Numerical Analysis of Ground Surface Settlement Induced by Double-O Tube Shield Tunneling

Transcription

1 Numerical Analysis of Ground Surface Settlement Induced by Double-O Tube Shield Tunneling Shong-Loong Chen 1 ; Shen-Chung Lee 2 ; and Yu-Syuan Wei 3 Abstract: This paper is a case study of the Taoyuan International Airport Access Mass Rapid Transit system, the first project in Taiwan constructed with Double-O-Tube (DOT) shield tunneling. The advancing DOT shield tunneling served to induce ground settlement during construction, which thus impacted the safety of buildings and facilities in neighboring areas. A three-dimensional finite-element program was introduced to simulate the DOT shield tunneling process. Five consecutive rounds were excavated by a tunnel-boring machine from a constructed section; then the longitudinal and transverse ground surface settlements were investigated. Three soil models a Mohr-Coulomb (MC) model, a Hardening Soil (HS) model, and a Hardening Soil model with small strain (HS-Small) were used during the numerical analysis. Six monitoring sections along the tunnel alignment and field monitoring data were selected for the investigation. From this study, the ground surface settlements analyzed by the MC model were clearly less than those of the other two models. Because the HS-Small model considered soil stiffness to decay nonlinearly with increasing strain amplitude, it thus showed more-realistic modeling compared to the MC and HS models. This phenomenon was especially evident in the soft-soil stratum. This case study sheds some light on future projects of similar nature. DOI: /(ASCE)CF This work is made available under the terms of the Creative Commons Attribution 4.0 International license, Introduction The Taoyuan International Airport of Taiwan is a crucial gateway for passengers. For rapid and convenient transportation, the High Speed Rail Bureau established the Taoyuan International Airport Access (TIAA) Mass Rapid Transit (MRT) project to connect transportation hubs, such as the Taipei Railway Station, Taoyuan International Airport, and the High Speed Rail Station. The conventional tunnel cross section of the MRT system in Taiwan is a separated-twin-tube layout. Given the increasing awareness of environmental protection and sustainable development, and for the sake of upgrading shield tunneling technology, an advanced Double-O-Tube (DOT) shield tunnel was introduced for the TIAA MRT project, the first such case in Taiwan. The DOT shield tunnel is composed of two circular cross sections, one on each the right and left sides, that are horizontally integrated into a double-o shape. The idea to simultaneously excavate two tunnels in parallel using one tunnel-boring machine (TBM) was first proposed in Japan in the early 1980s. The DOT shield tunnel has an optimized cross section, enabling the most efficient use of underground space (Chow 2006). Compared with separated-twin-tube shield tunneling, the DOT shield tunnel may pass narrower underground corridors, meaning the impact on nearby structures is minimized. Moreover, cross-passages between 1 Professor, Institute of Civil and Disaster Prevention Engineering, National Taipei Univ. of Technology, 1, Sec. 3, Zhongxiao E. Rd., Taipei 10608, Taiwan (corresponding author). f10391@ntut.edu.tw 2 Graduate Student, Graduate Institution of Engineering Technology- Doctoral, National Taipei Univ. of Technology, 1, Sec. 3, Zhongxiao E. Rd., Taipei 10608, Taiwan. sclee.geo@msa.hinet.net 3 Institute of Civil and Disaster Prevention Engineering, National Taipei Univ. of Technology,1, Sec. 3, Zhongxiao E. Rd., Taipei 10608, Taiwan. wei.yu.syuan@gmail.com Note. This manuscript was submitted on March 4, 2014; approved on March 19, 2015; published online on January 25, Discussion period open until June 25, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Performance of Constructed Facilities, ASCE, ISSN / (10)/$ two separated tubes are not required in the DOT shield tunnel, which reduces construction risk. From environmental protection, sustainable development, and technique improvement viewpoints, DOT tunneling is superior to conventional twin-tube tunnel projects. The ground surface settlement from tunneling can be estimated using either empirical formulation or numerical analysis. Numerical analysis, which is capable of handling complicated boundary conditions, has become a popular tool in the prediction of tunnelinginduced ground surface settlement (Chen et al. 2012). A threedimensional finite-element program was used in this study. Thus, both the longitudinal and transverse settlements were investigated in this paper. The mechanical behaviors of soils may be modeled at various degrees of accuracy. The linear elastic perfectly-plastic Mohr- Coulomb (MC) model is often used to model soil behavior in general. This model involves five parameters, namely the two elastic parameters from Hook s law (Young s modulus, E; and Poisson s ratio, ν), two parameters from Coulomb s failure criterions (friction angle, φ; and cohesion, c), and the dilatancy angle, ψ. In fact, the stiffness behavior below the failure contour is assumed to be linear elastic according to Hooke s law. Hence, the model has limited capability to accurately model deformation behavior before failure (Brinkgreve 2005). Thus, the Mohr-Coulomb model could be used to obtain a first estimate of deformations (order of magnitude), and a more-sophisticated constitutive model and parameters should be considered for geotechnical engineering applications. In contrast to a linear elastic perfectly-plastic model, the yield surface of a hardening plasticity model is not fixed in principal stress space but rather can expand due to plastic straining (Brinkgreve et al. 2012). The Hardening Soil (HS) model is an advanced model for simulating the behavior of different types of soil. When subjected to primary deviatoric loading, soil shows a decreasing stiffness and simultaneously, irreversible plastic strains develop. The HS model involves friction hardening to model the plastic shear strain in deviatoric loading and cap hardening to model the plastic volumetric strain in primary compression. Due to the two types of hardening, the model is also accurate for ASCE J. Perform. Constr. Facil.

2 problems involving a reduction of mean effective stress, and at the same time a mobilization of shear strength in excavation works (Brinkgreve 2005). The HS model can generally be considered as a second-order model for soils. The HS model assumes elastic material behavior during unloading and reloading. However, the strain range in which soils can be considered truly elastic is tight. With increasing strain amplitude, soil stiffness decays nonlinearly. If this nonlinear variation of soil stiffness at small strains is considered in the analysis of soil structure interactions, the analysis results improve considerably (Benz 2007). Based on the advanced HS model, Thomas Benz combined the small-strain idea with the HS model, namely the Hardening Soil Model with small-strain stiffness (HS-Small model). The use of the HS-Small model can predict the settlement trough above a shield tunnel (Benz 2007). Therefore, the HS-Small model was also selected in this study for the simulation of ground settlement caused by DOT shield tunneling, and its long-term displacements were compared with those analyzed by the MC and HS models. Elevated section Cut & cover section Fig. 1. Layout of the CA450 A project Overview of the Engineering Case The TIAA MRT project stretches 53.1 km from downtown Taipei City at the northern end to Chungli City at the southern end. The 3.6-km-long Contract CA450 A was selected for this study, as shown in Fig. 1 (Gui and Chen 2013). CA450 A consists of an elevated section, two cut-and-cover sections, and the DOT shield tunnel that is the focus of this study, which lies beneath the Danshui River and extends approximately 1.6 km (Yih and Lin 2008). The DOT section is located beneath even ground with elevations of approximately 4 m at the Taipei end and approximately 3 m at the Sanchong end. The ground layer is located at the alluvium layer of the Danshui River Basin. Its geological formation mainly consists of sediments of the Quaternary Period: clay, silt, and gravels. Fig. 2 provides the geological profile. The groundwater level was found at m below ground surface, as indicated in Table 1. DOT section, L=1548m Cut & cover section and station A1 Fig. 2. Geological profile of the CA450 A project ASCE J. Perform. Constr. Facil.

3 Table 1. Basic Engineering Information on the Monitoring Sections Monitoring section Ground surface EL (m) Overburden depth (m) Groundwater level from ground surface (m) Field monitoring settlement (mm) Diameter = 6.2 m 5.2 m 11.4 m Fig. 3. Typical cross section of the DOT segment lining The DOT tunnel-boring machine had a silkworm cocoon-like cross section mainly consisting of two conjoining circles; it was an earth pressure balance machine (EPBM). The cross-sectional area of excavation was 56 m 2. If it were converted to a single circle, the equivalent diameter (D equ ) was 8.5 m. The DOT tunneling was primarily supported by concrete segment lining, which was 30 cm thick and 120 cm wide, and each ring of lining was constructed of 11 segments (Ju et al. 2008), as shown in Fig. 3. During the construction, six monitoring sections were surveyed at the construction site (Fig. 1), labeled as Monitoring Section 1 6. The basic engineering information on these six monitoring sections is provided in Table 1. The layout of the settlement points at each monitoring section is shown in Fig. 4 (Yih and Lin 2008). The TIAA MRT project started in 2006 and is expected to open for traffic in December According to publications by the High Speed Rail Bureau, 94.5% of the construction work had completed as of October Numeric Analysis Method, Soil Models and Parameters The numerical program used in this study was Plaxis 3D version 2012, a three-dimensional finite-element program. The assumptions and simplifications for numerical analysis, constitutive models, material parameters, contraction parameters, and analysis procedures are described in subsequent subsections. Assumptions and Simplifications The actual construction site and shield tunneling works were complicated and impossible to fully replicate in a numerical analysis; thus, some assumptions and simplification were required: 1. The geometry of the DOT cross section is mainly composed by two circles which radii are 3.1 m and 0.6 m, respectively, as shown in Fig. 5. The studied DOT tunnel is located in a weak soil stratum. To avoid the prevention of any possible mechanism in the soil and any influence of the outer boundary, the model extended 60 m [approximately seven times the equivalent tunnel diameter (D equ )] horizontally both ways from the tunnel center line; i.e., in total, 120 m wide along the x axis. The vertical boundary stretched from the ground surface down to the gravel layer (GM). In this study, 60 m was considered along the z axis. In the longitudinal direction, a 12-m-long section was supposedly already constructed, followed by the excavations of five 1.2-m-long consecutive rounds. To understand the predeformation behaviors, a length of 60 m was extended from the excavation face of the last phase. Thus, the total length along the y axis was 78 m, as shown in Fig Six construction phases were simulated in the numerical analysis. It included one 12-m-long constructed section and five consecutive excavation rounds. A scheme of this longitudinal section is illustrated in Fig. 7. Fig. 4. Typical settlement point layout at a monitoring section ASCE J. Perform. Constr. Facil.

4 H = 6.2 m 5. The primary support of the tunnel was the concrete segment lining, which was represented by the elastic plate elements. 6. For urban shield tunnels, there were always shallow overburden depths and gaps existing between the concrete segment and the surrounding soils during the process of tunneling. Thus, the contraction cp was used to reflect the reduction of the tunnel cross-sectional area. The contraction parameters (cp ) are a significant factor to the tunnel deformation behaviors. 7. Hydrostatic pore water pressure was assumed to occur in the analysis. 8. For simplicity, the procedures of grouting for gaps and the jack forces on the existing segments were not assigned in the numerical analysis. The settlement caused by the buildings and vehicles was also excluded from this study. R1 = 3.1 m W = 11.4 m Soil Models Fig. 5. Geometry of the DOT cross-section The mechanical behavior of soils may be modeled with various degrees of accuracy. The linear elastic perfectly-plastic MohrCoulomb (MC) model is a well-known model for geotechnical analysis, but the studied DOT tunnel is located in alluvial deposits composed mostly of clay with low plasticity (CL) and silty-sands (SM), therefore, the advanced Hardening Soil (HS) model and Hardening Soil model with small-strain stiffness (HS-Small) were also adopted in this paper. Fig. 6. Three-dimensional finite-element mesh of DOT tunneling Mohr-Coulomb Model The Mohr-Coulomb model described here is officially called the linear elastic perfectly-plastic model with Mohr-Coulomb failure criterion. For simplicity, this model is called the Mohr-Coulomb model. This model is a combination of Hooke s law and the generalized form of Coulomb s failure criterion. The basic principle of the MC model is that strains are broken down into an elastic part and a plastic part (Fig. 8). The stiffness behavior below the failure contour is assumed to be linear elastic according to Hooke s law, given by a constant Young s modulus and Poisson s ratio. Hence, the model has a limited capability to accurately model deformation behavior before failure (Brinkgreve 2005). 3. The basic soil elements of the 3D finite-element mesh were the 10-node tetrahedral elements (Brinkgreve et al. 2012). The global coarseness of the mesh in this model was set at medium, but in the tunnel excavation area, the elements were refined, as shown in Fig The tunnel-boring machine was an earth pressure balance machine; thus, the support (chamber) pressure was required during tunnel excavation. The face pressures were assumed to cover a range of active lateral earth pressures in this study. Hardening Soil Model The HS model is an advanced model for simulating the behavior of different types of soil. A basic feature of the HS model is the stress dependency of soil stiffness. The relationship between the vertical strain (ε1 ) and the deviatoric stress (q) can be approximated well by a hyperbolic shape, as shown in Fig. 9. The advantage of the HS model over the MC model is not only the use of a hyperbolic stress strain curve instead of a bilinear curve but also the control of stress level dependency. When using the MC model, the user has to select a fixed value of Young s modulus, whereas for real soils, this stiffness depends on the stress level. However, the HS model uses the 12 m 5 x 1.2=6 m 60 m Constructed section Excavation section Ahead of the excavation face Fig. 7. Scheme of the longitudinal section of DOT tunneling ASCE J. Perform. Constr. Facil.

5 Shear modulus G/G0[-] Very Small Strains Small strains Larger strains deviatoric stress Fig. 8. Basic idea of an elastic perfectly-plastic model 1 1 asymptote failure line axial strain Fig. 9. Hyperbolic stress strain relation in the primary loading triaxial test reference confining pressure (p ref ) and commutates the confining stress-dependent stiffness modulus automatically. Unlike the MC model, the plastic strain originating from the yield cap is considered in the HS model. Hardening Soil Model with Small-Strain Stiffness As mentioned in the preceding subsection, the strain range in which soils can be considered truly elastic is very small. With increasing strain amplitude, soil stiffness decays nonlinearly (Brinkgreve et al. 2012). Plotting soil stiffness against strain (log) yields a characteristic s-shaped stiffness-reduction curve, as shown in Fig. 10. The soil stiffness used in the analysis of geotechnical structures should consider the very-small-strain stiffness and its nonlinear dependency on strain amplitude. Vardanega and Bolton (2013) investigated the normalizing shear modulus and shear strain of clays and silts. In a monotonic test, the secant stiffness G simply reduced progressively with shear strain γ, principally due to the separation or slippage of intergranular contacts as the shear strain increased. A database of the secant shear stiffness of 21 clays and silts was compiled from 67 tests; plots of G=G max versus shear strain also showed a similar curved shape to that indicated in Fig. 10 (Vardanega and Bolton 2014). In the analysis of geotechnical engineering, the very-small-strain stiffness and its nonlinear dependency on strain amplitude should be properly taken in account. In addition to all features of the HS model, the HS-Small model offers the possibility to do so. 1 1e -6 1e -5 1e -4 1e -3 1e -2 1e -1 Fig. 10. Schematic drawing showing the stiffness strain behavior of soil Material Parameters The material parameters selected for the concrete segments, MC model soils, HS model soils and HS-Small soils are described next. The choice of contraction parameter (c p ) is also described in this subsection. Concrete Segments The studied DOT shield tunneling was primary supported by a 30-cm-thick concrete segment with a uniaxial compressive stress of 45 MPa. The material constitutive law was considered as the linear elastic model. The input parameters for the concrete segments were t = thickness of concrete segment; in this study, t ¼ 0.3 m; γ = unit weight of concrete segments; in this studied project, γ ¼ 26 kn=m 3 ; E = Young s modulus of concrete; in this study, E¼ kn=m 2 ; and ν = Poison s ratio; ν ¼ 0.15 was used for the concrete segments. Soils of MC Model The MC model involves five parameters: (1) Young s modulus E, (2) Poisson s ratio ν, (3) friction angle φ, (4) cohesion c, and (5) dilatancy angle ψ. The parameter ψ comes from the use of a nonassociated flow rule, which was used to model a realistic irreversible change in volume due to shearing. The parameters of MC model with their standard units are as follows: E = Young s modulus (kn=m 2 ); ν = Poisson s ratio ( ); c = cohesion (kn=m 2 ); ϕ = friction angle ( ); and ψ = dilatancy angle ( ). Taking Monitoring Section 1 as an example, the soil parameters of the MC model are listed in Table 2 (Ke 2011). According to the suggestion of the Plaxis 3D manual, the order of dilatancy angle (ψ)isψ φ 30 (Brinkgreve and Broere 2004). In addition to the previously-given five parameters, the soil unit weight above phreatic level (γ unsat ) and below phreatic level (γ sat ) are necessary inputs for the analysis. As tunneling essentially unloads the soil, the elastic parameters correspond to the E ur and ν ur values employed in the HS and HS-Small models (Mathew and Lehane 2012). Because the concrete segment and the surrounding soils have different material properties, an interface parameter, R inter ¼ 0.7, was set to present the soil-strength reduction in the corresponding soil layers. Soils of HS Model The HS model requires the input of 10 parameters: 1. Three reference stiffness parameters at reference stress level p ref (default p ref ¼ 100 kpa in this study) (Peng et al. 2011): ASCE J. Perform. Constr. Facil.

6 Table 2. MC Model Soil Parameters for Monitoring Section 1 Soil layer Thickness (m) Soil type γ unsat (kn=m 3 ) γ sat (kn=m 3 ) E ur (kn=m 2 ) ν ur c ref (kn=m 2 ) φ ( ) Ψ ( ) SF , SM , SM , CL , SM , CL , SM , CL , SM , GM , Table 3. HS Soil Parameters for Monitoring Section 1 Soil layer Thickness (m) Soil type E ref 50 (kn=m2 ) E ref oed (kn=m2 ) E ref 50 for triaxial compression, E ref ur for triaxial unloading/reloading, and E ref oed for oedometer loading; 2. A power for the stress-level dependency of stiffness m; 3. Poisson s ratio for unloading/reloading (ν ur ); 4. Mohr-Coulomb strength parameters (c, φ, and ψ); 5. K o -value for normal consolidation (K nc o ); and 6. A parameter called the failure ratio R f, which is the ratio of q f =q a (Fig. 9). Excluding the parameters given in Table 2, the parameters for the HS model are listed in Table 3. Soils of HS-Small Model The HS-Small model was based on the HS model and contains most of the same parameters. Three additional material parameters are needed to describe the variation of stiffness with strain. They are the initial or very-small-strain shear modulus G o, reference shear modulus (G ref o ) at very small strains, and shear strain (γ 0.7 )at which G s ¼ 0.722G o. The shear modulus Go was calculated from Eq. (1)(Brinkgreve et al. 2012): c cos φ σ G o ¼ G ref 0 3 sin φ m o c cos φ þ p ref ð1þ sin φ The reference shear modulus G ref o at very small strains (ε < 10 6 ) for p ref ¼ 100 kpa was estimated from Eq. (2) (Benz 2007): G ref o ¼ 33 ð2.97 eþ2 ðmpaþ 1 þ e The threshold shear strain γ 0.7 was calculated as Eq. (3) (Brinkgreve et al. 2012): γ G o f2c 0 ½1 þ cosð2φ 0 ÞŠ σ 0 1 ð1 þ k oþ sinð2φ 0 Þg ð2þ ð3þ E ref ur (kn=m 2 ) ν ur e m k nc o SF 12,500 10,000 37, SM 20,000 16,000 60, SM 30,000 24,000 90, CL 13,200 10,560 39, SM 47,500 38, , CL 26,400 21,120 79, SM 62,500 50, , CL 30,000 24,000 90, SM 97,500 78, , GM 125, , , where m = power for stress-level dependency of stiffness (m ¼ 0.5 for the study); e = initial soil void ratio ( ); E ref 50 = secant stiffness in the standard drained triaxial test (kn=m 2 ); E ref oed = tangent stiffness for primary oedometer loading (kn=m 2 ); E ref ur = unloading/ reloading stiffness at engineering strains (kn=m 2 ); ν ur = Poisson s ratio for unloading/reloading (ν ur ¼ 0.20 for the study); G ref o = reference shear modulus at very small strains (kn=m 2 ); γ 0.7 = Shear strain at which G s ¼ 0.722G o ; K 0 = earth pressure coefficient at rest; σ1 0 = vertical principal effective stress (pressure negative) (kn=m 2 ); and σ3 0 = horizontal principal effective stress (pressure negative) (kn=m 2 ). The relevant HS-Small soil parameters of Monitoring Sections 1 are listed in Table 4. To ensure a small-strain stiffness larger than the large-strain stiffness, the G ref o of Soil Layers 9 and 10 in Table 4 used the values of G ref o ¼½E ref ur =2 ð1þν ur ÞŠ ð1þ10%þ. The data for layer thickness, soil type, and unit weights (γ unsat and γ sat ) are given in Table 2; thus, they are not listed here again. Definition of Contraction Parameters The concrete segments were erected inside the shield plate of the tunnel-boring machine (TBM); thus, a gap was existed between the segment and the surrounding soil after the segments detached from the TBM. Moreover, the disturbance of the excavation face, the variation of underground water, and the pitching and yawing advancing of TBM were also primary reasons for the ground surface settlements (Kao et al. 2008; Pinto et al. 2014). In the numerical analysis, a contraction parameter (c p ) was adopted to reflect the reduction of the tunnel s cross-sectional area. The contraction c p is different from the ground loss (υ). The ground loss (υ) is a conventional indicator, defined as the ratio of the volume of the settlement trough (per meter length of tunnel) to the notional excavated volume of the tunnel (Ahmed and Iskander 2011). According to the study carried out by Yang (2007) based on the Taipei urban MRT projects (separated-twin-tube shield R f ASCE J. Perform. Constr. Facil.

7 Table 4. HS-Small Soil Parameters for Monitoring Section 1 Soil layer E ref 50 (kn=m2 ) E ref oed (kn=m2 ) E ref ur (kn=m 2 ) ν ur e m G ref 0 (kn=m 2 ) G 0 (kn=m 2 ) γ ,500 10,000 37, ,009 21, ,000 16,000 60, ,070 65, ,000 24,000 90, ,027 81, ,200 10,560 39, ,170 91, ,500 38, , , , ,400 21,120 79, , , ,500 50, , , , ,000 24,000 90, , , ,500 78, , , , , , , , , tunneling), the ratios of c p =υ ranged from 1.39 to For a 20-m overburden depth shield tunneling, the corresponding c p was at the range of % if the ground surface settlements are between 10 and 15 mm. The studied DOT tunneling is the first project in Taiwan; no any contraction data can therefore be referenced. Considering the site geology, tunnel overburden depth, and the noncircular cross section shape, a contraction of 1.5% was adopted for the numerical analysis in this paper. Analysis Procedures The numerical analysis was executed with a three-dimensional finite-element program. The general analysis procedures are as follows: 1. The boundaries of soil contour in the x and y directions were defined. In this study, x min ¼ 60 m, x max ¼ 60 m, y min ¼ 0 m, and y max ¼ 78 m. 2. Soil stratigraphy was defined. The water level depth, soil parameters, and material models were set in this procedure. In this study, the soil depth was extended 60 m from the ground surface, i.e., z max ¼ 0 m and z min ¼ 60 m, as shown in Fig The DOT tunnel cross section and the longitudinal profile were created. The tunnel cross section is shown in Fig. 5, and the longitudinal profile is shown in Fig The plates (concrete segments) of tunneling were created. The contraction parameter (c p ) of plates was 1.5% for this study. Table 5. Ground Surface Settlements along the Tunnel Alignment Soil model Monitoring section Maximum ground surface settlement (max :u z ) (mm) Location of the maximum u z (m) 5. The perpendicular surface loads for each excavation faces were set. The surface loads were equal to active lateral earth pressures in the analysis. In the studied six monitoring sections, the surface loads were in the range of kpa. 6. The finite-element mesh was generated. The element s global coarseness was set to medium, but the meshes in the tunnel excavation area were refined. 7. The stage construction model was built. In addition to the initial phase, there were six construction phases in the analysis. The construction of a 12-m constructed section was simulated in Phase 1. Phases 2 6 represented the excavations and supports of five 1.2-m-long consecutive rounds, as shown in Fig. 7. During the analysis of each phase, the corresponding soils were deactivated, the water condition was set to dry, and the surface load for the excavation face and the plates (with contraction) were activated in each construction stages. 8. Execution of calculation. Once the calculation was completed, the results were displayed in the output program. Numeric Analysis Results and Discussion The calculation results and discussion according to the previouslydefined analysis procedures and parameters to yield the longitudinal and transverse ground surface settlements are described in the subsequent subsections. u z at the excavation face (mm) u z of excavation face/maximum u z (%) Location of the 10% of maximum u z (m) Mohr-Coulomb y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ 30.5 Hardening soil y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ 38.8 HS-small y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ y ¼ 30.9 ASCE J. Perform. Constr. Facil.

8 Longitudinal Settlements The longitudinal ground surface settlements along the tunnel center line (y axis) of the six monitoring sections are summarized in Table 5, and the settlement distributions along the y axis are shown in Fig. 11. From Table 5 and Fig. 11, it can be found that the values of the vertical ground surface settlements (u z ) analyzed by the MC model were the least among these three models, the u z of the HS-Small was in the middle, and the u z of the HS model was the biggest. The average ratio of maximum u zmc to u zhs Small and u zhs was approximately 77 and 57%, respectively. Except for the HS model result of Section 1, most of the maximum u z occurred in the vicinity of the tunnel portal. On the other words, the maximum u z occurred approximately two times the equivalent tunnel diameter (D equ ) behind the excavation face. On the MC and HS-Small models, the settlements at the excavation face reached 57 68% (approximately two-thirds) of the maximum u z during the process of tunneling. At the distance of 17.4 m (approximately two times D equ ) in front of the excavation face, the presettlements reached 10% of the maximum u z. While on the HS model, the settlements at the excavation face reached more than 80% of the maximum u z. At an average distance of 27.1 m (3.2 times D equ ) ahead of the excavation face, the presettlements reached 10% of the maximum u z. i.e., the presettlements analyzed by the HS model were also bigger than those of the MC and HSsmall models. Transverse Settlements The maximum ground surface settlements (maximum u z ) of the six monitoring sections with the field-monitoring data are listed in Table 6, and the ground surface settlement troughs with the fieldmonitoring data are indicated in Fig. 12. As mentioned before, the maximum u z values of the MC model were the least and the values of HS model were the largest among the studied three models. Due to the factors such as the construction procedures, surface pavement, traffic disturbance, wide-area ground subsidence, and human errors in surveying, the field-monitoring data sometimes did not fully coincide with the analysis values (Kao et al. 2008). Moreover, the long-term measured field data included the consolidation settlements that were not calculated in the numerical analysis; thus, some fieldmonitoring settlements are clearly bigger than the numerical results. Discussion From the analyses for the studied DOT tunneling described in preceding sections, it is clear that the ground surface settlements (u z ) analyzed by the MC model are the least among the three models; the settlements of HS model are the largest and the settlements of HS-Small lie in them middle of the adopted three models. The same results and situations were obtained if the studied DOT cross section was converted to an equivalent single-circular tunnel with a diameter (D equ ) of 8.5 m, as shown in Table 7. Fig. 11. Longitudinal ground surface settlement of the studied six monitoring sections ASCE J. Perform. Constr. Facil.

9 The differences of ground surface settlement caused by the different soil constitutive models can be discussed and inferred in terms of the following reasons: 1. In the MC model, the stiffness behavior below the failure contour is assumed to be linear elastic given by a constant Young s Table 6. Transverse Ground Surface Settlements of the Six Monitoring Sections Monitoring MC model HS model HS-small model Field monitoring section (mm) (mm) (mm) settlement (mm) modulus and Poisson s ratio (Fig. 8); thus, the model has limited capabilities to accurately model deformation behavior before failure (Brinkgreve 2005). The MC model did not consider the hardening cap; the plastic strains that originate from the yield cap were not considered in the analysis process. When using the MC model for tunnel excavation in the soft ground, it generally leads to a large pit bottom heave (Brinkgreve 2005), as shown in Fig. 13. These heave situation somewhat offset the settlement values above the tunnel crown. The HS model considers the stress dependency of stiffness and has hardening caps; for certain stress paths, the generated plasticity leads to larger deformations. The HS-Small model takes into account the very-small-strain soil stiffness and its nonlinear dependency on strain amplitude; thus, the HS-Small model allows for even more-realistic modeling compared with the MC and HS models. Fig. 12. Ground surface settlement troughs of the studied six monitoring sections Table 7. Longitudinal Ground Surface Settlements at Monitoring Section 1 of an Equivalent Single-Circular Tunnel (Dequ ¼ 8.5 m) Soil model Mohr-Coulomb Hardening soil HS-small ASCE Maximum ground surface settlement (max imum uz ) (mm) Location of the maximum uz (m) uz at the excavation face (mm) uz at the excavation face/maximum uz (%) Location of the 10% of maximum uz (m) y ¼ y ¼ 3.87 y ¼ y ¼ 34.5 y ¼ 41.2 y ¼ J. Perform. Constr. Facil.

10 Depth from ground surface (m) Conclusions Vertical displacements (mm) MC model HS model HS-Small Fig. 13. Displacement distributions along the depth (z axis) of Monitoring Section 1 of an equivalent single-circular shield tunneling DOT shield tunneling is a new technique compared to conventional separated-twin-tube shield tunneling. Three soil models, i.e., the Mohr-Coulomb model, Hardening Soil model, and Hardening Soil model with small-strain stiffness, were introduced in the numerical analysis for this study. Six monitoring sections along the tunnel alignment were investigated and analyzed. From the numerical results and the field monitoring data, the following observations were made: 1. Compared with the conventional separated-twin-tube shield tunneling, the ground surface settlement induced by Double- O-Tube shield tunneling is bigger. A larger contraction parameter c p should be considered during the process of numerical analysis in the design stage. 2. The ground surface settlements (u z ) analyzed by the Mohr- Coulomb model were less than those of HS and HS-Small models. In this study, the maximum u zmc to the maximum u zhs Small and maximum u zhs was approximately 77 and 57%, respectively. 3. From the distributions of longitudinal ground surface settlement, the maximum u z was located at approximately two times the equivalent diameter (D equ ) behind the excavation face. 4. On the MC and HS-Small models, the ground surface settlements at the tunnel excavation face were approximately two-thirds (63% in this study) of the maximum u z. At the distance of two times D equ ahead of the excavation face, the vertical ground surface settlements reached 10% of the maximum u z. The corresponding values of the HS model were obviously bigger than those of the MC and HS-Small models, as shown in Table Due to the linear elastic perfectly-plastic stress strain relationship characteristics and the constant elastic parameters of the MC model, as well as a large heave at the tunnel invert (Fig. 13), the ground surface settlements are always underestimated. However, the HS-Small model takes into account the very-small-strain soil stiffness and its nonlinear dependency on strain amplitude. Compared with the MC and HS models, the HS-Small model allows for even more-realistic modeling. When executing the numerical analysis for shield tunneling, except the general used MC model, it is recommended to check the tunnel deformation behavior with the advanced but more time-consuming HS-Small model. References Ahmed, M., and Iskander, M. (2011). Analysis of tunneling-induced ground movements using transparent soil models. J. Geotech. Geoenviron. Eng., /(ASCE)GT , Benz, T. 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