2. REVISIÓN DE LITERATURA
2.7 Microbiología ruminal
When investigating the horizontal strain ²h in the building it was found that hardly any tensile strain occurs in a 100m wide building with no eccentricity. Therefore additional analyses were performed in which the building had an eccentricity of e = 20m with respect to the centre line of the tunnel. Figure 5.11a shows the strain distribution over the length of the 5-storey building. The results for the zero-load, the 50kPa and the 100kPa case are presented. The increase (in terms of absolute value) in both compressive (negative sign) and tensile (positive sign) strain can be seen. In a previous section it was demonstrated how the soil stiffness in close proximity to the building controls the horizontal displacement of the soil in this region. A set of analyses using the modified soil model for the uppermost 6m of soil (see Figure 5.6) was undertaken with the eccentric building geometry. Figure 5.11b shows the strain distribution from these analyses. The lines for different load cases lie close together and coincide well with the zero-load case using the conventional soil model. This result reveals how the stiffness in the uppermost soil controls the strain development in the structure caused by tunnelling: On the one hand the higher soil stiffness reduces the horizontal soil movement whereas on the other hand it means the soil is more able to transfer this movement to the structure. The net result is an increase in horizontal strain.
This effect can be observed for all stiffness-load combinations. Figure 5.12a and b show the development of horizontal strain when the building load is increased. The plots are of a similar format to those shown in Figure 5.8 with the modification factors M²h for each load case normalized against the corresponding zero-load case. For the flexible structure the modification factors reduce slightly with increasing load. This is due to the absence of any stiff structure restraining the horizontal movement of the soil. Hence the reduction in modification factors is caused by the reduction in horizontal soil movement with increasing soil stiffness. If, however, a stiff structure is included into the analyses this picture changes: For the 1-, 3-, 5- and 10-storey buildings the horizontal strain (both compression and tension) in the structure increases steadily with building load. For both tensile and compressive strain the behaviour for each tunnel depth is very similar. The tensile strain is increased by approximately 100% when a load of 100kPa is applied compared to the zero-load case. For the compressive strain this increase is smaller giving a compressive strain that is 50% greater than in the corresponding zero-load case when 100kPa are applied.
-7.0x10-6 -6.0x10-6 -5.0x10-6 -4.0x10-6 -3.0x10-6 -2.0x10-6 -1.0x10-6 0.0x10+0 10.0x10-7 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 εh
Distance from tunnel CL [m] (a) Building stiffness: 5 storeys Building load: 0 kPa 50 kPa 100 kPa -7.0x10-6 -6.0x10-6 -5.0x10-6 -4.0x10-6 -3.0x10-6 -2.0x10-6 -1.0x10-6 0.0x10+0 10.0x10-7 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 εh (b) Building stiffness: 5 storeys
Building load, top layer: 0 kPa, modified 50 kPa, modified 100 kPa, modified 0 kPa, conventional
Figure 5.11: Horizontal strain distribution in structure (B = 100 m, e = 20 m, z0 = 34 m) for (a) standard soil model and (b) modified top layer.
These graphs, however, give no indication about the absolute magnitude of horizontal strain developed in the structure. Figure 5.13 shows that the strain drops significantly when normalizing the modification factors against the corresponding flexible case (note that in contrast to Figure 5.9 this graph has a logarithmic scale on the ordinate): As an example the data for tension and for the 34m deep tunnel are given, showing a significant reduction to values between 0.017 and 0.05 for the 1-storey stiffness compared to the flexible case. Combining these results with the curves in Figure 5.12b reveals that although there is a clear trend of increasing modification factor with load the modification factors themselves remain at a very low level. This becomes clear when plotting the modification factors against the relative axial stiffness α∗. Figure 5.14 includes all the load cases. The zero-load cases are marked with square symbols while the ‘realistic’ cases are represented by triangle symbols. All other cases are shown with a cross symbol. Because of the small scale chosen in this graph the increase in modification factors for all cases when load is considered can clearly be seen. The realistic cases, however, remain close to the corresponding zero-load square symbols.
Figure 5.14 also shows the design curves suggested by Potts & Addenbrooke (1997). It can be seen that some ‘weightless’ results lie above the curves for an eccentricity of e/B = 0.2.
0.5 1.0 1.5 2.0 0 10 20 30 40 50 60 70 80 90 100 M ε hc /M 0 ε hc Load [kPa] (a) z0 = 20m no stiffness 1 storey 3 storeys 0.5 1.0 1.5 2.0 2.5 0 10 20 30 40 50 60 70 80 90 100 M ε hc /M 0 ε hc (b) z0 = 34m 5 storeys 10 storeys diagonal (a) 0.5 1.0 1.5 2.0 0 10 20 30 40 50 60 70 80 90 100 M ε ht/M 0 ε ht Load [kPa] (a) z0 = 20m no stiffness 1 storey 3 storeys 0.5 1.0 1.5 2.0 2.5 0 10 20 30 40 50 60 70 80 90 100 M ε ht/M 0 ε ht (b) z0 = 34m 5 storeys 10 storeys diagonal (b)
Figure 5.12: Change of (a) M²hc and (b) M²ht with applied load. M²h normalized against corresponding zero-load case.
0.001 0.010 0.100 1.000 0 1 2 3 4 5 6 7 8 9 10 M ε ht/M fl ε ht
Building stiffness [Storeys] z0 = 34m 0 kPa 10 kPa 30 kPa 50 kPa 100 kPa
Figure 5.13: Change of tensile strain
modification factor M²ht with stiffness. M²htnormalized against corresponding flexi- ble case (0 storeys).
This is due to the changed initial conditions (i.e. no zone of reduced K0) used in these analyses, as discussed in Section 4.2.3. It is therefore not possible to compare the results of the present work directly with the study of Potts & Addenbrooke (1997). However, as the difference between the current data and their upper bound curves remains small it is still possible to use their design approach.
This graph reveals that the modification factors remain small with a maximum value of M²hc = 0.08 for the 1-storey building under a load of 10kPa, z0 = 34m. According to the design approach by Potts & Addenbrooke (1997) this means that the horizontal compressive strain in this type of structure is only 0.08 times the compressive strain found in the corre-
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.1 1.0 10.0 100.0 M ε ht (b) no load load (realistic) load design curve: e/b = 0.2 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.1 1.0 10.0 100.0 M ε hc α* Solid symbols: 20m tunnel Hollow symbols: 34m tunnel (a) design curve: e/B = 0.2
no load load (realistic), z0=20m load
Figure 5.14: Strain modification factors M²h together with the design curves by Potts & Addenbrooke (1997). 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.1 1.0 10.0 100.0 M ε ht Solid symbols: 20m tunnel Hollow symbols: 34m tunnel (b) no load load (realistic) load design curve: e/b = 0.2 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.1 1.0 10.0 100.0 M ε hc α*mod (a)
design curve: e/B = 0.2
Figure 5.15: Strain modification factors M²h versus a modified relative axial stiffness taking into account the change of soil stiffness beneath the foundation.
sponding greenfield situation. These greenfield values are given in Table 5.4. For the tensile strain (which is more critical in respect to building damage) the modification factor is even smaller: M²ht = 0.02 for the 1-storey structure mentioned above.
For calculating the relative axial stiffness α∗ the soil stiffness E
S considered in Equa- tion 2.29b is taken at half tunnel depth. For the results shown in Figure 5.14 the increase of ES due to the increase of p0 at this depth is taken into account. It can be seen that the difference in relative axial stiffness for each range of load cases is very small. Previously it was shown that it is the soil stiffness in the zone immediately beneath the building which controls the horizontal strain behaviour in the building. It is therefore straight forward to include this soil stiffness into the relative axial stiffness α∗. For this particular geometry the best curve fit can be achieved when taking the soil stiffness from a depth of x = 5.8m. Figure 5.15 shows the strain modification factors for all stiffness-load combination plotted
against the modified relative axial stiffness incorporating the soil stiffness at z = 5.8m. It can be seen that for each tunnel depth the data points follow a uniform line with a very small scatter.
Although choosing the soil stiffness at z = 5.8m seems to be an arbitrary choice the result demonstrates the significant influence of the soil stiffness below the structure’s foundation. Figure 5.15 shows different patterns for each tunnel depth. This is because the tunnel depth z0 is not included anymore in the modified relative stiffness α∗ while it was incorporated into the original formulation when the soil stiffness was taken from half tunnel depth.
In an engineering context the increase of modification factors for realistic stiffness-load combinations remains very small. These results lie very close to the design curves provided by Potts & Addenbrooke (1997). The scatter shown in Figure 5.14 is small compared to the potential error associated with the estimation of the structure’s stiffness.
5.5
Conclusions
This chapter shows the influence of the weight of a structure on its deformation behaviour caused by tunnelling induced ground subsidence. Loads of up to 100kPa were applied to structures with a stiffness representing 1 to 10-storey buildings. By varying the material properties of the soil profile the mechanisms which control this aspect of the soil-structure interaction problem were investigated. It was found that the load of the building alters the deformation behaviour of the soil in two distinct zones: At tunnel depth and in close proximity to the foundation of the building. At tunnel depth the effect of increasing mean effective stress p0 has been uncoupled from the change in lateral stress ratio σ0
h/σv0 and the consequences of both were analysed separately. It was found that the increase in p0 affects directly the volume loss VL. Adjusting the soil displacement to a common volume loss leads to a uniform soil movement for different levels of mean effective stress while σ0h/σ0v was kept constant. The lateral stress ratio σ0
h/σv0 in contrast influences the deformation field of the soil which consequently affects any structure above the tunnel. This demonstrates the complex character of the interaction problem: The load of the building changes the stress regime which influences the deformation mode of the soil around the tunnel which then affects the response of the building to the tunnelling induced subsidence. The increase in soil stiffness in close proximity to the structure has been found to influence the building response significantly. It
has been shown that the development of horizontal strain in the structure can be directly related to the soil stiffness beneath the structure.
The influence of building load on the deflection ratio and on horizontal strain has been investigated with a parametric study involving 50 nonlinear plane strain FE analyses for two different building geometries. It has been shown that in general the modification factors increase with increasing load. This effect is, however, small compared to the decrease of deflection ratio and horizontal strain with increasing building stiffness. Since the latter effect dominates, the graphs plotting modification factor against relative stiffness show little change when realistic building weight scenarios are included into the analyses. The results therefore lie close to the upperbound curves provided by Potts & Addenbrooke (1997) and provide further confidence in the use of these curves for practical design.
The influence of the soil-structure
interface
6.1
Introduction
In all analyses presented in the previous chapters it was assumed that the building and the underlying soil are rigidly connected and consequently no relative movement was modelled between the foundation and adjacent soil. This chapter focuses on the nature of this contact between soil and building. Interface elements, described in Section 3.2.4.4, were included into the 2D analysis to control the behaviour of the connection between soil and structure.
It will be shown that a separation between building and soil occurs when weightless buildings are modelled. If building load is included in the analyses no gap between soil and foundation develops. This chapter will therefore highlight the role of relative horizontal displacement within the soil-structure interface on tunnel induced building settlement. Using interface elements with low shear but high normal stiffness properties, it will be investigated how this movement affects ground and building deformation. It will be shown that horizontal soil movement close to the building foundation increases drastically, compared to conventional no-interface analysis, while horizontal strain within the building nearly vanishes. The results of a parametric study will conclude that the deflection ratios in various building geometries reduce when relative horizontal movement at the soil-structure interface is allowed.