Accuracy in any numerical analysis code depends on two things: the theoretical model underpinning the analysis, and the accuracy of the numerical method itself. Uncertainties also run through the whole of a geotechnical design calculation, from site investigation data through to construction.

The theoretical model underpinning LimitState:GEO is the theory of plasticity, which has a long history of application in geotechnical design. The majority of textbook stability calculations are based on this theory, or on simplifications of it.

LimitState:GEO is regularly benchmarked against a known set of limit analysis solutions from the literature. These verification tests are published and give useful guidance on the accuracy that can be expected across a range of problem types.

Accuracy also depends on nodal resolution. The core analysis method finds the critical translational mechanism that causes collapse, which gives good results across a wide range of problem types. Where rotational failure mechanisms are likely to be critical — a wall rotating about a pivot, for example — LimitState:GEO provides the default capability to model rotations at the edges of pre-defined solid objects. This produces a more conservative prediction of the collapse load, but because rotations are not permitted within pre-defined solid objects, certain highly confined problems may still see the true collapse load overestimated significantly.

Description text The Adequacy Factor is closely comparable to a Factor of Safety, but what it factors depends on which mode LimitState:GEO is running in. There are two modes: Factor Load(s) and Factor Strength(s).

• Factor Load(s) mode. The Adequacy Factor may be applied to any load and/or to the self weight of any body of material. The Adequacy Factor returned when the solve completes is the factor by which all the specified loads and self weights must be multiplied to cause collapse. This is equivalent to a Factor of Safety on load.

• Factor Strength(s) mode. The Adequacy Factor may be applied to any combination of material strengths, and by default is applied to all Mohr-Coulomb materials. The Adequacy Factor returned when the solve completes is the factor by which all the specified material strengths must be divided to cause collapse. This is equivalent to a Factor of Safety on material strength.goes here

Description textSolution accuracy in LimitState:GEO is controlled by the nodal resolution. Changing the nodal resolution alters the number and range of potential slip-lines from which the solver selects the critical solution. Increasing the nodal resolution will increase the solution accuracy, other than in the rare case described below, where a small increase in node count causes the Adequacy Factor to rise. Nodal resolution is set in the Analysis settings. goes here

For certain classes of problem — some bearing capacity problems, for example — the plastic collapse load for a symmetrical failure mechanism is identical to that for an asymmetrical mechanism. LimitState:GEO will often generate the symmetrical mechanism, but any asymmetry in the initial model set-up can skew the result towards the asymmetrical case, while still producing the same collapse load. Where the problem geometry is itself symmetrical, the most likely cause is numerical tolerance. The same explanation applies where the slip-lines appear symmetrical but the animated failure mechanism does not.

This relates to how nodes are distributed in the model, and should generally only produce a small change in Adequacy Factor of a few percent. By default LimitState:GEO uses a fixed total number of nodes for the problem. If the geometry is altered — for example by deleting a body of soil that plays no part in the collapse mechanism — the nodes that would have been placed in that body are redistributed elsewhere. This usually increases the accuracy of the solution and causes a minor reduction in the Adequacy Factor. Nodes are also placed on boundaries and on the water table, so modifying either can have the same effect.

To avoid this behaviour, change the nodal settings from a constant overall number to fixed nodal spacing.

This normally only happens when a coarse nodal resolution is in use. With a small increase in the number of nodes, the available slip-line locations may shift to positions that are slightly less favourable for collapse, which raises the Adequacy Factor. A large increase in nodal resolution should produce the expected decrease.

Some problems — the bearing capacity problem in cohesionless soils, for example — are extremely sensitive to changes in the input parameters. A change of a few degrees in the angle of shearing resistance can double the capacity in certain circumstances, and results from LimitState:GEO are subject to the same sensitivity.

A more useful question is: what change in input soil strength parameters would be required to generate the result produced by LimitState:GEO? Viewed this way, discrepancies typically reduce to a few percent.

LimitState:GEO is designed to work in either metric or imperial units, and the selected units are displayed in the Wizards, the Property Editor and the Reports. If parameters are only known in other units, the built-in Calculator provides common conversions for all relevant units.

This is typically caused by one of two conditions:

• The problem is geometrically locked. Either there is nowhere for the soil to deform into, or the soil has a high angle of shearing resistance and no feasible mechanism can be found for the given number of nodes. Check that the boundary conditions are correctly specified, and increase the number of nodes. This can also arise when a modelled slope is shallower than the angle of shearing resistance of the soil, in which case no factor on self weight will cause collapse.

• There is no fixed boundary anchoring the soil. Without one, any applied load simply causes the whole soil mass to fly off into space. Check that at least one fixed boundary exists. In certain circumstances a symmetry boundary condition can fulfil this role, since it acts as a fixed but perfectly smooth boundary. This can also arise when a modelled slope is steeper than the angle of shearing resistance of the soil, in which case no factor on self weight can prevent collapse.

This can occur in rare situations where a water table is present and the Adequacy Factor is applied to a body self weight in only part of the problem. Where the Adequacy Factor is applied to the self weight of a body, LimitState:GEO applies it to both the self weight and the water pressures within that body. If water pressures are factored in only one part of the problem, they will not be in equilibrium with the water pressures elsewhere unless the Adequacy Factor happens to equal 1.0. For this reason, applying the Adequacy Factor to the self weight of isolated bodies is not recommended.

LimitState:GEO provides a tension cutoff material type, which can be assigned to either Boundaries or Solids. Assigning a tension cutoff to a Boundary, beneath a footing, for example, permits breakaway of a cohesive soil from the footing. Assigning a tension cutoff to a Solid permits tension cracks to form within a body of soil, which is typically what is wanted in a slope stability analysis.

If a water table lies above a crack that forms, LimitState:GEO assumes the crack fills with water and applies water pressures to the sides of the crack. The crack will normally therefore be longer than in an equivalent case with no water present. The crack does not need to extend to the ground surface in order to fill with water.

Yes. To model a retaining wall failing by rotation about a single point, place the retaining wall on a rigid material and apply a no-tension cutoff material to the interface between the wall and the rigid base. Provided Allow rotations is set to Along edges, this set-up will normally produce a rotational failure mode.

Alternatively, if the wall is modelled using a Sheet Pile Wall element, an Engineered Joint can be used with its Fixity property set to Fixed Hinge.

LimitState:GEO works in general with 2D bodies, but a component that is essentially a 1D strut or rod transmitting load can be modelled in one of two ways:

• As a thin 2D Solid.

• As an Engineered Element, or one of its derived types such as a Soil Nail or Soil Reinforcement.