Openings in the lining of sprayed concrete lined (SCL) structures are common in mined stations where two or more tunnels intersect. The formation of an opening in a SCL structure results in redistribution of stresses in the concrete shell around it. The use of steel fibre reinforced (SFR) sprayed concrete, may prove adequate to reduce or eliminate the need for strengthening of the parent tunnel around the opening.

Considering a typical junction between two SCL tunnels, the main factors affecting the post-opening stress distribution as well as a proposed design approach are discussed in this article. The presented design philosophy, delivered significant health and safety, time, resource and environmental benefits by enabling a large number of openings to be successfully built without introducing any steel mesh/bar reinforcement or additional lining thickenings.

Common Practice

Introducing openings in SCL tunnels results in high compressive hoop forces at the sides of the opening and increased tensile forces (both hoop and longitudinal) and bending moments above and below.

The purpose of the design is to predict the final stress state in order to assess whether additional support is required. Basic design approaches include analytical/empirical solutions or two-dimensional (2D) numerical analyses. These design approaches however have limitations as they ignore the out-of-plane bending moments, the soil-structure interaction and the construction sequence, while assuming a linear elastic model for the SCL.

As a result, excessive stress changes are calculated around the opening, translated into reinforcement required to accommodate the tension/flexure and thickening of the SCL to install this reinforcement and resist possible compressive overstressing.

A thorough literature review of the available methods can be found in [8]. Three-dimensional (3D) numerical analyses, simulating the soil structure interaction and the construction sequence, overcome most of the aforementioned limitations.

It will be illustrated however, that even a full 3D Finite Element (FE) analysis may result in conservative designs if the plastic parameters of the SCL (in particular the post-crack residual tensile flexural strength) are ignored.

Design Approach for Steel Fibre Reinforced SCL

Steel fibres are mainly used with SCL to enhance the durability and ductility of the linings. Most of the tunnel design FE codes however, provide the option to model the SCL only as a linear elastic material. As a result, high tensile forces and bending moments are calculated around the opening, rendering necessary the use of reinforcement to accommodate the excessive tension/flexure.

The elastic-plastic “concrete damaged plasticity model” in FE code Abaqus (Dassault Systemes Simulia [3]), provides the option to simulate the SFR SCL as ideally elastic prior to compressive and tensile yield. The compressive strength and residual tensile strength parameters are considered in the post-yield states.

Furthermore, using the recommendations provided in [4] and [6] in line with the Eurocodes ([1], [2]) the capacity of the SFRC lining for sections under axial load and bending is checked using capacity limit curves [7] and through inspection output strains in the FE models.

Parametric Study

In order to compare the results of different design approaches, a parametric study was undertaken utilising the following three types of analysis:

  • 2D FE plane stress analysis (2D),
  • Full 3D FE analysis with ideal elastic SCL (elastic 3D),
  • Full 3D FE analysis using the concrete damaged plasticity model for the SCL (plastic 3D), where the tensile strength of the SCL was set at 300kPa and the compressive strength at 28MPa.

The parent tunnel was steel fibre reinforced SCL, 400mm thick with its axis at 25m below ground level. Three cross sections with almost equal cross sectional area and perimeter were examined:

i. “Circle” 10m diameter,

ii. “Horizontal” ellipse (H-Ellipse) 8.9m vertical diameter and 11.2m horizontal and

iii. “Vertical” ellipse (V-Ellipse) 11.2m vertical diameter and 8.9m horizontal.

Additionally, three different values were considered for the height aspect ratio (Ar=Circular Child tunnel height/ Parent tunnel height): 60%, 70% and 80%.

For simplicity, the soil in the 3D FE analyses was modelled as an isotropic, linear elastic material (Young’s modulus = 100MPa).

In the 2D plane stress analysis the parent tunnel geometry including the opening is being “unfolded” and flattened into a 2D surface and the developed shape is introduced in the FE model (see Figure 1). The pre-opening hoop and longitudinal stresses in the parent tunnel are assigned at the boundaries of the mesh.

For the sake of comparison these stresses have been taken from the 3D FE models although it is possible to use approximations given by empirical relationships or simplified 2D FE analyses. Figure 1 shows the resulted stress changes for the base case of a circular tunnel with Ar =60%, using the FE code Phase 2 (Rocscience).

The 3D FE analyses have been carried out using Abaqus. The results for the same example have been plotted in Figure 2.

Results of parametric study

The complete results of the parametric study are shown in the graphs of Figure 3. The most important conclusions are the following:

  • Hoop compressive stress changes at the sides of the opening were underestimated in most of the 2D analyses. Both 3D analyses results are similar. The shape and the aspect ratio did not affect the maximum values notably.
  • Hoop tensile stress changes above and below the opening were overestimated in 2D. The plastic 3D analyses predicted slightly higher values than the elastic results.
  • The longitudinal stress changes above and below the opening were considerably affected by the method of analysis. The 2D predicted significant tension, with lower values predicted by the elastic 3D. In the plastic 3D however, the stress changes were very small.
  • Higher bending moments above and below the opening were predicted in the elastic 3D compared to the plastic 3D analyses.
  • The effects of the shape and the aspect ratio did not follow a specific pattern. The aspect ratio affected mainly the stresses above and below the opening in the horizontal ellipse. Furthermore, both 3D analyses predicted slightly higher compressive stresses at the sides of the opening in the horizontal ellipse.

The following limitations of this study should be noted:

  • The conclusions are based on specific tunnel size and depth and ground properties. In order to draw more broadly applicable conclusions, the size and depth of the tunnel as well as the ground stiffness and the k0 will have to be varied.
  • Only openings in the primary lining of SCL tunnels were considered. The effect of the openings in final linings depend on the design principles (type of lining, design loads, waterproofing).
  • Openings in SCL shafts have not been assessed. Similar principles may apply there, however the initial and resulting stress states are different than in the SCL tunnels.
  • The effect of the excavation of the child tunnel and the stiffness of its connection to the parent tunnel have not been considered in this study.

Case Studies

The proposed design approach for openings in SFR SCL presented above was applied successfully in multiple instances. Two examples from Crossrail Farringdon Station are presented. Farringdon station comprises two ticket halls, two escalator/concourse tunnels, two platform tunnels, numerous cross passages and ventilation tunnels as well as four stub tunnels, all built using SCL techniques.

As the tunnels were constructed 85% in the Lambeth Group, Farringdon provided a unique insight in this challenging formation. The generally stiff-very stiff overconsolidated clays of the Lambeth Group included interbedded water bearing sand lenses, of random distribution. These, approximately 3m thick lenses, combined with the five geological faults that crossed the station imposed considerable risks on the SCL works.

BAM Ferrovial Kier (BFK) joint venture, the main contractor, appointed Dr. Sauer & Partners as specialist SCL designer. The design team was co-located within the BFK offices to provide rapid and effective design support. Key Dr. Sauer & Partners employees were also embedded into the BFK Engineering team to provide a degree of independence and assurance within the Contractor’s delivery team. An opportunity was identified by the team to improve the baseline programme by designing and constructing five additional temporary SCL structures to provide vital logistics supply routes to support tunnelling operations.

All five temporary structures included openings and were successfully designed and constructed without additional steel bar reinforcement and/or additional thickenings [5]. Two of these examples were the opening in cross passage CP1 and in reception chambers STE1 and STE2.


A temporary SCL connection adit (CP1- CH1) was designed and constructed between cross passage CP1 and concourse tunnel CH1, allowing CH1 to be built in advance of escalator barrel ES1 (see Figure 4), thus providing significant programme savings. The construction of the temporary adit was particularly difficult as CP1, constrained by its close proximity to the future escalator barrel ES1, had a cross section prescribed by the permanent works design.

This limiting factor resulted in an optimised breakout from CP1 towards CH1, which flared out from the breakout to allow more space for the tunnelling operations but still posed considerable logistic challenges.

CP1 is 7,200mm high and 6,200mm wide with a 250mm thick SFR SCL and the required opening in the CP1 was 5,385mm high resulting in an aspect ratio of 75%. The contractor had a strong preference to explicitly use SFR linings throughout to provide health and safety benefits, maximising the amount of mechanisation, reducing manual handling, eliminating working at height and steel fixing.

The opening was assessed following the proposed design approach and the results allowed the sole use of SCL without any additional reinforcement.

STE1 and STE2 Openings

At the eastern end of Crossrail Farringdon station, a temporary access shaft and two new cross tunnels were constructed to provide access to STE1 and STE2 chambers (see Figure 5). The purpose was to form a connection between the surface and the running tunnels for future first stage concrete and track slab works between Farringdon and Liverpool Street Station.

The temporary access shaft was constructed using precast concrete rings and sprayed concrete lining (SCL) techniques (part AS1 and AS2). Subsequently, two connection SCL tunnels (CT1 and CT2) were constructed and connected to STE1 and STE2. The TBM reception chambers STE1 and STE2 are 9,010mm high and 9,410mm wide with 400mm thick SFRC linings. The openings for CT1 and CT2 tunnels are 5,020mm high and 5,000mm wide with an aspect ratio of 55%. The openings were formed without any additional strengthening of the tunnel lining.

Demonstrating the main conclusions of the parametric study, two design models are compared in Figure 5: the elastic 3D FE model and the calculated hoop stresses with the corresponding capacity limit curve for STE2 is shown on the left and the plastic 3D FE model is shown on the right.

Implementing the residual tensile strength of the SFR SCL in the analysis has reduced the tension with a slight increase in the bending moments, without however any exceedance of the lining capacity.


The proposed design method when applied in tunnels and shafts brings important benefits. These benefits have been identified in Table 1 for three distinct categories: Health & Safety, construction (including time & cost savings and quality improvement) and environmental benefits.

To further quantify the benefits arising from openings without additional layers of SCL thickening and without steel bar and/or mesh reinforcement, a typical junction between a 10m diameter parent tunnel, 400mm thick and an 8m diameter child tunnel (Ar=80%) was considered. The savings in programme duration, material usage and CO2 emissions resulting from the avoidance of installing reinforcement and SCL thickening around the openings were assessed and are presented in Table 2.


Advanced design tools combined with the improved knowledge of material behaviour provide opportunities for improved designs. Every case however should be examined individually. The proposed design philosophy exploits the capabilities of non-linear 3D FE analysis and the plasticity characteristics of steel fibre reinforced SCL in order to optimise the design of openings in SCL tunnels. This approach has been applied successfully by Dr. Sauer & Partners in numerous projects. The avoidance of additional reinforcement permitted rapid construction progress and delivered considerable health and safety benefits by avoiding the need for manual handling, the need to work at height and steel fixing.

Extrapolating the savings discussed in Table 2 in a mined station with 20 openings for example, may result in savings of 120 days in programme duration, 90 tonnes of steel, 3,000m3 of concrete, 3,000m3 of excavated material and 1,000 tonnes of CO2 emissions.

This solution supported the industry drive of maximising the use of robotic and remote construction methods. In-tunnel and surface measurements during and after construction showed excellent correlation with the predicted tunnel deformations, thus validating the design approach and assumptions.