# Feature Focus

July 5, 2010

#### Background

The benefits associated with performing 3D slope stability analyses were expounded by Dr. Del Fredlund in the 1970s. Over the years a number of 3D methods of analysis have been researched. These methods have ranged from the method of columns to approaches based on variational calculus, and more recently, the use of dynamic programming. The interest in 3D slope stability analysis is largely based on the fact that the majority of slope stability failures are inherently three-dimensional in character. That is, the failure surface most often represents a variation on a dish-shaped surface. Therefore, any 2D representation is a significant simplification of the actual situation. It is quite surprising that geotechnical engineers have been as successful as they have been in using two-dimensional simplifications of three-dimensional geometries.

Industry has largely embraced a two-dimensional approach with respect to slope stability analysis as an accepted method of practice and acceptable design factors of safety generally range between 1.3 and 1.5. The calibration to well-instrumented failures has typically involved performing 2D back-analyzing of failed slopes and accepting the results as a “reasonable calibration”, even though the slope failed in a 3D manner.

#### The Problem

There is a fundamental difference between calculations of failed slopes performed using a 2D analysis as opposed to a 3D analysis. The difference in the 2D and 3D analysis is closely related to the geometry of the failed surface. A homogeneous slope with the same slip surface will result in a difference in the computed factor of safety depending upon whether a 2D analysis or a 3D analysis is performed.

The difference between a 2D and a 3D slope stability analysis depends upon the geometry, the number of soil layers, as well as the material properties involved. How much difference can there be between a 2D and 3D analysis? Differences in the range of 15% up to 50% have been documented in research literature. Gitirana (2007) documented differences encountered between various convex and concave slope configurations and are reproduced in the following figures. The results showed differences of up to 30% between a 2D and 3D analysis for classic benchmarks.

The potential, significant differences between a 2D and 3D analysis make it important to give consideration to performing 3D analysis on a more routine basis in industry. The following reasons are speculated as to why so few 3D analyses have been performed in geotechnical engineering practice:

• Lack of easy-to-use software tools: There have previously been few software tools available to for analyzing slopes of a 3D configuration.
• Lack of understanding: The geotechnical consulting community may have been unaware of the differences that can occur between a 2D and a 3D analysis. It may also not have been clear as to when the differences between a 2D and 3D analysis was significant.
• Current methodologies are good enough: There may have been a perception that existing 2D methods of analysis are good enough and that the factors of safety are conservative. This line of reasoning can result in: i.) slope that are over-designed to the detriment of the client’s pocketbook and, ii.)situations where the 2D analysis does not represent the actual conditions in the slope.

#### A Solution

SVSlope® 3D allows 3D slope stability analyses to become mainstream by allowing the easy creation and analysis of natural and man-made slopes. The extensive CAD-based interface allows easy creation of 3D geometries through use of a number of different paradigms (including quick and simple extrusion) that greatly simplify the representation of 3D models. The models are analyzed using the method of columns and the analysis method is therefore simply an extension of existing 2D limit equilibrium methods.

SVSlope® can also perform 2D analysis which allows quick and easy comparisons to be made between 2D and 3D analyses. The difference between these analysis methods and the factor of safety result can therefore be quickly ascertained. Three-dimensional limit equilibrium analyses provide continuity between existing geotechnical engineering practices and more realistic representations of field situations. The comparisons are simple and easy to perform.

Why perform 3D analysis? A 3D analysis is inherently a closer representation of the real-world geometry than a 2D analysis. Once factors of safety have been computed for a slope, the results offers advantages in design. Consider the following scenarios:

Figure 2: 3D Slope
• Levee analysis: For levees, the earth used for construction is generally quite costly. Levees can extend over many miles. Most existing designs are based on a 2D analysis. The levee structures may be over-designed and result in increased costs to construct.
• Earth storage: Often it is necessary in the mining industry to store earth material in a particular area. Making the slopes steeper can result in reduced costs as more material can fit on a particular parcel of land. A 3D analysis allows the calculation of more realistic factors of safety and allows the opportunity to design storage facilities which optimize design.
• Tailings piles: The land requirement for the storage of tailings piles can be costly. An optimized design performed using a 3D analysis allows for the storage of more tailings per unit area.
• Heap leach analysis: Larger amounts of ore can be extracted on a heap leach pile with steep side slopes. However, the increased side slope steepness results in a condition closer to failure. A 3D analysis can be used to more closely represent the geometry of the heap leach pile. It is important to accurately balance the slope angle design and the ore recovery.

There are many other examples where the application of a 3D analysis is of added value. We would encourage you to download our software and try out the slope stability analysis for yourself. Our engineers are ready to assist you and help you through the creation of slope stability models.

#### References

The modeling project we worked on had a 3D component which could not be reasonably modeled with existing 2D software. The team at SoilVision Systems Ltd. was helpful in training regarding the use of the SVSlope 3D product. The software worked well for the project at hand and we look forward to its continued use.

Amer Awad, Ph.D., P.Eng., Senior Geotechnical Engineer

The comparison between 2D and 3D factors of safety in the performed analysis indicated that 2D may be adequate for computations with relatively simple geometries of both ground and slip surfaces. [However], the factors of safety related to complex 3D geometries and stratigraphies are difficult to compute on the basis of 2D analyses. In these latter cases, 3D estimates (through 3D modeling) are surely more reliable.

Eng. Michele Calvello, Professor, Universita' degli Studi di Salerno, Dip. di Ingegneria Civile (DICIV)

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