Undrained footings
Undrained footings (vertical loads)
Undrained footing (weightless soil), vertical load
| Benchmark | 5.14 |
| Result | 5.2 |
| Discrepancy on Collapse Load | 1.16% |
| Discrepancy on Input Parameters | 1.16% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space.
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 5.1415 (Prandtl solution).
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing.
Undrained footing with surcharge (weightless soil), vertical load
| Benchmark | 6.14 |
| Result | 6.2 |
| Discrepancy on Collapse Load | 0.97% |
| Discrepancy on Input Parameters | 1.2% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 1 kN/m2 (permanent) , symmetrical half space.
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 6.1415 (Prandtl solution).
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing.
NOTES: Error on load = 1.0%. 'Benchmark' partial factor set with factor of 1.012
(i.e. 1.2%) on cu is required to give benchmark solution.
Undrained footing, vertical load
| Benchmark | 5.14 |
| Result | 5.2 |
| Discrepancy on Collapse Load | 1.16% |
| Discrepancy on Input Parameters | 1.16% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space.
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 1 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 5.1415 (Prandtl solution).
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing.
Undrained footing with surcharge, vertical load
| Benchmark | 6.14 |
| Result | 6.2 |
| Discrepancy on Collapse Load | 0.97% |
| Discrepancy on Input Parameters | 1.2% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 1 kN/m2, symmetrical half space.
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 1 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 5.1415 (Prandtl solution).
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing.
NOTES: Error on load = 1.0%. 'Benchmark' partial factor set with factor of 1.012
(i.e. 1.2%) on cu is required to give benchmark solution.
Undrained footing, flooded, vertical load
| Benchmark | 9.07 |
| Result | 9.13 |
| Discrepancy on Collapse Load | 0.66% |
| Discrepancy on Input Parameters | 1.2% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
WATER REGIME: Water table above footing and soil surface.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space.
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 1 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 5.1415 + 0.4*9.81 = 9.0655 (Prandtl solution).
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing.
NOTES: Weightless footing increases collapse load by weight of water displaced.
Error on load = 0.7%. 'Benchmark' partial factor set with factor of 1.012 (i.e.
1.2%) on cu is required to give benchmark solution.
Undrained footings (linear variation of cohesion with depth)
Undrained footing, vertical load, weightless soil, smooth base, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m
| Benchmark | 5.98 |
| Result | 6.09 |
| Discrepancy on Collapse Load | 1.85% |
| Discrepancy on Input Parameters | 1.85% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, footing base smooth.
SOIL PROPERTIES: c_u = 1 kN/m2 at surface, c_u gradient = 1kN/m2/m depth, soil unit
weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 5.98176
REFERENCE: Benchmark derived using ABC software, Martin (2004) User Guide for ABC.
Analysis of Bearing Capacity, Version 1.0, http://www-civil.eng.ox.ac.uk/people/cmm/software/abc/.
Undrained footing, vertical load, smooth base, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m
| Benchmark | 5.98 |
| Result | 6.09 |
| Discrepancy on Collapse Load | 1.85% |
| Discrepancy on Input Parameters | 1.85% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, footing base smooth.
SOIL PROPERTIES: c_u = 1 kN/m2 at surface, c_u gradient = 1kN/m2/m depth, soil unit
weight = 1 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 5.98176
REFERENCE: Benchmark derived using ABC software, Martin (2004) User Guide for ABC.
Analysis of Bearing Capacity, Version 1.0, http://www-civil.eng.ox.ac.uk/people/cmm/software/abc/.
Undrained footing, vertical load, weightless soil, full base adhesion, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m
| Benchmark | 6.61 |
| Result | 6.74 |
| Discrepancy on Collapse Load | 1.94% |
| Discrepancy on Input Parameters | 1.94% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, full adhesion on footing
base.
SOIL PROPERTIES: c_u = 1 kN/m2 at surface, c_u gradient = 1kN/m2/m depth, soil unit
weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 6.60906
REFERENCE: Benchmark derived using ABC software, Martin (2004) User Guide for ABC.
Analysis of Bearing Capacity, Version 1.0, http://www-civil.eng.ox.ac.uk/people/cmm/software/abc/.
Undrained footing, vertical load, full base adhesion, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m
| Benchmark | 6.61 |
| Result | 6.74 |
| Discrepancy on Collapse Load | 1.94% |
| Discrepancy on Input Parameters | 1.94% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, full adhesion on footing
base.
SOIL PROPERTIES: c_u = 1 kN/m2 at surface, c_u gradient = 1kN/m2/m depth, soil unit
weight = 1 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 6.60906
REFERENCE: Benchmark derived using ABC software, Martin (2004) User Guide for ABC.
Analysis of Bearing Capacity, Version 1.0, http://www-civil.eng.ox.ac.uk/people/cmm/software/abc/.
Undrained footing, vertical load, weightless soil, full base adhesion, c_u=1kN/m2 at surface, gradient = 2.0 kN/m2/m
| Benchmark | 7.6 |
| Result | 7.82 |
| Discrepancy on Collapse Load | 2.83% |
| Discrepancy on Input Parameters | 2.83% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, full adhesion on footing
base.
SOIL PROPERTIES: c_u = 1 kN/m2 at surface, c_u gradient = 2kN/m2/m depth, soil unit
weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 7.5966
REFERENCE: Benchmark derived using ABC software, Martin (2004) User Guide for ABC.
Analysis of Bearing Capacity, Version 1.0, http://www-civil.eng.ox.ac.uk/people/cmm/software/abc/.
Undrained footing, vertical load, full base adhesion, c_u=1kN/m2 at surface, gradient = 2.0 kN/m2/m
| Benchmark | 7.6 |
| Result | 7.82 |
| Discrepancy on Collapse Load | 2.83% |
| Discrepancy on Input Parameters | 2.83% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, full adhesion on footing
base.
SOIL PROPERTIES: c_u = 1 kN/m2 at surface, c_u gradient = 2kN/m2/m depth, soil unit
weight = 1 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 7.5966
REFERENCE: Benchmark derived using ABC software, Martin (2004) User Guide for ABC.
Analysis of Bearing Capacity, Version 1.0, http://www-civil.eng.ox.ac.uk/people/cmm/software/abc/.
Undrained footings (layered soils)
Undrained footing, vertical load, weightless soil, smooth base, upper layer c_u=1kN/m2, lower layer c_u=2 kN/m2
| Benchmark | 5.09 |
| Result | 5.17 |
| Discrepancy on Collapse Load | 1.59% |
| Discrepancy on Input Parameters | 1.59% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, footing base smooth.
SOIL PROPERTIES: Upper layer 0.5m deep, c_u = 1 kN/m2, lower layer c_u = 2 kN/m2,
soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: Upper bound = 5.31, Lower bound = 4.86, mean = 5.085.
REFERENCE: Merifield, R.S, Sloan, S.W., Yu, H.S. (1999) Rigorous plasticity solutions
for the bearing capacity of two-layered clays. Geotechnique, Vol. 49, No 4, pp 471-490.
COMMENT: Benchmark based on mean of an upper and lower bound.
Undrained footing, vertical load, weightless soil, smooth base, upper layer c_u=1kN/m2, lower layer c_u=0.667 kN/m2
| Benchmark | 4.28 |
| Result | 4.37 |
| Discrepancy on Collapse Load | 2.11% |
| Discrepancy on Input Parameters | 2.11% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, footing base smooth.
SOIL PROPERTIES: Upper layer 0.5m deep, c_u = 1 kN/m2, lower layer c_u = 0.667 kN/m2,
soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: Upper bound = 4.48, Lower bound = 4.07, mean = 4.275.
REFERENCE: Merifield, R.S, Sloan, S.W., Yu, H.S. (1999) Rigorous plasticity solutions
for the bearing capacity of two-layered clays. Geotechnique, Vol. 49, No 4, pp 471-490.
COMMENT: Benchmark based on mean of an upper and lower bound.
Undrained footing, vertical load, weightless soil, smooth base, upper layer c_u=1kN/m2, lower layer c_u=0.4 kN/m2
| Benchmark | 3.3 |
| Result | 3.47 |
| Discrepancy on Collapse Load | 4.78% |
| Discrepancy on Input Parameters | 4.78% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, footing base smooth.
SOIL PROPERTIES: Upper layer 0.5m deep, c_u = 1 kN/m2, lower layer c_u = 0.4 kN/m2,
soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: Upper bound = 3.47, Lower bound = 3.13, mean = 3.30.
REFERENCE: Merifield, R.S, Sloan, S.W., Yu, H.S. (1999) Rigorous plasticity solutions
for the bearing capacity of two-layered clays. Geotechnique, Vol. 49, No 4, pp 471-490.
COMMENT: Benchmark based on mean of an upper and lower bound.
Undrained footing, vertical load, weightless soil, rough base, upper layer c_u=1kN/m2, lower layer c_u=2 kN/m2
| Benchmark | 6.22 |
| Result | 6.31 |
| Discrepancy on Collapse Load | 1.38% |
| Discrepancy on Input Parameters | 1.38% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, full adhesion on footing
base.
SOIL PROPERTIES: Upper layer 0.5m deep, c_u = 1 kN/m2, lower layer c_u = 2 kN/m2,
soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: Upper bound = 6.50, Lower bound = 5.94, mean = 6.22.
REFERENCE: Merifield, R.S, Sloan, S.W., Yu, H.S. (1999) Rigorous plasticity solutions
for the bearing capacity of two-layered clays. Geotechnique, Vol. 49, No 4, pp 471-490.
COMMENT: Benchmark based on mean of an upper and lower bound.
Undrained footing, vertical load, weightless soil, rough base, upper layer c_u=1kN/m2, lower layer c_u=0.667 kN/m2
| Benchmark | 3.87 |
| Result | 3.96 |
| Discrepancy on Collapse Load | 2.28% |
| Discrepancy on Input Parameters | 2.28% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, full adhesion on footing
base.
SOIL PROPERTIES: Upper layer 0.5m deep, c_u = 1 kN/m2, lower layer c_u = 0.667 kN/m2,
soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: Upper bound = 4.08, Lower bound = 3.65, mean = 3.865.
REFERENCE: Merifield, R.S, Sloan, S.W., Yu, H.S. (1999) Rigorous plasticity solutions
for the bearing capacity of two-layered clays. Geotechnique, Vol. 49, No 4, pp 471-490.
COMMENT: Benchmark based on mean of an upper and lower bound.
Undrained footing, vertical load, weightless soil, rough base, upper layer c_u=1kN/m2, lower layer c_u=0.4 kN/m2
| Benchmark | 2.73 |
| Result | 2.85 |
| Discrepancy on Collapse Load | 4.2% |
| Discrepancy on Input Parameters | 4.2% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, symmetrical half space, full adhesion on footing
base.
SOIL PROPERTIES: Upper layer 0.5m deep, c_u = 1 kN/m2, lower layer c_u = 0.4 kN/m2,
soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: Upper bound = 2.88, Lower bound = 2.58, mean = 2.73.
REFERENCE: Merifield, R.S, Sloan, S.W., Yu, H.S. (1999) Rigorous plasticity solutions
for the bearing capacity of two-layered clays. Geotechnique, Vol. 49, No 4, pp 471-490.
COMMENT: Benchmark based on mean of an upper and lower bound.
Undrained footings (inclined loads)
Undrained footing (weightless soil), inclined load, tau=0.2c_u
| Benchmark | 4.92 |
| Result | 4.97 |
| Discrepancy on Collapse Load | 0.99% |
| Discrepancy on Input Parameters | 0.99% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (horizontal component = 0.2c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 4.920
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 0.4kN/m2 is equivalent to shear stress
of 0.2c_u on base.
Undrained footing (weightless soil), inclined load, tau=0.4c_u
| Benchmark | 4.65 |
| Result | 4.7 |
| Discrepancy on Collapse Load | 1.21% |
| Discrepancy on Input Parameters | 1.21% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (horizontal component = 0.4_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 4.647
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 0.8kN/m2 is equivalent to shear stress
of 0.4c_u on base.
Undrained footing (weightless soil), inclined load, tau=0.6c_u
| Benchmark | 4.3 |
| Result | 4.34 |
| Discrepancy on Collapse Load | 1.02% |
| Discrepancy on Input Parameters | 1.02% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (horizontal component = 0.6c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 4.298
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 1.2kN/m2 is equivalent to shear stress
of 0.6c_u on base.
Undrained footing (weightless soil), inclined load, tau=0.8c_u
| Benchmark | 3.81 |
| Result | 3.88 |
| Discrepancy on Collapse Load | 1.82% |
| Discrepancy on Input Parameters | 1.82% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (horizontal component = 0.8c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 3.814
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 1.6kN/m2 is equivalent to shear stress
of 0.8c_u on base.
Undrained footing (weightless soil), inclined load, tau=0.9c_u
| Benchmark | 3.46 |
| Result | 3.57 |
| Discrepancy on Collapse Load | 3.12% |
| Discrepancy on Input Parameters | 3.12% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (horizontal component = 0.9c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 3.458
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 1.8kN/m2 is equivalent to shear stress
of 0.9c_u on base.
Undrained footing (weightless soil), inclined load, tau=1.0c_u
| Benchmark | 2.57 |
| Result | 2.75 |
| Discrepancy on Collapse Load | 6.6% |
| Discrepancy on Input Parameters | 6.6% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (horizontal component = 1.0c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 2.571
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
COMMENT: This problem is challenging for most numerical methods because the theoretical
failure mechanism is infinitesimally small in area. If the problem is run with finer
and finer nodal spacing, the mechanism shrinks with the nodal spacing, and the solution
becomes more accurate.
Undrained footing (weightless soil), inclined load, sig_v=2.2c_u
| Benchmark | 1 |
| Result | 1 |
| Discrepancy on Collapse Load | 0% |
| Discrepancy on Input Parameters | 0% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 2.2c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 1.000
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
Undrained footing (weightless soil), inclined load, sig_v=2.6c_u
| Benchmark | 1 |
| Result | 1 |
| Discrepancy on Collapse Load | 0.01% |
| Discrepancy on Input Parameters | 0.01% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 2.6c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 1.000
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
Undrained footing (weightless soil), inclined load, sig_v=3.0c_u
| Benchmark | 0.98 |
| Result | 0.99 |
| Discrepancy on Collapse Load | 1.6% |
| Discrepancy on Input Parameters | 1.6% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 3.0c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 0.977
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
Undrained footing (weightless soil), inclined load, sig_v=3.4c_u
| Benchmark | 0.91 |
| Result | 0.93 |
| Discrepancy on Collapse Load | 2.31% |
| Discrepancy on Input Parameters | 2.31% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 3.4c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 0.913
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
Undrained footing (weightless soil), inclined load, sig_v=3.8c_u
| Benchmark | 0.8 |
| Result | 0.83 |
| Discrepancy on Collapse Load | 3.14% |
| Discrepancy on Input Parameters | 3.14% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 3.8c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 0.805
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
Undrained footing (weightless soil), inclined load, sig_v=4.2c_u
| Benchmark | 0.65 |
| Result | 0.67 |
| Discrepancy on Collapse Load | 3.37% |
| Discrepancy on Input Parameters | 3.37% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 4.2c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 0.647
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
Undrained footing (weightless soil), inclined load, sig_v=4.6c_u
| Benchmark | 0.43 |
| Result | 0.46 |
| Discrepancy on Collapse Load | 7.27% |
| Discrepancy on Input Parameters | 7.27% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 4.6c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 0.430
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
COMMENT: At this value of vertical load, the horizontal load is very sensitive to
small changes in vertical load. For a horizontal stress of 0.470, the theoretical
vertical stress required to cause collapse would be 4.54.
Undrained footing (weightless soil), inclined load, sig_v=5.0c_u
| Benchmark | 0.13 |
| Result | 0.18 |
| Discrepancy on Collapse Load | 25.19% |
| Discrepancy on Input Parameters | 25.19% |
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Horizontal load on footing (unit permanent load 2kN/m2).
BOUNDARY CONDITIONS: No surcharge, inclined load, (vertical component = 5.0c_u,
permanent).
SOIL PROPERTIES: c_u = 1 kN/m2, soil unit weight = 0 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 0.133
REFERENCE: Powrie (2004) Soil Mechanics: Concepts and Applications. Taylor &
Francis.
NOTES: Footing is 0.5m high,applied stress 2.0kN/m2 is equivalent to shear stress
of 1.0c_u on base.
COMMENT: At this value of vertical load, the horizontal load is very sensitive to
small changes in vertical load. For a horizontal stress of 0.183, the theoretical
vertical stress required to cause collapse would be 4.94.
Undrained buried footings (lateral loads)
Undrained buried footing, lateral load
| Benchmark | 1000 |
| Result | 1000.26 |
| Discrepancy on Collapse Load | 0.03% |
| Discrepancy on Input Parameters | 0.03% |
GENERAL DESCRIPTION: Simple footing located within soil body with horizontal surface.
ANALYSIS TYPE: Undrained, tension cutoff not modelled.
KEY DIMENSIONS: Below ground surface: footing width 1m, footing depth 1m. Above
ground surface: column width = 0.25m, column height = 0.5m.
ADEQUACY FACTOR LOADING: Vertical load and horizontal load on column (unit permanent
load 1kN/m2 on each).
BOUNDARY CONDITIONS: No surcharge, soil/footing interface smooth on sides, full
adhesion on base.
SOIL PROPERTIES: c_u = 100 kN/m2, soil unit weight = 20 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 1000
NOTES: lhs lateral pressure = -190 kN/m, rhs lateral pressure = 210 kN/m, base adhesion
= 100 kN/m. Total resistance = 190 + 210 + 100 = 500 kN/m. Adequacy factor = 500/0.5
= 1000.
Undrained buried footing, lateral load, tension cutoff
| Benchmark | 620 |
| Result | 620.13 |
| Discrepancy on Collapse Load | 0.02% |
| Discrepancy on Input Parameters | 0.02% |
GENERAL DESCRIPTION: Simple footing located within soil body with horizontal surface.
ANALYSIS TYPE: Undrained, tension cutoff modelled on lhs soil/footing interface.
KEY DIMENSIONS: Below ground surface: footing width 1m, footing depth 1m. Above
ground surface: column width = 0.25m, column height = 0.5m.
ADEQUACY FACTOR LOADING: Vertical load and horizontal load on column (unit permanent
load 1kN/m2 on each).
BOUNDARY CONDITIONS: No surcharge, soil/footing interface smooth on sides, full
adhesion on base.
SOIL PROPERTIES: c_u = 100 kN/m2, soil unit weight = 20 kN/m2.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 1000
NOTES: lhs lateral pressure = 0 kN/m (tension cutoff), rhs lateral pressure = 210
kN/m, base adhesion = 100 kN/m. Total resistance = 0 + 210 + 100 = 310 kN/m. Adequacy
factor = 310/0.5 = 620.