LimitState:GEO - Validation
LimitState:GEO verification results
This web page details the list of tests carried out using LimitState:GEO to verify its accuracy against known limit analysis solutions. These tests are run every time the software code is updated.
Except where indicated, all analyses are performed using the default coarse nodal density. Known exact benchmarks are used where available. Where unavailable, the mean of the best available upper and lower bounds are used. In these cases, the benchmark is not necessarily the exact solution and could in fact be higher than the LimitState:GEO result.
Results are presented in terms of deviation from benchmark collapse load and also in terms of change in input parameters required for the LimitState:GEO solution to match the benchmark solution. This latter approach matches a design approach that considers uncertainty in material parameters. It is particulary relevant where the collapse load is a highly non-linear function of the soil strength. For example a change of φ' by 5% can result in a change of footing bearing capacity by over 25% for certain simple footing problems on cohesionless soil.
In general, even when using the coarse nodal density, accuracy in most of the below tests varies from exact to ~5% in terms of the input parameters. Increased accuracy is straightforwardly achieved by increasing the nodal density.
An animated image and further details of each test including the source of the benchmark can be obtained by clicking on the relevant hyperlink. The input file used to generate the test result may also be downloaded.
Simulations ran on
07 September 2009, build
2.0.c.10784
Undrained footings
Undrained footings (vertical loads)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained footing (weightless soil), vertical load | 5.14 | 5.2 | 1.16 | 1.16 | download | |
| Undrained footing with surcharge (weightless soil), vertical load | 6.14 | 6.2 | 0.97 | 1.2 | download | |
| Undrained footing, vertical load | 5.14 | 5.2 | 1.16 | 1.16 | download | |
| Undrained footing with surcharge, vertical load | 6.14 | 6.2 | 0.97 | 1.2 | download | |
| Undrained footing, flooded, vertical load | 9.07 | 9.13 | 0.66 | 1.2 | download |
Undrained footings (linear variation of cohesion with depth)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained footing, vertical load, weightless soil, smooth base, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m | 5.98 | 6.09 | 1.85 | 1.85 | download | |
| Undrained footing, vertical load, smooth base, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m | 5.98 | 6.09 | 1.85 | 1.85 | download | |
| Undrained footing, vertical load, weightless soil, full base adhesion, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m | 6.61 | 6.74 | 1.94 | 1.94 | download | |
| Undrained footing, vertical load, full base adhesion, c_u=1kN/m2 at surface, gradient = 1.0 kN/m2/m | 6.61 | 6.74 | 1.94 | 1.94 | download | |
| Undrained footing, vertical load, weightless soil, full base adhesion, c_u=1kN/m2 at surface, gradient = 2.0 kN/m2/m | 7.6 | 7.82 | 2.83 | 2.83 | download | |
| Undrained footing, vertical load, full base adhesion, c_u=1kN/m2 at surface, gradient = 2.0 kN/m2/m | 7.6 | 7.82 | 2.83 | 2.83 | download |
Undrained footings (layered soils)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained footing, vertical load, weightless soil, smooth base, upper layer c_u=1kN/m2, lower layer c_u=2 kN/m2 | 5.09 | 5.17 | 1.59 | 1.59 | download | |
| Undrained footing, vertical load, weightless soil, smooth base, upper layer c_u=1kN/m2, lower layer c_u=0.667 kN/m2 | 4.28 | 4.37 | 2.11 | 2.11 | download | |
| Undrained footing, vertical load, weightless soil, smooth base, upper layer c_u=1kN/m2, lower layer c_u=0.4 kN/m2 | 3.3 | 3.47 | 4.78 | 4.78 | download | |
| Undrained footing, vertical load, weightless soil, rough base, upper layer c_u=1kN/m2, lower layer c_u=2 kN/m2 | 6.22 | 6.31 | 1.38 | 1.38 | download | |
| Undrained footing, vertical load, weightless soil, rough base, upper layer c_u=1kN/m2, lower layer c_u=0.667 kN/m2 | 3.87 | 3.96 | 2.28 | 2.28 | download | |
| Undrained footing, vertical load, weightless soil, rough base, upper layer c_u=1kN/m2, lower layer c_u=0.4 kN/m2 | 2.73 | 2.85 | 4.2 | 4.2 | download |
Undrained footings (inclined loads
Undrained buried footings (lateral loads)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained buried footing, lateral load | 1000 | 1000.26 | 0.03 | 0.03 | download | |
| Undrained buried footing, lateral load, tension cutoff | 620 | 620.13 | 0.02 | 0.02 | download |
Drained footings
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained footing with surcharge (weightless soil, phi'=20 degrees), vertical load | 6.4 | 6.52 | 1.84 | 1 | download | |
| Drained footing with surcharge (weightless soil, phi'=30 degrees), vertical load | 18.4 | 18.99 | 3.12 | 1.3 | download | |
| Drained footing with surcharge (weightless soil, phi'=40 degrees), vertical load | 64.2 | 67.75 | 5.25 | 1.5 | download |
Drained footings
Drained footings with water table
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained footing (phi'=30 degrees, gamma = 19.62 kN/m2), vertical load | 144.74 | 183.71 | 21.21 | 6.1 | download | |
| Drained footing, submerged (phi'=30 degrees, gamma = 19.62 kN/m2), vertical load | 72.37 | 91.85 | 21.21 | 6.1 | download |
Retaining walls (active pressures)
Undrained analyses
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained active smooth retaining wall | 1.5 | 1.5 | 0 | 0 | download | |
| Undrained active retaining wall, full adhesion | 2.07 | 2.1 | 1.16 | 1.16 | download | |
| Undrained active smooth retaining wall (adequacy on self weight) | 4 | 4 | 0 | 0 | download | |
| Undrained active smooth retaining wall, flooded (adequacy on self weight) | 1 | 1 | 0 | 0 | download | |
| Undrained active retaining wall, full adhesion (adequacy on self weight) | 5.14 | 5.19 | 0.93 | 0.93 | download |
Linear variation of cohesion with depth
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained active smooth retaining wall (weightless soil) | 3 | 3 | 0 | 0 | download | |
| Undrained active smooth retaining wall | 2.5 | 2.5 | 0 | 0 | download | |
| Undrained active smooth retaining wall (adequacy on self weight) | 6 | 6 | 0 | 0 | download |
Drained analyses
Retaining walls (passive pressures)
Undrained analyses
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained passive smooth retaining wall (weightless soil) | 2 | 2 | 0 | 0 | download | |
| Undrained passive retaining wall, adhesion=0.5c_u (weightless soil) | 2.39 | 2.4 | 0.38 | 0.38 | download | |
| Undrained passive retaining wall, full adhesion (weightless soil) | 2.57 | 2.6 | 0.93 | 0.93 | download | |
| Undrained passive smooth retaining wall | 2.5 | 2.5 | 0 | 0 | download | |
| Undrained passive retaining wall, full adhesion | 3.07 | 3.1 | 0.78 | 0.78 | download |
Linear variation of cohesion with depth
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained passive smooth retaining wall (weightless soil) | 3 | 3 | 0 | 0 | download | |
| Undrained passive smooth retaining wall | 3.5 | 3.5 | 0 | 0 | download |
Drained analyses
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained passive smooth retaining wall (phi' = 30 degrees) | 1.5 | 1.5 | 0 | 0 | download | |
| Drained passive smooth retaining wall (phi' = 40 degrees) | 2.3 | 2.3 | 0.02 | 0 | download | |
| Drained passive smooth retaining wall (phi' = 50 degrees) | 3.77 | 3.77 | 0 | 0 | download |
Drained analyses with water pressures
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained passive smooth retaining wall (phi' = 30 degrees) | 29.43 | 29.43 | 0 | 0 | download | |
| Drained passive smooth retaining wall (phi' = 30 degrees), wall submerged | 14.72 | 14.72 | 0 | 0 | download | |
| Drained passive smooth retaining wall (phi' = 30 degrees), wall half submerged | 25.75 | 25.77 | 0.06 | 0 | download |
Slope stability
Undrained slope stability
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained slope stability, 30 degree slope, failure through toe | 6.51 | 6.72 | 3.18 | 3.18 | download | |
| Undrained slope stability, 45 degree slope, failure through toe | 5.86 | 6.08 | 3.54 | 3.54 | download | |
| Undrained slope stability, 60 degree slope, rigid below level of toe | 5.25 | 5.35 | 1.96 | 1.96 | download | |
| Undrained slope stability, 70 degree slope, rigid below level of toe | 4.8 | 4.85 | 1.1 | 1.1 | download | |
| Undrained slope stability, 80 degree slope, rigid below level of toe | 4.33 | 4.34 | 0.33 | 0.33 | download | |
| Undrained slope stability, 90 degree slope, rigid below level of toe | 3.79 | 3.83 | 1.15 | 1.15 | download |
Drained slope stability (dry slopes)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained 0.5:1.0 slope, phi'=20 degrees, c'/gamma H = 0.15 | 1 | 1.06 | 5.84 | 4.1 | download | |
| Drained 0.5:1.0 slope, phi'=30 degrees, c'/gamma H = 0.15 | 1 | 1.05 | 4.84 | 2.9 | download | |
| Drained 0.5:1.0 slope, phi'=40 degrees, c'/gamma H = 0.15 | 1 | 1.02 | 1.99 | 1.1 | download | |
| Drained 1.0:1.0 slope, phi'=20 degrees, c'/gamma H = 0.15 | 1 | 1.09 | 8.31 | 5.3 | download | |
| Drained 1.0:1.0 slope, phi'=30 degrees, c'/gamma H = 0.15 | 1 | 1.11 | 9.77 | 5.8 | download | |
| Drained 1.0:1.0 slope, phi'=40 degrees, c'/gamma H = 0.15 | 1 | 1.1 | 9.38 | 4.9 | download |
Drained slope stability (with ru coefficient)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained 0.5:1.0 slope, phi'=20 degrees, c'/gamma H = 0.15, ru=0.25 | 1 | 1.07 | 6.73 | 5.6 | download | |
| Drained 0.5:1.0 slope, phi'=30 degrees, c'/gamma H = 0.15, ru=0.25 | 1 | 1.06 | 5.22 | 3.9 | download | |
| Drained 0.5:1.0 slope, phi'=40 degrees, c'/gamma H = 0.15, ru=0.25 | 1 | 1.04 | 3.46 | 2.6 | download |
Anchors
Anchors, no flow around mechanism (drained)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained anchor, D/B = 2, phi'=20 degrees, vertical load | 3.46 | 3.46 | 0.01 | 0 | download | |
| Drained anchor, D/B = 5, phi'=20 degrees, vertical load | 14.1 | 14.1 | 0.02 | 0 | download | |
| Drained anchor, D/B = 2, phi'=30 degrees, vertical load | 4.31 | 4.31 | 0.02 | 0 | download | |
| Drained anchor, D/B = 5, phi'=30 degrees, vertical load | 19.43 | 19.44 | 0.02 | 0 | download |
Anchors, no flow around mechanism (undrained)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained anchor (weightless soil), D/B = 2, vertical load | 3.69 | 3.74 | 1.41 | 1.41 | download | |
| Undrained anchor (weightless soil), D/B = 3, vertical load | 4.77 | 4.84 | 1.45 | 1.45 | download | |
| Undrained anchor (weightless soil), D/B = 4, vertical load | 5.53 | 5.6 | 1.29 | 1.29 | download | |
| Undrained anchor (weightless soil), D/B = 5, vertical load | 6.12 | 6.2 | 1.36 | 1.36 | download | |
| Undrained anchor (weightless soil), D/B = 10, vertical load | 7.97 | 8.1 | 1.57 | 1.57 | download | |
| Undrained anchor, D/B = 2, vertical load | 5.69 | 5.74 | 0.92 | 0.92 | download | |
| Undrained anchor, D/B = 3, vertical load | 7.77 | 7.84 | 0.9 | 0.9 | download | |
| Undrained anchor, D/B = 4, vertical load | 9.53 | 9.6 | 0.75 | 0.75 | download | |
| Undrained anchor, D/B = 5, vertical load | 11.12 | 11.2 | 0.75 | 0.75 | download | |
| Undrained anchor, D/B = 10, vertical load | 17.97 | 18.1 | 0.7 | 0.7 | download |
Rotational problems
Masonry arches
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Simple arch | 33.03 | 33.07 | 0.11 | 0.11 | download | |
| Simple arch with low friction joints | 20.46 | 20.46 | 0.02 | 0.02 | download |
Trapdoors (drained)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Drained trapdoor, D/B = 0.5, phi'=30 degrees, vertical load | 0.54 | 0.14 | 73.78 | 0 | download | |
| Drained trapdoor, D/B = 1, phi'=30 degrees, vertical load | 0.54 | 0.55 | 0.97 | 0 | download | |
| Drained trapdoor, D/B = 2, phi'=30 degrees, vertical load | 1.52 | 1.53 | 0.41 | 0 | download | |
| Drained trapdoor, D/B = 3, phi'=30 degrees, vertical load | 2.49 | 2.52 | 1.27 | 0 | download | |
| Drained trapdoor, D/B = 5, phi'=30 degrees, vertical load | 4.4 | 4.53 | 2.85 | 0 | download | |
| Drained trapdoor, D/B = 0.5, phi'=40 degrees, vertical load | 0.21 | 0.21 | 2.03 | 0 | download | |
| Drained trapdoor, D/B = 3, phi'=40 degrees, vertical load | 2.66 | 2.69 | 1.38 | 0 | download | |
| Drained trapdoor, D/B = 5, phi'=40 degrees, vertical load | 4.63 | 4.69 | 1.49 | 0 | download |
Soil nails (undrained wall)
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Undrained active smooth retaining wall, soil reinforcement, T = 0.0 kN/m/m, N = 0.0 kN/m/m (adequacy on self weight) | 4 | 4 | 0.09 | 0.09 | download | |
| Undrained active smooth retaining wall, soil reinforcement, T = 0.1 kN/m/m, N = 0.0 kN/m/m (adequacy on self weight) | 4.05 | 4.05 | 0.09 | 0.09 | download | |
| Undrained active smooth retaining wall, soil reinforcement, T = 0.1 kN/m/m, N = 1.0 kN/m/m (adequacy on self weight) | 5.05 | 5.05 | 0.07 | 0.07 | download |
Beams
| Simulation | Benchmark | LimitState:GEO Result | % Discrepancy on Collapse Load | % Discrepancy on Input Parameters | Download File | Comments |
| Loaded Beam with Fixed Boundary Supports | 16 | 16 | 0 | 0 | download | |
| Loaded Beam with Simple Supports | 8 | 8 | 0 | 0 | download |
