, respectively. horizontal twin tunnel complex at the tunnel invert. Looking to the resisted seismic-induced (6). The maximum resisted seismic-induced bending moments by the triple tunnel complex are bending moments along the tunnel perimeter, it can be noted that, at the normalized perimeter of 33.37% less than that of the rectangular tunnel complex while 6.55% more than the equivalent about 0.375, 0.5, and 0.625, the resisted moments in case of the triple tunnel complex are about horizontal twin tunnel complex at the tunnel invert. Looking to the resisted seismic-induced 30.20% more while, at the crown level, about 79.86% more than at the rectangular tunnel complex. bending moments along the tunnel perimeter, it can be noted that, at the normalized perimeter From the conclusions drawn, it is evident that the triple tunnel complex resists more of about 0.375, 0.5, and 0.625, the resisted moments in case of the triple tunnel complex are about seismic-induced bending moments than that of the equivalent horizontal twin tunnel complex 30.20% more while, at the crown level, about 79.86% more than at the rectangular tunnel and the rectangular tunnel complex. The produced surface heaves are the least among the three complex. shapes as well. This highlights the performance of a triple tunnel complex against the transversal From the conclusions drawn, it is evident that the triple tunnel complex resists more seismic- seismic vibrations. induced bending moments than that of the equivalent horizontal twin tunnel complex and the rectangular tunnel complex. The produced surface heaves are the least among the three shapes as Maximum thrust (kN/m) Appl. Sci. 2020, 10, 334 20 of 22 7. Limitations Since this study comprises of a new, unconventional shape that lacks analytical solutions, the reliability of results is based on the comparison of seismic-induced bending moments and thrusts results with the analytical solutions of the reference model. For more authenticity, analytical solutions addressing this particular shape are needed to develop. Apart from this, experimentation using centrifuge must be conducted in order to validate and compare the results. Currently, the literature lacks research regarding this unique shape. Hence, on the basis of the reference model, the Mohr-Coulomb model modified for incorporating the e ect of cyclic stresses using viscous damping and moduli increment is used in order to compare the results. Since the earthquake also results in the shear modulus degradation with the development of shear strains, advanced models like the Hardening strain with small strain sti ness (HS ) or the soft soil model should also be used. The results should small be compared and more refined. 8. Future Work This research is focused on the detailed parametric study of the triplet tunnel complex and its comparison with the other tunnel shapes numerically. In this research, continuous tunnel lining is used with the minimal internal structure thickness for the analyses. Therefore, the conclusions are valid for that condition. It is recommended that the e ect of segmental lining and fortification of the tunnel complex using a thicker internal structure should also be evaluated. 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Published: Jan 2, 2020

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