ABSTRACT
Hard rock formations with layered, anisotropic geological structures are common in Norway and design for rock support under such ground conditions has been traditionally done with an empirical approach, assisted with engineering rock mass classification. In most cases, rock stability has been achieved using fibrereinforced sprayed concrete combined with rock bolts, and sometimes ribs of reinforced sprayed concrete (RRS concrete) and bolt spiling.
However, the discontinuous character and more complex ground behaviour of layered rock can lead to design challenges, as experienced in construction of the new Skarvberg road tunnel in northern Norway. A significant portion of the tunnel exhibited consistent overbreak, delamination problems and a tunnel failure.
In this article, the ground behaviour and rock support performance at different locations of the tunnel are investigated to find a basis for design optimisation of rock support under similar ground conditions. A site investigation programme formed the basis for further assessments and analyses with a hybrid design methodology and the numerical code UDEC (Itasca).
The work identified the main challenges of classification systems to capture ground behaviour and derive optimal support design in layered rocks. It has resulted in the development of, among others, a specific ground behaviour classification for layered ground and a new, optimised RRS-support concept for layered rock masses of very poor quality (e.g., rock mass quality (Q) ~ 0.1–1).
1 INTRODUCTION
Layered hard rock masses with anisotropic geological structure are common and typically exhibit persistent and weak bedding planes, which are a significant source of mechanical weakness. For tunnelling, the ground behaviour of layered rock is therefore different and more complex than that of blocky rock masses without a dominant weak orientation. Such complexity results from the interaction of several engineering geological parameters, such as joint spacing and persistence, bed thickness, mechanical properties of joints, tunnel span, roof geometry, and in-situ rock stresses, as well as the characteristics of the rock reinforcement.
The design of permanent rock support also turns more challenging. Some examples have been addressed by authors like Perras and Diederichs (2009) and Diederichs (2020) from case studies in Canada and Australia, respectively. Similar cases with tunnel stability problems and/or design challenges have been also found in Norwegian tunnels, such as the North Cape tunnel in which unforeseen and significant roof stability problems, over long tunnel sections, resulted in high support consumption (Melby et al. 2002; Palmstrom, personal communication 2023). The recent construction of the new Skarvberg tunnel showed extensive sections with roof overbreak, delamination problems, and a tunnel failure, resulting in a significant increase of the required rock support (Bøgeberg and Skretting 2021; Gildestad and Bakkevold 2021).
Some of the challenges can be attributed to limitations of current design methods, such as empirical classification systems being unable to capture and describe the basic ground properties controlling the anisotropic ground behaviour of layered rocks. As noted by authors like Palmstrom and Broch (2006), Palmstrom and Stille (2006), Marinos et al. (2005), Anagnostou and Pimentel (2009), Palmstrom (2009), Vibert and Vaskou (2011), Høien et al. (2019), and Terron-Almenara and Li (2023), the well-established and widely used classification systems are built upon the assumption of structural isotropy; these include the Rock Mass Rating (RMR) of Beniawski (1973; 1989), the Q-system (Barton et al. 1974; NGI 2015), and the Geological Strength Index (GSI) of Hoek (1994).
Alternatively, analytical solutions based on the Voussoir beam analogue of jointed rock roofs may be also used to evaluate the roof stability of an excavation, as suggested in Sofianos (1996) and Diederichs and Kaiser (1999), among others. However, such an approach also presents limitations in predicting roof stability due to challenges for some of the mentioned analytical solutions to simulate tunnel shape and jointing, the effect of in-situ stresses and rock support, and also the failure mechanisms of the beds (Oliveira and Pells 2014; Bakun-Mazor et al. 2009; Abousleiman et al. 2021, 2023).
With the use of a numerical approach based on the Distinct Element Method (DEM), detailed analyses of tunnel stability in layered, discontinuous rock masses can be performed. However, numerical methods applied for the analysis of discontinuum ground also have limitations, as noted by Starfield and Cundall (1988), Oliveira and Pells (2014), and Walton and Sinha (2022).
Hence, there is a lack of specific design methods that integrate different methodologies of assessing ground behaviour plus adequate rock support designs for anisotropic, layered ground.
The design gap led research work (Terron-Almenara et al. 2023) to develop a hybrid approach, built on a retrospective stability analysis of more than one hundred hard rock tunnel cases, including anisotropic rock masses, from Norway and internationally.
Here, the new Skarvberg tunnel is studied as an example to demonstrate the limitations of the current empirical methodology used in Norway (NPRA 2020, 2022a) for tunnel rock support design in layered rocks. Two main objectives of the study were: to find a basis for developing improved design recommendations for layered ground; and, practical implementation and testing of a hybrid approach.
The performance of the current design methodologies was numerically studied at the new Skarvberg tunnel by comparing the tunnel stability with empirically based and hybrid-based designs. As a result, this article presents a new design procedure for tunnel rock support in layered rock masses, based on the application of a hybrid methodology (Terron-Almenara et al. 2023) in the anisotropic rock masses at Skarvberg.
In this context, a new classification for layered rock masses called Layered Ground Behaviour Classification (LGBC) is also proposed. This is intended as a supplementary design tool.
Finally, a new and optimised rock support concept – consisting of modified ribs of sprayed concrete called Crown-RRS (C-RRS) – is proposed for the reinforcement and support of horizontally layered rock masses of quality Q 0.1–1. The numerical analyses performed for the proposed C-RRS support concept showed tunnel stability and an associated potential for a reduction in rock support consumption.
Hence, in addition to an improvement in tunnel stability, optimisation with the use of hybrid designs can also pose a beneficial contribution to the environment.
2 NEW SKARVBERG HIGHWAY TUNNEL
A major upgrade has been undertaken by the Norwegian Public Roads Administration (NPRA) on the E69 highway to North Cape, including construction of the subsea North Cape tunnel and the Honningsvåg tunnel, completed in the late 1990s, and more recently the 3.5km-long Skarvberg tunnel (see Figure. 1a). The new Skarvberg tunnel is D-shaped, 12.5m-wide, and was excavated by drill-and-blast. Its rock support design is based on empirical rock mass classifications. The main elements of the permanent rock support are shotcrete and rock bolts, as well as RRS support arches.
The geology was characterised mainly as hard rock with a distinct anisotropic, layered rock mass structure. The rocks belong to the Kalak Formation, mainly composed of sequences of metasandstones and mica schists disposed sub-horizontally and intersected by sub-horizontal, 0.1m–1m thick intrusions of metagabbro. The rock mass structure is formed by three main joint sets as shown in the rosette diagrams made from joint registrations during construction (Figure. 1b).
From aerial photography over the tunnel alignment, up to nine weakness zones were identified (Figure. 1b). The geometrical correlation between the structures recognised on the surface and those encountered (and mapped) as weakness zones at the tunnel level, during construction, confirmed the weakness zones to be vertical to subvertical (Figure. 1c). In addition, minor fracture zones were also encountered, having similar strike and dip but a lower degree of jointing and shearing.
Tunnel construction saw a significant deviation between forecast and encountered distribution of rock mass classes, and rock support. While only 15% of ‘very poor quality’ rock mass of Class IV was forecast in the tender studies, based on Q-logging, the proportion met during construction was 51.6% of at least Class IV (see Table 1).
This difference was mostly related to the frequent occurrence of tunnel roof instabilities, caused by the combination of layered rock mass structure and insufficient horizontal confinement in long sections of the tunnel, and limitations of empirical systems used in tender design to forecast such behaviour.
Several tunnel sections were supported with RRS arches and bolt spiling. Despite the heavy rock support measures in locations with very poor rock mass quality, a roof failure occurred at Profile 3 + 162 (see Figure. 2). The failure occurred in a tunnel section with mapped Q 0.1 and supported with single (Si)-RRS 30/6 spaced c/c 2m, radial bolts 4m-long, at c/c 2m, and bolt spiles in the crown. Failure occurred in the centre of the roof and extended about 9m behind the tunnel face. The centre part of the RRS arches in the flat tunnel roof was visibly buckled downwards, causing the development of tensional fractures in the shotcrete.
In addition, frequent instabilities during the excavation of the tunnel were observed in the form of delamination, rock fall, and over-break when the rock mass was exposed immediately after each advance. Several more site investigations were conducted and the findings used by the contractor`s specialist consultant to derive an adjusted support design. The encountered rock conditions finally lead to an increased use of RRSarches and rebar bolt spiles corresponding to factors of 13.4 and 6.6, respectively, higher than the tender forecast (Gildestad and Bakkevold 2021). The tunnel section at Profile 3 + 162 is further studied in this article, together with a monitored tunnel section at Profile 2 + 227. Locations are shown in Figure. 1.
3 DESIGN OF TUNNEL SUPPORT
Horizontally layered rock masses of poor quality, in Norway The design of permanent rock support in Norwegian tunnels is based on an empirical approach. Rock support design in Scandinavian hard rock tunnelling is similarly based on the utilisation of the rock mass as a load-bearing structure. This is achieved by conserving – or improving – the self-bearing capacity of the rock mass with rock reinforcement measures, typically a combination of bolts and fibre-reinforced sprayed concrete that form part of the permanent support.
In rock masses of poor quality the load-bearing support normally has also the installation of RRS arches. In the Q-system, different configurations – or designs – of RRS support are available by adjusting the longitudinal centre spacing, thickness, the number of steel layers – Single (Si) or Double (D) – and the number of steel rebars in the RRS arches. This approach permits wide design – and construction – flexibility to suit different loading conditions.
The design of rock support in Norwegian tunnels must additionally comply with the national design guidelines for road tunnels as published by NPRA in Pedersen et al. (2010), and the subsequent revisions (NPRA 2020, 2022a). The guidelines are basically a simplification of the Q-system (Table 1).
The guidelines, however, give no specific design recommendations for rock support in anisotropic, horizontally layered rock masses. Instead, experienced geologists apply some mapping adjustments and recommendations to derive representative values of Q-parameters that reflect best the expected ground response of layered rocks. These can consider: joint roughness number (Jr) and joint alteration number (Ja) of the most unfavourable joint set – i.e., the bedding planes; the value of the stress reduction factor (SRF) to represent the impact of in-situ stresses in relation to the main joint directions; and, assessment of representative rock quality designation (RQD) values to account for both the bedding and the cross-joints, such as by considering volumetric joint count (Jv), as suggested by Palmstrom (1982, 2000) and NGI (2015).
A frequent design solution to reinforce and support layered rock masses has been to use RRS arches combined with bolt spiling (a pre-reinforcement measure above and ahead of the face), resulting in a thicker and stronger beam of reinforced rock beds (illustrated with dark brown colour in Figure. 3). They also tie the load-bearing support (RRS) to competent and undetached ground above the tunnel roof, restricting deflection and providing the needed ground-RRS-arch interaction. In this context, the main functionality of the RRS arches is to hold ground pressure and provide a resistance force against radial deformations (thick black arrows in the figure).
Bolt spiling is a pre-reinforcement measure of the rock mass for poor conditions. The method of pre-reinforcement installs steel bolts above the tunnel crown and extending ahead of the face, prior to advancing the excavation (see also Figure. 3). Its stabilising effect has three main characteristics: (a) maintain the arched roof geometry; (b) reinforce both longitudinally and radially, generating a protective vault (grey-shaded colour in figure); and, (c) help load transfer and arching in the tunnel direction, thus a more even distribution of ground load.
The bolt spiling method falls within the category of an umbrella arch (UA) reinforcing system (Oke et al. 2014a). Design practice in Norwegian hard rock tunnelling is primarily based on experience and basic empirical design recommendations, advising use of bolt spiling when Q < 0.6. This leads to designs where the actual (and necessary) interaction between the ground, tunnel support and bolt spiling remains unaccounted for – or, in other words, the rock support design is principally independent of the beneficial (and known) stabilising effect of bolt spiling.
4 GROUND BEHAVIOUR OF HORIZONTALLY LAYERED ROCK MASSES
The analysis of deformational behaviour in tunnels has been traditionally linked to the Convergence Confinement Method (CCM), an analytical elastoplastic model for weak and isotropic rocks. However, in hard and layered rock, the persistent and often weak planes of bedding have a discontinuous character that invalidates the premise and, therefore, the use of CCM.
The following summarises the main geometrical and engineering geological parameters controlling ground behaviour of layered rock.
4.1 Failure Mechanics of Jointed Roof Beds
The mechanics of tunnel roof beds have been studied at least since Fayol (1885) when the study of stability was mostly based on the classic beam theory for elastic and continuous beams. However, cross-joints in bedded rock formations reduce the allowable beam tensile strength and invalidate the continuum approach in favour of the jointed or Voussoir beam analogue approach.
The essential principle of the Voussoir concept is that jointed, discontinuous rock beams can develop moment resistance from the generation of a compression arch between the upper beam midspan and the lower abutment. With this approach, roof deflection and beam stress can be used to evaluate roof bed failure in relation to the intrinsic elastic properties of the rock, bed geometry, and span of the opening.
Four basic failure modes of Voussoir roofs were categorised by Diederichs and Kaiser (1999) (see Figure. 4).
Buckling (Figure. 4a) and crushing (Figure. 4b) in multi-layered rock masses would be expected for a high ratio of span to bed thickness, typically greater than 10. If the rock is hard, buckling failure is produced when moment loading exceeds moment capacity of a bed; where rock material is relatively weak, failure by crushing can be initiated at the upper midspan and at the lower support (hinges) by an excess of compressive stress. Both buckling and crushing failures would be accompanied by interbed slip and delamination, causing bed cracking and roof deflection.
For low span to bed thickness ratios, however, the beds are considered thick and shear failure (Figure. 4c), can take place for shear loads in excess of shear resistance at the abutments. A fourth failure type is diagonal tensile rupture (Figure. 4d), which also can occur under low ratios of span to bed thickness.
4.2 Further Parameters Controlling Layered Ground
Other parameters like the joint spacing and joint persistence have also a direct influence on the extent of the dome of loosened rock formed above the tunnel, hence on the ground loads. In-situ rock stress also controls ground behaviour since horizontal confinement usually contributes to roof arching and stability. However, such stresses are seldom accounted for in the Voussoir solutions.
Similarly, rock mass structure and changes in rock stiffness across the geological sequence can contribute to stress reorientation and fluctuation in magnitude, which can lead to misinterpretation of the stress state. Other important parameters for roof stability analysis are geometry and reinforcement.
4.3 Proposed Classification
A classification of ground behaviour for layered ground has been elaborated in Table 2. This proposed Layered Ground Behaviour Classification (LGBC) combines the basic failure modes of jointed rock beams (Figure. 4) and the relevant engineering geological parameters discussed. It has categories of Layered Ground Behaviour Type (Layered GBT, or LGBT).
The LGBC aims to supplement a hybrid procedure for tunnel rock support design in layered and hard rock masses, as proposed by Terron-Almenara et al. (2023). The main purpose of such classification is to better anticipate ground loading conditions (approximate distribution and size).
Final, hybrid designs of permanent rock support should, however, be performed on the basis of an elaborated analysis process. According to Terron- Almenara et al. (2023), such a hybrid procedure should principally be used when rock mass quality is Q < 1 in anisotropic and hard rock masses. Defining a lower boundary may be challenging and use of LGBC not recommended, as rock mass anisotropy is scale- and stress-dependent. As such, the relative size of span to bed thickness along with in-situ stress conditions should be evaluated in each case when Q is very poor. Some authors like Barton (1998) and Brady and Brown (2006) suggest that Q < 0.1 may behave more isotropically as a result of denser jointing.
Therefore, several rock mechanical parameters and geomechanical systems should be employed when performing a classification of LGBT.
The LGBC is similarly built from civil rock tunnelling experience where in-situ rock stresses were not especially high to create stability problems related to brittle failure of rock. The classification is, therefore, limited to ground conditions subject to low-moderate stresses, i.e., in-situ stresses not more than about 10 MPa.
As observed in Table 2, the LGBC is divided into three main vertical blocks – ‘Ground Conditions’, ‘Ground Behaviour’ (or failure mode), and ‘Support Loading’ (or design considerations).
Each of the six different LGBT categories is defined by a set of characteristics found in the corresponding horizontal rows for each category. The categories are grouped into two subgroups, ‘a’ and ‘b’, which describe two different confinement conditions: ‘Low’ for rock masses subject to low in-situ stresses (maximum horizontal stress typically below 5 MPa) with a horizontal to vertical stress ratio and k0 < 1; and, ‘Moderate’ representing rock masses where the maximum horizontal stress is in the order of 5 MPa–10 MPa, and a horizontal to vertical stress ratio k0 > 1.
For the former, ‘a’, subgroup the rock masses present challenges to the arch and often lead to a higher propensity for tunnel instabilities and a greater need of tunnel support. On the other hand, subcategory ‘b’ is where the horizontal confinement contributes to rock arching and the rock mass can take a greater share of the ground load.
In the absence of stress measurements, best estimates can be based on overburden, topography, rock mass structure, and the geological/tectonic context of the site. This can allow application of the LGBC early on a project and interpretations are then update as excavations proceed.
The categories I, II and III represent decreasing joint spacing (relative to tunnel span) and quality of joint surfaces, i.e., declining rock mass quality. Categorisation between I, II and III is primarily based on tunnel span to bed thickness ratio.
Figure. 5 shows failure mechanisms that may arise upon excavation for different categories and subgroups. The cross-joints are truncated at almost every bedding plane. The extent, geometry, and location of the loosening zones over the excavation can vary if persistent cross-joints cut both the bedding and the excavation.
5 GROUND CONDITIONS AT KEY PROFILES
Roof failure during the construction of the new Skarvberg tunnel motivated additional site investigations and upgraded tunnel support designs. Site investigations were focused at two locations – Profiles 3+162 and 2+227, respectively.
5.1 Rock Mass Mapping
Mapping shows that the rock mass is predominantly layered metasandstones and thin intercalations of metagabbro (Figures. 6 and 7). From face mapping at Profile 3 + 162, the rock mass was characterised by a well-marked and thin lamination, joint surfaces with poor conditions, unstable tunnel abutments with overbreak and flat roofs, and roof delamination. The assessment of RQD was primarily based on measurements in the vertical direction. Cross-joints were also accounted for, through the study of Jv, to adjust and derive a final RQD representative of the overall jointing degree at the face. This resulted in Jv of approx 32 joints/m3 and RQD 10%–20% at profile 3 + 162.
A core hole was drilled at Profile 3 + 180 with a length of 18m and at an angle of 45° pointing towards Profile 3 + 162, reaching an area about 12m–13m above the tunnel roof in the section. Both the lithological sequence and rock mass structure logged were projected to Profile 3 + 162 as observed in the logged layers 1 and 2 (Figure. 6) of the metagabbro. In general, the rock mass was characterised by Q 0.1, RMR 30–35, and a GSI 25–30. A summary of the geomechanical classifications is presented in Table 3.
The mapping at the second study location, at Profile 2 + 227 (Figure. 7), shows slightly better rock mass conditions. The resulting Jv was approx 22 joints/m3 and RQD 35–45%. The other data were Q 0.3–0.4, RMR 35–40, and GSI 30–35.
5.2 Joint and Rock Properties
At the two study locations, three main joint sets were identified – bedding and two sets of cross-joints. Each joint set was characterised on-site with the assessment of the Joint Roughness Coefficient (JRC), Joint Compressive Strength (JCS), the roughness number in the Q-system (Jr), and measurements of joint spacing (S) and persistence (P). As shown in Table 4, joint conditions at Profile 3+162 were significantly worser than those at 2+227.
Rock testing was performed in samples retrieved outside the failure zone (Profile 3 + 162), both from core holes and from samples collected at the face during construction. The strength anisotropy was also studied in intact rock samples. With the relatively low strength anisotropy and the laboratory scale of the samples, the main source of anisotropy was interpreted to be mechanical weakness introduced by the penetrative and weak bedding planes. Density of the rock material was also tested, finding 27 kN/m3 for metasandstone, 31 kN/ m3 for metagabbro.
5.3 In-situ Rock Stresses
Estimation of the in-situ stress state for underground works for a particular site should be based on the broader geological and stress context of the region.
Bedrock has traditionally been subdivided into two main tectonic belts in northern Norway, one of Precambrian age with crystalline rocks like gneiss and granites, and another of Cambrian-Silurian age representing fractured metasediments. While relatively large horizontal stresses have been reported in the former, rocks of the Cambrian-Silurian belt have been generally characterised by lower stresses, which applies to the region of Skarvberg tunnel.
Both the magnitude and the orientation of horizontal stresses can be influenced by the rock mass structure and the degree of jointing. If the general lineament patterns in the region of Finnmark are considered, some degree of rotation of the major horizontal stresses (oriented N-S) should be expected to take place and align with the mentioned structures.
5.4 Deformation Monitoring
During construction, convergence measurements were taken some tens of metres behind the face.
This limited anticipation of some sort of instability or trend that might have anticipated the failure at Profile 3 + 162. The available deformation records at the failure area were derived from comparison of scanned tunnel profiles before and after the event, which gave a total deflection of the centre roof of about 150mm–200 mm.
Four multi-point borehole extensometers (MPBX) were also installed vertically in the centre roof to study the behaviour of the layered rock over time and the extent of loosening zones. The measurements were also utilised for calibration process in the numerical analyses of tunnel stability.
The measured vertical displacements at different anchor depths in extensometers at Profiles 2 + 227 and 2 + 231 were measured for a period of three months. Considering that on average, a 4m long excavation round was taken per day and the characteristics of the hard and anisotropic rock mass (Q ~ 0.3–0.4), displacements appear to occur in connection to block movements, its associated dilation, and possible rock detachment. Some differences in the distribution of vertical displacements measured at the anchors placed at different depths were also observed. Such response may be interpreted either as rock mass movements mass occurring at any depth between 4m and 12m, as the beneficial reinforcement effect of the 5m long rock bolts stabilising the arch roof, or a combination.
6 ANALYSIS METHODOLOGY
Four numerical models were run to study the ground behaviour and the performance of different support designs Table 5. The pairs of models A1–A2 and B1–B2 cover an empirical and a hybrid design approach for both study sections, Profiles 3+162 and 2 + 227.
A summary of the analysis methodology based on a hybrid approach (Terron-Almenara et al. 2023) is presented in Table 6.
- Step 1. Identification of ground behaviour and assessment of potential failure mechanisms based on the evaluation of, among other rock mechanical parameters, the rock mass structure and competence, jointing conditions, tunnel geometry, and the in-situ stresses. The ground conditions are categorised to the classification presented by Terron-Almenara et al. (2023) for hybrid design. The LGBC is utilised to select the LGBT category for best to the rock mass conditions.
- Step 2. Specific site investigations are recommended in such hybrid methodology for anisotropic rock masses when rock mass quality Q < 0.4 and/or GSI < 40. The resulting set of rock mechanical properties is then utilised, especially in the analytical solutions in Step 4, and in the numerical calculations in Step 5.
- Step 3. Empirical and basic estimates of rock support design are derived from well-established classifications for hard rock tunnelling like the RMR, the Q-system, or the empirical classification proposed by NPRA (NPRA 2022a). The aim was to obtain a basic estimate of empirical rock support design concerning rock bolting, thickness of sprayed concrete, and the design of RRS arches.
- Step 4. The authors selected three analytical solutions based on limit equilibrium analysis of Voussoir roof beds, like the ones proposed by Lang and Bischoff (1982), Diederichs and Kaiser (1999), and Abousleiman et al. (2021), chosen since their joint application can capture the actual ground and support behaviour of the jointed roof beds.
- Step 5. The numerical analyses in the models summarised in Table 5 are conducted with the numerical code UDEC v5.0 (Itasca 2011). It is a twodimensional numerical program based on the distinct element method (DEM), treating the rock mechanical problem as an assemblage of distinct, interacting, and deformable blocks; it solves the equations of motion and contact forces between blocks (Cundall 1980), permitting simulation of large displacements together with block deformation (Eberhardt 2023).
The four models A1, A2, B1 and B2 were calibrated before performing the analyses. The exerted loading conditions on the support systems in each of model were then compared with the calculated resistance and capacity of such support systems. Since the mode of shotcrete failure in hard rock masses not subject to high stresses is primarily related to shear and bending, the analyses then focused on the stability analysis of these parameters.
By further evaluation and comparison of the distribution and size of the support loading and factor of safety (FS) in each of the pair models A1–A2 and B1–B2, it was possible to assess design optimisation possibilities.
7 SET UP OF THE NUMERICAL MODELS
The UDEC models are built in plane-strain conditions, with elasto-plastic Mohr–Coulomb material, and the non-linear Barton-Bandis joint model (Barton and Bandis 1990). Such a combination of material and joint models is intended to be representative of the studied rock mass conditions where rock displacements are not only related to shear translations through existing joints but also to buckling failure of rock when subject to loading.
The individual rock blocks were subdivided into a mesh of finite-difference elements, the size of the mesh established on the basis of the rock mass conditions, the dominant failure mechanisms, and the size of the excavation. As such, the maximum element length was set to not exceed a value of 1m in the UDEC models, in line with modelling recommendations given by, among others, Lorig and Varona (2013) and Itasca (2011).
Boundary conditions were set first by an external geometry or box of 100m × 100m that contains the geological model and the tunnel in its centre. The external boundaries were constrained to zerohorizontal movement in the vertical walls of the box, and zero-vertical movement in the horizontal (top and bottom) sides of the box, to prevent the model rotating. Both in-plane and out-of-plane in-situ stresses were also applied. The modelled tunnel geometry was based on a D-shaped, 12.5m span tunnel, and updated to match the actual excavation profiles.
Jointing in the models was simulated to replicate the actual rock mass structure. However, some simplifications – typically one of the approaches Chen et al. (2001) – were included since the presence of joint contacts in UDEC modelling normally occupy a relatively large computational memory.
The four models were calibrated before performing the analyses. Tunnel deformations registered in monitoring were utilised as a basis for backcalculations. Rock and joint properties obtained from field and lab investigations were adjusted through an iterative process until consistent with measured behaviour. Bulk modulus (K) and shear modulus (G) of rock were also for the UDEC models.
Calibration of numerical models performed on the basis of deformation monitoring in hard rock tunnels is a widely used procedure in rock engineering. As pointed out by Sakurai (2017), it provides a rather useful posteriori rock engineering indicator reflecting the true response of a set of rock mass properties to tunnel excavation. However, the same author along with Walton and Sinha (2022) advises that the use of such a back-analysis process normally involves limitations and assumptions.
For the two studied tunnel sections, the main assumptions and considerations for the modelling and calibration processes were:
- Constitutive are assumed to capture the behaviour of layered hard rock and distinct joints subject to low levels of horizontal stress confinement;
- Field and laboratory investigations are representative of the ground conditions;
- No evidence of time-dependent or creep deformations;
- Displacements registered in the four MPBX and from several tunnel were assumed representative and measurements reliable;
- UDEC calculations are performed in computational steps or stages, which provide a representative simulation of the sequential installation of support.
- Material properties of the rock support elements are not subject to calibration;
- It is assumed that rock displacement is the parameter that best defines the behaviour of layered and hard rock subject to relatively low stresses. However, various combinations of input parameters used in the back-analyses can also yield a similar response.
As noted by Walton and Sinha (2022), however, there can always be remaining possibilities for reliability improvement since every parameter added to the backanalyses intrinsically adds a source of uncertainty. Due to the limitations of the methodologies (i.e., rock testing, in-situ testing, rock mass classification and mapping, numerical method) involved in the study, uncertainty and subjectivity can still remain. In that sense, we believe that the involvement and integration of different design tools and approaches as suggested in a hybrid approach by Terron-Almenara et al. (2023) have contributed to the identification of possible deviations and to reduce the level of uncertainty.
Before excavation in the models, the models were run in elastic conditions to equilibrium. Then, the full face excavation was computed, and the support installed sequentially behind the face. Bolt spiling ahead of the face was also modelled at the two studied locations.
With regards to the modelling of RRS support, UDEC permits the construction of composite beam support that may simulate RRS in the tunnel direction. The modelling of RRS-support requires definition of normalised beam sections to derive equivalent beam properties
8 GROUND BEHAVIOUR AND SUPPORT PERFORMANCE
8.1 Summary of Results
The results for model A1 (Figure 8) clearly indicate that the failure of the tunnel support occurs due to flexural failure of the RRS support. The unfavourable combination of a wide excavation span combined with a flat roof and too short bolt lengths, too large centre distance of bolts, and insufficient horizontal confinement did not contribute to rock mass arching. This resulted in an excess of ground load not taken by the rock mass nor by the roof bolts, and then transferred onto the RRS.
By using a hybrid approach, as in model A2, proposing an improved support design has been possible; in that, rock support elements are dimensioned to become loaded to a more optimal level. Hence, an improved load sharing in the rock support can be realised. Obviously, model A2 requires a generally heavier support design than that in A1. In turn, it provides stability whilst limiting oversupporting.
In terms of the shear loading of rock bolts in the four UDEC models, the calculations showed that the shear load was, in general, rather low, mainly in the range of 5kN–8kN for all four models with one maximum finding of 18kN (in model A1).
When comparing models B1 and B2, the results suggest an improvement of the rock arching in the latter, which naturally results in a slight reduction of the support loading. The latter improvement in the loading conditions of the hybrid support in the B2 model can be visualised from the comparison of loading values of the support system between models B1 and B2 in Table 7. Besides the limited magnitude in the load reduction of the support systems in the hybrid B2 model, the improved loading condition has still allowed for an optimisation of the rock support design from the use of modified RRS arches. A summary of the results is presented in Table 7.
9 FINAL DISCUSSIONS AND RECOMMENDATIONS
The study of ground behaviour and support performance in the new Skarvberg tunnel has enabled the evaluation of rock mass conditions influencing the design of rock support in layered rock masses of poor quality.
As such, the application of a hybrid design methodology allowed for design optimisation as so indicated in the numerical results for models A2 and B2.
Layered rock mass conditions require a more comprehensive characterisation of the ground and the combination of different analysis methods. With a rational combination of the mentioned approaches and methods, including the Voussoir beam models, the authors were able to predict the ground behaviour of layered rock and derive more optimal and cost-effective support designs.
It should be noted that the main goal of this hybrid methodology has been to provide a complementary tool for ground characterisation of layered rocks and the assessment of permanent rock support design. Practitioners should, therefore, be aware that further elaborated design work may be needed to derive final, detailed designs.
As observed, a hybrid approach still contains an empirical essence since part of the rock mass characterisation and support assessments are based on the application of several rock mass classifications. Although a detailed study with such an analytical approach would require more specific information on, among other parameters, the joint spacing, rock stiffness, and the level of horizontal confinement, simple analyses using the Voussoir beam model can still help to predict roof stability and the needs of support on the basis of roof -deflection and -loading.
In light of this discussion, it is obvious that the type and amount of rock mechanical information needed for more elaborated analyses with such a hybrid procedure may theoretically place the use of such hybrid procedure more towards detailed design and/or the construction stages of a tunnel project. However, the structure of this procedure is conceived for use at any stage of tunnel construction as more rock information is gained.
In looking to design optimisation, the results obtained for models A2 and B2 with the application of a hybrid methodology, combined with UDEC calculations, show that such procedure can contribute to reduced amounts of support without compromising tunnel stability. Use of a hybrid approach demands more knowledge of the rock mass conditions and ground response which may appear, a priori, more expensive and time consuming, but it would be quickly compensated, as extra costs, possible delays, and safety concerns related to tunnel instabilities can be significantly reduced.
There was an overall optimisation in the use of bolts of different lengths, with combinations of 4m and 3m bolts in the hybrid designs providing a notable reduction in rock support consumption when compared to empirical recommendation with 5m and 4m bolts. Put in an economic perspective, in terms of 2022 prices for tunnel construction in Norway, a saving of about Euro 300,000 may have been achievable by the approach in only 175m length of tunnel. Savings of time and carbon were not considered in the analysis.
Although such hybrid methodology has been proven rather effective to predict ground behaviour and support design in layered rocks, some additional remarks should be given to practitioners intending to use this hybrid methodology approach in other projects. Note that the methodology should be only used in underground rock conditions comparable to those studied in this article.
10 CONCLUSIONS
The current empirical approaches in Norway for design of rock support has been investigated in layered rock masses of poor rock quality (Q < 1) and subject to low horizontal confinement of the new Skarvberg tunnel.
The approaches exhibit limitations in characterising ground behaviour. A hybrid approach, combined with numerical calculations performed with UDEC, showed it was possible to establish a better and wider description of the failure mechanisms. This study demonstrated that a significant optimisation of the support design would be possible, as shown in the studied models A2 and B2.
The presented results show the importance of conserving or improving the self-bearing capacity of the layered and jointed rock or Voussoir beams to arch and take part in the ground load. In addition, a comprehensive site investigation campaign was found to be important.
Rock reinforcement ahead of the face with spiling together with rock bolts and shotcrete is important, and actively contributed to ground stabilisation and tunnel stability. Ground load taken by the rock mass itself and/or by the bolts is then only transferred to the RRS support to a limited extent, hence allowing for design optimisation.
The results showed a significant reduction of the load on support systems in rock mass qualities Q 0.3–0.4, which permitted an optimisation of the ordinary full-profile Si-RRS-arches into a support concept or proposal to reinforce only the crown (Figure 9). The satisfactory behaviour and stability observed in the numerical results for C-RRS-support should enable the use of this or equivalent designs in tunnel projects with ground conditions comparable to those studied in model B2.
More case studies in hard, layered rocks will contribute to development of the approach.
DECLARATIONS:
The authors confirm that there are no known conflicts of interest associated with the publication of this article, and that are no financial or non-financial interests that has affected the outcome of this work.
This paper was originally published online in Rock Mechanics and Rock Engineering Journal, from Springer, in August 2024, under a Creative Commons Attribution 4.0 International Licence (http://creativecommons.org/licenses/by/4.0/ ). Open access funding provided by NTNU. This article has been prepared under a PhD project jointly financed by NPRA and the Norwegian Railway Administration (Bane NOR). The authors also wish to acknowledge the financial support of Sweco Norge AS and the Norwegian Tunnelling Association (NFF). As permitted under the particular open access facility, this version of the original paper has been abridged and edited for space, and images adapted to house-style. The original paper is available in full at https://doi.org/10.1007/s00603-024-04082-3.
Datasets generated during this study are available from the corresponding author (Jorge Terron-Almenara) upon reasonable request.
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