Design and Construction for Tunnel Face Stability: Theoretical and Modeling Approach

Tunneling is considered to be among the most important projects in all countries worldwide. However, interspersed, some tunnels rise to problems of instability during excavation. This chapter is a case study of the tunnel of “Djebel El Kantour” which is part of the East–West Algerian Highway. Face stability is the most critical problems that affect the subject of our research. This study is carried out via analytical and numerical methods based on the instability relationship, characteristics of the ground and the geometry of the tunnel, to draw conclusions and recommendations for overcoming this problem.


Introduction
The instability problem of the tunnel face has occurred during the construction of several tunnels in the world ( Several studies have been conducted in this regard: [1][2][3], and various stabilization techniques of tunnels face were used: 1. Fiberglass method of FIT (injection tube) was applied for the first time in 1988 HST Link Roma -Fiorenze(Italy); 2. The technique of shotcrete.
The tunnel face is located at kilometer point (KP 230 + 586.5), which is located inside the tunnel of «Djebel El Kantour". The main problem in this tunnel is the instability of the face which was reported since the beginning of the project, especially in northern the tunnel because of two key factors: the quality of the ground (Marly sandstone clay) and low coverage. In this research finite element simulation were conducted using the software ANSYSE in order take into account the staged construction technique for better estimation the vertical and longitudinal deformations, as well as the failure mechanisms to the front of the tunnel face.
To solve this problem, many techniques have been used to stabilize the face, but the technique did not yield the expected results. Therefore, the prime contractor applied a new technique called the Fiberglass Technique (FIT). However, it proved inadequate in this case, due to its high cost and the limited effectiveness. This is mainly due to the poor mastery of the excavation method, which in turn, was not suitable to this type of rocks. In this study, we try to demonstrate, via a numerical modeling tool, the relationship between the attack section and the deformation field on the Tunnel face.

Case study. Djebel El Kantour tunnel
T4 tunnel is located in the north-east of the department of Constantine. It crosses Djebel El Kantour from south to north with a total length of 2500 m. Its cover is higher than 15 m, and reaches 224 m in maximum points (Figure 1).
The section of the tunnel was chosen according to the geometric characteristics, the geological and geotechnical data tests performed on the ground in question as well as the height of the cover. To take into account the natural conditions of the surrounding terrain, an arched profile has been adopted to ensure the stability of the structure and the service conditions during the constructions process.

Geological and geotechnical parameters of the study
The design of the tunnel was performed on the basis of a geological and geomechanical survey conducted from recent geotechnical survey includes the following investigations: • Geological surveys conducted by geologists' experts; • A recognition campaign by core drilling, in situ and laboratory tests.
It noted that any study must lead to the acquisition of the following information with the maximum possible degree of reliability, considering the wide range of technical resources currently available in the geological survey field:  • Structural geological and hydrogeological conditions and the natural stress state of the ground to be tunneled; • The physical characteristics, the strength and deformability of the geological bodies affected by the excavation: • The hydrogeological conditions in the rock mass.
Geology of the area crossed by the tunnel is essentially of Cretaceous age (Telliennes Tablecloths) and consists of marl and limestone in the form of strongly folded and sheared blocks (Figure 2). These are covered by Quaternary deposits consisting of clays, silts and conglomerates.  The design of the tunnel was carried out on the basis of geological and geotechnical studies. The results of RMR classification are presented in Table 1.
The table below ( Table 2) shows the value of the rock classification (Rock Mass ratings) determined after application of the Total rating.
In our case, the rocks are of marl-clay-sandstone type ( Table 3).

Collapse problem of the tunnel face at PK 230 + 586.5
This tunnel consists of two tubes spaced 22 m. The problem of collapse occurred on the southern side of the tunnel in the right tube. The RMR classification results obtained on the Southern side during the day that preceded the crisis was similar to the classification results of the opposite side of the tunnel, which also suffers from the same problem of instability, but with a technique linked to the soil stabilization.
As we dig in the initially stable soil, the preexisting stress state has changed. Indeed, the stress on the excavation contour vanishes: the decompression phenomenon. This change in the stress state appears only in an area surrounding the Tunnel face: the influence area of the face. It extends over a length towards the front edge which is of the same order of magnitude as the diameter of the tunnel according to the measurements performed on several displacement starts [4,5].
The usual methods for calculating the tunnel's, Tunnel face stability are resulting from experimental studies [6], extrusion testing in laboratory [7] Semi-empirical and theoretical which mainly the approach of calculating the rupture [8,9].
In our case, the experiment shows that the ruptures of the Tunnel face can mobilize important volumes of ground.
The first systematic studies on the face instability of the tunnels dag in the soft soil carried out by [10] were used to characterize the stability conditions starting from a stability parameter coefficient (Figure 3).
The stability coefficient N is defined in [10].
Where; γ: density of the rock. Q u: Shearing resistance (Figure 4). The Figure 5 gives an indication of the relation between the amount of real stability and awaited deformations.
In our case, the parameters required for the calculation of the stability coefficient N are the following:  The obtained result for the stability coefficient is N = 6.45, which means that the tunnel face is unstable.
In our case, the Tunnel face is unstable; therefore, we try to find the value of the pressure of supporting σ_T suitable to be applied in order to decrease this state towards an Elastoplastic deformation.
The interval of σ_T is calculated starting according to the following formula: In this case, the pressure to be exerted on the Tunnel face will lie between the two following values:  The state of stress in the ground is considerably greater than the strength properties of the material even in the zone around the face. For this consideration based for the results of the diagnosis phase, the techniques to be applied for the application of the supporting pressure on the Tunnel faces are as follows:
Both methods assure the rigidity of the core of ground ahead of the face, and therefore the conditions of stability in that ground, have a decisive effect on that deformation response and determine how an arch effect is triggered and consequently the tone of the stress-strain response in the whole tunnel. Relation between the stability coefficient and the face supporting according to [12]. On the other hand, they are difficult to apply this theoretical approach in the domains of soft rocks, flysch and soils, give insufficient consideration to the effects of natural stress states and the dimensions and geometry of an excavation on the deformation behavior of a tunnel and fail to take account of new constructions systems [13].
However, it does not give adequate consideration to the construction stages and therefore it does not constitute a fully integrated method of design and construction. To do this, our analysis of the deformation response continued using the numerical modeling which is able to consider stress states in the ground that are not of the hydrostatic type, which take due account of gravitational loads and which also calculate the effects which the various construction stages have on the statics of a tunnel by simulating the real geometry of lining structures and the sequence and the distance.

Numerical analysis
In engineering practice, different design methods tend to be used; in this study, advanced numerical modeling was used due to its ability to predict vertical and longitudinal deformations; as well as the failure mechanisms at the front of the tunnel face [14,15]. It can indeed be used to simultaneously take into account constraints and anisotropic materials, tunnel advance stages and any pre-containment and cavity containment intervention. In this work, the use of a calculation code through finite element method according to the execution situation [16][17][18]. The numerical parameter used in the simulation as already mentioned in the Table 3 resulting from the geotechnical investigation of the zone in question, where the behavior criteria used in the simulation is Drucker-Prager criterion, which as a generalization of the Mohr-Coulomb criterion for soils. The criterion is based on the assumption that the octahedral shear stress at failure, it depends linearly on the octahedral normal stress through material constants. The results indicate that the action of the surrounding terrain on the tunnel based on the attack section R. The main input parameters are the mesh network of elements which determines the domain to which the analysis applies, the geomechanical properties of each element, the surrounding conditions and the loads acting (Figure 6).
Numerical simulations allowed obtaining practical results of the radial and longitudinal displacements in the figure and table below:

Longitudinal displacement
The following diagram shows the extrusion of different attack section based on the distance in front of the face (Figure 7).

Radial displacements vertical displacements
The vertical and longitudinal deformations and changes of the critical zone that occur in the tunnel are linked to attack section R. When the maximum value of the attack section "R" is equal to 5 m, the corresponding Maximum Vertical Displacement (Ux) is equal to 0.53 m, and Longitudinal Deformation in front of the Tunnel face can reach a maximum of 65 m.
In the case where the radius R = 3.5 m attack, the maximum vertical displacement (Ux) is 0.2 m. So, it is 3 times less than the previous case, and similarly for Longitudinal Deformation in front of the Tunnel face which does not exceed 50 m. it is shown that simulation results are consistent with the observed extent and those obtained in literature. (Figure 8).

Horizontal displacements
We studied the horizontal displacement of the solid rock in vertical section for all cases of attack sections. The (Figure 9) shows the horizontal displacements along a vertical section for various attack sections R.
The maximum horizontal displacement Uh is the edge of the excavation to tend towards zero displacement at a considerable distance from the tunnel. With a difference between the displacements, values of every driving section R compared to another.

Conclusion and recommendations
To ensure the stability of the Tunnel face and minimize its stress concentrations and deformations; the exploitation of this study's results with the inclusion of