Rotational problems
Masonry arches
Simple arch
| Benchmark | 33.03 |
| Result | 33.07 |
| Discrepancy on Collapse Load | 0.11% |
| Discrepancy on Input Parameters | 0.11% |
ANALYSIS TYPE: Drained
WATER REGIME: Dry conditions
KEY DIMENSIONS: Wall height 1m.
ADEQUACY FACTOR LOADING: Total vertical load 1kN (load 100kN/m2 over 0.01m).
BOUNDARY CONDITIONS: Fixed supports.
BLOCK PROPERTIES: dry unit weight = 23 kN/m3
JOINT PROPERTIES: phi = 30 degrees, no-tension cutoff model used
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 33.03.
REFERENCE: LimitState:RING 2.0 solution.
COMMENT:
Simple arch with low friction joints
| Benchmark | 20.46 |
| Result | 20.46 |
| Discrepancy on Collapse Load | 0.02% |
| Discrepancy on Input Parameters | 0.02% |
ANALYSIS TYPE: Drained
WATER REGIME: Dry conditions
KEY DIMENSIONS: Wall height 1m.
ADEQUACY FACTOR LOADING: Total vertical load 1kN (load 100kN/m2 over 0.01m).
BOUNDARY CONDITIONS: Fixed supports.
BLOCK PROPERTIES: dry unit weight = 23 kN/m3
JOINT PROPERTIES: phi = 14.036 degrees, no-tension cutoff model used
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 20.46.
REFERENCE: LimitState:RING 2.0 solution.
COMMENT:
Trapdoors (drained)
Drained trapdoor, D/B = 0.5, phi'=30 degrees, vertical load
| Benchmark | 0.54 |
| Result | 0.14 |
| Discrepancy on Collapse Load | 73.78% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 0.5m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 1.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 30 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: 0.71. Benchmark = 0.5(1 - 0.71) = 0.145.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 0.5. To achieve active failure a baseline passive load of 0.5 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Drained trapdoor, D/B = 1, phi'=30 degrees, vertical load
| Benchmark | 0.54 |
| Result | 0.55 |
| Discrepancy on Collapse Load | 0.97% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 1m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 1.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 30 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: Upper bound = 0.47, Lower bound = 0.45, mean = 0.46. Benchmark = 1(1 - 0.46) = 0.54.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 1.0. To achieve active failure a baseline passive load of 1.0 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Drained trapdoor, D/B = 2, phi'=30 degrees, vertical load
| Benchmark | 1.52 |
| Result | 1.53 |
| Discrepancy on Collapse Load | 0.41% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 2m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 2.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 30 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: Upper bound = 0.26, Lower bound = 0.22, mean = 0.24. Benchmark = 2(1 - 0.24) = 1.52.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 2.0. To achieve active failure a baseline passive load of 2.0 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Drained trapdoor, D/B = 3, phi'=30 degrees, vertical load
| Benchmark | 2.49 |
| Result | 2.52 |
| Discrepancy on Collapse Load | 1.27% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 3m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 3.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 30 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: Upper bound = 0.19, Lower bound = 0.15, mean = 0.17. Benchmark = 3(1 - 0.17) = 2.49.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 3.0. To achieve active failure a baseline passive load of 3.0 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Drained trapdoor, D/B = 5, phi'=30 degrees, vertical load
| Benchmark | 4.4 |
| Result | 4.53 |
| Discrepancy on Collapse Load | 2.85% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 5m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 5.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 30 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: Upper bound = 0.15, Lower bound = 0.09, mean = 0.12. Benchmark = 5(1 - 0.12) = 4.40.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 5.0. To achieve active failure a baseline passive load of 5.0 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Drained trapdoor, D/B = 0.5, phi'=40 degrees, vertical load
| Benchmark | 0.21 |
| Result | 0.21 |
| Discrepancy on Collapse Load | 2.03% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 0.5m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 1.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 40 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: 0.58. Benchmark = 0.5(1 - 0.58) = 0.21.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 0.5. To achieve active failure a baseline passive load of 0.5 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Drained trapdoor, D/B = 3, phi'=40 degrees, vertical load
| Benchmark | 2.66 |
| Result | 2.69 |
| Discrepancy on Collapse Load | 1.38% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 3m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 3.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 40 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: Upper bound = 0.13, Lower bound = 0.10, mean = 0.115. Benchmark = 3(1 - 0.115) = 2.655.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 3.0. To achieve active failure a baseline passive load of 3.0 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Drained trapdoor, D/B = 5, phi'=40 degrees, vertical load
| Benchmark | 4.63 |
| Result | 4.69 |
| Discrepancy on Collapse Load | 1.49% |
| Discrepancy on Input Parameters | 0% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Trapdoor width 1m, soil cover depth 5m.
ADEQUACY FACTOR LOADING: Vertical active load on trapdoor (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, rough trapdoor. Baseline passive vertical load on trapdoor (unit load 5.0kN/m2).
SOIL PROPERTIES: c'=0, phi' = 40 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: F/gammaDB: Upper bound = 0.09, Lower bound = 0.06, mean = 0.075. Benchmark = 5(1 - 0.075) = 4.625.
REFERENCE: Smith C.C. (1998) Limit Loads for an Anchor/Trapdoor Embedded in an Associative Coulomb Soil. Int. J. Numer. Anal. Meth. Geomech., 22, pp 855-865.
COMMENT: Benchmark result is relative to 5.0. To achieve active failure a baseline passive load of 5.0 kN/m2 was applied to the trapdoor. Error on input parameter not given since load error is small, and exact true solution not known.
Soil nails (undrained wall)
Undrained active smooth retaining wall, soil reinforcement, T = 0.0 kN/m/m, N = 0.0 kN/m/m (adequacy on self weight)
| Benchmark | 4 |
| Result | 4 |
| Discrepancy on Collapse Load | 0.09% |
| Discrepancy on Input Parameters | 0.09% |
GENERAL DESCRIPTION: Simple retaining wall, horizontal soil surface, soil reinforcement at mid depth
ANALYSIS TYPE: Undrained, tension cutoff not modelled
KEY DIMENSIONS: Wall height 1m, reinforcement length in soil 0.75m.
ADEQUACY FACTOR LOADING: Applied to soil self weight
BOUNDARY CONDITIONS: No surcharge; wall on smooth base; soil-wall interface smooth
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 1 kN/m3
REINFORCEMENT PROPERTIES: Pullout resistance = 0.0 kN/m/m, Lateral resistance 0.0 kN/m/m
BENCHMARK SOLUTION: 4.00
REFERENCE: LimitState:GEO manual, Appendix C.
Undrained active smooth retaining wall, soil reinforcement, T = 0.1 kN/m/m, N = 0.0 kN/m/m (adequacy on self weight)
| Benchmark | 4.05 |
| Result | 4.05 |
| Discrepancy on Collapse Load | 0.09% |
| Discrepancy on Input Parameters | 0.09% |
GENERAL DESCRIPTION: Simple retaining wall, horizontal soil surface, soil reinforcement at mid depth
ANALYSIS TYPE: Undrained, tension cutoff not modelled
KEY DIMENSIONS: Wall height 1m, reinforcement length in soil 0.75m.
ADEQUACY FACTOR LOADING: Applied to soil self weight
BOUNDARY CONDITIONS: No surcharge; wall on smooth base; soil-wall interface smooth
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 1 kN/m3
REINFORCEMENT PROPERTIES: Pullout resistance = 0.1 kN/m/m, Lateral resistance 0.0 kN/m/m
BENCHMARK SOLUTION: 4.05
REFERENCE: LimitState:GEO manual, Appendix C.
Undrained active smooth retaining wall, soil reinforcement, T = 0.1 kN/m/m, N = 1.0 kN/m/m (adequacy on self weight)
| Benchmark | 5.05 |
| Result | 5.05 |
| Discrepancy on Collapse Load | 0.07% |
| Discrepancy on Input Parameters | 0.07% |
GENERAL DESCRIPTION: Simple retaining wall, horizontal soil surface, soil reinforcement at mid depth
ANALYSIS TYPE: Undrained, tension cutoff not modelled
KEY DIMENSIONS: Wall height 1m, reinforcement length in soil 0.75m.
ADEQUACY FACTOR LOADING: Applied to soil self weight
BOUNDARY CONDITIONS: No surcharge; wall on smooth base; soil-wall interface smooth
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 1 kN/m3
REINFORCEMENT PROPERTIES: Pullout resistance = 0.1 kN/m/m, Lateral resistance 1.0 kN/m/m
BENCHMARK SOLUTION: 5.05
REFERENCE: LimitState:GEO manual, Appendix C.