Application of a hyperbolic model to municipal solid waste

An understanding of the stress–strain behaviour of landfilled waste is important in landfill design. Based on evaluation of numerous strain–strain curves obtained from triaxial compression testing of samples of municipal solid waste (MSW) ranging from fresh to degraded, it is proposed that the stress–strain behaviour of MSW under loading follows a non-linear elastic (hyperbolic) model. The hyperbolic model is typically described using σ_ult and E, but can also be described using c′ and φ′ in conjunction with three other parameters (K, n and R_f). The use of the parameters K, n and R_f to describe the stress–strain behaviour may be particularly useful for MSW, because it is often difficult to obtain values of σ_ult and E. Stress–strain data from 15 datasets comprising 57 individual triaxial tests have been compiled. These data originated both from published studies and from the authors' own laboratory testing of large intact and recompacted samples of MSW from three different landfills in Canada. Best-fit hyperbolic model parameters K, n and R_f were determined for 12 of these datasets (comprising 50 individual triaxial tests), and upper- and lower-bound values of K, n and R_f were determined for the 90% confidence level. By using these upper- and lower-bound values, the five-parameter hyperbolic model was effectively reduced to a two-parameter (c′–φ′) model. It is proposed that the resulting lower and upper bounds of the stress–strain curves plotted using the proposed lower and upper bounds of K, n and R_f in conjunction with site-specific c′–φ′ values can reasonably embrace the experimental strain–strain curves up to an axial strain of 20%, even given the significant variability of the waste samples considered. This approach is given further credence as it yields a reasonable prediction of the stress–strain behaviour when compared with the last three datasets (comprising seven individual triaxial tests), which had not been included in the statistical analysis.