1 Interaction of Rock Mass, Tunnel Boring Machine and Segmental Lining
Mechanized tunnelling involves a complex interaction of loads and acting forces, which needs to be taken into account (Fig. 1):
The temporary face must be supported against the effects of rock mass pressure and water pressure or seepage pressure, respectively. The pressure of the cutterhead FCW and possible support pressures FSP serve this purpose. Both must be applied with the help of the jacking forces FTF.
At the same time, the temporary face serves as an abutment. It must be sufficiently “competent” so that the jacking forces can be applied. If this is not the case and there is no possibility of compensating for this in another way, the jacking forces will drop (cf. section 1.4.5).
The cutterhead pressure FCW as well as the torque must be sufficiently large to allow for cutting the rock.
The frictional forces between the shield and the ground Ffr must be overcome. The jacking forces FTF must also be sufficiently dimensioned for this purpose.
The trailer load of the back-up FBUS must also be moved with the jacking forces.
1 | Interaction of TBM, segmental lining and rock mass
Thus, taking into account a safety margin ΔF, the jacking forces must be dimensioned in such a way that they can ensure the required cutter wheel pressure FCW, the support pressure FSP, as well as overcoming the frictional forces Ffr and the trailer load of the back-up FBUS (force equilibrium in the horizontal direction, Fig. 1).
The jacks strut against the segmental ring. The segments must be dimensioned against the expected maximum jacking force. At the same time, it must be ensured that a minimum value of jacking force is acting on the segmentel rings in order to maintain the pre-stress in the sealing gaskets of the circumferential joints and thus ensure the tightness of the segmental lining, as well as to guarantee that the first „floating“ segmental rings are kept in position.
Since tunnel boring machines are generally top-heavy, an additional requirement is that greater jacking forces are applied in the invert area than in the roof area. This results in a moment that compensates for the head load and thus permits control steering of the tunnel boring machine (Fig. 1). However, this is only possible if – as already mentioned – the temporary face provides a sufficiently competent abutment or – if this is not the case – appropriate measures are taken to compensate (cf. section 1.4.5).
1.2 Properties of Jointed Rock Masses
The essential properties of jointed rock masses can be described and simulated with the “Anisotropic Jointed Rock Model (AJRM)”, which has been used successfully for many years. A more detailed description of the AJRM can be found in [1, 2, 3, 4]. Fig. 2 shows a typical example of a sedimentary rock mass with approximately horizontal bedding parallel joints, which are partially filled with clay, and steeply dipping joints. These steep joints frequently end at the bedding parallel joints. The strength and deformation behavior of the rock mass is determined by the intact rock and the discontinuities.
For stresses below the strength, one can assume linear-elastic behavior for most rock mass types. However, sedimentary rocks, clay shales and also gneisses do not always behave isotropically in the elastic range. The compressibility perpendicular to bedding or schistosity is often greater than parallel to it. This property can be described in good approximation by the assumption of a transversal isotropy with the help of five elastic constants: the Young‘s modulus parallel and perpendicular to bedding E1 and E2 , two Poisson‘s ratios ν1 and ν2 and the shear modulus G2. In the case shown in Fig. 2, an elastically isotropic deformation behavior can be assumed, which can be described by the Young‘s modulus and the Poisson’s ratio.
With regard to strength, a distinction is made between the strength of the unfractured intact rock σcIR and the shear strength on the discontinuities (bedding parallel joints & joints), which in practice can be described by a friction angle φB / φJ and a cohesion cB / cJ. The shear strengths on the discontinuities are usually considerably smaller than the intact rock strength and thus decisive for the stability of structures in rock.
Due to the different characteristics of the discontinuities, the permeability of the rock mass parallel and perpendicular to bedding is often also different and thus anisotropic.
The table in Fig. 2 shows examples of typical characteristic values of the Bunter formation with a pronounced anisotropy of strength and also of permeability.
The calculations illustrated in the following have been carried out for the example of TBM tunneling in a Bunter formation with these characteristic values (Fig. 2) at an overburden of around 40 m above the tunnel’s roof and a groundwater table at the ground surface (cf. Fig. 1).
1.3 Groundwater and Seepage Flow
If tunnel excavation is carried out below the groundwater table and water can enter in the area of the temporary face and shield, then a seepage flow directed toward the tunnel is triggered. In this case, which is the basis for the following considerations, seepage pressures and uplift forces act on the rock mass. If no water can enter in the area of the shield or via the temporary face, then the full water pressure acts on the temporary face, shield and segmental lining, and uplift forces act on the rock mass.
The corresponding forces can be determined with the aid of seepage flow analyses. Such calculations have been carried out for the example case with the finite element mesh shown in Fig. 3. In case of seepage flow, the distribution of equipotentials changes over a wide area. Therefore, a large calculative section (600 m x 1200 m x 145 m) is required for these calculations. The boundary conditions are shown in detail in Fig. 3.
3 | FE mesh and boundary conditions for seepage flow analyses
Fig. 4 shows the calculated distribution of equipotential lines in the vicinity of the tunnel, which result from the seepage flow directed towards the tunnel. Assuming an anisotropic permeability of the rock mass (kfh >> kfv, see Fig. 2), there is a clear concentration of the equipotential lines and thus of the hydraulic gradient above and below the shield and the segmental lining (Fig. 4, left). As a result, significantly higher seepage pressures (S) act in the vertical direction than in the horizontal direction. Furthermore, there is practically no lowering of the groundwater table at the ground surface.
For comparison, Fig. 4 shows on the right the distribution of equipotential lines that results in the case of isotropic permeability of the rock mass: in this case, there is a significant and extensive lowering of the groundwater table at the ground surface. The distribution of equipotential lines around the tunnel is nearly symmetrical, the seepage pressures in vertical direction are clearly smaller, however, the seepage pressures directed to the temporary face are larger than in the case of anisotropic permeability.
These results show very clearly that the anisotropy of the permeability has a major influence both on the forces acting in the area of the temporary face, shield and segmental lining and on the changes in the groundwater table at the ground surface. This is an effect that must not be neglected in planning and execution.
1.4 Stresses and Deformations
1.4.1 Calculative Section and FE Mesh
For the calculation of stresses and deformations, a much smaller calculative section is sufficient (see yellow marking in Fig. 3). In addition to the rock mass, the FE mesh used reproduces in detail the cutting wheel with openings as well as the shield and the segmental rings (cf. detail of the FE mesh in Fig. 5; position of the detail: see red rectangle in Fig. 3).
5 | FE mesh, detail
At the beginning of the calculation, an open steering gap is simulated between the shield and the rock mass, which in the case considered is 4 cm thick at the roof and 2 cm thick at the bottom. The first segmental ring is located within the shield and is therefore not embedded in the annular gap mortar. The second segmental ring is embedded in fresh annular gap mortar. The mortar pressure is taken into account in the calculation. The following segmental rings are embedded in hardened annular gap mortar. The dead weight of the first two segmental rings must be held by frictional forces in the circumferential joints between the first, second and third segmental rings. Corresponding jacking forces are required for this.
1.4.2 Assumptions and Calculative Steps
The example case already explained was considered (cf. chapter 1.2). Beforehand seepage flow analyses were carried out – assuming that groundwater can flow in the area of the face and the shield. This way, the uplift forces and seepage pressures were calculated (cf. chapter 1.3) and then introduced in the calculations of stresses and deformations.
The calculations of stresses and deformations have been performed in a total of ten calculation steps. The first calculation step is used to simulate the in-situ stress state. In calculation steps 2 and 3, excavation and support of an 85 m long tunnel section are simulated. The result forms the initial state for the subsequent calculation of a step-by-step excavation in calculation steps 4 to 10. In each of these calculation steps, the excavation of a 2 m long tunnel section is simulated. The following factors are taken into account: the cutting wheel with contact pressure at the face, the excavation, the construction of the segmental ring, the fixation of the segmental ring’s position with the aid of the jacking forces, the grout injection pressure in the area of the previously installed segmental ring, the hardened grout in the area of the segmental rings further back.
1.4.3 Support of the Temporary Face
In one of the calculations, it was assumed that the bedding parallel joints enter the temporary face at an angle of 30° (Fig. 6). Apart from that, the assumptions of the example case apply.
In the calculations, the contact pressure of the cutting wheel against the temporary face was varied. It was shown that resulting forces of 3542 kN and 5000 kN are not sufficient to stabilize the temporary face. In order to ensure the stability of the temporary face under the assumptions made, forces of 15 000 to 20 000 kN would be required (Fig. 6). This clearly shows that such considerations of the stability of the temporary face, taking into account the spatial position of the discontinuities, the anisotropy of strength and permeability as well as the seepage flow, are important for the correct design of the tunnel boring machine for heading in jointed rock masses.
6 | Influence of cutting wheel pressure on displacements of temporary face
A practical example where a very high groundwater level and the resulting seepage flow pressure led to problems with regard to the stability of the temporary face is the Hallandsås Tunnel on the railway line from Malmö to Gothenburg in Sweden (Fig. 7). More detailed information on this can be found in .
1.4.4 Loads on Shield and Segmental Lining
In further calculations, a horizontal bedding was assumed. The assumptions of the example case apply in all other respects. These calculations show that a rock mass volume of around 26 m height moves down onto the shield and thus also onto the subsequent segmental rings (Fig. 8, left). The schematic diagram sketched on the right hand side of the calculation result, illustrates the process caused by bedding and jointing, which also corresponds to observations of roof failures during conventional tunnelling in sedimentary rock. In this process, the steering gap in the roof area closes, and the shield mantle deforms under the load of the rock mass (Fig. 9). The segmental rings experience the displacements shown in Fig. 10 in the various construction stages, which must be superposed to obtain the final displacement pattern. The resulting moments and normal thrusts are shown in Fig. 11. For the sake of accuracy, it should be mentioned that the stress concentrations acting in the longitudinal joints due to the limited load transfer area, against which the segments are to be designed with an appropriate tensile reinforcement, are not shown here.
8 | Displacements and zones with exceeding of strength along discontinuities
Credit/Quelle: WBI, 
For comparison, additional calculations were also executed assuming a rock mass without groundwater. The resulting displacements are significantly smaller in such case, but still large enough to close the steering gap so that the shield is loaded. In this case, too, a loosened rock volume forms above the roof, but it reaches only about half as high as when interacting with a seepage pressure for anisotropic permeability.
Apart from the requirement that load assumptions are to be determined specifically for each project under consideration of the statements of the geotechnical expert, the recommendations of the DAUB for static calculations of shield tunnelling machines  request that a vertical load on the shield must be considered as additional load case, if tunnel heading is to be carried out in horizontally stratified rock with the risk of formation of rock wedges along the discontinuities in the roof area. The additional vertical load due to these rock wedges should amount to at least σV = 0.5 * D * γRocks, as a minimum . This corresponds to a rock wedge of about 5 m height, which is considerably less than results from the calculations explained above, with and also without the influence of groundwater.
A more accurate calculation is therefore necessary and important for the correct design of the shield as well as the segmental lining.
1.4.5 Transfer of Jacking Forces Into the Segmental Ring
As explained in chapter 1.1, the segmental rings serve as abutments for the jacks. The forces are transferred from the jacks to the contact surfaces in the circumferential joints and lead to stress concentrations there, which result in tensile splitting forces in the segments, as shown in Fig. 12 for an example project [3, 7]. To be able to design the segments accordingly, the maximum jacking forces, which are composed of the components shown in Fig. 1, must be determined in the design phase. In the case considered in chapter 1.4.4, force components required to overcome the friction of the clamped shield also contribute significantly to the magnitude of the jacking forces.
On the other hand, the sealing gaskets located in the circumferential joints between the segmental rings need to be compressed. This necessity leads to minimum jacking forces that must be achieved.
As already mentioned, the temporary face must also provide a sufficient abutment so that the jacking forces can be applied. The authors know various cases from practice of TBM tunneling in EPB mode in jointed rock, in which the rock mass strength at the temporary face was so low and/or the stability of the temporary face was not given, so that it was not possible to apply the required jacking forces. As a result, the jacking forces dropped repeatedly, problems arose with steering the tunnel boring machine and with the positional stability and tightness of the segmental rings. Supplementary compressed air support (EPB & partial filling & compressed air) had to be provided to enable proper driving. Corresponding observations were made, for example, in a section of the Neue Schlüchterner Tunnel in the strata of the upper Bunter formation .
12 | Tensile splitting forces resulting from jacking forces for a project example
Credit/Quelle: [3, 7]
2 Reflections on the Annular Gap Mortar
2.1 Bi-Component Mortar
The use of bi-component mortar for annular gap filling has advantages from the point of view of construction operation as well as with regard to the uplift forces resulting from fresh mortar. However, from the authors‘ point of view, such mortar is not suitable for tunneling in rock in most of the cases, because complete filling of the annular gap, which is required for a sound bedding of the segmental ring, cannot be guaranteed for the following reasons:
It can or must be assumed that the cavity in the area of the shield is stable at least in some sections of the tunnel. In such case, the steering gap in the roof area remains open. As a result, the bi-component mortar can flow towards the temporary face. Consequently, no grout pressure can be built up and the annular gap remains open in the roof area.
A practical example where this has been observed is the Boßler Tunnel, which was excavated with a tunnel boring machine in the course of the new railway line from Stuttgart to Ulm in Germany. Extensive post-grouting was required in the roof area after driving (Fig. 13, [9, 10]).
In addition, the joints in sedimentary rocks, such as sandstones, locally may have opening widths, into which the bi-component mortar can also flow off. Also in such case, a complete filling of the annular gap with bi-component mortar cannot be guaranteed.
13 | Two-component mortar, average grout take during post-grouting of annular gap of Eastern tunnel tube of Boßler Tunnel
2.2 Cement Mortar
Cement mortars for annular gap grouting usually have low cement contents with a high water-cement-ratio. As a result, the Young’s modulus is small and develops only slowly. The complete bedding of the segmental ring may therefore only be achieved at larger distances from the temporary working face. In addition, the development of the Young‘s modulus depends on the drainage conditions and thus on the kf-value of the rock mass. For example, the stiffness modulus of a mortar with a cement content of 50 kg/m³ develops much more favorably under drained than under undrained conditions (Fig. 14, [11, 3]).
14 | Oedometric tests on annular gap mortar in drained and undrained condition
Credit/Quelle: [11, 3]
For a project in Israel, oedometric tests on a cement mortar under drained conditions showed that even the fresh, not yet set mortar has a modulus of elasticity of 5 MPa, which in the given case was sufficient for bedding of the segmental ring, if the effective mortar injection pressure amounted to at least 1 bar and was kept upright for a certain period of time to allow for consolidation of the mortar (Fig. 15, ). In such case, the rock mass must be sufficiently permeable to allow the mortar to release water. It should be noted that the modulus of elasticity required for a sufficient bedding as well as the effective grout injection pressure required for grouting must be determined on a project-specific basis, taking into account the respective boundary conditions (regarding this as well as other requirements on the mortar see ).
15 | Oedometric test on cement mortar
In the case of low permeabilities of the rock mass (undrained conditions), it must be demonstrated by testing that the grout will set even without water release. In this case, it is particularly important during tunnel heading to apply a sufficiently high grout injection pressure and to keep it constant over a certain period of time in order to create hydrostatic conditions. If this is ensured, sufficient bedding of the segmental rings in many cases can be achieved also under such conditions until the grout sets.
However, special considerations are required if conditions are to be expected in which layers of different permeability are present in the tunnel cross-section so that different drainage conditions are present, which can lead to uneven bedding of the segmental ring. This may be the case, for example, in the alternating sequences of low-permeable claystones and higher-permeable sandstones that are frequent in sedimentary rocks.
To prevent the segmental rings from floating, the mortar must have a minimum shear strength (). This must be ensured with the composition and verified by testing.
3 Cutting the Rock
For tunnelling in jointed rock, the common tests for determining abrasiveness, such as the Cerchar abrasiveness test, are necessary and helpful, but not sufficient.
Even if these tests show an only slightly abrasive rock, considerable wear can occur during tunnelling. The following effects are just a few examples:
Grinding effect when water enters e.g. during heading in quartzitic sandstones with clayey binders
One-sided wear of due to clogging non-rotating cutter discs in claystones (see also section 3.3)
Wear in alternating layers of claystone/sandstone or in mixed-face conditions with fault zones.
Corresponding considerations must be made in time so that the tunnel boring machine and the heading are designed accordingly.
3.2 Blocky Ground
Depending on the spatial position, the spacing and the characteristics of the discontinuities, rock wedges may form at the temporary face in fractured rock. In these cases, the rock is not crushed into rock pieces (chips) at the temporary face, as it is meant to be. Rather, the rock wedges are torn from the rock mass at the temporary face and then move in an uncontrolled manner in front of the cutterhead, which must act as a rock crusher in such a case. The rock wedges can cause considerable damage to the cutting tools and the cutterhead itself, as well as to the subsequent transport system. This phenomenon, known as “blocky ground”, has already occurred in a number of tunnel headings in rock. Examples are the Hallandsås Tunnel in Sweden  and the Neuer Schlüchternen Tunnel in Germany . If such conditions are to be expected, the openings in the cutterhead must be limited in size, e.g. by means of so-called grill bars (steel struts), so that the size of the rock blocks entering the transport system is limited to a permissible level. At the same time, the cutterhead and the cutting tools must be designed accordingly (reinforcement, wear protection, possibility of simple and fast tool changes). Also, tool changes must be taken into account in planning and costing.
Sedimentary rocks often occur as alternating sequences of low-permeability claystones or siltstones and higher-permeable sandstones or calcareous sandstones (cf. e.g. typical stratigraphic sequences of the formations of Keuper, Jurassic, Bunter). The mudstones often are slaking rocks. They decompose to clay when dried out and subsequently exposed to water. This can be observed in surface outcrops exposed to weathering.
During TBM heading in such formations, especially below the groundwater table, have repeatedly shown problems with clogging. Such observations were made, for example, during the excavation of the Filder Tunnel (Stuttgart 21) in the alternating sequence of mudstones and permeable sandstones of the Stubensandstein formation below the groundwater table . Such phenomena were also observed during the excavation of the Neuer Schluechterner Tunnel in the alternating sequence of claystones and sandstones of the Upper Bunter formation . Due to the clogging, the cutters were blocked, and unilateral wear occured. As a result, a large number of cutting tool changes became necessary (Fig. 16, ). Furthermore, there was a significant decrease in the advance rate. The clogging phenomena in combination with the higher rock strength of the sandstone layers lead to an increase in the required cutting pressure and torques. The temperatures at the cutterhead increased.
16 | Clogging in claystones, wear of cutter discs – examples
Credit/Quelle: WBI (links), Arge ATCOST 21 (rechts)
Extensive investigations were carried out on this subject in connection with the Filder Tunnel . Laboratory tests showed that after drying and subsequent addition of water, crushed mudstone samples decompose to a medium plastic clay, which, in terms of its plasticity and consistency, falls exactly within the range of soils that are highly susceptible to clogging . During TBM tunnelling, the claystones are first crushed into smaller pieces (chips). They are exposed to elevated temperatures at the cutterhead (see above) and can therefore dry out. On the one hand, water can flow in through the permeable sandstone layers. Furthermore, water is added in connection with conditioning and cleaning. In addition, the claystones are “mechanically processed” during excavation. It is therefore obvious that these slaking rocks disintegrate under the given conditions during tunnelling and that, as a consequence, clogging phenomena occur.
Formation of rock chips, “mechanical processing” and increased temperatures are influencing factors that cannot be changed. The only possible countermeasure is therefore to minimize the quantities of water added. All waters added in connection with operation (cleaning, conditioning) should be minimized and immediately drained off. The water inflow from the rock mass (sandstone layers) can be minimized or prevented by (supplementary application of) compressed air. A successful example of this is the excavation of the Filder Tunnel in the sections located in the Lias α formation, also below the groundwater table, which was carried out without EPB, under compressed air, and did not experience any problems with clogging .
Future TBM headings in formations with slaking rock will require appropriate considerations and further investigations to better deal with clogging phenomena.
In TBM tunnelling, there is a complex interaction between the tunnel boring machine, the ground and the segmental lining. Especially for tunnel heading in jointed rock, these interactions must be taken into account in planning and construction, to avoid considerable problems that can lead to construction time and cost overruns.
An essential prerequisite for this is the understanding as well as the realistic description and simulation of the stress and deformation behaviour as well as the permeability of the rock mass, in particular the frequently existing anisotropies of strength and permeability. A suitable model for this purpose is the Anisotropic Jointed Rock Model (AJRM).
In this article, the interaction of the overall system consisting of tunnel boring machine, ground and segmental lining is explained in principle. Based on the example of a Bunter formation, the realistic description of the rock mass with the aid of the AJRM is described. Subsequently, selected results of finite element calculations are presented, which were carried out on the above-mentioned overall system considering the interactions. It is shown that the discontinuity fabric, the anisotropy of strength and permeability and the seepage flow have considerable influence on the stability of the temporary working face, on the loads and deformations in the area of shield and segmental lining and also on the suitability of the temporary working face as an abutment. This results in essential conditions for the design of the tunnel boring machine (e.g. jacking forces, design of shield, design of segments, requirement for compressed air support, etc.). If the relevant properties of the rock mass are not properly taken into account and the interaction of ground, tunnel boring machine and segmental lining is not adequately simulated, there is a risk that the tunnel boring machine and the segment lining will not be adequately designed and that problems will occur during tunnel heading.
In addition, during TBM excavation in jointed rock, special conditions exist with regard to annular gap filling and rock cutting (wear, blocky ground, clogging), which require appropriate measures. This is also dealt with in the present article.
In the past, difficulties have frequently arisen during TBM tunnelling in jointed rock. These have led to an exceeding of the planned construction times and costs. Along the new lines planned by Deutsche Bahn, a number of long tunnels in jointed rock are planned. Due to their length, they are suitable for mechanized tunnelling. With this article, the authors would like to highlight the relevant issues and thus contribute to better cost and schedule reliability of future projects.