In order to see how a tunnel rock arch reinforced by fully grouted rock bolts and shotcrete is working, the functioning of vertical and horizontally reinforced soils should be explored first.

While the vertical and horizontal reinforcement of soils has developed following the use of fully grouted bolts to reinforce a tunnel carrying rock arch, they should be described as their functionality is similar to that of the reinforced rock arch and shotcrete, and is easier to understand.

Vertical reinforcement

Vertical soil reinforcement was studied (Combarieu) between 1975 and 1985. It was later formalised in case of stone columns by a recommendation (RFG number 111 2eme trimestre 2005).

The theoretical works of Combarieu showed the functioning of soil reinforced by vertical inclusions. The inclusions are considered as friction piles, or friction and end bearing piles.

The transfer of the loads brought about by a fill or a general foundation slab to a soil reinforced by inclusions occurs through an arching effect between the inclusions. The loading of the inclusions takes place along a transfer length where the strain of the soil and the inclusions are equal, and where the shear strength capacity of the soil-inclusion contact is sufficient. This shear strength value may be the critical condition for the inclusions spacing. The capacity of shear strength development along the inclusion is linked to the soil horizontal stress (see Figure 1).

The upper portion of the inclusion is in compression and is loaded along the transfer length (negative friction) while the lower portion behaves as a friction pile and returns the load to the surrounding soil located between the inclusions. This load transfer is valid if the modulus of the soil located below the tip of the inclusion is of the same magnitude as the modulus of the soil where the inclusions are embedded. In case the modulus of the soil below the inclusion tip is higher, a portion or the total load will be carried to the tip (see Figure 2).

The bearing capacity of the reinforced soil is made up of two capacities:

  • Internal capacity: the bearing capacity of very inclusion is Estimated
  • Outer capacity: the bearing capacity of the reinforced soil is estimated based on the Terzaghi approach for a piles group, or by computing the bearing capacity of a surface foundation slab resting on a soil with an improved cohesion. This last approach is similar to a circular rupture of the cohesive foundation soil.

Soil nailing

The nailing of excavation slopes was developed in France between 1972 and 1974 on temporary slopes at the enlargement of a railway line in Versailles by the contracting joint venture of Bouygues and Solétanche (Rabesajet, Toudic 1974). And for stabilising tunnel entrances at the A8 motorway construction site by Campenon Bernard (Launay, 1974). In the latter case, the principles of NATM were applied for stabilisation of the slopes.

The nailing computation was done assuming that each nail was bringing a stabilising force on the least stable circular circle. The nails were working against the sliding forces. As with the NATM, the carrying capacity of the shotcrete skin was considered as limited to the loosened zone between four nails. The zone was loosened during the excavation phase.

Contrary to vertical reinforcement, the inclusions, or nails, are in tension. The first Clouterre guideline of 1991 considered the shotcrete skin as a floor resting on four poles (the nails) loaded by the horizontal active pressure, which is proportional to depth. The 2002 update following FEM modelling of the soil behaviour between the nails recommended considering a skin pressure much lower than that proposed in 1991.

The maximum pressure is encountered at the nail (equal to the nail tension force) and to zero at the centre of the shotcrete plate. It is interesting to emphasise the fact that reinforced earth has a similar approach.

In the two editions of the Clouterre guideline the overall stability of the reinforced slope is performed using the modified Bishop method taking into account the nails working in tension. The shear line crosses the reinforced soil mass and the nails are locally loaded as a pile under a horizontal force located at its upper end.

Rock arch design

The design of a tunnel rock arch taking into account the stabilising effects of the fully grouted bolts is a challenging task. Several methods are at the disposal of the designer. Among those approaches the following ones are available:

  • Modelling of the bolts section and length by means of special elastic beam elements within an F.E.M model. The link between the bolt and the soil/rock has the same strain.
  • Model the reinforced rock arch zone in increasing the cohesion of the rock arch area in accordance with the theory of homogeneity as proposed by E. Greuel, 1993 for cohesive soil or K. Gharbi 1994 for cohesive and friction soil.

The two models, and particularly the former, are limited as they do not completely reproduce the behaviours and the measurements encountered on sites. They give too much of a weighting to the shotcrete shell in the carrying capacity of the provided support (including bolts) contrary to the stresses measured within shotcrete shell.

Backgrounds

At the time of development of NATM between 1962 and 1975, Kastner, Pacher and Rabcewicz proposed to estimate the reinforced rock arch carrying capacity based on shear lines through the entire support and the appearance of arching effect between the radial grouted bolts and the soil-rock. This would be based on model tests, theoretical approaches and results of measurements in tunnels under construction.

The phenomenon of the transfer of the load towards the bolts, described above for vertical reinforcement of soil and nailing of slopes, is also encountered in a tunnel arch reinforced by grouted bolts. These results have been described in Rabcewicz (1964, 1965, 1969, 1971) and Rabcewicz et al (1972, 1973).

Modelisation

The transfer of overburden load towards the grouted bolts was more or less intuitive until now. In order to analyse and describe its functioning, it was decided to use the most up to date three dimensional FEM program, which has sufficient computation power to model in details the behaviour of the reinforced rock arch. The results obtained were described in detail in the master paper of Lelong (2009).

The studied section has a 6m radius; the support is composed of 6m long, 20mm diameter fully grouted bolts every square meter of arch. The rock has a Mohr-Coulomb elastic-plastic law.

The initial isotropic geostatic stress at axis of tunnel is equal to 0.9MPa. The utilised FEM model is the three dimensional CESAR program of LCPC. In order to avoid the usual inaccuracies it is necessary to model each bolt and its connection with the soil/rock. It requires a very precise modelling which involves many nodal points. The final model includes 100,000 nodes, 30,000 volumetric elements as well as 1,800 connection nodes, it was later simplified to 55,000 nodes.

Two major points must be underlined that fit the model to reality:

  • The outer ends of the bolts are not allowed to sustain tension.
  • The stress between the bolt and the surrounding soil/rock is a Mohr Coulomb relationship.

The tunnel excavation is modelled by a 30 per cent deconfining coefficient before placement of the bolts. In a first approach the shotcrete shell was not modelled. It will later be introduced to check the results of the modelling with measurements in a tunnel under construction where the NATM was applied. Finally the bolts were modelled with and without anchor plates.

Results

Internal deformation of the reinforced arch

Figures 4a and 4b show the distribution of the deformations between the bolts in three dimensions. In spite of the absence of support between the bolts at tunnel excavation periphery there is no failure of the soil/rock and the displacement is limited (2 to 3mm). The shape of the equal displacement curves shows the build up of arching effect (vertical section at mid-distance between two rows of bolts and along a section through the row of bolts).

As described by (Rabcewicz 1972 and 1973) the radial stress applied to the reinforced arch is transferred as well by friction in the bolts (tension) and into the reinforced arch by compression (see figure 5). The green zone is in tension and will therefore be carried by the shotcrete shell which can be associated to the reinforced arch. The weight of this zone is very limited and therefore the shotcrete shell can be thin. It must be mentioned that the FEM results given have been obtained by means of a two dimensional modelling.

Stresses within the reinforced rock arch

When designing the support of a tunnel, the radial and tangential stresses applied to the support must be known. Based on the results of the model and taking into account the progressive de-confinement taking place after placement of the bolts, it is possible to make the following conclusions:

a. As far as the radial stress is concerned, it is ‘maintained’ within the reinforced arch at a higher value than without reinforcement. The radial stress value corresponding to the deconfinement ahead of the excavation face (30 per cent in the assumed case) is located 2m within the reinforced arch. With regards to the deformations it means that smaller deformations will occur outside the reinforced zone or smaller settlements at the ground surface in case of a shallow tunnel. At the tunnel excavation periphery the radial stress is nil.

b. The most important result is the displacement of the maximum tangential stress location (plastic radius) away from the reinforced arch with deconfinement increase (equivalent to time) as well as a large decrease of the tangential stress at the tunnel excavated periphery. The stresses are pushed away from the tunnel. This fact can be very useful in the sequences of tunnel excavation when stages excavations are required. For example the placement of the bench support will be more flexible in terms of time allowance.

The tangential stress distribution loads the reinforced arch in a manner similar to the soil weight in case of an outdoor soil nailed excavation or a vertically reinforced soil.

Stresses distribution within bolts without anchoring plate

As introduced earlier, the bolts have been introduced in the model without plates or shotcrete shell. The stresses distribution along the bolt is shown on Figure 6.

The bolt length origin is at the edge of the tunnel excavation. A loading tension zone appears on a 4m length and an unloading tension zone on a 2m length. The point of maximum tension is located at the point of maximum tangential stress. In a similar manner as the tangential stress, the tension within the bolt will build up progressively with de-confinement or time until it reaches its maximum value.

The maximum friction between the bolt and the ground must be compatible with the compressive stress around the bolt-grouted zone and the available shear stress between the bolt and the ground. Combarieu’s idea of negative friction along an inclusion is confirmed.

Stresses distribution within a bolt with anchoring plate

The introduction of anchoring plates (200 by 200mm) changes slightly the distribution of stresses and deformations between the bolts heads (toward the plates). The unsupported surface is smaller, but away from the periphery of the tunnel excavation the totally de-confined zone has a similar extent compared to the case without plates.

The tension stresses distribution along the bolt is different from what was encountered without plate (see Figure 7). It shows that when a ‘stiff’ support component relative to the ground stiffness is introduced it ‘catches’ the loads. This distribution of stresses is to be compared to the one described in the soil nailing (Clouterre additive, 2002).

As far as the radial and tangential stress field is concerned in a plan at mid distance between two rows of bolts it is similar to what is founded with plates.

Examples of measured stresses in bolts in various tunnels

The three examples described are tunnels where the support was composed of fully grouted bolts and a thin shotcrete shell. The examples (see Figure 7) were given by Louis (Le soutènement par boulonnage et béton projeté) at the 1977 AFTES meeting in Paris.

They show that the stresses distribution along bolts may vary a lot from one bolt to the next one even when the ground conditions is homogenous (Marl at the Las Planas tunnel A8, 1975) or slightly heterogeneous at Marseille (Marl and limestone).

The example (see Figure 8) is the connecting chamber of the Sèvres-Achères sewage system. The crown of the chamber has been excavated within the plastic clay of Paris. It can be seen that the stresses distribution along the bolts is also changing from one bolt to the other.

Conclusions

The modelling approach, with examples, shows that the distribution of the stresses along a fully grouted bolt is heterogeneous.

It is linked to the relative stiffness of the support that can be provided on the periphery of the tunnel excavation; anchoring plate and/or shotcrete shell. Dependent on the proper placement of the plate against the ground and/or the connection of the shotcrete to the ground the distribution will vary. But most important, the arching effect in between the bolts will in any case develop and therefore determine the functioning of the reinforced arch.

Shotcrete shell

A shotcrete shell has been used in a 13m diameter tunnel excavated in Phylite (GSI=25; C=250 kPa; =32°; Erm=370MPa). The support is composed of a 100mm thick shotcrete shell and 20mm diameter 5m long fully grouted bolts every square meter. The overburden height is equal to 100m at tunnel axis ( o=2,500kPa).

The loading of the bolts, development of arching and a very small load on the shotcrete have been founded in the FEM model results. Symmetrically, on both sides of the tunnel axis, appears a zone where the pressure is higher ( r=130-150kPa). These areas correspond to the maximum deformation points (13mm). The pressure on the remaining portion of the shotcrete shell varies between 50 to 100kPa. The pressure is low and roughly equal to two to four per cent or the initial radial stress. This example has also been modelled without any shotcrete. The equilibrium has been obtained with a convergence of 16mm. The shotcrete shell has limited the convergence but does not change the functioning of the reinforced arch.

Design of the support (grouted bolts and shotcrete)

The functioning of a reinforced arch was outlined previously with regards to inner and outer deformations, distribution of the radial and tangential stresses around and inside the reinforced arch and distribution of the stresses along bolts with or without anchoring plate. The following conclusions can be drawn:

a. The appearance of an arching effect between the bolts is true. It allows the built up of reinforced arch around the tunnel excavation within which the tangentia l stress is high away from the tunnel excavation and low at the border. b. The loading of the reinforced arch is progressive and develops with time and convergence.

c. The distribution of stresses along the bolts is related to the provision of a shotcrete shell and/or of anchoring plates. The relative stiffness of the shell or of the anchoring plate has an influence on the stress distribution along the bolts.

d. Providing a thin shotcrete shell (100mm) has a similar effect as an anchoring plate.

e. It must be emphasised that with or without shotcrete shell or anchoring plate, the reinforced arch (including radial bolts) is able to carry the greatest portion of the overburden load with limited convergences.

These conclusions allow a design of the tunnel support to be proposed based on a shear surface through the reinforced arch and the shotcrete shell in a manner similar to what is done in case of soil nailing.

The shape of this surface cannot be circular due to the shape of the tunnel excavation surface. The surface or shear line will be a logarithmic spiral as the normal to the bolts will have a constant shear angle with the shear line. This shear angle is computed on the Mohr circle based on the normal and shear stress along the shear line.

Along this shear line, the principal stresses are 1= =tangential stress and 3= r=radial stress. The values of these two stresses vary within the reinforced arch. If in order to compute the shear angle the values at the periphery of the excavation are used, the estimated value will be on the conservatively safe side.

The location of the shear surface must be assumed taking into account the original stress eld and/or the sequences of excavation. This surface is described by Rabcewicz (1969) and by Rabcewicz and G. Golser (1973). It is related to the confining effect of the shotcrete shell, the bolts and steel arch and to the geotechnical characteristics of the ground.

When computing the carrying capacity of the support in accordance with his approach, the weight of the reinforced arch is correctly estimated and it allows a decrease to the overall cost of the support without jeopardising the safety of the tunnel stability. It is easy to use and it allows a quick and correct estimate of the support capacity but, as its authors have always strongly recommended, it must not be put in practice without continuous convergence measurements and therefore follow up of the behaviour of the support with time.

This method has been utilised in numerous projects for the last 10 years under low and high overburden, in elastic or plastic ground conditions with success.

Conclusions and applications

The reinforced arch with fully grouted bolts model presents a certain number of conclusions that are important in the way to implement grouted bolts and shotcrete shell.

1. The bolt loading is triggered by tunnel convergence. This convergence must not be counteracted by a too stiff shotcrete shell which would limit the loading of the bolts and the built up of the reinforced arch.

2. If convergence measurements do not show stabilisation, an increase of the support will be necessary using grouted bolts and shotcrete. The bolts must be placed first and the shotcrete extra thickness in a second stage. As a matter of fact, if the new shotcrete is placed first, the stiffness of the total shotcrete shell will be higher and it will limit the new convergence avoiding as a consequence the development of the assumed carrying capacity of the newly placed bolts. It should be pointed out that this reasoning must take into account the overburden height as the tangential stress must be sufficiently high to ‘squeeze’ every bolt.

3. The squeezing of the bolts by the ground has an important consequence on the request by many technical specifications on the pull out tests of bolts. As a matter of fact, the pull out tests results will depend on the actual convergence of the tunnel periphery. When the reinforced arch will have completely developed it will be impossible most of the time to pull out the bolt and it will break at the level of the screw thread of the bolt head.

4. The development of the tangential stress with convergence and therefore time. It shows that its value decreases at the tunnel periphery and that, when the total carrying capacity of the bolts is obtained, this value is low and in fact close to zero. Then, when a two stage excavation is performed in a tunnel, the bench excavation will take place with a tangential stress value above the excavated sidewall very low as the higher values have been pushed away from the sidewall. The stability of the sidewall has improved a lot and the risk of landslide before placement of the support has decreased. The use of grouted bolts as support has improved the safety of the works.

5. The location of the anchoring plate versus the excavated surface does not change the efficiency of the bolts as with or without the plate, the tension capacity of the bolt is similar and the reinforced arch is mobilised in the same manner.

6. The load that is carried by the shotcrete shell is limited as much as the relative stiffness of the shell is low, with reference to the ground one. This functioning is equivalent to the transfer of the load at the ends of the piles.

7. The shear line computation proposed by Rabcewicz and Golser which is similar to the computation of a nailed wall is a correct approach to modelling the functioning support (composed of a reinforced arch and shotcrete shell). Relatively simple to put into practice it allows estimation of its carrying capacity. It outlines the ‘weight’ of the reinforced arch and therefore the capacity of the ground to support itself with rather little support materials.

8. It is then finally necessary to remember that the observations of convergences, and the follow up actions all along the works, are the basis for security of the support. It is especially clear when keeping in mind all the unknowns that exist within the geotechnical parameters, and also in the stress field in the original ground.