Figure 1
Anchored embedded retaining wall.
Figure 2
Embedded wall under construction.
Figure 3
Geometry of the problem
Table 1
Material parameters.
| sand | concrete | ||
|---|---|---|---|
| Young Modulus | E [MPa] | 80 | 30000 |
| Poisson’s ratio | ν [-] | 0.25 | 0.20 |
| Cohesion | c [kPa] | 0.0 | - |
| Friction angle | Φ [o] | 34 | - |
| Unit weight | γ [kN/m3] | 18 | 25 |
Figure 4
Finite element mesh: a) general view; b) cross-section of the model for z0 = 2 m.
Figure 5
Range of passive and active zones near the anchor block for z0 = 2 m.
Figure 6
Force-displacement curves for the block without contact elements, surcharge thickness z0 = 2 m, incompressible behaviour of sand at yielding and various pulling force locations.
Figure 7
Force-displacement curves for the model with contact elements of different friction angle δ, surcharge thickness z0 = 2 m, incompressible behaviour of sand at yielding and the pulling force location h = 2 m.
Figure 8
Block’s displacement and mesh deformation in the ultimate state: a) h = 0.5 m; b) h = 2.0 m.
Figure 9
Variations of the ultimate force value with respect to its location and contact conditions for Z0 = 1 m.
Fig. 10
Variations of the ultimate force value with respect to its location and contact conditions for z0 = 2 m.
Table 2
Influence of tendon attachment location and dilatancy on ultimate force for z0 = 1 m.
| ψ | contact conditions | Fult h = 0.5 m, kN | Fult h = 2 m, kN | Fult h = 0.5/Fult h = 2×100, % |
|---|---|---|---|---|
| 0° | no contact elements | 977 | 2270 | 43.0% |
| δ = 0° | 657 | 1925 | 34.1% | |
| 5° | no contact elements | 1230 | 2486 | 49.5% |
| δ = 0° | 733 | 2053 | 35.7% | |
| 10° | no contact elements | 1404 | 2643 | 53.1% |
| δ = 0° | 789 | 2152 | 36.7% |
Table 3
Influence of tendon attachment location and dilatancy on ultimate force for z0 = 2 m.
| ψ | contact conditions | Fult h = 0.5 m, kN | Fult h = 2 m, kN | Fult h = 0.5/Fult h = 2×100, % |
|---|---|---|---|---|
| 0° | no contact elements | 1743 | 3741 | 46.6% |
| δ = 0° | 1305 | 3333 | 39.2% | |
| 5° | no contact elements | 2244 | 4187 | 53.6% |
| δ = 0° | 1434 | 3483 | 41.2% | |
| 10° | no contact elements | 2583 | 4470 | 57.8% |
| δ = 0° | 1571 | 3693 | 42.5% |
Figure 11
Scheme of pressures on the block.
Table 5
Coefficients of earth pressure for different contact friction.
| δ | Kpn | Kan |
|---|---|---|
| 0° | 3.5371 | 0.2827 |
| 1/3ϕ | 4.8707 | 0.2577 |
| 2/3ϕ | 6.0623 | 0.2395 |
| ϕ | 6.7123 | 0.2280 |
Table 6
Passive earth pressure for different contact friction and embedment z0 = 1 m.
| δ | ep1, kPa | ep2, kPa | Eph, kN |
|---|---|---|---|
| 0° | 84.04 | 590.84 | 1012.3 |
| 1/3ϕ | 115.73 | 813.60 | 1394.0 |
| 2/3ϕ | 144.04 | 1012.65 | 1735.0 |
| ϕ | 159.48 | 1121.23 | 1921.1 |
Table 7
Passive earth pressure for different contact friction and embedment z0 = 2 m.
| δ | ep1, kPa | ep2, kPa | Eph, kN |
|---|---|---|---|
| 0° | 208.83 | 830.87 | 1559.6 |
| 1/3Φ | 287.56 | 1144.12 | 2147.5 |
| 2/3Φ | 357.92 | 2672.94 | 2672.9 |
| Φ | 396.30 | 1576.72 | 2959.5 |
Table 8
Comparison of ultimate pullout forces for different contact friction and embedment z0.
| z0 = 1m | z0 = 2m | |||||
|---|---|---|---|---|---|---|
| δ | Fult anal, kN | Fult FEM, kN | Fult anal/Fult FEM×100, % | Fult FEM, kN | Fult anal, kN | Fult FEM/Fult anal×100, % |
| Φ | 1921.1 | 2221 | 86% | 2959.5 | 3680 | 80% |
| 2/3Φ | 1750.03 | 2193 | 79% | 2672.9 | 3564 | 75% |
| 1/3Φ | 1394.0 | 2112 | 66% | 2147.5 | 3448 | 62% |
| 0° | 1012.3 | 1925 | 53% | 1559.6 | 3333 | 47% |