Tunnel face stability

The same as in conventional tunneling construction, the tunnel face stability is of major importance in the pipe jacking construction, which aims to ensure safety against soil collapse in front of the cutting face. Some internal pressure in the heading chamber must be maintained to support the tunnel face in soft ground and the support pressure must be kept above a certain threshold, or the face is unstable and there is the risk of tunnel collapse (Chambon & Corte, 1994). In the conventional literature on tunneling, the face is seen as “enemy”. However, the ADECO (Analysis of COntrolled DEformations) has shown success in using the ground ahead of the tunnel face core as a stabilization measure, which can be seen as “friend” of the designer and contractor (Kim & Tonon, 2010). Besides, Lunardi (2000, 2008), by making full use of the most recent knowledge, calculating power and advance technologies, proposed the A.DE.CO.-RS approach offers a simple guide with which tunnels can be classified in one of three fundamental behavior categories and presented the countermeasures with preconfinement and confinement , as shown in Figure 1.5 and Figure 1.6.

Tunnel face stability is one of the most critical issues that should be achieved during mechanical tunnel excavation, which also plays an important role in influencing the ground deformation. For underground works, the consecutive construction stage is not the final stage before the tunnel is finished and subjected to external loads predicted at the design stage, but the intermediate construction stage. The effects of the disturbance caused by excavation have not been completely confined by the final lining yet, which becomes very sophisticated. A number of studies have concerned on tunnel face stability,

including analytical or based on limit-analysis calculation (Anagnostou & Kovari, 1996;

Davis, Gunn, Mair, & Seneviratine, 1980; Jancsecz & Steiner, 1994; Leca & Dormieux, 1990; Mühlhaus, 1985; Pinyol Puigmartí & Alonso Pérez de Agreda, 2013), numerical simulations (Chen, Tang, Ling, & Chen, 2011; Z. Zhang, Hu, & Scott, 2011) and experimental investigations (Kamata & Mashimo, 2003; Kim & Tonon, 2010; Kirsch, 2010) both for conventional and pipe jacking tunnel with various geological conditions.

For conventional tunneling, Anagnostou and Kovari (1994, 1996) analyzed the face stability of slurry shield driven and earth pressure balanced (EPB) tunnel to have a better understanding of tunnel face collapse mechanism by using sliding mechanism model, which consists of a wedge and a right-angled prism that extends from the tunnel crown to the surface. Furthermore, Guilhem Mollon (2009a, 2009b) used two deterministic finite element models to present a probabilistic analysis of a shallow circular tunnel driven by a pressurized shield in the frictional and/or cohesive soil, which is based on the upper-bound method of the limit analysis theory and considered both of the ultimate limit state (ULS) and serviceability limit state (SLS). It was found that SLS can be used alone for the assessment of the tunnel reliability. Depend on the results of previous studies, the proposed two rotational failure mechanisms for the active and passive cases, taking account the entire circular tunnel face instead of an inscribed ellipse to this circular area, which behaved more consistent with the rotational rigid-block movement observed in the experimental tests (Mollon, Dias, & Soubra, 2011).

However, few literatures can be found on the study of the face stability of pipe jacking tunnel and what is more, there are not so many reports focusing on the face stability analysis of jacking tunnel in frozen ground can be found. In a sense, the face stability analysis of conventional shield and pipe jacking tunnel can be made by using the similar failure mechanical models if making the assumption that the influence of construction technology and procedure can be ignored. Therefore, the face stability analysis of pipe jacking tunnel in frozen ground is done by using the similar approach of conventional tunneling in this thesis.

Figure 1.5 Tunnel face behavior category (Lunardi, 2008).

Figure 1.6 Preconfinement and confinement for conventional tunneling (Lunardi, 2008).

1.4.1.1 General analytical solutions of face stability

The mechanical behavior of geomaterials is very sophisticated and, till now, there is no mathematical model can completely describe the actual behavior. Therefore, drastic idealization is necessary to only capture the essential characters within the theoretical model for practical applications. As we know, the geomaterials are not linearly elastic or perfect plastic, but always behave elastoplasticity and even rheological property.

Stability analysis for a boundary problem of a deformable continuum must satisfy basic physical conditions, including stress equilibrium equations, compatibility equations and constitutive equations. Finding a complete analytical solution that satisfies all the three conditions is difficult and sometimes impossible. In order to make the problem relative simplification and tractable, either equilibrium analysis or plastic limit analysis can be used to describe the stability problems.

1.4.1.2 Limit equilibrium analysis

So far, the limit equilibrium method is the most frequently used analysis approach for the stability of geotechnical structures, which applies a static equilibrium condition between forces and moments acting on the soil mass and the strength mobilized in the soil for the most critical collapse mechanism, which uses the global equilibrium condition rather than equilibrium conditions at every point in the soil mass and neglects the constitutive and compatibility condition altogether (Kim & Tonon, 2010).

Anagnostou and Kovari (1994) showed the effects of slurry penetration as an essential factor to affect the face stability of slurry shield driven tunnel by taking into consideration the time-dependency of the slurry penetration distance and the pressure gradient applied on the face. The factors to influence the slurry infiltration, including characteristic grain size, the excess pressure and slurry concentration, were also discussed. Based upon the silo theory (Janssen, 1895), they presented a simple model which idealizes the three-dimensional failure mode of the tunnel face to estimate the required face support pressure for earth pressure balanced tunnel (Anagnostou &

Kovari, 1996). The model is composed of a wedge and a prism as shown in Figure 1.7(a). The forces acting on the wedge at face are listed in Figure 1.7(b). The tunnel face is considered to be stable when the limit equilibrium condition is achieved for the wedge and prism. The soil in this model is idealized as a rigid-plastic material and the Mohr-Coulomb failure condition is assumed.

Figure 1.7 Sliding mechanism of EPB tunnel (Anagnostou & Kovari, 1996).

According to the equilibrium equations and Mohr-Coulomb yield criterion, the effective support pressure depends linearly on the size of the forces acting on the wedge and shear forces depend linearly on the cohesion. By carrying out a dimensional analysis, the general form of the limit equilibrium equation can be obtained as follows:

𝜎_𝑇^′ = 𝐹₀𝛾^′𝐷 − 𝐹₁𝑐 + 𝐹₂𝛾^′∆ℎ − 𝐹₃𝑐∆ℎ

𝐷 Eq. 1.1

where F0 to F3 are dimensionless coefficients that depend on the friction angle φ, c and φ are the effective shear strength parameters, γ’ is the submerged unit weight, D is the tunnel diameter, Δh=h0-hF, and hF presents the piezometric head in the chamber. The equation takes the effect of seepage force into account by prescribing a constant piezometric head in the chamber and ahead of face. However, for the pipe jacking tunnel in the frozen ground, the water in the soil is frozen and therefore, in the calculation of the required pressure of tunnel face, the effect of underground water is ignored.

Jancsecz and Steiner (1895) proposed a method to evaluate the required face support pressure for slurry shield by using a model composed of a wedge and a prism as shown in Figure 1.8. The soil arching effect above the tunnel was considered and a three-dimensional earth pressure coefficient for different values of the friction angle was suggested, which is based on the limit equilibrium method.

Figure 1.8 Wedge and prism model (Jancsecz & Steiner, 1994).

𝜎_𝑇𝑈 = 𝛾𝐷 4𝑐𝑜𝑠𝜑( 1

𝑡𝑎𝑛𝜑+ 𝜑 −𝜋

2) Eq. 1.2

where, σTU is the uniform normal support pressure, D is the tunnel diameter, γ represents the unit weight of soil and φ is the angle of internal friction.

1.4.1.3 Limit analysis

The upper and lower bound stability solutions were derived for collapse and for assessment of the risk of blow-out failure caused by excessively high slurry pressure with a plane strain cross section by Davis (1980), which has taken into account the effects of both tunnel depth and cover-to-diameter ratio. Assuming constant undrained shear strength with depth, the kinematically admissible upper bound and statically admissible lower bound plasticity solutions for idealized plane strain tunnel heading were proposed. The stability ration N, defined by Broms and Bennermark (1967), equals to the difference between the total overburden stress in the ground at the axis of the tunnel and the tunnel pressure divided by the undrained shear strength, as shown in Figure 1.9.

𝑁 =𝜎_𝑠 + 𝛾(𝐶 + 𝐷 2⁄ ) − 𝜎_𝑇

𝑠_𝑢 Eq. 1.3

where σs stands the surcharge pressure, γ is the total unit weight of the ground, C is the cover depth, D represents the tunnel diameter, σT is the applied face support pressure at the center of the face and su is the undrained shear strength.

Figure 1.9 An idealization of shield tunneling.

Leca and Dormieux (1990) have investigated the face stability of tunnel against collapse and blow-out cases. Three upper bound solutions are derived from the

consideration of mechanisms based on the motion of rigid conical blocks. Bound solutions give bracketed estimation of required face support pressure: upper and lower solutions. The upper bound solution is found by considering a kinematically admissible failure mechanism. The external work done to the system exceeds the work dissipated inside the system. The lower bound solution is found by taking a statistically admissible stress distribution into consideration, which does not violate the yield criterion. The external work done to the system cannot constitute an unconfined plastic flow. The model is composed of one or two conical blocks as show in Figure 1.10.

Figure 1.10 Mechanism (a) MI and (b) MII (Leca & Dormieux, 1990).

The upper bound solution for required face support pressure, σT, against collapse associated with mechanism MI and MII can be determined by finding the σp that satisfies the inequality equation:

𝑁_𝑠𝑄_𝑠+ 𝑁_𝛾𝑄_𝛾≤ 𝑄_𝑇 Eq. 1.4

where, the loading parameters, Qs, Qγ and QT, are defined as follows:

𝑄_𝑠 = (𝐾_𝑝− 1)𝜎_𝑠 𝜎_𝐶+ 1

Eq. 1.5 𝑄_𝑇 = (𝐾_𝑝− 1)𝜎_𝑇

𝜎_𝐶+ 1 𝑄_𝛾 = (𝐾_𝑝− 1)𝛾𝐷

𝜎_𝐶

The lower bound solution for required face support pressure against collapse is obtained by calculating the force equilibrium with the mechanism shown in Figure 1.11. For

lower bound solution, Qs, Qγ and QT are calculated by using Eq. 1.6 and Ns and Nγ are calculated as follows:

𝑁_𝑠 = 𝐾_𝐴

Eq. 1.6 𝑁_𝛾 = 𝐾_𝐴(𝐶

𝐷+ 1)

Figure 1.11 A lower bound solution for collapse (Leca & Dormieux, 1990).

As mentioned above, many theoretical models had been proposed to interpret the heading face mechanism of conventional tunnel face. However, there are few studies on the tunnel face stability in frozen ground, much less of pipe jacking in cold regions.

In the following Chapter 2, the parametric study was conducted by using numerical simulation method. At the same time, the face deformation mechanism was analyzed and the optimal face support pressure with various conditions were calculated by using a new proposed calculation model.