Characterization of Variability of Unit Weight and Shear Parameters of Municipal Solid Waste
Publication: Journal of Hazardous, Toxic, and Radioactive Waste
Volume 25, Issue 2
Abstract
The safety and stability of municipal solid waste (MSW) slopes are governed by unit weight (γ), cohesion (c), and friction angle (ϕ) of the MSW. Variability associated with the unit weight, cohesion, and friction angle of MSW is a major problem in the design of landfills because it negatively affects the performance of the slope. Variability associated with these properties may trigger catastrophic slope failures. The reported studies on the reliability-based design of MSW landfills adopted either Gaussian or lognormal distributions based on a reasonable approximation. The limitations are apparent when a coefficient of variation (COV) is higher. The accuracy of reliability-based designs depends on the selection of best-fit continuous and extreme value distributions (such as Gumbel and Weibull) that can model a high degree of variability precisely. The present study has undertaken to propose a suitable statistical model that gives a better representation of variability by optimizing the statistical parameters. A high degree of variability associated with the unit weight, cohesion, and friction angle of MSW is also investigated. A novel approach is proposed to determine reliable continuous probability density functions (PDFs) that can be fitted to the database consisting of 184 sample points collected from the most comprehensive experimental studies reported in the literature. The best-fit PDFs are recommended by optimizing the mean and standard deviation such that errors associated with quantiles (Q–Q), percentiles (P–P), and cumulative distribution functions (CDFs) are as minimum as possible. This study signifies the selection of optimized PDFs for the representation of parameter variability, and it is proved that the probability of failure is either underestimated or overestimated considerably when other conventional PDFs are chosen. The recommended mean, COV, and PDF can be useful in the reliability-based design of engineered MSW landfills and for judging the performance of existing MSW slopes.
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Acknowledgments
Financial support for this project was provided by the Science and Engineering Research Board (SERB), which is a statutory body of the Department of Science and Technology, Government of India (Grant No. SR/FTP/ETA-026/2012), and partially by the Government of India, Ministry of Human Resource Development.
Notation
The following symbols are used in this paper:
- c
- cohesion of MSW (kPa);
- fX(x)
- probability density function;
- g(x)
- performance function;
- h
- height of the landfill slope (m);
- PfMP
- probability of failure of MSW slope;
- Xi
- generated random variables;
- experimentally reported variable;
- x
- vector containing generated random values;
- x*
- vector of collected values;
- α
- slope angle of the landfill with horizontal (°);
- βMP
- reliability index against slope failure-Morgenstern price method;
- γ
- unit weight of MSW (kN/m3);
- ɛCDF
- CDF error function;
- ɛPP
- percentile error function;
- ɛQQ
- quantile error function;
- μi
- mean of the random variable;
- σi
- standard deviation of the variable; and
- ϕ
- internal friction angle of MSW (°).
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Journal of Hazardous, Toxic, and Radioactive Waste
Volume 25 • Issue 2 • April 2021
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Received: Jun 3, 2020
Accepted: Oct 7, 2020
Published online: Dec 9, 2020
Published in print: Apr 1, 2021
Discussion open until: May 9, 2021
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