As the underground environment becomes ever more congested, more rigorous assessment of the effects of new construction on existing structures and construction safety is required. This, combined with the current drive to provide sustainable, safe, cost-effective underground structures within a stringent legislative, health and safety and approvals framework, demands innovative solutions from tunnel engineers.
Recent modelling of challenging soil-structure interaction problems in two-dimensional (2-D) and three-dimensional (3-D) finite element analyses in Asia have shown that proposed contractor’s alternatives and reference designs have proved not only that the proposed tunnel solution could be adopted, but that it also provided a more robust and environmentally acceptable solution. The increase in computing power and improvement in software algorithms have now reached a stage at which full 3-D modelling is a viable tool for tunnel design.
This paper looks at two projects that the author worked on in Asia and describes the use of 2-D and 3-D soil-structure interaction models that have been developed by Arup to achieve a better design solution.
Alternative tender proposal – Project A, Asia
The project will form a core element of the local mass transit railway network. It will comprise of a 3.8km underground passenger railway, providing a strategic link between two existing rail systems (figure 1). The tendered design and build contract will form an extension to the southern section of the western line, linking to the eastern line, which includes an overrun to an existing station to accommodate the connection.
The alignment is located within a very dense, highly congested urban environment, so any construction method including extensive cut-and-cover excavation would create a major environmental impact, with increased traffic congestion, associated increase in pollution and increased travel times. Tourists extensively visit the local area; any major construction works will have a negative effect on the retail sector and the overall image of the area.
The employer’s reference design consultants working paper stated that the use of a TBM was not feasible, as there was insufficient separation between the two tracks, little cover and no space for launch or extraction shafts. Their scheme design involved a cut-and-cover excavation directly above the existing running tunnels, with less than 2.2m cover from the crown of the existing tunnels to the excavation base.
Arup, working closely with the contractor, Nishimatsu Construction Company (NCC), developed an alternative solution for the tender proposal. This was achieved by modifying the alignment and producing detailed 2-D finite element analyses to assess changes in stresses around the existing tunnels and the resulting distortions from the proposed tunnelling operations. It was proved not only that the bored tunnel could be adopted, but that is also provided a more robust and environmentally acceptable solution.
Existing conditions
The proposed rail extension is located close to the waterfront within a highly built up district. The bored tunnel alignment of the southern section of the link, from the new station to the existing station will run in a stacked configuration beneath a 21m wide road with multi-storey piled foundation structures along both sides and multiple buried utilities beneath the road surface. Towards the end of this road, the alignment turns through a tight 245m radius curve beneath a historic monument, which is currently being renovated into a boutique shopping complex and six star hotel. The tunnels then unstack and climb to a very shallow depth with less than a diameter of cover and run beneath a wider road where the alignment passes above the existing mass transit running tunnels (figure 2) where it connects to the existing terminal station overrun tunnel box of the eastern line.
Physical constraints on the horizontal alignment include; the existing horizontal separation of the centre lines of the overrun tunnels at the eastern end of the alignment, a historic 5-star hotel to the north of the alignment, and another piled foundation public building and associated facilities to the south of the alignment. In addition to the existing constraints it is essential to maximise the distance between the proposed twin-bore tunnels, to minimise the effect of the second bore on the first.
Physical constraints on the vertical alignment include; the existing level of the overrun tunnel at the eastern end of the alignment, an existing pedestrian subway tunnel, the existing mass transit running tunnels and an existing drainage box culvert.
The clear spacing between the external faces of the proposed tunnel linings is 2.16m, and the minimum clear space between the external underside face of the proposed tunnel lining and the existing mass transit tunnel lining is 2.12m. The available data shows that the existing mass transit tunnels are 4.9m i.d precast concrete segmental linings. The original lining was formed using six segments and a key, 165mm thick and 900mm wide. The nominal distance between the tunnel centres is 13.1m, with a clear spacing between the external faces of the linings of 7.9m.
The reclamation fill at the site is typically described as a clayey silty gravely sand, the marine deposits are typically described as a soft clayey silt, or a losses clayey silty sand, and the alluvium is typically described as a clayey silty gravely sand. As-built records indicate that the lower half to two-thirds of the existing Up Track tunnel is resting on rock, while the Down Track is entirely embedded in rock. The face records also indicate that boulders and corestones are likely above rockhead reflecting the variable weathering profile of the granite stratum.
The modelling
Design analyses were carried out to estimate the predicted movements and lining stresses of the existing tunnels resulting from construction of the proposed bored tunnels, including sensitivity checks of the critical parameters, both longitudinal and transverse to the lining. Finite element modelling was carried out to take account of the inherent stiffness of the existing tunnels, and the soil-structure interaction effects, to allow the ground pressure changes around the existing tunnels, as a result of the new tunnels construction to be estimated.
Based on anticipated TBM advance rates, the TBM would take about 3-4 days to cross the zone of influence of the existing tunnels, for each of the Up Track and Down Track tunnels. Compared to the cut-and-cover excavation, where the excavation would be open for months, this is a huge advantage in limiting the length of time that the existing running tunnels are potentially ‘at risk’.
To act as a base case, the existing bending moments and hoop thrusts in the existing running tunnels were calculated using analytical methods (using a continuum analysis, in an isotropic medium, based on Muir Wood and Curtis (1975/86) methods, and using Duddeck and Erdmann’s (1982) formulae), for a cross-check of the finite element analyses perpendicular to the existing tunnels. Changes in stresses from the finite element analyses parallel to the existing tunnels were imposed on the empirical model to calculate the predicted magnitude of bending moment increases.
A sensitivity study was also conducted on all key input data, including critical soil parameters, properties of the ‘excavation void’, the use of a pipe-pile TBM ‘cradle’ and the % volume loss to get an understanding of the factors influencing the design.
2-D plane strain finite element analyses were carried out using the Oasys SAFE finite element computer programme. The initial analyses showed that before construction of the proposed bored tunnels the existing running tunnel segmental lining experiences sagging moments at the crown and hogging moments at the walls, due to the difference between the vertical and horizontal loads. The situation would be reversed to some extent, when excavation of the proposed tunnels above the existing tunnels occurs, as the vertical stress is reduced and the existing tunnel moved slightly upwards due to stress relief above the tunnel. The net result is a lower hoop stress in the existing tunnel and a slight reduction in the bending moments, due to the slight upward deformation.
The results showed that the predicted hoop thrusts and bending moments are within the lining capacity curve for all load cases, whether calculated using a traditional empirical approach, using a bedded-beam-spring model approach, or using a finite element analysis approach, see Figure 3.
The multiple lining capacity curves shown on this figure result from the sensitivity analyses that were carried out regarding the properties of the existing running tunnels.
Project conclusions
While the analyses showed that crossing of the existing mass transit tunnels could be safely achieved using a TBM rather than the conforming cut-and-cover scheme, unfortunately NCC were not awarded the contract on this occasion. During the tender period our proposal was presented to the mass transit railway company and they provided positive feedback and comments on the proposal. Construction of the extension has now commenced in Asia.
Alternative tender proposal – Project B, Asia
As before, the alignment is located within a very dense, urban, highly congested environment, so any construction method including extensive cut-and-cover excavation would create a major environmental impact, with increased traffic congestion, associated increase in pollution and increased travel times.
Arup, working closely with the contractor developed an alternative solution for the tender proposal. The conforming tender solution comprised of a double-cell rectangular cut-and-cover tunnel solution. A tender alternative of an Overlapping Multi-Face (OMF) Slurry TBM was proposed.
The advantages of a OMF shield are; no need to construct cross-passages, reduced cross-sectional area resulting in less spoil, less grout required to fill the void between the extrados of segments and excavated profile and a reduced zone of influence. However, there is limited experience of this type of TBM outside of Japan.
This tender alternative produced an underground structure consisting of twin 7m i.d circular tunnels installed simultaneously, which formed a structure with an internal maximum clear dimension of 13.3m (figure 4). This allowed the structure to stay within the same corridor as the cut-and-cover tunnel, but had the advantage of avoiding most of the disruption caused by cut-and-cover methods, especially so when the alignment is under a main road.
Existing conditions
The route of this new railway line lies within a reclaimed land with reclamation fill comprising of mainly sand with occasional clay/silt over alluvium deposits of sandy clayey silty soils. Beneath these strata is the completely decomposed granite of sandy silt of intermediate to high plasticity. There are only a few instances of marine deposits present in the form of isolated lenses along the fill/Alluvium interface. Areas along the route had undergone different phases of ground treatment to improve the fill for surrounding development.
The modelling
Each length of the segmental lining was composed of three types of reinforced Pre-Cast Concrete (PCC) segments; one central wall, two “Y” shaped (one larger, one small) and eight standard segments.
The i.d was 7m, with a 6.3m centre to centre spacing of the centrelines for the OMF tunnel.
Given the shape of the OMF segmental lining and the complex soil-structure interaction between the fill (a soft granular reclaimed fill) and the tunnel lining, the use of traditional empirical methods to analyse the OMF tunnel were considered to be too simplistic and inappropriate in this particular scenario (however an equivalent single bore tunnel was analysed using these methods to act as a benchmark).
The Oasys SAFE 2-D finite element programme was used as the basis for the design calculations with Oasys LS-DYNA 3-D finite element programme used for verification and 3-D effect checks.
For the previous OMF segmental linings designed and constructed in Japan and China the designer used a bedded-beam-spring model to design the lining. The main advantage of numerical modelling over this method is that it allows soil-structure interaction effects; it takes account of the surrounding ground and there is no need to estimate the sub-grade reaction, which is a difficult parameter to define. Also, such beam-spring models include only linear elastic soil behaviour, which requires substantial designer’s intervention and experience to iterate to the correct value.
The 2-D modelling was first calibrated against the results of the settlement assessments that had been obtained from Oasys TUNSET. Anisotropy has been identified as a crucial soil behaviour that affects the pattern of the surface settlement trough; isotropic soils tend to produce wider troughs. The fill was therefore modelled as an anisotropic soil in order to produce a close correlation between the FE computed surface settlement and the settlement trough predicted using an empirical approach, whereby the trough is assumed to follow a Gaussian distribution profile.
It would be unconservative to use this method for calculating the structural forces within the lining, so for analyses that were used for the structural design of the tunnel, and not for assessing the ground movement effects on third parties, a ‘wished-in-place’ analysis, with no volume loss was performed.
Plain strain 2-D finite element simulations were initially performed to study the performance of the segmental lining under normal loading conditions and to investigate the sensitivity of the structure under different ground and loading conditions. Such analyses allowed an understanding of the variation of design forces and identification of critical design parameters for the design of the tunnel structure. A wide range of 2-D analyses were undertaken to study the structural forces under the following conditions: wished-in-place tunnel – base Case analysis, range of volume losses up to 1%, variation in tunnel elevation, surface surcharge loading, variation in ground stiffness, variation in ground treatment and variation in groundwater level.
Additional sensitivity studies were undertaken to compare the effects of: Modelling joints via a thin layer of no tension elements at the joints, modelling joints via an equivalent reduced Young’s Modulus of concrete using an empirical reduction factor and modelling a continuous ring using the full Young’s Modulus of concrete.
The 3-D modelling was performed as an advanced design during the tender assessment period, when it was used as a design tool to prove the adequacy of the OMF design. It was also intended to provide the assurance to all parties with respect to the behaviour of the segmental concrete lining under normal operational conditions and also under impact loading.
Due to the highly complex ground response, the tunnel face slurry pressure control and annulus grouting pressures during TBM excavation were not included in the model, instead the ground loss caused by tunnelling was modelled using an induced ground loss approach (or a stress relaxation approach). This ground loss value had been discussed and agreed with the tunnelling contractor, and supported by case histories from similar excavation using similar TBMs.
Figure 5a shows the 3-D model of a pair of the linings for the OMF tunnel designed with staggered segments so it is without cruciform joints. Figure 5b shows the model used to assess influence of construction sequence. Initially a single ring model was used to establish a base design case. This was followed by a second model incorporating two rings of tunnel lining with staggered radial joints. This allowed the study of the difference in the tunnel performance when staggered joints were provided in the design. Finally the model was extended into a full 3D model to provide an insight to the behaviour of the tunnel lining during construction and also under impact loading.
The 3-D models were also used in the design analyses to study; sensitivity of the fill stiffness; potential stiffer soils on one side of the tunnel where ground treatment was expected in different areas along the route; different groundwater conditions; different tunnel elevations; effects of future surcharge loading for the provision of future works; and segments with/without bolts.
Figure 6a shows the computed hoop stress of the tunnel linings. Figure 6b shows the computed bending moment of the tunnel lining plotted along the axis of the lining. The 3-D models showed that tunnel installed using the OMF TBM was adequate under all the design scenario considered in the design.
Project conclusions
Arup have since completed a reference design of an OMF segmental lining and are awaiting a suitable opportunity to use it upcoming project. Through the analysis conducted to date a thorough understanding of the way this lining works has developed along with its sensitivities. Internal design notes have been produced that have been circulated worldwide to assist with any scheme that might adopt this type of lining for a transportation tunnelling project.
Conclusions
The increase in computing power and improvement in software has reached a stage where full 3-D modelling is becoming a viable tool for tunnel design, and it is now being used regularly by Arup in the design of challenging soil-structure interaction problems assessing the effects of proposed works on adjacent existing structures.
Complex 3-D modelling requires an experienced analyst to set up the model and analysis and it may be that they do not have a tunnelling background. It is therefore important to systematically record the assumptions and results of the analysis, which should be technically reviewed by an experienced tunnel engineer. The use of empirical calculations is still important and should be used to benchmark and validate the 3-D analysis to ensure the predictions are within the range of expected values. It is also essential to carry out sensitivity studies to understand which are the critical variables and input parameters in the design.
This paper has shown just a few examples of innovative contractor’s alternatives and reference designs that will help the industry move forward and embrace new technology and techniques. I believe that some of the 3-D finite element analyses that Arup are currently running are setting standards for the industry to follow. The analyses not only justify contractor’s alternatives but help in setting monitoring trigger levels once the project commences on site.
Geometry at proposed crossing of existing running tunnels: View extracted from 3D fly-through Extract from 2D FE mesh Sample output of analysis plotted onto lining capacity curves: From Duddeck and Erdmann approach From Beam & Spring model approach Map and section and plan of the tunnel crossing Geometry of OMF segmental tunnel lining 3D model: OMF tunnel segmentation Full 3D Model Computed bending moments Sample output from alternative OMF bored tunnel analysis: Computed hoop stress from 3D model Cross section of the OMF segmental lining Fig 4
