**4. 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].

$$N = \frac{\sigma\_- \text{s} - \sigma\_- \text{T}}{\text{Q}\_- \text{u}} + \frac{\gamma.(\text{C} + \text{R})}{\text{Q}\_- \text{u}} \tag{1}$$

**5**

**Figure 3.**

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

The obtained result for the stability coefficient is N = 6.45, which means that the

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

The interval of σ\_T is calculated starting according to the following formula:

σ −σ γ + ( ) ≤+ ≤ s T u u

2 4

− σ ( <sup>+</sup> ) ≤+ ≤ 5 4 T

≥σ ≥ 5 5 13,17.10 Pa 6,97.10 Pa <sup>T</sup>

In this case, the pressure to be exerted on the Tunnel face will lie between the

σT **[ . ] ( ).** ≈ ≈ 0 7 untill 1 MPa

5 5 14.10 2.10 . 25 5 2 4 3,1.10 3,1.10

.C R

Q Q (2)

• The tunnel radius R = 5 m. γ = 4 3 2.10 N / m ; Qu =3,1.105 Pa;

The required σT an Elastoplastic deformation the following:

*Formation of three characteristic zones during the digging of a tunnel (Lunardi 1993) [11].*

*DOI: http://dx.doi.org/10.5772/intechopen.96277*

towards an Elastoplastic deformation.

• The cover C = 25 m;

tunnel face is unstable.

N [2 untill 4]

two following values:

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 surface load; σ = <sup>5</sup> <sup>s</sup> 14.10 Pa and σ = <sup>T</sup> 0 ; *Design and Construction for Tunnel Face Stability: Theoretical and Modeling Approach DOI: http://dx.doi.org/10.5772/intechopen.96277*

• The cover C = 25 m;

*Slope Engineering*

γ (kN/m3

*Geotechnical parameters.*

**Table 3.**

The design of the tunnel was carried out on the basis of geological and geotech-

The table below (**Table 2**) shows the value of the rock classification (Rock Mass

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 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

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

( ) *<sup>N</sup>* σ −σ γ + <sup>=</sup> <sup>+</sup> \_s \_T .C R

The **Figure 5** gives an indication of the relation between the amount of real

In our case, the parameters required for the calculation of the stability

<sup>s</sup> 14.10 Pa and σ = <sup>T</sup> 0 ;

Q \_u Q \_u (1)

nical studies. The results of RMR classification are presented in **Table 1**.

) 20 E (MPa) 200 C (kPa) 50–160 ϕ °( ) 25

In our case, the rocks are of marl-clay-sandstone type (**Table 3**).

**4. Collapse problem of the tunnel face at PK 230 + 586.5**

the measurements performed on several displacement starts [4, 5].

mobilize important volumes of ground.

from a stability parameter coefficient (**Figure 3**). The stability coefficient N is defined in [10].

ratings) determined after application of the Total rating.

**4**

Where;

γ: density of the rock.

Q u: Shearing resistance (**Figure 4**).

stability and awaited deformations.

• The surface load; σ = <sup>5</sup>

coefficient N are the following:

• The tunnel radius R = 5 m. γ = 4 3 2.10 N / m ; Qu =3,1.105 Pa;

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: N [2 untill 4]

$$
\mathbf{2} \le \frac{\sigma\_s - \sigma\_\mathbf{T}}{\mathbf{Q}\_u} + \frac{\gamma\_\mathbf{r}(\mathbf{C} + \mathbf{R})}{\mathbf{Q}\_u} \le 4 \tag{2}
$$

$$
\mathbf{2} \le \frac{\mathbf{14.10^\circ} - \sigma\_\mathbf{T}}{\mathbf{3,1.10^\circ}} + \frac{\mathbf{2.10^\circ}.(2\mathbf{5} + \mathbf{5})}{\mathbf{3,1.10^\circ}} \le 4
$$

The required σT an Elastoplastic deformation the following:

$$13,17.10^5 \text{Pa} \ge \sigma\_\text{T} \ge 6,97.10^5 \text{Pa}$$

In this case, the pressure to be exerted on the Tunnel face will lie between the two following values:

σT **[ . ] ( ).** ≈ ≈ 0 7 untill 1 MPa

#### **Figure 5.**

*Relation between the stability coefficient and the face supporting according to [12].*

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.

**7**

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

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

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.

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 [16–18]. 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

Numerical simulations allowed obtaining practical results of the radial and

The following diagram shows the extrusion of different attack section based on

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

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

surrounding conditions and the loads acting (**Figure 6**).

longitudinal displacements in the figure and table below:

**5.1 Longitudinal displacement**

the distance in front of the face (**Figure 7**).

Tunnel face can reach a maximum of 65 m.

obtained in literature. (**Figure 8**).

**5.2 Radial displacements vertical displacements**

*DOI: http://dx.doi.org/10.5772/intechopen.96277*

systems [13].

**5. Numerical analysis**

*Design and Construction for Tunnel Face Stability: Theoretical and Modeling Approach DOI: http://dx.doi.org/10.5772/intechopen.96277*

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.
