Figure 1.
Overall schematic diagram of tunnel model.
Figure 1.
Overall schematic diagram of tunnel model.
Figure 2.
Photo of indoor model box.
Figure 2.
Photo of indoor model box.
Figure 3.
Layout plan of displacement meter for vertical convergence deformation of tunnel (in mm).
Figure 3.
Layout plan of displacement meter for vertical convergence deformation of tunnel (in mm).
Figure 4.
Layout of vertical displacement meter in tunnel (in mm).
Figure 4.
Layout of vertical displacement meter in tunnel (in mm).
Figure 5.
Layout plan of displacement meter for horizontal convergence deformation of tunnel (in mm).
Figure 5.
Layout plan of displacement meter for horizontal convergence deformation of tunnel (in mm).
Figure 6.
Layout of horizontal displacement meter in tunnel (in mm).
Figure 6.
Layout of horizontal displacement meter in tunnel (in mm).
Figure 7.
Layout of measuring points for deep settlement of soil (in mm).
Figure 7.
Layout of measuring points for deep settlement of soil (in mm).
Figure 8.
Loading process of the model tests.
Figure 8.
Loading process of the model tests.
Figure 9.
Tunnel settlement curve.
Figure 9.
Tunnel settlement curve.
Figure 10.
Vertical convergence deformation curve of tunnel.
Figure 10.
Vertical convergence deformation curve of tunnel.
Figure 11.
Transverse convergence deformation curve of tunnel.
Figure 11.
Transverse convergence deformation curve of tunnel.
Figure 12.
Deep settlement curve of soil (parallel to tunnel direction).
Figure 12.
Deep settlement curve of soil (parallel to tunnel direction).
Figure 13.
Deep settlement curve of soil (perpendicular to tunnel direction).
Figure 13.
Deep settlement curve of soil (perpendicular to tunnel direction).
Figure 14.
Settlement of each measuring point of tunnel segment under different ground surcharge.
Figure 14.
Settlement of each measuring point of tunnel segment under different ground surcharge.
Figure 15.
Vertical convergence deformation of each measuring point of tunnel segment under different ground surcharge.
Figure 15.
Vertical convergence deformation of each measuring point of tunnel segment under different ground surcharge.
Figure 16.
Settlement of each measuring point of tunnel segment at different tunnel depths.
Figure 16.
Settlement of each measuring point of tunnel segment at different tunnel depths.
Figure 17.
Vertical convergence deformation of each measuring point of tunnel segment at different tunnel depths.
Figure 17.
Vertical convergence deformation of each measuring point of tunnel segment at different tunnel depths.
Figure 18.
Transverse convergence deformation of tunnel center point under different ground surcharge positions.
Figure 18.
Transverse convergence deformation of tunnel center point under different ground surcharge positions.
Figure 19.
Transverse convergence deformation of each measuring point of tunnel segment under different ground surcharge positions.
Figure 19.
Transverse convergence deformation of each measuring point of tunnel segment under different ground surcharge positions.
Figure 20.
Deep settlement curve of soil parallel to tunnel direction.
Figure 20.
Deep settlement curve of soil parallel to tunnel direction.
Figure 21.
Deep settlement curve of soil perpendicular to tunnel direction.
Figure 21.
Deep settlement curve of soil perpendicular to tunnel direction.
Figure 22.
Calculation results of deep settlement of soil parallel to the tunnel direction.
Figure 22.
Calculation results of deep settlement of soil parallel to the tunnel direction.
Figure 23.
Calculation results of deep settlement of soil perpendicular to the tunnel direction.
Figure 23.
Calculation results of deep settlement of soil perpendicular to the tunnel direction.
Figure 24.
Interaction between Poisson’s ratio μ and elastic modulus E on settlement ω.
Figure 24.
Interaction between Poisson’s ratio μ and elastic modulus E on settlement ω.
Figure 25.
Influence of different soil quality on vertical deformation of tunnel.
Figure 25.
Influence of different soil quality on vertical deformation of tunnel.
Figure 26.
Influence of different soil quality on tunnel settlement.
Figure 26.
Influence of different soil quality on tunnel settlement.
Figure 27.
Variation of stress with soil layer thickness Z underground surcharge.
Figure 27.
Variation of stress with soil layer thickness Z underground surcharge.
Figure 28.
Stress isolines of different soils.
Figure 28.
Stress isolines of different soils.
Figure 29.
Three-dimensional finite element model.
Figure 29.
Three-dimensional finite element model.
Figure 30.
Deformation diagram of tunnel.
Figure 30.
Deformation diagram of tunnel.
Figure 31.
Dimensionless comparison diagram of tunnel settlement under different ground surcharges.
Figure 31.
Dimensionless comparison diagram of tunnel settlement under different ground surcharges.
Figure 32.
Dimensionless comparison diagram of vertical convergence deformation of tunnel under different ground surcharges.
Figure 32.
Dimensionless comparison diagram of vertical convergence deformation of tunnel under different ground surcharges.
Figure 33.
Dimensionless comparison diagram of tunnel transverse convergence deformation at different ground surcharge positions.
Figure 33.
Dimensionless comparison diagram of tunnel transverse convergence deformation at different ground surcharge positions.
Figure 34.
Dimensionless comparison diagram of deep settlement of soil parallel to the tunnel direction.
Figure 34.
Dimensionless comparison diagram of deep settlement of soil parallel to the tunnel direction.
Figure 35.
Dimensionless comparison diagram of deep settlement of soil perpendicular to the tunnel direction.
Figure 35.
Dimensionless comparison diagram of deep settlement of soil perpendicular to the tunnel direction.
Figure 36.
Dimensionless comparison diagram of vertical convergence deformation of the tunnel under different burial depths.
Figure 36.
Dimensionless comparison diagram of vertical convergence deformation of the tunnel under different burial depths.
Table 1.
Similarity constant of indoor model test.
Table 1.
Similarity constant of indoor model test.
Physical Quantity | Similarity Relation | Similarity Constant | Physical Quantity | Similarity Relation | Similarity Constant |
---|
Geometric dimensions | Basic quantity | 15.5 | Pressure | | 16.75 |
Elastic modulus | Basic quantity | 16.75 | Axial force | | 4024 |
Strain | | 1 | Bending stiffness | | 57720 |
Stress | | 16.75 | Axial stiffness | | 3724 |
Displacement | | 15.5 | Shear stiffness | | 3724 |
Table 2.
Geometric parameters and material characteristics of tunnel model.
Table 2.
Geometric parameters and material characteristics of tunnel model.
| Outer Diameter of Segment (m) | Segment Inner Diameter (m) | Segment Thickness (m) | Ring Width (m) | Elastic Modulus of Segment (MPa) | SEGMENT Poisson’s Ratio |
---|
Prototype | 6.200 | 5.504 | 0.348 | 1.200 | 34,500 | 0.2 |
Model | 0.400 | 0.356 | 0.022 | 0.077 | 2060 | 0.3 |
Table 3.
Geometric parameters and material properties of tunnel connecting bolts.
Table 3.
Geometric parameters and material properties of tunnel connecting bolts.
| Bolt Length (m) | Diameter of Bolt (m) | Number of Bolts | Elastic Modulus of Bolt (MPa) | Poisson’s Ratio of Bolts |
---|
Prototype | 0.400 | 0.030 | 17 | 200,000 | 0.30 |
Model | 0.027 | 0.002 | 6 | 33,800 | 0.32 |
Table 4.
Physical and mechanical indexes of dry sand.
Table 4.
Physical and mechanical indexes of dry sand.
Density (g) | Moisture Content (%) | Internal Friction Angle (°) | Cohesion (kPa) | Compressive Modulus (MPa) |
---|
1.495 | 0.23 | 29 | 0 | 2.89 |
Table 5.
Test conditions.
Table 5.
Test conditions.
Test Number | Ground Surcharge Position | Total Thickness of Soil Layer | Tunnel Buried Depth | Sand for Test |
---|
1 | Eccentricity 0 m | 1.2 m | 0.6 m | Dry sand |
2 | Eccentricity 0.2 m | 1.2 m | 0.6 m | Dry sand |
3 | Eccentricity 0.4 m | 1.2 m | 0.6 m | Dry sand |
4 | Eccentricity 0.6 m | 1.2 m | 0.6 m | Dry sand |
5 | Eccentricity 0 m | 1.1 m | 0.5 m | Dry sand |
6 | Eccentricity 0 m | 1.2 m | 0.6 m | Dry sand |
7 | Eccentricity 0 m | 1.3 m | 0.7 m | Dry sand |
8 | Eccentricity 0 m | 1.4 m | 0.8 m | Dry sand |
9 | Eccentricity 0 m | 1.2 m | 0.6 m | Wet sand |
Table 6.
Working conditions of finite element three-dimensional numerical model.
Table 6.
Working conditions of finite element three-dimensional numerical model.
Test Number | Ground Surcharge Position | Tunnel Buried Depth | Type of Soil |
---|
1 | Eccentricity 0 m | 9.3 m | Sand |
2 | Eccentricity 3.1 m | 9.3 m | Sand |
3 | Eccentricity 6.2 m | 9.3 m | Sand |
4 | Eccentricity 9.3 m | 9.3 m | Sand |
5 | Eccentricity 0 m | 7.75 m | Sand |
6 | Eccentricity 0 m | 9.3 m | Sand |
7 | Eccentricity 0 m | 10.85 m | Sand |
8 | Eccentricity 0 m | 12.4 m | Sand |