Schweiger_ NUMGE_2002.pdf - Plaxis

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distance from tunnel axis [m] 0 10 20 30 40 50 60 70 80 90 100 0 -5 horizontal displacements [mm] -10 -15 -20 -25 -30 -35 -40 -45 -50 -55 ST1 ST3 ST4 ST5 ST6 ST7 ST8 ST9 ST10 ST11 ST12 -60 Figure 3. Calculated horizontal displacements at surface - analysis B Figure 4 plots surface settlements for the elastic-perfectly plastic analysis with a specified volume loss of 2% and the even wide scatter in results is indeed not very encouraging. The significant effect of the vertically and horizontally restrained boundary condition used in ST5 is apparent. However in the other solutions no obvious cause for the differences could be found except that the lateral boundary has been placed at different distances from the symmetry axes and that the specified volume loss is modelled in different ways. The range of calculated values for the surface settlement above the tunnel axis is between 1 and 25 mm and for the crown settlement between 17 and 45 mm respectively. The normal forces in the lining and the contact pressure between soil and lining do not differ that much (variation is within 15 and 20% respectively), with the exception of ST9 who calculated significantly lower values. distance from tunnel axis [m] 0 10 20 30 40 50 60 70 80 90 100 5 0 vertical displacements [mm] -5 -10 -15 -20 -25 -30 -35 ST1 ST2 ST3 ST4 ST5 ST6 ST8 ST9 ST10 ST11 ST12 -40 Figure 4. Calculated surface settlements - analysis C After comparing all results submitted, a second round of calculations has been performed. All authors were asked to redo their analysis with the lateral boundary placed at a distance of 100 m from the tunnel axis with horizontal displacements restrained. By doing so all solutions for analyses A and B were within acceptable limits, for analysis C however, still significant differences in results were obtained, although the range of scatter was reduced (Figure 5). These differences are most likely due to the way different software handles the specified volume loss. Again this is a strong case for developing guidelines and reference examples how to model this (and other) excavation problems.
distance from tunnel axis [m] 0 0 10 20 30 40 50 60 70 80 90 100 vertical displacements [mm] -5 -10 -15 -20 ST1 ST3 ST5 ST7 ST8 ST9 ST10 -25 Figure 5. Calculated surface settlements - analysis C with lateral boundary at 100 m 3. Deep excavation 3.1. Geometry, basic assumptions and computational steps The general layout of the problem follows from Figure 6 and the following additional specifications have been given: - plane strain - influence of diaphragm wall construction is neglected, i.e. initial stresses are calculated without the wall, then wall is "wished-in-place" - diaphragm wall modelling: beam elements or continuum elements (E b = 30.0e6 kPa, ν = 0.15, d = 0.8 m) - interface elements between wall and soil - horizontal hydraulic cut off at -30.00 m is not considered as structural support, the same mechanical properties as for the surrounding soil are assumed - hydrostatic water pressures correspond to water levels inside and outside excavation (groundwater lowering is performed in one step before excavation starts) - anchors are modelled as rods, the grouted body as membrane element which guarantee a continuous load transfer to the soil - given anchor forces in Figure 1 are design loads Computational steps to be performed: stage 0: initial stress state (given by σ' v = γz, σ' h = K o γz, K o = 0.43) stage 1: activation of diaphragm wall and groundwater lowering to -17.90 m stage 2: excavation step 1 (to level -4.80 m) stage 3: activation of anchor 1 at level -4.30 m and prestressing stage 4: excavation step 2 (to level -9.30 m) stage 5: activation of anchor 2 at level -8.80 m and prestressing stage 6: excavation step 3 (to level -14.35 m) stage 7: activation of anchor 3 at level -13.85 m and prestressing stage 8: excavation step 4 (to level -16.80 m) Distance and prestressing loads for anchors follow from Figure 6.
Page 1 and 2: RESULTS FROM NUMERICAL BENCHMARK EX
Page 3: locations which are indicated in Fi
Page 7 and 8: 3.3. Comments on solutions submitte
Page 9 and 10: measurement (corrected) -80 -70 -60

Schweiger_ NUMGE_2002.pdf - Plaxis

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