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Program of numerical simulation
| Height of cave (h/m) | Cave span (D/m) | Pile diameter (d/m) | Distance from the bottom of the cavity to the bottom of the pile (m) | |
|---|---|---|---|---|
| 1 | 3 | 3, 4, 6 | 1.0 | 3 |
| 2 | 2, 3, 4 | 6 | 1.0 | 3 |
Mechanical parameters of the prototype limestone material and pile
| Material | ρ (g/cm3) | σ c (MPa) | E (MPa) | c (kPa) | φ (°) |
|---|---|---|---|---|---|
| Strongly weathered limestone | 2.48 | 28.3 | 3,000 | 800 | 32 |
| Moderately weathered limestone | 2.7 | 88 | 14,000 | 1,200 | 38 |
| Pile | 2.48 | — | 24,000 | 2,060 | — |
Mechanical parameters of similar materials
| Mix proportion | ρ (g/cm3) | σ c (MPa) | E (MPa) | c (kPa) | φ (°) |
|---|---|---|---|---|---|
| Q:G:C:R:D:L = 66:10:10:4:4:6 | 1.788 | 1.93 | 328.93 | 32.38 | 35.50 |
| Q:G:C:R:D:L = 80:3:3:6:6:2 | 1.763 | 0.62 | 42.07 | 19.91 | 32.03 |
| Q:G:C:R:D:L = 66:12:12:4:4:2 | 1.727 | 2.57 | 448.53 | 38.21 | 36.01 |
Loading load-level design
| Tag (times) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Load class (kN) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
Program of physical model test simulation
| Height of cave (h/cm) | Cave span (D/cm) | Pile diameter (d/cm) | Distance from the bottom of the cavity to the bottom of the pile/cm | |
|---|---|---|---|---|
| 1 | 10 | 10, 13.3, 20 | 3.3 | 10 |
| 2 | 6.7, 1, 13.3 | 20 | 3.3 | 10 |
Material parameters
| Similar material | γ (kN/m3) | E (MPa) | υ | c (kPa) | φ (°) |
|---|---|---|---|---|---|
| Strongly weathered limestone | 24.8 | 2,000 | 0.3 | 30 | 32 |
| Moderately weathered limestone | 27 | 14,000 | 0.25 | 300 | 38 |
| Pile | 25 | 24,000 | 0.2 | — | — |
Targeted parameters of the similar materials obtained using the corresponding ratio of similitude
| Similar material | ρ (g/cm3) | σ c (MPa) | E (MPa) | c (kPa) | φ (°) |
|---|---|---|---|---|---|
| Strongly weathered limestone | 1.67 | 0.63 | 66.67 | 17.77 | 32 |
| Moderately weathered limestone | 1.8 | 1.95 | 311.11 | 26.67 | 38 |
| Pile | 1.67 | — | 533.33 | 45.7 | — |