June 16, 2009
The unique ability of SVSlope to search for the most critical slip surface has application in the area of balefill slope stability analysis. In a balefill, the incoming waste stream is compacted into rectangular bales prior to landfilling. Balefills are operated separately from landfills, where the incoming waste is usually condensed in-situ by compactors. The study outlined in this article required the slope stability analysis of a proposed vertical extension to a balefill. Why use dynamic programming? Conventional geotechnical analysis methods are generally limited to well-defined failure modes, which may not occur in landfills due to the presence of unknown but preferential slip surfaces. Conventional models assume a stress distribution to solve an indeterminate problem. The application of dynamic programming with a stress-based analysis allowed the consultant to avoid drawbacks associated with conventional methods of slices.
The analyzed design may be seen above. Stability analyses of landfills are complex, as the stress-strain relationship of municipal solid waste has not been resolved due to uncertainties, scalability of lab results, and multiple failure mechanisms working in parallel.
In this particular analysis, the landfill was composed of a series of bales which made the analysis process somewhat complex. Due to the construction of the landfill, interfaces between materials were anticipated to represent preferential locations for slip surfaces.
Advanced landfilling techniques, such as baling, introduce additional complexities at bale interfaces and lifts. Moreover, conventional, well-defined failure surfaces may not develop within the waste mass due to the presence of preferential failure surfaces, defined by liner systems, lifts, and abandoned work faces. Therefore, it is essential to demonstrate the impact of waste strength parameters on the slope stability of balefills, taking into account concurrently the potentially irregular geometry of the failure surface as it will be further analyzed in the sequence.
Specifically, the analysis was performed in a two stage process: (i) calculation of stress distribution, and (ii) application of an optimization technique to identify the most probable failure surface. The stress analysis was performed using a finite element formulation and the location of the failure surface was located by Dynamic Programming optimization method. To further reduce uncertainties, a sensitivity analysis was performed, evaluating the effect of different waste strength ratios between the existing and piggy-backed, vertical expansion of the landfill.
Dynamic programming was selected for this analysis because of its ability to determine the most reasonable slip surface in an unrestrained way. Given the complex geometry of the situation the location of a potential slip surface was unknown.
In the analysis at hand, the resulting slip surfaces were categorized into four groups based on the location and shape of the slip surfaces. Some of the resulting slip shapes may be seen in the figures below. The critical slip surfaces were generally found to run parallel to the interfaces between waste bodies, thus resulting in a translational slip. The critical slip shape more closely resembles that of a non-circular failure.
If you are interested in this type of analysis the Dynamic Programming method is implemented in our SVSlope software package. Please visit our ordering page for pricing and purchase information, or contact us directly.
- Kremen, A. and Tsompanakis, Y, 2009, APPLICATION OF DYNAMIC PROGRAMMING TO EVALUATE THE SLOPE STABILITY OF A VERTICAL EXTENSION TO A BALEFILL, accepted for publication in Waste Management & Research ( PDF)