Drained footings
Drained footing with surcharge (weightless soil, phi'=20 degrees), vertical load
| Benchmark | 6.4 |
| Result | 6.52 |
| Discrepancy on Collapse Load | 1.84% |
| Discrepancy on Input Parameters | 1% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Drained.
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'=0, phi' = 20 degrees, soil unit weight = 0 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 6.3994 (Nq value).
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing.
NOTES: Error on load = 1.9%. 'Benchmark' partial factor set with factor of 1.010
(i.e. 1%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 19.8 degrees.
Drained footing with surcharge (weightless soil, phi'=30 degrees), vertical load
| Benchmark | 18.4 |
| Result | 18.99 |
| Discrepancy on Collapse Load | 3.12% |
| Discrepancy on Input Parameters | 1.3% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Drained.
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'=0, phi' = 30 degrees, soil unit weight = 0 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 18.4011 (Nq value).
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing.
NOTES: Error on load = 3.7%. 'Benchmark' partial factor set with factor of 1.013
(i.e. 1.3%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 29.7 degrees.
Drained footing with surcharge (weightless soil, phi'=40 degrees), vertical load
| Benchmark | 64.2 |
| Result | 67.75 |
| Discrepancy on Collapse Load | 5.25% |
| Discrepancy on Input Parameters | 1.5% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Drained.
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'=0, phi' = 40 degrees, soil unit weight = 0 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 64.1952 (Nq value)
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing
NOTES: Error on load = 5.7%. 'Benchmark' partial factor set with factor of 1.015
(i.e. 1.5%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 39.6 degrees.
Drained footings
Drained footing with surcharge (weightless soil, c'=1 kN/m2, phi'=20 degrees), vertical load
| Benchmark | 21.23 |
| Result | 21.24 |
| Discrepancy on Collapse Load | 0.04% |
| Discrepancy on Input Parameters | 1% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Drained.
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'=1 kN/m2, phi' = 20 degrees, soil unit weight = 0 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 21.2341 (= Nq+Nc = 6.3994+14.8347)
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing
NOTES: Error on load = 2.1%. 'Benchmark' partial factor set with factor of 1.010
(i.e. 1.0%) on c' and tan(phi)' is required to give benchmark solution. Corresponding
values of c'and phi' are 0.990, and 19.8 degrees respectively.
Drained footing with surcharge (weightless soil, c'=1 kN/m2, phi'=30 degrees), vertical load
| Benchmark | 48.54 |
| Result | 50.16 |
| Discrepancy on Collapse Load | 3.23% |
| Discrepancy on Input Parameters | 1.3% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Drained.
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'=1 kN/m2, phi' = 30 degrees, soil unit weight = 0 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 48.5407 (= Nq+Nc = 18.4011+30.1396)
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing
NOTES: Error on load = 3.8%. c' = 1.013, phi' = 30.33 degrees is required to give
theoretically exact solution of 50.4489. Corresponding error on input soil properties,
c' and tan(phi') = 1.32%.
NOTES: Error on load = 3.8%. 'Benchmark' partial factor set with factor of 1.013
(i.e. 1.3%) on c' and tan(phi)' is required to give benchmark solution. Corresponding
value of c'and phi' are 0.987, and 29.7 degrees respectively.
Drained footing with surcharge (weightless soil, c'=1 kN/m2, phi'=40 degrees), vertical load
| Benchmark | 139.51 |
| Result | 147.3 |
| Discrepancy on Collapse Load | 5.29% |
| Discrepancy on Input Parameters | 1.7% |
GENERAL DESCRIPTION: Simple footing located on horizontal soil surface.
ANALYSIS TYPE: Drained.
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'=1 kN/m2, phi' = 40 degrees, soil unit weight = 0 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 139.5083 (= Nq+Nc = 64.1952+75.3131)
REFERENCE: Chen (2007). Limit Analysis and Soil Plasticity, J. Ross Publishing
NOTES: Error on load = 5.8%. 'Benchmark' partial factor set with factor of 1.017
(i.e. 1.7%) on c' and tan(phi)' is required to give benchmark solution. Corresponding
values of c'and phi' are 0.983, and 39.5 degrees respectively.
Drained footing (phi'=20 degrees, gamma = 1 kN/m2), vertical load
| Benchmark | 1.43 |
| Result | 1.72 |
| Discrepancy on Collapse Load | 17.13% |
| Discrepancy on Input Parameters | 6.5% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 0 kN/m2, symmetrical half space, footing base rough.
SOIL PROPERTIES: c'=0 kN/m2, phi' = 20 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 1.427 (Ngamma/2 value)
REFERENCE: Smith, C.C. (2005) Complete limiting stress solutions for the bearing
capacity of strip footings on a Mohr-Coulomb soil. Geotechnique, 55 (8), October,
pp 607-612.
NOTES: Error on load = 20.7%. 'Benchmark' partial factor set with factor of 1.065
(i.e. 6.5%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 18.8 degrees.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution. The Terzaghi bearing capacity formula using the EC7
recommended formula for N_gamma = 2*(Nq-1)*tan(phi) gives a solution of 1.97, an
error of 38.1%.
Drained footing (phi'=30 degrees, gamma = 1 kN/m2), vertical load
| Benchmark | 7.38 |
| Result | 9.36 |
| Discrepancy on Collapse Load | 21.21% |
| Discrepancy on Input Parameters | 6.1% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 0 kN/m2, symmetrical half space, footing base rough.
SOIL PROPERTIES: c'=0 kN/m2, phi' = 30 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 7.377 (Ngamma/2 value)
REFERENCE: Smith, C.C. (2005) Complete limiting stress solutions for the bearing
capacity of strip footings on a Mohr-Coulomb soil. Geotechnique, 55 (8), October,
pp 607-612.
NOTES: Error on load = 26.9%. 'Benchmark' partial factor set with factor of 1.061
(i.e. 6.1%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 28.5 degrees.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution. The Terzaghi bearing capacity formula using the EC7
recommended formula for N_gamma = 2*(Nq-1)*tan(phi) gives a solution of 10.05, an
error of 36.2%.
Drained footing (phi'=40 degrees, gamma = 1 kN/m2), vertical load
| Benchmark | 42.78 |
| Result | 56.37 |
| Discrepancy on Collapse Load | 24.1% |
| Discrepancy on Input Parameters | 5.6% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 0 kN/m2, symmetrical half space, footing base rough.
SOIL PROPERTIES: c'=0 kN/m2, phi' = 40 degrees, soil unit weight = 1 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 42.78 (Ngamma/2 value)
REFERENCE: Smith, C.C. (2005) Complete limiting stress solutions for the bearing
capacity of strip footings on a Mohr-Coulomb soil. Geotechnique, 55 (8), October,
pp 607-612.
NOTES: Error on load = 31.7%. 'Benchmark' partial factor set with factor of 1.056
(i.e. 5.6%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 38.4 degrees.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution. The Terzaghi bearing capacity formula using the EC7
recommended formula for N_gamma = 2*(Nq-1)*tan(phi) gives a solution of 53.0, an
error of 23.9%.
Drained footing with surcharge (c'=0 kN/m2, phi'=20 degrees, gamma = 15 kN/m2), vertical load
| Benchmark | 170.45 |
| Result | 175.22 |
| Discrepancy on Collapse Load | 2.7% |
| Discrepancy on Input Parameters | 1.8% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 20 kN/m2 (permanent) , symmetrical half space,
footing base rough.
SOIL PROPERTIES: c'=0 kN/m2, phi' = 20 degrees, soil unit weight = 15 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 170.45
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/.
NOTES: 'Benchmark' partial factor set with factor of 1.018
(i.e. 1.8%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 19.7 degrees.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution.
Drained footing with surcharge (c'=0 kN/m2, phi'=30 degrees, gamma = 15 kN/m2), vertical load
| Benchmark | 553.38 |
| Result | 576.1 |
| Discrepancy on Collapse Load | 3.9% |
| Discrepancy on Input Parameters | 1.5% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 20 kN/m2 (permanent) , symmetrical half space,
footing base rough.
SOIL PROPERTIES: c'=0 kN/m2, phi' = 30 degrees, soil unit weight = 15 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 553.38
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/.
NOTES: 'Benchmark' partial factor set with factor of 1.015
(i.e. 1.5%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 29.6 degrees.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution.
Drained footing with surcharge (c'=5 kN/m2, phi'=20 degrees, gamma = 15 kN/m2), vertical load
| Benchmark | 247.13 |
| Result | 251.19 |
| Discrepancy on Collapse Load | 1.6% |
| Discrepancy on Input Parameters | 0.8% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 20 kN/m2 (permanent) , symmetrical half space,
footing base rough.
SOIL PROPERTIES: c'=5 kN/m2, phi' = 20 degrees, soil unit weight = 15 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 247.13
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/.
NOTES: 'Benchmark' partial factor set with factor of 1.008
(i.e. 5.3%) on c' and tan(phi)' is required to give benchmark solution. Corresponding
values of c' and phi' are 4.96 kN/m2 and 19.85 degrees respectively.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution.
Drained footing with surcharge (c'=5 kN/m2, phi'=30 degrees, gamma = 15 kN/m2), vertical load
| Benchmark | 711.5 |
| Result | 735.52 |
| Discrepancy on Collapse Load | 3.3% |
| Discrepancy on Input Parameters | 1.1% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 20 kN/m2 (permanent) , symmetrical half space,
footing base rough.
SOIL PROPERTIES: c'=5 kN/m2, phi' = 30 degrees, soil unit weight = 15 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 711.5
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/.
NOTES: 'Benchmark' partial factor set with factor of 1.011
(i.e. 1.1%) on c' and tan(phi)' is required to give benchmark solution. Corresponding
values of c' and phi' are 4.95 kN/m2 and 29.7 degrees respectively.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution.
Drained footing with surcharge (c'=5 kN/m2, phi'=40 degrees, gamma = 15 kN/m2), vertical load
| Benchmark | 2656.95 |
| Result | 2827.73 |
| Discrepancy on Collapse Load | 6.0% |
| Discrepancy on Input Parameters | 1.5% |
ANALYSIS TYPE: Drained.
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 20 kN/m2 (permanent) , symmetrical half space,
footing base rough.
SOIL PROPERTIES: c'=5 kN/m2, phi' = 40 degrees, soil unit weight = 15 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 2656.95
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/.
NOTES: 'Benchmark' partial factor set with factor of 1.015
(i.e. 1.5%) on c' and tan(phi)' is required to give benchmark solution. Corresponding
values of c' and phi' are 4.93 kN/m2 and 39.6 degrees respectively.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution.
Drained footings with water table
Drained footing (phi'=30 degrees, gamma = 19.62 kN/m2), vertical load
| Benchmark | 144.74 |
| Result | 183.71 |
| Discrepancy on Collapse Load | 21.21% |
| Discrepancy on Input Parameters | 6.1% |
ANALYSIS TYPE: Drained.
WATER REGIME: Dry
KEY DIMENSIONS: Footing width 1m.
ADEQUACY FACTOR LOADING: Vertical load on footing (unit permanent load 1kN/m2).
BOUNDARY CONDITIONS: Surcharge = 0 kN/m2, symmetrical half space, footing base rough.
SOIL PROPERTIES: c'=0 kN/m2, phi' = 30 degrees, soil unit weight = 19.62 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 144.74
REFERENCE: Smith, C.C. (2005) Complete limiting stress solutions for the bearing
capacity of strip footings on a Mohr-Coulomb soil. Geotechnique, 55 (8), October,
pp 607-612.
NOTES: Error on load = 26.9%. 'Benchmark' partial factor set with factor of 1.061
(i.e. 6.1%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 28.5 degrees.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution. The Terzaghi bearing capacity formula using the EC7
recommended formula for N_gamma = 2*(Nq-1)*tan(phi) gives a solution of 197.2, an
error of 36.2%.
Drained footing, submerged (phi'=30 degrees, gamma = 19.62 kN/m2), vertical load
| Benchmark | 72.37 |
| Result | 91.85 |
| Discrepancy on Collapse Load | 21.21% |
| Discrepancy on Input Parameters | 6.1% |
ANALYSIS TYPE: Drained.
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: Surcharge = 0 kN/m2, symmetrical half space, footing base rough.
SOIL PROPERTIES: c'=0 kN/m2, phi' = 30 degrees, soil unit weight = 19.62 kN/m3.
PARTIAL FACTOR SET: Unity.
BENCHMARK SOLUTION: 72.37
REFERENCE: Smith, C.C. (2005) Complete limiting stress solutions for the bearing
capacity of strip footings on a Mohr-Coulomb soil. Geotechnique, 55 (8), October,
pp 607-612.
NOTES: Error on load = 26.9%. 'Benchmark' partial factor set with factor of 1.061
(i.e. 6.1%) on tan(phi)' is required to give benchmark solution. Corresponding value
of phi' is 28.5 degrees.
COMMENT: Result obtained using medium nodal density. This type of bearing capacity
problem involves a complex network of sliplines and requires a finer nodal spacing
to achieve a good solution. The Terzaghi bearing capacity formula using the EC7
recommended formula for N_gamma = 2*(Nq-1)*tan(phi) gives a solution of 98.6, an
error of 36.2%. This result is half that of the equivalent dry case. NB The unit
weight of the footing was set to 9.81 kN/m3 in order that it had no effective weight.