Civil and Structural engineering

Case Study

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Söderström Tunnel Connector

  • Detailed solid modelling of a cable anchored concrete tunnel connector and surrounding rock

  • Nonlinear analysis involving contact assessments

  • Stability of connector proved for all considered loading conditions

ELU Konsult is involved with various contracts for the Stockholm City Line project and, as part of the ELU-Golder HB partnership, it provides technology support and review of contract documents for the Söderström tunnel on behalf of its client, Banverket. ELU used LUSAS Civil & Structural to carry out a finite element analysis of a proposed tunnel connection at Söder Mälarstrand. Load transfer mechanisms between the concrete tunnel and the rock were investigated to ascertain the magnitude of stresses and forces at the connection, in the anchorage cables, and in the rock itself due to permanent, variable and accidental loading to the immersed concrete tunnel.


The Stockholm City Line is a 6km long commuter train tunnel running beneath central Stockholm, with two new stations at Odenplan and T-Centralen. It is being built by the Swedish Transport Administration in close co-operation with the City of Stockholm, Stockholm County Council and Stockholm Transport, SL. When finished in 2017 the new line will double the capacity for rail traffic through the centre of Stockholm

The City Line passes mostly through rock but in the waters of Söderström, between Riddarholmen and Söder Mälarstrand, it runs through an immersed concrete tunnel constructed from three prefabricated tunnel elements, each approximately 20m wide a+nd 10m high. The elements are divided into two cells, one 12m wide, taking two rail tracks, and one, 5m wide, for services and rescue purposes. The tunnel is supported at locations along its length by three pile groups and a caisson founded on bed rock. Concrete connectors at each end of the tunnel secure it to the rock mass with movements being accommodated at the Northern end. 

Tunnel connector

The reinforced concrete tunnel connector at the Southern end extends approximately 20m into the mountain tunnel and is shaped with a tapered heel. Rock anchors, extending a minimum of 20m backwards from the heel of the connector and a minimum of 10m transversely to the tunnel wall at one outer end of the connector, are used to tie the connector to the rock mass and restrain it against any imposed loadings. Between the attachment points the cables can move freely without transmitting forces to the rock.

Plan view Elevation

Schematics of initial proposed Southern connection

Various load combinations needed to be assessed using LUSAS. These included permanent actions comprising load from the surrounding rock, self weight, water pressure and support displacement. Variable loads comprised traffic loads, water level variations and change of temperature. Accidental actions considered a variety of potential ship impacts and large-scale shifting of the bedrock.

Rock and tunnel connector analysed with LUSAS

Tunnel connector model showing contact region (green) and location of longitudinal and transverse anchorages


CAD model geometry representing a 70m long x 80m wide x 50m high volume of rock and tunnel was imported directly into LUSAS prior to defining the material properties, supports and various loading conditions that needed to be assessed. The rock and the concrete tunnel connector were modelled using 20-noded volume elements. Bar elements represented the longitudinal and transverse anchorage cables. Joint elements modelled the contact between the rock and the tunnel and allowed frictional forces between these to be taken into account. To verify the model built, the coefficient of friction at the contact surfaces between the concrete tunnel and the rock was set to zero and a single load case with just the anchorage cable tensions was applied. From this, initial stresses in the rock around the anchorage points, and stress transfer and stress levels in the concrete and the rock heel could be evaluated. Because of the interfaces used in the model a nonlinear analysis had to be undertaken.

Stress distribution in the rock just behind the longitudinal cables

Stress distribution in the rock just behind the longitudinal cables

Stress in the rock at distances of 1m, 3m and 4.5m behind the transverse rock anchorages

Accidental loading

For a number of the accidental loadcases considered, different coefficients of friction for the contacting concrete tunnel and rock surfaces were used to evaluate the effect on the results obtained. The effects of a horizontal or vertical displacement of the main tunnel, both of which apply a torque to the connector, and a longitudinal pulling force on the connector itself were examined in great detail, with stresses in the rock and anchorage cables, and stresses in contacting regions of the concrete and the rock being of particular interest.

Displacement and stress distributions calculated by LUSAS for these various loadcases and combinations were plotted on a number of slice sections through the model. In addition to slice sections at and in the vicinity of the cable anchorage points, horizontal sections were located at the mid-height of the tunnel, and at distances of 4.5m, 10m, and 15m below the tunnel base. A longitudinal vertical section and a slice section inclined at 15 degrees towards Söderström (north) and 15 degrees to the east (to correspond with a fracture zone in the rock) enabled a detailed comparison to be made between the results from the LUSAS analysis and analytical results by others.

Representative Results Plots

The following images illustrate the types of results plots created to evaluate the magnitude of stresses and forces at the connection, in the anchorage cables, and in the rock itself due to permanent, variable and accidental loading to the immersed concrete tunnel.

Longitudinal vertical slice section


Stress distribution on the vertical slice section


Stress distribution in the rock heel 


Prestressing force in anchorage cables


Stress distribution on a horizontal section though the tunnel and connector 


Stresses in rock mass showing regions of localised high stress

In Summary

The results obtained with LUSAS showed that the tensions and deformations arising in the rock from the applied loading to the tunnel connection were reasonable taking into account the friction between the concrete tunnel and the rock. The forces in the anchoring cables for both the rear anchor and cross anchorage were shown to increase slightly as a result of accidental loadings. This increase was greatest in the transverse anchors but did not exceed 10% of initial prestressing force. Overall, the results indicated that the concrete tunnel connection will remain stable for all analysed loading conditions.

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