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Earth pressure reduction factor λE in dependence on the wall's geometry_
| Earth pressure reduction factor λE | H (m) | |||||||
|---|---|---|---|---|---|---|---|---|
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
| b (m) | 1 | 26.0 | 22.3 | 19.6 | 17.5 | 15.8 | 14.5 | 13.3 |
| 2 | 56.2 | 47.1 | 40.8 | 36.1 | 32.4 | 29.5 | 27.0 | |
| 3 | 91.7 | 74.6 | 63.6 | 55.7 | 49.7 | 45.0 | 41.2 | |
| 4 | 100.0 | 100.0 | 88.3 | 76.6 | 67.9 | 61.2 | 55.7 | |
| 5 | 100.0 | 100.0 | 100.0 | 98.7 | 86.9 | 77.9 | 70.7 | |
| 6 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 95.3 | 86.3 | |
Earth pressure reduction factors λE for a typical bridge abutment (H = 8_0 m, b = 4_0 m) and standard vertical surface load (q = 25 kPa)_
| Backfill type | ρIL | ρTB | ρb | ϕb | ES/ETB | λE |
|---|---|---|---|---|---|---|
| kN/m3 | kN/m3 | kN/m3 | ° | kN/m | % | |
| Case A | ||||||
| Medium sand | 19.00 | 0.00 | 19.00 | 35.0 | 164.8 | 0.0 |
| Tyre–sand | 19.00 | 5.40 | 7.67 | 29.6 | 25.4 | 84.6 |
| Tyre–LECA | 5.25 | 5.40 | 5.38 | 27.0 | 77.1 | 53.2 |
| Tyre–rubber | 5.40 | 5.40 | 5.40 | 26.8 | 77.5 | 53.0 |
| Case B | ||||||
| Medium sand | 19.00 | 0.00 | 19.00 | 35.0 | 200.0 | 0.0 |
| Tyre–sand | 19.00 | 5.40 | 7.67 | 29.6 | 64.2 | 67.9 |
| Tyre–LECA | 5.25 | 5.40 | 5.38 | 27.0 | 117.5 | 41.2 |
| Tyre–rubber | 5.40 | 5.40 | 5.40 | 26.8 | 118.0 | 41.0 |
| Case C | ||||||
| Medium sand | 19.00 | 0.00 | 19.00 | 35.0 | 219.0 | 0.0 |
| Tyre–sand | 19.00 | 5.40 | 7.67 | 29.6 | 17.1 | 92.2 |
| Tyre–LECA | 5.25 | 5.40 | 5.38 | 27.0 | 76.8 | 64.9 |
| Tyre–rubber | 5.40 | 5.40 | 5.40 | 26.8 | 77.7 | 64.5 |
Shear strength parameters of tyre–filling interface_
| Filling material | Friction angle Δ | Cohesion c | Determination coefficient R2 |
|---|---|---|---|
| (°) | (kPa) | ||
| Medium sand | 29.6 | 0.77 | 0.962 |
| LECA aggregate | 27.0 | 0.08 | 0.994 |
| Rubber aggregate | 26.8 | 0.50 | 0.983 |
Shear and normal stresses along the tyre bale–LECA interface_
| Bale no. | Area A | Normal load V | Failure load Hf | Normal stress σ | Shear stress τ | Shear stress τcal | Error estimation |
|---|---|---|---|---|---|---|---|
| (m2) | (kN) | (kN) | (kPa) | (kPa) | (kPa) | (%) | |
| P-1 | 2.686 | 22.2 | 12.00 | 8.27 | 4.47 | 4.28 | 4.28 |
| 28.4 | 14.22 | 10.57 | 5.29 | 5.46 | 3.00 | ||
| 38.4 | 20.41 | 14.30 | 7.60 | 7.35 | 3.37 | ||
| 44.0 | 22.79 | 16.38 | 8.48 | 8.41 | 0.87 | ||
| P-2 | 2.712 | 22.2 | 11.62 | 8.19 | 4.28 | 4.24 | 0.96 |
| 28.4 | 14.59 | 10.47 | 5.38 | 5.41 | 0.49 | ||
| 38.4 | 19.86 | 14.16 | 7.32 | 7.28 | 0.57 | ||
| 44.0 | 22.69 | 16.22 | 8.37 | 8.33 | 0.42 | ||
| P-3 | 2.726 | 22.2 | 11.30 | 8.14 | 4.15 | 4.22 | 1.83 |
| 28.4 | 14.56 | 10.42 | 5.34 | 5.38 | 0.71 | ||
| 38.4 | 19.23 | 14.09 | 7.05 | 7.24 | 2.63 | ||
| 44.0 | 22.25 | 16.14 | 8.16 | 8.29 | 1.53 | ||
Basic dimensions and weights of tyre bales_
| Bale no. | Number of tyres | Length L | Width B | Hight H | Area A | Volume V | Weight G | Unit weight γAVG |
|---|---|---|---|---|---|---|---|---|
| (m) | (m2) | (m3) | (kg) | (kg/m3) | ||||
| P-1 | 135 | 2.070 | 1.310 | 0.747 | 2.712 | 2.026 | 1038 | 512.43 |
| P-2 | 135 | 2.040 | 1.317 | 0.757 | 2.689 | 2.034 | 1022 | 502.50 |
| P-3 | 135 | 2.050 | 1.310 | 0.740 | 2.686 | 1.987 | 1012 | 509.24 |
| P-4 | 135 | 2.040 | 1.323 | 0.737 | 2.699 | 1.989 | 1034 | 519.83 |
| P-5 | 135 | 2.070 | 1.317 | 0.750 | 2.726 | 2.045 | 1049 | 513.05 |
| P-6 | 135 | 2.060 | 1.295 | 0.750 | 2.668 | 2.001 | 1032 | 515.80 |
| Avg. | 135 | 2.055 | 1.312 | 0.747 | 2.697 | 2.014 | 1031 | 512.14 |
Basic material characteristics of the filling materials_
| Filling material | Granulation | Weight density | Moisture | Friction angle | Cohesion | State |
|---|---|---|---|---|---|---|
| (mm) | (kN/m3) | (%) | (°) | (kPa) | ||
| Medium sand | 0.25–1.00 | 18.5 ± 0.5 | 12.6–12.8 | 35.2 | 0 | Loose / medium concentrated |
| LECA aggregate | 8–20 | 3.2 | 18.7–22.2 | 35.3 | 0 | Loose |
| Rubber aggregate | 4–20 | 4.2 | 9.8–11.0 | 20.5* | 10.5* | Loose |
Shear and normal stresses along the tyre bale–medium sand interface_
| Bale no. | Area A | Normal load V | Failure load Hf | Normal stress σ | Shear stress τ | Shear stress τcal | Error estimation |
|---|---|---|---|---|---|---|---|
| (m2) | (kN) | (kN) | (kPa) | (kPa) | (kPa) | (%) | |
| P-1 | 2.686 | 22.2 | 14.01 | 8.27 | 5.22 | 5.47 | 4.58 |
| 28.4 | 18.24 | 10.57 | 6.79 | 6.78 | 0.18 | ||
| 38.4 | 23.00 | 14.30 | 8.56 | 8.90 | 3.74 | ||
| 44.0 | 25.71 | 16.38 | 9.57 | 10.08 | 5.05 | ||
| P-2 | 2.712 | 22.2 | 13.86 | 8.19 | 5.11 | 5.42 | 5.73 |
| 28.4 | 18.61 | 10.47 | 6.86 | 6.72 | 2.10 | ||
| 38.4 | 23.00 | 14.16 | 8.48 | 8.82 | 3.82 | ||
| 44.0 | 28.03 | 16.22 | 10.34 | 9.99 | 3.45 | ||
| P-3 | 2.726 | 22.2 | 16.45 | 8.14 | 6.03 | 5.40 | 11.80 |
| 28.4 | 17.80 | 10.42 | 6.53 | 6.69 | 2.40 | ||
| 38.4 | 24.70 | 14.09 | 9.06 | 8.78 | 3.25 | ||
| 44.0 | 28.41 | 16.14 | 10.42 | 9.94 | 4.81 | ||
Shear and normal stresses along the tyre bale–rubber aggregate interface_
| Bale no. | Area A | Normal load V | Failure load Hf | Normal stress σ | Shear stress τ | Shear stress τcal | Error estimation |
|---|---|---|---|---|---|---|---|
| (m2) | (kN) | (kN) | (kPa) | (kPa) | (kPa) | (%) | |
| P-1 | 2.686 | 22.2 | 12.88 | 8.27 | 4.80 | 4.68 | 2.57 |
| 28.4 | 16.15 | 10.57 | 6.01 | 5.84 | 2.96 | ||
| 38.4 | 21.32 | 14.30 | 7.94 | 7.72 | 2.83 | ||
| 44.0 | 24.51 | 16.38 | 9.13 | 8.77 | 4.04 | ||
| P-2 | 2.712 | 22.2 | 12.18 | 8.19 | 4.49 | 4.64 | 3.11 |
| 28.4 | 15.46 | 10.47 | 5.70 | 5.79 | 1.52 | ||
| 38.4 | 20.64 | 14.16 | 7.61 | 7.65 | 0.51 | ||
| 44.0 | 23.62 | 16.22 | 8.71 | 8.69 | 0.21 | ||
| P-3 | 2.726 | 22.2 | 12.34 | 8.14 | 4.53 | 4.61 | 1.89 |
| 28.4 | 15.88 | 10.42 | 5.83 | 5.76 | 1.10 | ||
| 38.4 | 20.51 | 14.09 | 7.52 | 7.61 | 1.17 | ||
| 44.0 | 22.20 | 16.14 | 8.14 | 8.65 | 5.85 | ||