LimitState recently secured a contract to supply Network Rail with their groundbreaking geotechnical software, LimitState:GEO, which uses new technology to rapidly evaluate the safety of geotechnical constructions such as slopes, retaining walls and foundations.

Network Rail has purchased a multi-user network license which means the LimitState software can potentially be used by engineers in company offices nationwide. LimitState will also provide Network Rail with training in using the software in conjunction with new European design standards, the Eurocodes, which became mandatory on 1 April. The introduction of the Eurocode for geotechnical design marks a paradigm shift in the way geotechnical constructions will be designed. More...

Did you know that there are several ways of quickly selecting multiple objects of a similar type in both LimitState:RING and LimitState:GEO?

Basic - Use CTRL and Select

By holding down CTRL whilst clicking, you can select multiple objects - if these are of the same type then their properties will be displayed in the Property Editor for you to edit. This is useful if you have a small number of similar objects to select and modify.

Advanced - Use Rectangle Select and the Property Editor

In both LimitState:RING and LimitState:GEO, you can select a large block of objects by choosing the 'Rectangle Select' tool and drawing a rectangle around the objects of interest. This method is useful if you have a large number of objects to modify and / or want to ensure that you have not excluded one by mistake.

•  Dragging from left to right gives a red rectangle, which selects all objects that are completely enclosed within it.
•  Dragging from right to left gives a green rectangle, which selects all objects that it touches or encloses.

Once the objects are selected, you can filter out specific types using the drop-down menu at the top of the Property Editor and then modify the common properties of  these en masse (see Figure).

Alternatively, both LimitState:RING and LimitState:GEO also allow you to filter the objects before you select them:

•  In LimitState:RING you can select only contact surfaces by clicking Select > Contact surfaces Only.
•  In LimitState:GEO, you have even more control. Clicking Select > Filter... brings up the Filter dialog. Here you can choose to select one or more types from Vertices, Boundaries, Solids, The Water Pressure Table or Slip-lines (Select All is the default).

In both cases, to avoid later confusion, you should remember to set the selection filter back to normal before continuing to work with your model.

Download this application note as a pdf

Introduction

This Application Note outlines the principles applied when performing a slope stability analysis using LimitState:GEO.

In a conventional slope stability analysis (e.g. using the method of slices) a pre-determined slip surface is assumed and the stability of the failing soil mass is evaluated by comparing resisting and disturbing forces/moments. Usually many trial slip surfaces are investigated and the most critical one identified. This typically requires specification of a search zone and entry and exit points, and can be very sensitive to the shape of slip surfaces used (e.g. circular or non-circular).In contrast the general purpose limit analysis procedure used by LimitState:GEO does not require the form of the collapse mechanism to be pre-specified. However, the use of a general purpose procedure does mean that an particular approach must be adopted to identify the critical failure mechanism.

Slope Stability Limit Analysis

In LimitState:GEO, it is necessary to drive the problem to collapse by applying a multiplier (or Adequacy factor) to an unfavourable load.

In a foundation problem this is conceptually straightforward: the load on the foundation is increased until the underlying soil fails, indicating that the ultimate limit state has been reached.

Similarly, in a slope stability problem the self weight of the soil forming the slope could be increased until collapse occurs. However, a simple example will help show that this is not necessarily the best approach, particularly for problems involving purely frictional soils. Thus see Figure 1, which shows a brick placed on a plank of wood. For a given angle of inclination of the plank, the brick will either be stable or unstable. However, factoring up the weight of the brick will not affect its stability, i.e. applying the Adequacy factor to the self weight of the brick will not drive the problem to failure (and will typically return a solution of *unstable* or *locked* in LimitState:GEO).

Alternatively, consider a laboratory model of a slope stability problem with the model contained within a tank, such that the tank may be pivoted about one end as depicted in Figure 2. In order to establish how close to the point of stability the slope is, the tank could be slowly tilted from the horizontal to a steeper and steeper angle α_crit until failure occurs. The larger this angle the more stable the slope.

Typically a factor of safety is required in terms of a factor (F) on soil strength such that the slope collapses with soil properties c'/F and tan φ'/F. The problem then becomes one of finding F such that α_crit = 0¹. 

Alternatively, from a Eurocode 7 perspective (Design Approach 1, Combination 2, and Design Approach 3), a specified factor is applied to the soil strength and stability evaluated. In this context a value of α_crit ≥ 0 indicates stability. As will be seen, either of these principles can be applied when using LimitState:GEO. 

Application in LimitState:GEO

Tilting the tank is analogous to modifying the body forces exerted by any mass of soil or structure. Within the frame of reference of the tank, the vertical body force becomes mg cosα and a horizontal body force is introduced mg sinα, as shown in Figure 2b, where m is the mass of the body and g the acceleration due to gravity.

In LimitState:GEO, horizontal body forces can be introduced using the Seismic Actions facility in the Property Editor. By setting the Horizontal Accel. k_h (g) to 1.0, Adequacy (on k_h) to True (and ensuring Adequacy is not set on any other parameter), this requires the software to find the horizontal acceleration required to cause collapse. This will be returned as the Adequacy Factor (AF).

This can be converted to an equivalent value of α_crit using the expression α_crit = tan⁻¹(AF). Thus the problem is stable if AF ≥ 0.0.

It is important to note that:

1. Whereas in normal usage stability corresponds to AF ≥ 1.0 (e.g. for a foundation stability problem), in this special case a value of AF ≥ 0.0 is required.
2. The significance of the order of magnitude of AF will differ from conventional usage. For example, a 24.8^o slope of soil of friction angle 30^o is just stable with a factor of safety of 1.25 on soil strength. This corresponds to a value of α_crit = 5.2^o (or AF = 0.091). It is thus recommended to conceptually interpret the Adequacy factor as an angle α_crit = tan⁻¹(AF).

A worked example of a slope stability problem using LimitState:GEO may be found in Application Note LS-AN2.