Insights on squeezing behavior from Saint-Martin-la-Porte galleries

In the context of the Saint-Martin-la-Porte survey project of the Lyon-Turin railway link, an access gallery (SMP2) was first excavated across a Carboniferous formation, where tectonized productive Houiller was met at a depth of 300 m. It exhibited a highly squeezing behavior, characterized by large, time-dependent and anisotropic deformation. Recently, a new survey gallery (SMP4) began to be excavated along the axis of the future base tunnel at a depth of about 600 m. Squeezing conditions have been met again when SMP4 crossed the same Carboniferous formation. Practical problems have been encountered related to the large and anisotropic closure of the cross-section and the instability on the tunnel face. On the basis of previous studies and numerical analyses of carried out for SMP2, the proposed methods are extended to SMP4 conditions. Numerical modeling is performed using FLAC3D code and the various phases of excavation and specific support installation are considered. The efficiency of the compressible elements in reducing the stress in the support system is demonstrated.


Introduction
As part of the Trans-European Transport Network (TEN-T) Project, the Lyon-Turin railway is a key element of the Mediterranean Corridor. It will connect France and Italy through a 57.5 km base tunnel under the Alps. In Saint-Martin-la-Porte in France, a survey project is underway to study the geological environment of one of the most complex areas of the Lyon-Turin base tunnel ( figure 1a). An access gallery (SMP2) was first excavated to reach the future base tunnel to provide access for the excavation of the base tunnel. A tectonized Carboniferous formation was encountered at a depth of 300-330 m, where productive Houiller was encountered. It presents a very heterogeneous stratified and fractured structure, composed of schist and/or Carboniferous schist, sandstone and a large proportion of clastic rock. Due to the poor mechanical properties of the rock mass, squeezing behavior was observed around the tunnel. It is characterized by large, time-dependent and often anisotropic convergence around the tunnel wall. Observation and convergence measurement show an elliptical deformation of the tunnel section with a high convergence up to 2 m, which produces severe problems for the excavation and support process. On the basis of the intensive field monitoring, a number of studies have been carried out on SMP2 to analyze the response of the rock masses and of the specific support systems during and IOP Conf.  The geological context of the SMP4-PS is very complex. The rock mass is very heterogeneous both in the longitudinal and radial directions (figure 2). Several discontinuity planes are present. The proportion of Carboniferous shales/coal, which is more deformable, is much higher from chainage 10310 to 10337 m than in the following parts.  In the present study, we focus on the part of SMP4-PS beyond the collapsed zone after chainage 10310 m. Based on the previous research of SMP2, numerical simulation of SMP4-PS is performed with the finite difference code FLAC3D considering the various excavation and support methods. The constitutive parameters of the rock mass are adjusted.

Excavation and support method
SMP4-PS was excavated at a rate of about 0.6 m/day. The yielding support system used in SMP4-PS is presented in figure 3. In the first stage, a horse-shoe section was excavated and a light support system was installed using steel ribs with sliding joints. In the second stage, at about 11 m from the tunnel face, the invert was excavated leading to a circular section and new support elements were added including four to eight compressible concrete (HiDCon) elements depending on the local amount of deformation. No final lining was installed in SMP4-PS as this part will be enlarged to full size later.

Mean convergence of SMP4-PS
The mean convergence of SMP4-PS has been monitored and analyzed using the convergence law proposed by Sulem et al. (1987aSulem et al. ( , 1987b written as: where T is a characteristic time related to the time-dependent properties of the system, X is a parameter related to the distance of influence of the tunnel face, ∞ is the instantaneous convergence obtained in the case of an infinite rate of face advance, m is a parameter related to the ratio between the timedependent convergence and the instantaneous convergence, n is a constant, usually taken equal to 0.3. The average values obtained from SMP2 of 4 parameters of the convergence law are applied considering the tunnel size effect for SMP4-PS: T = 20 days; X = 7.6 m; m = 18 and n = 0.3. The only parameter to fit is the instantaneous convergence C∞x for the two stages of excavation and support installation (Liu, 2020). The average convergence is analyzed by fitting the deformation of the tunnel section with a circle We take into account the two stages of excavation and support installation: (A) excavation of the tunnel section and (B) installation of the yielding support system. The obtained parameters and the predicted final mean convergence of the sections are summarized in table 1.

Numerical simulation
The in-situ conditions of SMP-PS field works are complex and some simplifications have been considered in the model. In accordance with the assumptions made by the project engineers in the design reports, the in-situ stress in Houiller formation is assumed to be 8.5 MPa for SMP2 and 16.2 MPa for SMP4. We assume that the galleries are circular and opened in one step. The ground is very heterogeneous. Reinforcement system including bolts and anchors is applied to improve the properties of the highly fractured ground. This reinforcement system is not explicitly modeled and the influence of these elements is included in the properties of the equivalent homogenized ground.  The constitutive models for the ground used here are the same as those used for modeling SMP2 (Tran Manh et al., 2015). The ground response is highly anisotropic because of the heterogeneity of rock mass. As a fixed direction of anisotropy cannot be identified, the average behavior is studied. The rock mass is simulated with the isotropic visco-elastic-plastic model CVISC (Itasca, 2017) with the aim to simulate the average response of the tunnel. This model has been widely used in numerical simulations of rock squeezing behavior (Bonini et al., 2009;Tran-Manh, 2014

Results
As laboratory data are not available to characterize the mechanical properties of the rock mass, the constitutive parameters of the ground can be obtained from back analysis of the convergence data. In order to constrain the model and reduce the number of parameters to calibrate, the elasto-plastic parameters are first determined by fixing the same values for the Poisson's ratio ν, the friction angle φ, the tension limit σt and the dilation angle ψ as those of SMP2. The two remaining parameters (Young's modulus E and cohesion c), which have much greater influence on the convergence magnitude, are fitted by using the time-independent part of the convergence law. For that, 3D time-independent numerical modeling is performed with a Mohr-Coulomb elasto-plastic model. As for example, the numerical simulation of the convergence of the section at chainage 10326 m is shown in figure 5 together with that obtained from the convergence law.    Table 3. Constitutive parameters of the ground of SMP2 and SMP4.

Conclusions
In the previous studies of SMP2 (Vu et al., 2013; Tran-Manh et al., 2015), a procedure of field data processing of the cross-section convergence and a numerical model have been proposed to analyze the large time-dependent and anisotropic deformation observed in the squeezing Carboniferous formation.
In the present work, the numerical model and the values of the constitutive parameters used in SMP2 have been applied and adjusted to SMP4-PS. Numerical modeling has been performed using FLAC3D for the sections exhibiting high convergence. The specific excavation and support installation process has been considered and the constitutive parameters of the ground have been adjusted in order to account for the different stiffness of the rock mass at greater depth. CVISC model permits to well reproduce the time-dependent convergence and stress state in the support. The different values of the constitutive parameters in the different zones of the gallery reflect the high heterogeneity of the ground. The performance of the HiDCon elements is demonstrated. They permit a significant reduction of the stress in the support system and prove to be highly efficient for tunneling in squeezing ground.