The estimation of tunnel displacements is always a highly complicated matter, both in terms of continuum modelling as well as in cases of discontinuous modelling of the rock mass using appropriate software. Research and practical experience have shown that rocks characterised by hard foliation lead to asymmetrical displacements that are directly orthogonal to the foliation plane.

Calculation with a closure form or with a continuum modelling in a classical representation will not provide a sufficiently accurate estimate for this type of problem.

This paper provides an alternative calculation method for asymmetrical displacements in cases of predominant foliation using such non-conventional tools as finite element modelling (FEM) software (Plaxis-2D), based on the experiences in part of the excavations for Lot E52 (Wolf) and H51 (Pfons-Brenner) during the construction of the Brenner Base Tunnel on the Austrian side.


The Brenner Base Tunnel is a major rail project in the Alps that crosses the border between Austria and Italy. Construction involves years of major tunnelling to create two parallel main running tunnels joined by cross passages at regular intervals, plus other major underground structures such as emergency stop caverns, shafts and adits, and an exploratory tunnel (between and approx 10m below the running tunnels).

Construction is being undertaken on a number of lots and is being executed using both tunnel boring machines (TBMs) and drill and blast method (D&B). The tunnel length is 64km and will connect Innsbruck (Austria) and Fortezza (Italy). Over 50% of the approx. 230 km of galleries and tunnels needed to construct the strategic rail transport project have now been excavated (see Figure 1).

 From north to south, the Brenner Base Tunnel crosses the following major tectonic units: the Innsbruck quartz phyllite zone; the Penninic and sub-Penninic units of the Tauern window; a narrow eastern Alpine zone; Tertiary intrusions along the Periadriatic fault; and, finally, the south Alpine Brixen granite (see Figure 3). Overall, schists and phyllites are the main lithologies, totalling some 60%.

1 Construction of Lot H51 for the most part runs through the Penninic Buenden schists.


The tunnelling works include many important junctions of main tunnels, caverns, cross pages and adits in various locations and arrangements. For this study, tunnels of particular interest include a 281m-long cross tunnel (made up of Ch. 0-180m of 161m2 cross section tunnel, already excavated in Lot E52, and Ch. 180-281m in cross cavern (CC) of 212m2 section) as well as the first 200m of the central tunnel (CT) of 104m2 section for the St. Jodok emergency stop in Lot H51 on the Austrian side, starting from the end of the 3.2km-long ‘Wolf’ access adit (see Figure 2).

The cross cavern (CC) and first 200m length of the central tunnel (CT) lie entirely in the Lower Buenden schist sequences. These are folded with interlayered, closely alternating sequences of graphitic calcareous phyllite (‘black phyllite’) and calcareous schist, with the graphitic calcareous phyllites as the dominant lithology.

In contrast to the calcareous schists, the graphitic calcareous phyllites have a higher stratified silicate content and a lower calcareous and quartz content and are, therefore, less solid. The uniaxial compressive strength (UCS) of the graphitic calcareous phyllites ranges from 25MPa to 50MPa (rock); those of the calcareous schists are 50MPa to 100MPa (rock). The higher stratified silicate content of the calcareous phyllites means that they tend to fracture into thin plates, while the calcareous schists fracture into plates of greater thickness along the foliation. In addition, the calcareous phyllites can be distinguished from the lighter calcareous schists by their dark grey colour (graphite content).

The largely homogeneous and monotonous rock mass of the Lower Buenden schist in the project area under consideration has a stratified structure in which the foliation inclines moderately steeply (30°-50°) in a NNW direction and thus runs approximately parallel to the relevant tunnel axis of the cross connection tunnel (CCT) and the central tunnel (CT).

No faults occur in the rock area considered, only slickenside surfaces that are parallel to sub-parallel to the foliation.

The joints are dominated by a steep (on average 70°) eastward direction of inclination. These joints thus run approximately perpendicular to the tunnel axis or incline steeply in the direction of excavation.

The joint spacing in the cross cavern (CC) is small and joint persistence of greater than 8m was observed.

In contrast to the cross cavern (CC), the spacing of these joints is significantly greater in the central tunnel (CT), where for the most part only single joints occur and their persistence is rarely more than 3m. These eastward inclined joints very often show healing with quartz and calcite.

There was no groundwater inflow into either excavation; only a 0.4 l/s inflow of mountain water could be detected at the end of the borehole, coming from a 190m-long radial exploratory borehole to the north in the cross connection tunnel (CCT).


In Lot E52, the influence of the axis-parallel strike direction of the foliation in the cross connection tunnel (CCT) and in the access ramp (AR) to the exploratory tunnel clearly showed strongly asymmetrical displacements. Both tunnel structures are located in the lower Buenden schists, with almost identical rock conditions.

The displacement patterns are approximately the same in both tunnels, in terms of absolute amount, temporal displacement development, and orientation. The displacements caused damage to the extension or to the shotcrete lining of both tunnels (shearing at the transition between the top heading and the bench, cracking and spalling).

In order to prevent damage to the shotcrete lining, deformation slits were left open in the left-hand shoulder area and only closed (with shotcrete) after the displacements had abated.5

The rock behaviour and the size of the rock deformations were dependent on the joint density and on minor changes in the schist orientation.

Analysis and back-calculations of the displacements at Lot E52 provide an opportunity to calibrate the model more accurately. Table 1 lists the geotechnical parameters of the rock mass for the lower Buenden schists.


Strenger Tunnel is a two-tube tunnel, each tube approx.5.8km-long between Flirsch and Pians in Tyrol.

Construction of the tunnel involved excavation through quartz phyllites, quartzite schists and quartzites of the Landeck quartz phyllite zone. The strike direction of the foliation is almost parallel to the axis of the tunnel over long stretches, with inclination angles of 60°-70°, and fault systems of the so-called Stanzertal line also occurring parallel to this.

Highly compressive conditions with an asymmetrical displacement pattern had to be cut through over a length of several kilometres. Graz University of Technology2 simulated these displacements using the discrete element method (see Figures 4(a) and 4(b)). The analysis by (TU Graz considered that the rhombohedral chips that are typical of phyllite were pushed together in the left-hand shoulder area, resulting in a strong dilatation with the displacement transverse to the stress. In contrast, the right-hand side shows slippage along the foliation.2

In our opinion, this model assumption can be extended using an FEM analysis in order to estimate the absolute magnitudes of the expected displacements.


The model is based upon Euler’s theory. The Austrian Society for Geomechanics (OeGG) guidelines for the geotechnical planning of underground structures with cyclic tunnelling describes this rock behaviour as ‘GVT (rock behaviour type) 6’ or ‘buckling’3, i.e., the buckling of thin strata, often in combination with shear failure.

As a methodical approach, a critical modulus of elasticity is determined in the calculation model only for the delimited ‘effective’ strata that can trigger strong displacements transverse to the stress. All other areas are modelled with the predicted modulus of elasticity of the rock. The effective strata for this model were assumed to be approx. 5 times that of the plastic zone, considering the flow of the phenomena behind the zone and also to consider displacements over time.

The primary stress of the overburden acts as a force on the anisotropic rock, see Figure 6.

Only the projected component of the primary stress acts along the parallel axis of the foliation on the strata, which react statically like a bundle of slender beams. The forces parallel to the strata thus generate instabilities along the foliation levels near the cavity.

Assuming that a substantial part of the primary stress acts parallel to the schist and that this effect is assumed to be the critical normal force (Ncr), a critical modulus of elasticity for the rock can be calculated by assuming a certain buckling length (‘beam’ articulated on both sides):

1 Ecr  = Ncr • L2/ π2 • I

In Equation 1, I is the moment of inertia of the hypothetical cross-section of the ‘beam’ and L is the free buckling length. The buckling length is the distance between two joints that are perpendicular to the foliation levels. The geometric properties of the ‘beam’ result from the joint density and the height of such a single ‘beam’ within the strata affecting the deformation. Here, depth of the calculation model corresponds to the base, and joint spacing to the length; the ‘beam’ height can be varied within the plastic zone, which represents the critical zone of the problem.

The model was calibrated for the effects in the cross connection tunnel (CCT) and calculated as a continuum model using Plaxis 2D. The overburden is about 340m, while the tunnel radius is some 7.5m with a plastic zone of some 2.1m in thickness. The rock parameters given in Table 1 were used. The buckling length was determined at 10m on the basis of the working face recordings.5

The height of the ‘beam’ is now varied between 1.45m and a maximum of 2.10m (plastic zone) and thus different ‘critical’ moduli of elasticity are determined in order to optimally represent the actual displacements. Table 2 shows the moduli of elasticity for different construction locations (in Chainage, or Tunnel Metres (TM)) and compares the displacements calculated using FEM with those actually measured.5

Figure 8 shows a graphical comparison between the measured deformation line5 and the calculated deformation line.

It is obvious from this simple reverse calculation that the measured deformations in the CCT can be covered with a very narrow range of values for a ‘beam height’. The high sensitivity of the critical modulus of elasticity with regard to beam height and buckling length makes it rational to perform model calculations using different parameter pairs.

MODEL APPLICATION Central Tunnel (CT) The central tunnel (CT) has a radius of approx. 5m at the St. Jodok emergency stop. Due to the spatial proximity and the parallel tunnel axes, the geological situation is assumed to be almost identical to that of the cross connection tunnel (CCT); the rock parameters of Table 1 can thus be applied unchanged. The calculation in this case was also made with an overburden of 340m. The plasticised radius is 6.4m. It was assumed for the calculation that the height of the ‘beam’ varies between 1.45m and 1.80m only, to take into account different phenomena inside the plastic zone.

Owing to the significantly higher joint spacing recorded for the working face6, the buckling length was increased to between 15m and 20m. At first glance, it seems implausible to permit a longer buckling length than the tunnel diameter. However, during strata buckling, the entire rock significantly deforms, therefore granting the ‘effective’ strata a sufficient deformation path for buckling over the entire length of the joint spacings.

The measured radial displacements6 for selected locations (chainages) of the central tunnel (CT) were significantly lower than in the cross connection tunnel (CCT). The reasons for this are a smaller cross-section size and a significantly greater buckling length

For the central tunnel (CT), the variance of the documented joint distances and a medium and a low ‘beam height’ (derived from reverse calculations of the cross connection tunnel (CCT)) were, therefore, selected as parameter pairs.

Model calculations were made using these parameters (See Table 3).

Table 3 shows that, despite a significant variation of the input parameters, the calculated displacements consistently show the same order of magnitude as the displacements actually measured. The model results are therefore only slightly sensitive to the selected critical modulus of elasticity, which makes it much easier to estimate the correct model parameters.

Deformation slits were also made in the shotcrete shell of the central tunnel (CT) in order to absorb the expected displacements with minimal damage. As soon as the displacement curve had flattened out, the deformation slits were closed (shotcrete).6

Cross Cavern (CC)

The cross cavern (CC) represents the extension of the cross connection tunnel (CCT).

The tunnel radius of the cross cavern (CT) is approx. 9m, and the main rail running tubes branch off from here, to the North and South directions. Using the rock parameters from Table 1 this results in a plasticised radius of approx. 11.5m with a plastic zone of approx. 2.5m. The cross-section was excavated with partial excavations of the top heading, bench and invert slab.

Three types of temporary displacements can thus be assessed in this structure: comparison following top heading excavation; comparison following bench excavation; and comparison following invert excavation.

It should be noted that the final displacements of the cavern due to subsequent excavation of the four outgoing main tubes were not considered in the model.

Table 4 shows the maximum radial displacements during the various excavation phases.6 The data show that despite the larger cross-section, the displacements measured in the cross cavern (CC) are lower than the displacements of the cross connection tunnel (CCT). The significantly lower joint density in the CC is assumed to be the main cause.

Based upon the documented joint distances6 of 15m to 20m, the buckling length in the cross cavern (CC) was therefore set to 15m and the ‘beam height’ varied within the range of values previously determined from the cross connection tunnel (CCT).

Table 5 shows the results of the calculation of the displacements following top heading excavation and following full-circle excavation, as well as the variation of critical moduli of elasticity on the basis of the buckling length and ‘beam height’.

Also in the case of the large cross cavern (CT), the model calculations show a good approximation to the maximum radial displacements actually measured.6


The influence of a very pronounced discontinuity structure on asymmetric displacement behaviour was analysed for the Brenner Base Tunnel on the basis of selected excavations in two construction lots, E52 and H51. The dependence of the displacements on the discontinuity orientation and the discontinuity density is shown both in the actual construction and in the calculation model.

The methodology presented here permits the asymmetric displacements due to strata buckling to be estimated using FEM calculations. Calculation is carried out with a critical modulus of elasticity according to Euler’s theory, with an estimated ‘beam height’ and the buckling length as the most important input parameters.

While the strata thickness and thus the decisive ‘beam height’ must be estimated or determined from reverse calculations of excavation operations, the buckling length can be determined directly from the joint spacing of the joint systems that are oriented perpendicularly to the foliation levels.

Further investigations should permit a better estimation of the parameter pairs of ‘beam height’ and buckling length or the definition of possible application limits.

Sufficient knowledge of such strata, derived from preliminary explorations, will allow realistic displacement dimensions and displacement vectors to be determined in the planning phase. This will in turn permit the oversize, supports, deformation slits and installation sequences to be optimised according to the expected asymmetric displacements.