In the January 2003 issue of T&TI, the authors introduced this second update of the Q-system for rock mass qualification. Emphasis was placed on the application of fibre reinforced sprayed concrete (Sfr) even in the lowest rock mass qualities, and the recent changes in rock support practice and material properties. The paper is continued below.

Calculation of deformation

Figures 9, 10 and 11 show the deformations in relation to the thickness and maximum load for the three models with 5, 10 and 20m span. Lines are drawn for both the roof and the walls for each load ranging from 0.1 to 2.0 MN.

In Figure 9 the maximum deformation in the roof in a 25cm thick rib in 5m span with high walls is 2mm when the maximum load is 2.0MN. It can be seen in Figure 9 that the deformations of the walls, compared to the roof, are far less influenced by the thickness of the ribs. This is most distinct under high loads. In the model the load is much higher in the roof than in the walls. A line drawn at 1mm deformation is considered as an acceptance limit in a 5m span after the permanent support is installed.

In Figure 10 the maximum deformation in the roof in a 25cm thick rib, in a 10m wide tunnel is 23mm when the maximum load is 2.0MN. The maximum deformation of the walls is 25mm with maximum load = 2.0 MN. In the model with a 10m span the deformation of the walls has an opposite development compared to a 5m span. In 10m spans the deformation of the walls is more reduced with increased thickness of the ribs than the roof. This is most pronounced with high loads, i.e. 1.5MN and 2.0 MN. A line drawn at 5mm deformation is considered an acceptance limit in a 10m span after permanent support is installed. These acceptance limits are based on practical experience in different spans.

In Figure 11 the maximum deformation in the roof is calculated to be 470mm in a 25cm thick rib in a 20m wide tunnel when the maximum load is 2.0MN. The maximum deformation in the walls under the same conditions is 250mm. This is largely ruled by the shape of the model with the 20m wide span that has relatively low walls. This difference between roof and walls is most pronounced with high loads 0.45MN-2.0MN. As in the 10m span the deformation of the walls is more reduced than the roof with increased thickness, particularly with high loads.

In Figure 11 a line drawn at 30mm deformation is considered as an acceptance limit in a 20m span after the permanent support is installed. For high loads, in the order of 2.0MN the diagram indicates a thickness of 75cm in the rib in order to remain under the 30mm line. But in most cases the arch is higher than in the model, and a 70cm thickness may be sufficient to avoid deformations greater than 30mm. And the “basic” support is likely to give more than the calculated 0.30MPa. Another reason why the calculated deformations may be too high for the 20m span is the application of the same anchored strength of the springs at the invert for all three spans. By adjusting the anchored strength of the springs for 5m and 20m span relative to the strength for the 10m span, which is calibrated, the deformation will be increased for 5m span and reduced for 20m span. The spring strength has to be increased many times its original magnitude (1,000 kN) in order to give a significant reduction in deformation in the 20m span. If the radius of curvature in the crown is reduced, the deformations will also be reduced.

In most cases high loads will cause deformations, which will lead to tension cracks in the crown. After moderate deformation the reinforcement bars will start to act. Because of this, it is very important to place most of the reinforcement bars in the lower layer (furthest off from the rock surface). Based on the deformation curves in Figures 9, 10 and 11 it is possible to recommend the optimum thickness of the ribs. This thickness should not allow too much deformation in the permanent structure, but should also avoid over-support.

Analysis of the number of rebars

The application of the calibrated STAAD-analysis makes it possible to calculate the necessary number of reinforcement bars in the ribs. It also gives a recommendation where to place the reinforcement in the ribs relative to the rock surface.

Figures 12 shows the number of reinforcement bars per rib in a tunnel related to thickness and load for a 10m span. This is based on the bending moment and deformations calculated in STAAD. Cases with too large deformation are avoided. For 5m span the expected borderline for unwanted deformations is set to 1mm in the RRS for permanent support. For 10m and 20m span the limit for accepted deformation is set to 5mm and 30mm respectively. The inset in the diagram shows RRS with one or two layers of rebars for each thickness.

Hence, the thickness 0.25m and 0.4m are shown for both single and double layers. For double layers in each load class, for instance 950kN, two columns are shown. The right hand column represent the number of rebars in the lower layer (most important with highest number of rebars, marked 950 –2 (kN), while the left hand columns indicate the number of rebars in upper layer, marked 950 (kN). The sum of these two columns has to be used in combination with the deformation diagrams in order to design ribs for different load (support pressure) and span.

In general, double layers, which can take higher loads than single layers of the same thickness, should be preferred if the total thickness is sufficient for two layers. It can be seen from the histograms in Figure 12 that a thickness of 0.25m combined with 200kN load in a 10m span requires a large number of reinforcement bars and combined with rock bolts in order to compensate for the large deformations. In these cases, the rebars will in large extent take over the bending moment after opening of cracks or partial crushing of the concrete. However, large deformations with possibility for shear failure should be avoided. If shear failure is expected, increasing number of rock bolts and cross reinforcement of the ribs is recommended.

RRS-calculations in the Q-chart

The calculated thickness for different loads (= support pressure) linked to rock mass qualities has been compared with practical cases in Norwegian tunnels. Most data used originates from the Frøya Subsea Tunnel (1), the Lærdal Tunnel (25km long and up to 1500m overburden) and the E18 twin tube highway tunnels in Vestfold County, South of Oslo.

Based on the calculations described above, the recommended thickness, number of rebars and spacing between the ribs has been placed in the rock support chart linked to rock mass quality, Q. For each Q-value (0.001, 0.004, 0.01, 0.04, 0.1 and 0.4) with 5m, 10m and 20m span, required thickness, number of rebars and spacing is given in the Q-chart. Similar to the thickness of the sprayed concrete in the original Q-chart published in 1993, the same thickness of the ribs can be followed from lower left to upper right. But because of the increasing spacing between the ribs with increasing Q-values the gradient is lower for the ribs than for even layers of sprayed concrete.

The same spacing is recommended between the ribs for similar Q-value irrespective of span. The net load on each rib of the same strength should be about the same, because the reduced support pressure compensates for the increased spacing with increased rock mass quality, Q (Figure 13).

For a Q = 0.001 there is no spacing between the ribs for 20m span. That means a continuous spraying of reinforced ribs with 70cm thickness in addition to the temporary support comprising of 12cm of Sfr + Bc/c1.5m. The ten reinforcement bars are distributed over the 1m wide rib.

In practical cases the layer of Sfr might be 25cm, and the spacing of the rock bolts might be 1.1m in addition to spiling bolts before installing the RRS. Here, the thickness of the RRS can be reduced with the corresponding increase in thickness of the Sfr ? 25cm – 12cm = 13cm. In other cases, the ribs spacing (centre/centre) is given for each case.

Between the different boxes which show calculated thickness, number of rebars and spacing between the ribs, interpolation is recommended for improving the support. For Q = 0.001 it is often more economic to apply cast concrete arches (CCA). However, in cases with changing profiles or small weakness zones it is practical and, hence more economic to use RRS.

It should be stressed that support pressure might vary significantly related to corresponding Q-values (Figure 4 in Part 1, January 2003, T&TI). Therefore, in the lower rock mass qualities it is wise to observe the deformations some time after temporary support, before making the design for the RRS.

In better rock mass qualities stress reduction often occurs during deformation. Hence, the rock mass takes a large part of the load after deformation, reducing a need for extra support. This can be controlled by deformation measurements.

Conclusions and discussion

For absorbing the deformations in rock masses of low quality, the toughness of sprayed concrete should be high. Based on laboratory tests and observations in tunnels it has been possible to incorporate the deformation energy for different rock mass qualities, Q, in the rock support chart. Design of rock support can be improved by changing to higher quality of fibres or by increasing the amount of fibres. This is in accordance with the guidelines and technical specifications of the Norwegian Concrete Association publication no. 7. When high stresses occur, it is recommended to move up one toughness class because of the high forces and the long term deformations.

In the lower rock mass qualities (Q<0.1 for 10m span) the Q-support chart published in 1993 (2); recommends application of RRS or cast concrete arches (CCA) in addition to fibre reinforced sprayed concrete (Sfr) and rock bolts (B). No design model has been available for construction of the RRS.

The research work referred to in this paper is based on the computer program STAAD, which gives deformation and bending moments in RRS that are dependant on the thickness and number of rebars for different loads (support pressure) and span. The analytical work has been compared to, and calibrated with deformation measurements and numerical analyses of tunnels of approximately 10m span. The calculated deformations agree well with the observed ones. For 5m and 20m span there are few practical examples where RRS is applied. Therefore, some uncertainties concerning the deformations and bending moments for 5m and 20m span exist. Just a few examples of 22m-23m span is recorded with deformation measurements. Hence, it is recommended that support with RRS in small and large spans should be done with some care. Regular observations of deformations, after installing the temporary support, will provide guidance in the design of the permanent support with RRS in extremely poor rock masses.

Generally, higher safety can be expected when crossing the border from the reinforcement category 7 to 8, as the addition of the RRS to the temporary support with Sfr + B will give a sudden substantial increment in support. This sudden increment may be smoothed if some part of the temporary layer of Sfr is taken as a part of the rib close to the borderline. It is important to remember that the ribs shall carry not only the rock mass above, but also the distributed load from the rock mass between the ribs. In the lowest Q-values in reinforcement category 9, the Q-system published in 1993 recommended CCA. However, practical experience and analyses show it is possible to replace any CCA with RRS for all rock mass qualities.

Small deformations and the first part of large deformations of RRS are usually elastic, dependent only on the concrete, irrespective of the reinforcement, without any cracking of the concrete. The first deformation is not dependent on the reinforcement. The reinforcement will start to act gradually during the deformations. Sufficient reinforcement in the RRS, may prevent further deformation and collapse if the design is correct related to the rock mass quality, Q.

For practical reasons it should be mentioned that all reinforced ribs of sprayed concrete have to be combined with rock bolts evenly distributed throughout the arch. Usually the spacing is 1.5m. This helps to avoid or reduce shear failure during large deformations. It is important that the deformations have to be controlled before the final installment of RRS. Sometimes large deformations may occur in the lower part of the walls. If no cast concrete ring is installed in the invert, then it is very important to install extra rock bolts through the lower part of the ribs, near the invert in order to avoid unwanted deformations or collapses.

The most important parameters for designing of RRS are support pressure taken from the Q-value, span, geometry and accepted deformation.

Related Files
Figure 13
Figure 11
Figure 9
Figure 12
Figure 10