Building stiffness was the fundamental parameter examined in the original work of Potts & Addenbrooke (1997). In their study they varied both bending stiffness EI and axial stiffness EA independently of each other and investigated the influence of these variations on the deformation behaviour of a surface structure. The main results of their work were discussed in Section 2.4.6.2. This section presents the results of tunnel induced soil movements beneath a surface structure of variable stiffness. The aim was to achieve a better understanding of the tunnel-soil-structure interaction.
The nature of this interactive problem can be seen in Figure 4.8a and b which profiles horizontal and vertical soil movement, respectively, for a section at 6m offset from the tunnel centre line (z0 = 20m). Results are presented for 100m wide buildings with 1, 3, 5 and 10
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0.000 Depth [m] Horizontal displacement [m] greenfield 1 storey 3 storeys 5 storeys 10 storeys (a) 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 -0.002 0.000 0.002 0.004 0.006 0.008 Depth [m] Vertical displacement [m] green field 1 storey 3 storeys 5 storeys 10 storeys (b)
Figure 4.8: Vertical profile of horizontal (a) and vertical (b) soil displacement at x = 6m. Data are for greenfield and for 100m wide structures, z0 = 20m. Negative horizontal dis- placement indicates movement towards the tunnel, positive vertical displacement indicates downwards movement.
storeys. In addition soil movements obtained from a greenfield analysis are included.
The maximum horizontal greenfield displacement (in terms of absolute value, the negative sign refers to movement towards the tunnel) along the vertical line is reached just above the tunnel axis depth of z0 = 20m. From there it reduces towards the surface but increases over the top 6m and shows a surface horizontal displacement of Shx = -1.8mm. At the surface the horizontal soil movement is altered drastically by the presence of a structure; for example it changes to Shx = -0.08mm for a 1-storey building. For this case the displacement then increases with depth and becomes larger than that obtained for greenfield conditions at a depth of approximately 5m. Below this depth a higher building stiffness leads to higher horizontal displacements, although the difference remains small. This trend continues well below tunnel axis depth.
The vertical greenfield displacement (Figure 4.8b) shows an increase from its surface value of Sv= 3.9mm to Sv= 6.1mm at a depth of z = 15m. It then reduces before changing to up-
0.0 5.0 10.0 15.0 20.0 25.0 30.0 0.000 0.010 0.020 0.030 Depth [m] Vertical displacement [m] Crown green field 1 storey 3 storeys 5 storeys 10 storeys
Figure 4.9: Vertical profile of vertical soil displacement along a line above the tunnel CL, x = 0m. Positive values refer to down- wards movement. 0.0 5.0 10.0 15.0 20.0 25.0 30.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Depth [m] i [m] GF 1 storey 3 storeys 5 storeys 10 storeys
Figure 4.10: Point of inflection for surface and subsurface settlement troughs. Data for greenfield and 100m wide buildings, z0= 20m
wards movement at z = 23.5m. This response persists when building stiffness is introduced. However, the magnitude of settlement reduces with increasing building stiffness over approx- imately the top 18m of soil. Below this depth the influence of building stiffness becomes less significant. The vertical displacement along a vertical line above the tunnel centre line (x = 0m) shown in Figure 4.9 displays the same trend. Near to the surface the settlement reduces with building stiffness. Immediately above the tunnel crown the influence of building stiffness on the vertical soil movement is not significant.
Comparing the horizontal soil movement profiles of Figure 4.8a with the profiles of vertical movements shown in Figure 4.8b and Figure 4.9 demonstrates that horizontal soil movement close to the soil surface is much more influenced by the building’s stiffness than the vertical movement is in this zone.
The previous two graphs showed the variation of the magnitude of vertical settlement with depth. In order to investigate how the shapes of subsurface settlement troughs are altered by the presence of a building the position of the point of inflection, i, is shown against depth z in Figure 4.10. This figure includes the same greenfield and building cases as plotted in the previous figures. In general i decreases with depth. This shows that subsurface settlement troughs become narrower and (considering the increasing settlement found in the previous graph) deeper. The distribution of i with depth for greenfield conditions has been discussed
in Section 2.2.2. The trend of an over proportional decrease of i near to the tunnel and an over proportional increase next to the ground surface as described by Grant & Taylor (2000), see Figure 2.11 on Page 40, can be seen in this figure. The greenfield surface settlement trough shows a width of i = 11.5m. This is in good agreement with the empirical formula (Equation 2.15, Page 36), which predicts i to be i = 0.5 × z0 = 10m.
Building stiffness changes this distribution over approximately the upper 8.5m of soil by increasing i. Between this depth and z ≈ 2m the results for the 1, 3, 5 and 10-storey buildings coincide but then diverge towards the surface with higher stiffnesses showing larger values of i. This widening of the settlement trough with increasing overlying stiffness (in this case due to the building) is in agreement with centrifuge tests performed by Hagiwara et al. (1999) and discussed in Section 2.2.2. In their tests they investigated the influence of the stiffness of a soil layer overlying a clay strata in which a tunnel excavation was investigated.
The results presented in this section demonstrate how the stiffness of a surface structure alters the soil displacements. These changes have been found to be significant close to the ground surface. In the vicinity of the tunnel the influence of building stiffness on vertical ground movement is insignificant. The horizontal displacement, however, changes close to the tunnel although the differences between greenfield and building cases remain small.