A simplified 3D model for tunnel construction using tunnel boring machines.pdf
外文翻译-简化的3D隧道建设模型为隧道建筑使用隧道机器
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A simplifi ed 3D model for tunnel construction using tunnel boring machines H. Mroueh *, I. Shahrour Laboratoire de Me canique de Lille (UMR 8107), Universite des Sciences et Technologies de Lille, F-59655 Villeneuve dAscq, France Received 5 September 2006; received in revised form 21 November 2006; accepted 28 November 2006 Abstract This paper includes a presentation of a simplifi ed three-dimensional numerical model for the prediction of soil movement induced during tunnel construction using tunnel boring machines (TBM). The model is based upon the generalization of the convergence-con- fi nement concept to 3D tunnel construction. It uses two parameters (Ldecand adec) which stand for the length of the unlined zone and the partial stress release, respectively. The value of the parameter Ldeccan be taken equal to the tunnel diameter, while the value of adeccan be determined by fi tting the model to empirical formula, and then adjusted based on settlement registered during tunnel construction. The capacity of the model is illustrated through an application to a shallow tunnel in soft soil. The comparison of the numerical results to those suggested by diff erent authors shows good agreement. ? 2006 Elsevier Ltd. All rights reserved. Keywords: Tunnel boring machine; TBM design; Finite element method; Three-dimensional; Non-linear; Shield tunnelling; Convergence-confi nement 1. Introduction Construction of tunnels in soft soils induces generally soil movement, which could seriously aff ect the stability and integrity of existing structures (pile foundations, build- ings.). In order to reduce such movement, in particular in urban areas, contractors use more and more the tunnel boring machines (TBM) for the construction of tunnels. Indeed, thanks to the application of a face pressure and to the temporary support, the TBM allows to reduce the soil disturbance due to tunneling, providing enhanced safety to existing structures (Herrenknecht, 1998; Kuri- hara, 1998; Kuwahara, 1999). Analysis of the impact of the tunnel construction using TBM on the soil movement requires the solution of large 3D non-linear soilstructure interaction problem. Non- linearity results from the non-linear behavior of geomateri- als, the condition at the soilstructure interface (soil grouting-lining, soil shield,) and the evolution of the geometry during excavation. The 3D aspect is due to the signifi cant stress disturbance and soil movement induced ahead the excavation front. 3D elastic analyses conducted by Panet and Guenot (1982) showed ground convergence at the tunnel face which was equal to about 27% of the total settlement. Higher values, up to 50%, were observed in fi eld measurements and computational analyses in soft ground (Moraes, 1999). Finite element modeling of the tunnel construction using TBM requires also the consider- ation of the complex tunnel process which includes the advance of the TBM, the application of the face pressure, the soil excavation, the installation of an immediate sup- port behind the rotating front, the installation of the defi n- itive support (lining ring) and the tail void grouting. A realistic consideration of these issues in the 3D calculation constitutes a high challenge (Dias et al., 2000; Cheng et al., 2002; Galli et al., 2004), because of the large eff ort for numerical modeling and calculation and the large uncer- tainties concerning the interaction between the shield and the soil, the behavior of the grouting, and the distribution of the tail void. Consequently, the use of this approach in tunnel design is still limited, because it requires important 0886-7798/$ - see front matter ? 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2006.11.008 * Corresponding author. E-mail address: Hussein.Mrouehpolytech-lille.fr (H. Mroueh). /locate/tust Tunnelling and Underground Space Technology xxx (2007) xxxxxx Tunnelling and Underground Space Technology incorporating Trenchless Technology Research ARTICLE IN PRESS Please cite this article in press as: Mroueh, H., Shahrour, I., A simplifi ed 3D model for tunnel construction using tunnel ., Tunnel. Underg. Space Technol. (2007), doi:10.1016/j.tust.2006.11.008 modeling eff ort and computational time. In order to over- come this diffi culty, a simplifi ed method is proposed in this paper to model the TBM tunneling process using a three- dimensional model based on the convergence-confi nement method (Panet and Guenot, 1982) with two release param- eters: adecand Ldec, which stand for the partial stress release and the length of the unlined zone, respectively (Fig. 1). This method can be easily implemented and employed using existing programs based on either the fi nite element or the fi nite diff erence method. The paper presents successively, the proposed method, its application to a model tunnel and the sensitivity of the method to the release factors adecand Ldec. 2. Presentation of the numerical model Numerical modelling of the tunnel construction using TBM constitutes a hard task, because it requires consider- ation of complex aspects such as the soil excavation, the overcut or annular space between the jacking pipe and the excavation, the application of the face pressure, the installa- tion of the defi nitive support constituted of lining rings and thegroutingoftheannularspace.Italsorequiresthedescrip- tionofthenon-linearbehaviorofboththesoilandthelining and the condition at the soilstructure interface. Modelling ofthetunnelconstructionisalsothree-dimensional,because the TBM induces an important stress disturbance and soil movement ahead the excavation front. Modelling of the annular space between the ground and the lining extrados is still problematic, because of the diffi culties to collect eff ec- tive data on the distribution and grouting of this space. Up to now, it seems very diffi cult to consider the above- mentioned issues in the practical design of tunnels. In order to overcome this diffi culty, a simplifi ed method is proposed in this paper to model the TBM process using a three- dimensional model based on the convergence-confi nement method (Panet and Guenot, 1982). This method uses a step-by-step procedure. Each step corresponds to the pro- gression of the tunnel face by a distance Llin(Fig. 1). At each step of the procedure, the stress release around the tunnel head is modeled using the parameters adecand Ldec, which stand for the ratio of the stress release and the length of the unlined zone, respectively. The calculation procedure at the step (incr) includes: (a) Determination of the incremental force resulting from the soil excavation (DF). This force is equal to the diff erence between the nodal force vector (F(incr) due to the external forces (self-weight, surface loads, front pressure,.) and the nodal internal forces at the previous step incr-1; calculation of DF is carried out using the following expression: DF F incr ? Z t Vincr Berincr?1dV1 V(incr)represent the volume of the soil mass at the step (incr); Beis the strain interpolation matrix which contains the spatial derivatives of the interpolation functions (e = Beu; u nodal displacement); r(incr?1) denotes the stress tensor at the previous step (incr- 1).In order to take into account the partial deconfi ne- ment resulting from the tunnel construction process (overcut, injection of the annular void, installation of the defi nitive tunnel support,.), a parameter adec is used for considering the partial release on the unsupported section of the tunnel; the length of this section is assumed to be equal to Ldec. The incremen- tal nodal force vector in this section (DF) is trans- formed using the following expression: DF 0 adec? DF2 (b) Activation of the lining elements located in the new section and a full release of stresses in this section. (c) Applicationofthefacepressurep(Fig.1);thepressure is assumed to be constant with depth; it corresponds to a compressed-air pressure TBM. Note that this pres- sure can vary with depth to model slurry shield machines or earth pressure balance (EPB) machines. The soil movement is controlled through the partial releasefactoradecandtheparameterLdecwhichenableusers to consider the infl uence of the void space and grouting around the tunnel. The determination of these parameters can be carried out by an adjustment procedure using empir- ical models and measurements during tunnel construction. The following section presents the application of the proposed method to a model tunnel, which will be followed by a sensitivity analysis of the model to the variation of the partial release parameters adecand Ldec. This analysis allows the elaboration of a methodology for the determina- tion of these factors. Ldec revtementcoulis Phase i Phase i+1 dec*(i-1) dec*(i) (1dec)*(i) lining grouting Step i+1 Step i Llin p Fig. 1. Method used for the tunnel construction using TBM. 2H. Mroueh, I. Shahrour / Tunnelling and Underground Space Technology xxx (2007) xxxxxx ARTICLE IN PRESS Please cite this article in press as: Mroueh, H., Shahrour, I., A simplifi ed 3D model for tunnel construction using tunnel ., Tunnel. Underg. Space Technol. (2007), doi:10.1016/j.tust.2006.11.008 3. Application to a tunnel model The proposed method has been implemented in the fi nite element code PECPLAS which provides fl exible features for the analysis of three-dimensional and non-linear soil structure interaction problems (Shahrour, 1992; Mroueh and Shahrour, 1999). This program uses a sparse storage scheme for the stiff ness matrix, and the bi-CGSTAB itera- tive method (Van der Vorst, 1992) coupled to the SSOR preconditioning operator (Successive Symmetrical Over- Relaxation) for the solution of the resulting linear systems. 3.1. Geometry and numerical parameters Fig. 2 shows the tunnel model geometry. The tunnel is characterized by its outer diameter D = 7.5 m, depth H = 2.5 D and lining thickness e = 0.5 m. The distance of the tunnel centre to the bottom boundary (rigid substra- tum) is assumed to be equal to 2.5D. The soil behavior is assumed to be governed by an elas- tic perfectlyplastic constitutive relation based on the MohrCoulomb criterion with a non-associative fl ow rule. The yield function and the plastic potential are given by f psinu ffi ffi ffi ffiffi J2 p cosh ? ffi ffi ffi ffiffi J2 3 r sinusinh ? C cosu3 g psinw ffi ffi ffi ffiffi J2 p cosh ? ffi ffi ffi ffiffi J2 3 r sinusinh4 where C, u and w designate the soil cohesion, friction angle and dilatancy angle, respectively; p, J2and h stand for the mean stress, second invariant of the deviatoric stress tensor and Lode angle, respectively. Their expressions are given by p rii=35 J2 1 2 sij? sijwhere sij rij? pdij6 h 1 3 sin?1? 3 ffi ffiffi 3 p 2 : J3 J3=2 2 ! where J3 sij? sjk? ski 3 7 Table 1 summarizes the characteristics of both the soil and the lining. Homogeneous silty sand is considered with the following characteristics: friction angle u = 27?, cohesion C = 5 kPa, dilatancy angle w = 5?, Youngs modulus E = 30 MPa, and Poissons ratio m = 0.3. The lining is as- sumed to be governed by a linear-elastic behavior with a Youngs modulus E = 35,000 MPa and a Poissons ratio m = 0.25. The initial stress in the soil media is determined using a coeffi cient of lateral earth pressure at rest K0= 0.5 and an eff ective bulk unit weight of the soil of c0= 10 kN/m3. 3.2. Finite element mesh Finite element analysis was carried out using the mesh presented in Fig. 3. This mesh consists of 2214 20-nodes hexahedral elements, which give rise to 10,494 nodes and 28,471 degrees of freedom. The lateral boundaries of the model are located a distance 4D from the tunnel axis in order to minimize their interaction with the tunneling con- struction. The longitudinal length of the mesh is fi xed to 8D, and the tunnel excavation is performed for a fi nal posi- tion of 4D. This mesh is used to illustrate the application of the proposed method. In tunnels design, an enhanced mesh must be used in order to well capture the soil deformation and the development of plasticity around the tunnel. An extension of the lateral boundaries of the soil mass should also be considered. 3.3. Calculation process Computation was carried out in 12 steps using the fol- lowing parameters for the excavation modelling: ratio of stressrelease adec= 0.5,length oftheunlinedzone Ldec= 1D, and length of the excavated section at each step Llin= D/3. The face pressure is assumed to be uniform and equal to p r0 h, where r 0 h stands for the initial axial stress at the tunnel axis. 3.4. Results 3.4.1. Settlement along longitudinal profi les Fig. 4a shows the evolution of the surface soil settlement along the longitudinal axis (AAP0) during the tunnel con- struction. It can be observed that the maximal surface set- tlement increases with the tunnel progression, and tends to stabilize at a value of wsurf max 0:07%D (D denotes the tunnel outer diameter. The stabilisation of the surface settlement H = 2.5D D = 7.5m e= 50 cm Fig. 2. Numerical example used for the illustration of the model performances. Table 1 Properties of geomaterials used in the tunnel model GeomaterialE (MPa)mc0(MPa)u (?) w (?)c (kN/m3) Soil300.30.00527520 Lining35,0000.2525 H. Mroueh, I. Shahrour / Tunnelling and Underground Space Technology xxx (2007) xxxxxx3 ARTICLE IN PRESS Please cite this article in press as: Mroueh, H., Shahrour, I., A simplifi ed 3D model for tunnel construction using tunnel ., Tunnel. Underg. Space Technol. (2007), doi:10.1016/j.tust.2006.11.008 8D4D 4.5D x z y u = 0 v = 0 u = 0 u = v = w = 0 v = 0 8D4D 4.5D x z y u = 0 v = 0 u = 0 u = v = w = 0 v = 0 Fig. 3. 3D Finite element mesh used in numerical analysis (2214 20-node elements; 10,494 nodes; 28,471 ddl). Fig. 4. Reference example: vertical displacement along longitudinal section: (a) at the ground surface, along the line (AA0) and (b) at the tunnel crown, along the line (BB0). 4H. Mroueh, I. Shahrour / Tunnelling and Underground Space Technology xxx (2007) xxxxxx ARTICLE IN PRESS Please cite this article in press as: Mroueh, H., Shahrour, I., A simplifi ed 3D model for tunnel construction using tunnel ., Tunnel. Underg. Space Technol. (2007), doi:10.1016/j.tust.2006.11.008 is observed after an excavation length of 3D). It can be noted that the surface settlement (wa) at the tunnel face is constant during the tunnel progression. It is equal to 0.03%D, which corresponds to 46% of the maximal value of settlement at the end of the simulation wsurf max. The amount of settlement induced just before the lining installation (wa+ wb) is about 77% of wsurf max (0.05%D), which means that 31% of the total settlement is induced in the unlined zone of the tunnel. This result shows that 23% of the total settlement (wc ) is due to the complete release of the confi ne- ment (1 ? adec). Table 2 summarises the proportion of settlement, in comparison with some published results. It can be noted that these values are in good agreement with observed or computed values reported by various authors. The amount of settlement in the front of the tunnel face waappears higher than reported values, but the cumulative settlement wa+ wbis in good agreement. Note that these values highly depend on the factors adecand Ldec. 3.4.2. Crown displacement Fig. 4b shows the variation of vertical displacement along the longitudinal axis (B?B0) during the tunnel con- struction, at the tunnel crown location wcr. It can be observed that the major part of the crown displacement results from the TBM progression. Indeed, 40% (respec- tively 90%) of the total displacement at the tunnel crown is observed at the TBM passage (respectively at the lining activation). After the lining installation, the displacement shows a rapid stabilization around the value wcr max 0.16%D. The spreading of displacements from the tunnel to the surface can be analysed through a softening coeffi cient or factor of diff usion Rdif, according to (AFTES, 1999): Rdif wsurf max=w cr max 8 Vertical displacements at the soil surface and the tunnel crown give Rdif= 0.4, which means that 40% of the vertical displacement at the crown tunnel is transmitted to the sur- face. This value agrees with empirical approaches and in situ observations. Ward and Pender (1981) reported val- ues for the diff usion coeffi cient varying from 0.2 (for sands) to 0.74 (for over-consolidated clays), while Sagaseta (1987) reported values between 0.2 (for frictional material) and 0.67 (for low frictional clay). 3.4.3. Settlement in a cross direction Fig. 5 shows the evolution of the settlement in the trans- verse section along the axis C ? C0. It can be observed that a moderate settlement appears (0.01%D) when the tunnel face is about 1D behind the cross section (C? C0), then the settlement increases when the tunnel face crosses the traverse section and tends to stabilize when the distance between the tunnel face and the section (C ? C0) exceeds +2D. Numerical results illustrated in Fig. 5 were used for the determination of the parameters of Peck formula (Peck, 1969): the location of the point of infl ection of the settle- ment curve i, the length of the settlement profi le Ls and the volume loss at the ground surface vs. Results are summarised in Table 3a. It is noted that the distance i and the length Ls decrease with the progression of the tunnel face, and tend to stabilise to a value of i = 1.17D when the relative distance between the cross sec- tion and the tunnel face exceeds +1D. The volume loss at the surface is estimated to Vs= 0.26%Vexc, where Vexc denotes for the volume of excavated soil. The parameters of Peck formula can be estimated from semi-empirical methods. Table 3b shows a comparison of thenumericalresultswiththeempiricalexpressions proposed by Table 2 Soil settlement along the longitudinal axis (A ? A0) wa/wsurf max(%) w
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