Modelling of long-term ground response to tunnelling under St James's Park, London

Following a tunnel excavation in low-permeability soil, it is commonly observed that the ground surface continues to settle and ground loading on the tunnel lining changes, as the pore pressures in the ground approach a new equilibrium condition. The monitored ground response following the tunnelling under St James's Park, London, shows that the mechanism of subsurface deformation is composed of three different zones: swelling, consolidation and rigid body movement. The swelling took place in a confined zone above the tunnel crown, extending vertically to approximately 5 m above it. On the sides of the tunnel, the consolidation of the soil occurred in the zone primarily within the tunnel horizon, from the shoulder to just beneath the invert, and extending laterally to a large offset from the tunnel centreline. Above these swelling and consolidation zones the soil moved downward as a rigid body. In this study, soil-fluid coupled three-dimensional finite element analyses were performed to simulate the mechanism of long-term ground response monitored at St James's Park. An advanced critical state soil model, which can simulate the behaviour of London Clay in both drained and undrained conditions, was adopted for the analyses. The analysis results are discussed and compared with the field monitoring data. It is found that the observed mechanism of long-term subsurface ground and tunnel lining response at St James's Park can be simulated accurately only when stiffness anisotropy, the variation of permeability between different units within the London Clay and non-uniform drainage conditions for the tunnel lining are considered. This has important implications for future prediction of the long-term behaviour of tunnels in clays.

Numerical simulation of long-term twin-tunnel behaviour at St James's park

The twin-tunnel construction of the Jubilee Line Extension tunnels beneath St James's Park was simulated using coupled-consolidation finite-element analyses. The effect of defining different permeabilities for the final consolidation stage was investigated, and the performance of a fissure softening model was also evaluated. The analyses suggested an unexpectedly high permeability anisotropy for soil around the tunnel crown, possibly due to stress-induced permeability changes, or low-permeability laminations. Also, the permeability profile and lining conductivity were found to differ between the tunnels. Inclusion of the fissure model gave a narrower settlement trough, more alike that in the field, by preferentially softening simple shear behaviour. Long-term settlements at the site continue to increase at an unexpectedly high rate, suggesting the possibility of creep or unexpected soil softening during excavation. © 2012 Taylor & Francis Group.

The rise heights of low-and high-Froude-number turbulent axisymmetric fountains

We present the results of an experimental investigation across a broad range of source Froude numbers, 0. 4 ≤ Fr 0 ≤ 45, into the dynamics, morphology and rise heights of Boussinesq turbulent axisymmetric fountains in quiescent uniform environments. Typically, these fountains are thought to rise to an initial height, z i, before settling back and fluctuating about a lesser (quasi-) steady height, z ss. Our measurements show that this is not always the case and the ratio of the fountain's initial rise height to steady rise height, λ = z i/z ss, varies widely, 0. 5 ≈ λ ≈ 2, across the range of Fr 0 investigated. As a result of near-ideal start-up conditions provided by the experimental set-up we were consistently able to form a vortex at the fountain's front. This enabled new insights into two features of the initial rise of turbulent fountains. Firstly, for 1. 0 ≈ Fr 0 ≈ 1. 7 the initial rise height is less than the steady rise height. Secondly, for Fr 0 ≈ 5. 5, the vortex formed at the fountain's front pinches off, separates from the main body and rises high above the fountain; there is thus a third rise height to consider, namely, the maximum vortex rise height, z v. From our observations we propose classifying turbulent axisymmetric fountains into five regimes (as opposed to the current three regimes) and present detailed descriptions of the flow in each. Finally, based on an analysis of the rise height fluctuations and the width of fountains in (quasi-) steady state we provide further insight into the physical cause of height fluctuations. © 2011 Cambridge University Press.

The rhythm of fountains: The length and time scales of rise height fluctuations at low and high Froude numbers

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers 0.3 ≤ Fr 0 ≤ 40 and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of Fr0. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of Fr 0) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high Fr0 we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, Strtop, based on experimental measures of the fountain top, defined such that Strtop = 1 would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high- Fr 0 fountains we find Strtop ≈ 0. 9. © 2013 Cambridge University Press.