Geotechnical problems become more complex as more and more space is used up in urban areas.
This has led to a need to improve understanding of ground behaviour and to have a more comprehensive, but accessible, technique for analysing problems.
Over the past three years, Arup Geotechnics has built on the experience and expertise of Arup's Advanced Technology Group to analyse geotechnical problems using 3D finite element modelling.
All the 3D models described here were generated using Altair's Hypermesh and analysed using Oasys LS-Dyna software. Results were extracted using Oasys D3PLOT post-processor. The LS-Dyna program uses an explicit time-stepping method to make 3D modelling practical for complex nonlinear geotechnical problems.
The models were created with simple single-point hexahedral eight-noded elements with higher order eight-points elements in critical areas of the meshes. The number of elements was intentionally made large to give confidence in the accuracy of the predictions.
Despite the nonlinear nature of the behaviour being modelled, with many thousands of elements, the computational effort needed to analyse the 3D models remains acceptable. Continued development and advances in computer technology will inevitably improve the computing time which will make this type of modelling more attractive to general practitioners.
However, the software is at present costly and not generally available. More importantly, its use requires significant expertise both in finite element technology and in modelling of material behaviour.
Deep excavations and retaining structures Figure 1 shows a 3D model of a proposed 40m deep excavation in central London for one of the future Crossrail stations, produced to predict ground movements associated with the proposed construction works.
The 1/8symmetry model for a square 35x35m excavation used a small strain, non-linear soil model (BRICK model, Simpson 1992, Pillai 1996), with non-linear material properties modelling the equivalent 'anisotropic' behaviour of a diaphragm wall.
Predicted ground movements are shown in Figure 2.
The 3D model consisted of 8,700 eight-point elements and it took less than four hours to complete an eight-stage construction sequence involving complex non-linear soil and structure models. Doubling the size of the model to 1/4 symmetry model, to study the inclusion of a capping beam at ground level, and reducing the use of eight-point elements remote from the retaining structure, did not increase computation time.
Piled raft A
1/4symmetry 3D piled raft model was used to investigate the behaviour of the piled raft foundation of a multi-storey building in London's Docklands in the east of the city.
Each of the piles was explicitly created with the core of the building modelled as the load transfer structure. As shown in Figure 3, a 3D single pile model was calibrated against load test results from test piles carried out at the site before producing the 3D model.
The model (Figure 4), consists of 14,300 elements. It took two and a half hours to complete the single stage loading analysis. This allowed the model to be used for sensitivity analyses with different load combinations. The computed piled raft settlement is shown in Figure 5. Further details of the 3D modelling undertaken for the project are given in Nicholson et al 2002.
Sprayed concrete lined tunnels Sprayed concrete lined (SCL) tunnels are being used increasingly for underground construction as they offer flexibility in choice of geometry of the openings.
Ground movement and stability of construction depends heavily on early age stiffness and strength of the sprayed concrete, where excavation speed for each stage of face advance is generally less than a single shift of eight hours.
3D models were created to represent the construction sequence involved in SCL construction; excavation was simulated explicitly, metre-bymetre. Early age concrete stiffness and strength were incorporated in the model (Figure 6) and the small strain, non linear BRICK model with anisotropy provision was used to model tunnelling induced ground movement (Simpson et al 1996).
A monitored trial tunnel in London clay was back-analysed and the settlement trough computed from the single SCL tunnel advance matches well with the measured value (Figure 7).
Construction required about 90 excavation stages for the very complex geometry (Figure 8) and computation was completed in 50 hours for the sizeable 100,000 element model.
Ground movement is explicitly computed from such a sequence without having to resort to the introduction of volume loss through stress relaxation or imposed volume change. Figure 9 shows deformation computed for the tunnels, which is used for damaged assessment.
References Nicholson DP, Morrison PRJ, Pillai AK (2002). Piled raft design for high rise buildings in east London, UK.
Pillai AK (1996). Review of the BRICK of soil behaviour. MSc dissertation, Imperial College, London.
Simpson B (1992). 32nd Rankine Lecture: Retaining structures - displacement and design. Geotechnique, 42, 4, 539-576.
Simpson B, Atkinson JH and Jovicic V (1996). The influence of anisotropy on calculations of ground settlements above tunnels.
Proc Intnl Symp Geotechnical Aspects of Underground Construction in soft ground. City University, London. Balkema.
Torp-Petersen G, Zdravkovic L, Potts DM and St John HD (2003). The prediction of ground movements associated with the construction of deep station boxes. Saveur, J (ed): Proceedings of the ITA World Tunnelling Congress 2003 - (Re)Claiming the Underground Space. Amsterdam, 12-17 April 2003. Balkema.