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Analysis

Overview

To perform an analysis, on the Analysis menu click Solve. Alternatively this command can be accessed via the button on the toolbar; the keyboard shortcut for the command is F5.

The analysis procedure first allocates nodes to all zones and generates a list of potential slip-lines.

An initial analysis is then undertaken and the solver iterates towards the optimal solution by progressively adding slip-lines at critical positions (see Theory). Stages in the solution are displayed on the Status bar.

By default, the output displayed in the Output pane from an analysis is restricted to the critical load case and failure adequacy factor only. To enable the display of all iteration data, go to the Preferences dialog in the Tools menu,select the Solve tab and check the option to Display iteration information in output window.

The Solver

A solver is required to find the critical collapse load factor and associated collapse mechanism. The internal forces in the structure must satisfy all specified yield constraints; these are set up for a particular problem by LimitState:GEO.

The solver used by LimitState:GEO is Mosek, a powerful interior point linear programming solver. In LimitState:GEO, Mosek is called as a subroutine and, to maximize efficiency, the problem data is passed via memory.

Prior to solving, LimitState:GEO runs a number of pre-solve checks. These are:

Analysis Settings

Overview

The project Property Editor parameters (as shown above) provide key control over the type and accuracy of the solution to be obtained.

Nodal Density

The nodal density controls the resolution and accuracy of the solution obtained (see Nodal Density).

Water Table

This setting controls whether the water table is enabled or disabled during the analysis (see Enabling the Water Table).

Long Term Analysis

This setting controls whether the problem solves as either a long term (typically drained) or short term (typically undrained) problem as described in Analysis Modes. If multiple scenarios (see Multiple Scenarios) are defined with differing individual long term/short term settings, then this parameter will display ‘Varies’. Changing this setting to ‘True’ or ‘False’ will change the long term/short term setting for all the scenarios.

Model Rotations

This setting controls whether the analysis is carried out as a translational analysis or with rotations permitted at Solid edges (see Solution Type).

Seismic Actions

This setting controls whether pseudo static horizontal and or vertical accelerations are applied to the problem (see Setting seismic parameters). One or both accelerations may have an Adequacy factor applied to them .

Setting and Previewing the Nodes

Solution accuracy is determined by the number of nodes utilised in the solution as described in Section .. The number of nodes to be used may be set using the Nodal Density setting in the the Project level parameters accessible in the Property Editor. The settings are Coarse, Medium, and Fine. It is recommended that initial scoping calculations are carried out in Coarse mode which typically generates solutions within a few seconds. For determination of the solution for final accuracy, the setting should be changed to Fine.

At any time, it is possible to view the arrangement of nodes prior to solve to check that these are as required. To do this click on the Preview Nodes button . This function may also be accessed via the Preview Nodes menu item on the Analysis menu. It is necessary to click Unlock afterwards to edit the problem parameters.

For advanced use, the Nodal Density may be set to Custom . The user has two options on how to control the Nodal density:

Target Number

Set this to the total number of nodes that the software will attempt to use when solving the problem. The software will normally be able to meet this target within a few percent. Altering this value will cause the Scale Factor on the Baseline Nodal Spacing to change, thus altering the Actual Nodal Spacing:

Actual Nodal Spacing = Baseline Nodal Spacing / Scale Factor

Note: The Actual Nodal Spacing is calculated by the software to determine the spacing required to achieve the Target Number of nodes and cannot be directly modified by the user. Modifying the Target Number will automatically cause the Scale Factor to change.

Scale Factor

A global factor used to scale the Baseline Nodal Spacing to achieve (or alter) the Target Number of nodes.

Actual Nodal Spacing = Baseline Nodal Spacing / Scale Factor

i.e. doubling the Scale Factor causes the number of nodes used along boundaries to double and the number of nodes used in solids to quadruple.

Note: Modifying the Scale Factor will automatically cause the Target Number to change.

Setting the Baseline Nodal Spacing is described in Setting Nodal Distribution.

Setting Nodal Distribution within Geometry Objects

The baseline nodal spacing within Geometry objects may be set by selecting the required object and modifying the following parameter(s) in the Property Editor:

Boundary object

Nodal spacing: this is the baseline spacing along the Boundary object.

Solid object

Linear nodal spacing: Click the to view the x-spacing and y-spacing. These specify the baseline spacing on a rectangular grid within the solid object. The software will position the grid within the solid appropriately.

If it is expected that failure will not occur in certain geometry objects (e.g. concrete elements) then setting a large nodal spacing in these objects will ensure computational resources are not wasted.

Analysis Results

Collapse Load Factor Found

Following an analysis the critical collapse load factor or ‘adequacy factor’ will be displayed in the Output pane. This is the factor that when applied to all ‘live’ loads (i.e. loads that have had Adequacy applied to them) causes collapse. This load factor may also be called a margin of safety.

When assessing a design using a design code analysis with partial factors applied to loads, a value of this factor of greater than or equal to 1.0 indicates that the design is safe. A value less than 1.0 indicates that it is unsafe.

No Solution Found

‘Locked’ result It is possible that the applied load can be increased without limit. In this case the problem can be described as being geometrically ‘locked’. This result will occur if a highly constrained body of soil is modelled with a large angle of shearing resistance. The result can also occur in a slope problem involving a frictional material when the adequacy factor is applied to the self weight; here it will often be found that the self weight can be increased without affecting stability. (As an analogy consider a book resting on a slightly sloping table; if the book is initially in stable equilibrium then simply making the book progressively heavier will never lead to the book sliding off the table.) Further discussion of these issues may be found in the Section Insoluble Problems.

‘Unstable’ result

It is possible that no solution can be found because material in the problem is ‘unstable’ under its own self weight and/or other applied forces. i.e. no viable equilibrium state can be identified. This result will typically occur if a body of soil is loaded, but has no viable means of resisting the load. For example, the ‘unstable’ result will occur in a slope problem involving a frictional material when the slope angle is greater than the angle of friction of the soil. (As an analogy consider a book resting on a steeply sloping table; if the book is not initially in stable equilibrium then increasing or reducing the weight of the book will not affect this, and the book will slide off the table.) Further discussion of these issues may be found in the Section Insoluble Problems.

‘Terminated’ result If the user aborts the analysis (see below for details on how to do this) then a ‘terminated’ status message will be reported. Note also that the software will internally abort an analysis if the number of iterations required is excessive (though this should very rarely happen).

‘Unknown’ result

The Mosek solver used by the software is very robust but will occasionally encounter numerical difficulties, leading to failure to find a solution of definite status (i.e. will fail to find a value for the ‘adequacy factor’ or the ‘locked’, ‘unstable’ or ‘terminated’ results). If this occurs then an ‘unknown’ status message will be reported. To overcome this it is worth trying to solve the problem again, initially in completely unchanged form, and subsequently after very minor changes have been made to one or more of the following: nodal density, material properties, loading regime. If the problem persists please contact LimitState support.

Aborting an Analysis

After the Mosek solver is started, LimitState:GEO then waits for a solution to be found. To abort this process, the user should click on the red stop button on the toolbar or press the Esc key to abort the analysis and return control to the user.

Lock and Unlock

After a solution is found, the slip-line mechanism is displayed in the viewer window, and the solution is ‘locked’. A ‘locked’ solution prevents any modification to the problem geometry or properties, but allows access to the properties of individual slip-lines, pressure distributions on individual blocks and animation of the mechanism. It is possible to animate the mechanism (see Animations), click on individual slip-lines to determine normal and shear forces or stresses on the line (see Slip-lines), and display pressure diagrams for individual blocks (see Pressure distributions).

To unlock the problem to allow editing of the problem parameters, click the unlock button or select Unlock on the Analysis menu.