Table 1
Parameters of soils.
| No | Symbol | Soil type | γ | φ’ | c’ | ψ | E0 | ν |
|---|---|---|---|---|---|---|---|---|
| kN/m3 | ° | kPa | ° | MPa | - | |||
| 1 | Ia | Sandy-clay | 20.9 | 1.45 | 18.0 | 14.5 | 21.5 | 0.317 |
| 2 | Ib | Sandy-clay | 20.9 | 12.5 | 14.0 | 1.25 | 17.0 | 0.322 |
| 3 | Ic | Sandy-clay | 20.9 | 10.0 | 11.0 | 1.00 | 12.5 | 0.304 |
| 4 | Id | Sandy-clay | 20.9 | 6.0 | 9.0 | 0.60 | 7.5 | 0.327 |
| 5 | Ie | Gravel | 18.8 | 38.0 | 1.0 | 14.00 | 127.0 | 0.220 |
| 6 | IIa | Peats/organic soil | 11.5 | 1.6 | 10.2 | 0.16 | 0.85 | 0.350 |
| 7 | IIIa | Sandy-silt/silty-clay | 18.8 | 6.0 | 12.0 | 0.60 | 4.5 | 0.347 |
| 8 | IIIb | Fine sand/clay-sand | 20.0 | 33.0 | 1.0 | 9.00 | 60.0 | 0.307 |
| 9 | IVa | Sandy-clay/clay-sand | 22.0 | 18.5 | 33.0 | 1.85 | 27.5 | 0.332 |
| 10 | IVb | Sandy-clay/clay-sand | 21.3 | 16.5 | 26.0 | 1.65 | 22.0 | 0.278 |
| 11 | zasypka | Gravel | 16.5 | 31.0 | 1.0 | 7.00 | 46.0 | 0.250 |
| 12 | nasyp | Sand | 20.0 | 33.0 | 50.0 | 9.00 | 80.0 | 0.25 |
Figure 1
Numerical model for initial state.
Figure 2
Numerical model after excavation.
Figure 3
Numerical model for final stage.
Figure 4
Numerical model – 1st variant.
Figure 5
Numerical model – 2nd variant.
Figure 6
Numerical model – 3rd variant.
Table 2
Maximum values of horizontal (ux) and vertical (uz) displacements and changes of pipe diameter (ΔD, ΔD%).
| 1st variant | 2nd variant | 3rd variant | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ux | uz | ΔD | ΔD % | ux | uz | ΔD | ΔD % | ux | uz | ΔD | ΔD % | |
| Time | mm | mm | % | mm | mm | % | mm | mm | % | |||
| After foundation of the pipe | -4 | -38 | -8 | -1.28 | -6 | -38 | -9 | -1.38 | -25 | -82 | -44 | -6.81 |
| I stage of embankment | 6 | -39 | -8 | -1.31 | 6 | -39 | -9 | -1.40 | -17 | -83 | -44 | -6.81 |
| II stage of embankment | 19 | -42 | -10 | -1.54 | 22 | -41 | -10 | -1.55 | 35 | -85 | -44 | -6.87 |
| III stage of embankment | 29 | -44 | -12 | -1.84 | 33 | -43 | -11 | -1.77 | 48 | -85 | -45 | -6.99 |
| IV stage of embankment | 44 | -48 | -15 | -2.34 | 48 | -45 | -14 | -2.22 | 66 | -85 | -46 | -7.15 |
| V stage of embankment | 67 | -51 | -20 | -3.06 | 74 | -47 | -20 | -3.05 | 94 | -85 | -49 | -7.70 |
| VI stage of embankment | 96 | -55 | -26 | -4.02 | 110 | -49 | -27 | -4.22 | 138 | -83 | -54 | -8.43 |
| Final stage | 139 | -61 | -35 | -5.40 | 190 | -53 | -42 | -6.64 | 290 | -80 | -65 | -10.21 |
Figure 7
Changes of pipe diameter in time.
Figure 8
Deformations of pipe in time.
Table 3
Comparison of FOS for different types of beddings depending on the stage of construction.
| Time | 1st variant | 2nd variant | 3rd variant | 4th variant |
|---|---|---|---|---|
| I stage of embankment | 3.80 | 3.65 (-3.9 %) | 3.60 (-5.3 %) | 3.00 (-21.1 %) |
| II stage of embankment | 2.70 | 2.65 (-1.9 %) | 2.55 (-5.6 %) | 2.05 (-24.1 %) |
| III stage of embankment | 2.20 | 2.10 (-4.5 %) | 2.05 (-6.8 %) | 1.65 (-25.0 %) |
| IV stage of embankment | 1.80 | 1.75 (-2.8 %) | 1.70 (-5.6 %) | 1.35 (-25.0 %) |
| V stage of embankment | 1.50 | 1.45 (-3.3 %) | 1.40 (-6.7 %) | <1.0 |
| VI stage of embankment | 1.35 | 1.30 (-3.7 %) | 1.25 (-7.4 %) | <1.0 |
| Final stage | 1.00 | 1.00 (0 %) | 1.00 (0 %) | <1.0 |
| Average difference | -3.4 % | -6.2 % | -23.8 % |