# LimitState:GEO?

**LimitState: GEO Analysis**For most geotechnical structures, sound design requires a sufficient margin of safety against failure. To achieve this goal, the most likely potential failure mechanism must be identified. Stability analyses can then quantify the corresponding safety margin to ensure that the structure is safe and economical.

Limit equilibrium (LE) analysis has been used for decades to find the critical failure surface and its associated factor of safety. In this approach, one assumes the failure geometry which defines a potential sliding mass and then solves the global equilibrium equations to determine the safety factor associated with that particular surface. The process is repeated until the critical results are obtained. While the process has an extensive record of success, it becomes difficult when dealing complex geotechnical structures. Two fundamental problems exist with LE analysis. The first potential problem is locating the critical surface. The geometry of this surface is usually assumed (plane, circle, log spiral) and for simple, homogenous problems, such an assumption is practically accurate. For complex problems ‘intuition’ is needed or involved search processes for general shaped slip surfaces (dynamic programming) need to be utilized. The second potential problem has to do with its statics. The general LE problem is statically indeterminate requiring assumptions which are usually related to internal forces. Often, what appears to be critical surface actually reflects an inadmissible statics (interslice forces acting outside the sliding mass, negative normal stress over the slip surface). Consequently, often ‘judgment’ is required to determine the admissibility of critical results.

The alternative to LE, which has gained momentum in recent years is finite element (FE) analysis. To check the margin of safety, variations of the Strength Reduction Method (SRM) method, originally proposed by Zienkiewicz, have been implemented in some codes. The soils’ strength is being reduced successively until the analysis diverges. Divergence is an awkward criterion for solving simultaneous differential equations. However, for simple problems the results from Finite Element analysis are similar to LE analysis but without assuming the failure mechanism. Reports in the literature show that for complex (and not so complex) problems, the non-converging solution may be highly sensitive to many aspects, including mesh representation of the continuum. FE analysis requires much more attention to detail than LE and produces a multitude of information that is not directly relevant to failure. This information is usually ignored although it may imply whether the intermediate results produced in the progressive computational process are reasonable (what if they are not reasonable, e.g., negative normal stresses within the continuum?).

For different reasons, both LE and FE may not be ideal design tools for assessing failure potential of complex geotechnical structures. Conversely, Limit Analysis (LA) is a tailor-made analysis for assessing complex failures, generating optimal failure mechanisms utilizing rigorous plasticity theory (upper bound theorem). Its mechanics consider energy and work done along failure surfaces over which the failure criterion is satisfied, rendering a system that is in global equilibrium. The required input data is not more than that needed for LE and its output is focused on the objective of the analysis, i.e., find the critical results. While stating the objective sounds simple, the numerical process of solving the governing equations can be exhaustive. LimitState:GEO is an extremely efficient tool, built on new technology applicable to numerous geotechnical problems. It provides a consistent and complete stability analysis solution. Please navigate through the dropdown menu to further realize how LimitState:GEO could benefit you.

**One product, many applications**

LimitState:GEO makes use of modern computing power to identify failure mechanisms in seconds, including those that cannot be identified using conventional ultimate limit state analysis software, and which might take a lifetime to identify manually. To achieve this, the powerful and efficient numerical analysis procedure ‘Discontinuity Layout Optimization’ (DLO) is used to provide an automatic means of identifying very accurate limit analysis solutions. LimitState:GEO can handle problems with any geometry or loading condition, which means that the engineer no longer needs to resort to application-specific ‘hand-type’ calculations, or the plethora of in-house spreadsheets and/or software applications that attempt to automate these. However, unlike other general analysis methods (e.g. non-linear finite element analysis), problems can be set up quickly and solutions can easily be checked by hand using the free-body diagrams output in the report.