A constitutive model for municipal solid waste considering mechanical creep and biodegradation-induced compression

Abstract

A constitutive model is developed to describe the stress–strain–time behavior for decomposing municipal solid waste (MSW) within a critical state soil mechanics framework. The model is an extension of the Modified Cam-Clay plasticity model. In this model, three sources contribute to the hardening of MSW due to volumetric strain: time-independent plastic volumetric strain, time-dependent volumetric mechanical creep strain, and time-dependent volumetric strain due to the biodegradation (decomposition) of MSW. The MSW model was evaluated through numerical analyses of large-scale one-dimensional compression tests in the laboratory and the field and the reported vertical and horizontal deformations of a MSW landfill. The associated model parameters were obtained by compositional analysis of the waste, from values reported in the literature, and by fitting numerical results to observed behavior. For the laboratory compression test, the best-fit numerical simulation over-predicted the early settlement but converged on the experimental values after 200 days. Initially, the calculated vertical strains in the field-scale test deviated from the measured strains by up to 10% over the 398-day period of the test. However, numerical results after adjusting model parameters to provide the best fit with the measured strains resulted in a maximum deviation of less than 3% over the test duration. The calculated vertical displacements of the MSW landfill were consistent with field measurements. However, the calculated horizontal displacements were significantly lower than the measured values. Sensitivity studies showed that the time-dependent settlement predicted by the model is highly sensitive to the biodegradation rate of MSW. The good agreement between numerical values and observed vertical deformations for the SWEAP section on the MSW landfill suggests that the model has the potential to assess the performance of subsystems in landfills (e.g., the performance of a side slope liner system subject to landfill settlement). However, the discrepancy between predicted and observed horizontal displacements suggests that the numerical model can be improved by incorporating deviatoric creep deformations in the constitutive model.

Appendices

Appendix 1

See Table 8.

Table 8 Constitutive models for mechanical behavior of soft clays and waste

Appendix 2: Derivation of Eq. (10b)

As shown in Fig. 1, for a waste element at a state point at B, with volumetric age t_v, volumetrically creeps in time period $\Delta t = \Delta t_{{\text{v}}}$ at a constant effective stress, the waste would shrink by an amount as follows:

$$\left| {\Delta e} \right| = \psi \ln \left( {1 + \frac{{\Delta t_{{\text{v}}} }}{{t_{{\text{v}}} }}} \right) = \left( {\lambda - \kappa } \right)\ln \left( {1 + \frac{{\Delta p_{{\text{c}}}^{{\prime }} }}{{p_{{\text{c}}}^{{\prime }} }}} \right)$$

(26)

Solving for $\Delta p_{{\text{c}}}^{{\prime }} /p_{{\text{c}}}^{{\prime }}$ obtains:

$$\frac{{\Delta p_{{\text{c}}}^{{\prime }} }}{{p_{{\text{c}}}^{\sqrt 2 } }} = \left[ {\left( {1 + \frac{{\Delta t_{{\text{v}}} }}{{t_{{\text{v}}} }}} \right)^{{\psi /\left( {\lambda - \kappa } \right)}} - 1} \right] = \frac{\psi }{\lambda - \kappa }\left( {\frac{{\Delta t_{{\text{v}}} }}{{t_{{\text{v}}} }}} \right) + \frac{1}{2!}\frac{\psi }{\lambda - \kappa }\left( {\frac{\psi }{\lambda - \kappa } - 1} \right)\left( {\frac{{\Delta t_{{\text{v}}} }}{{t_{{\text{v}}} }}} \right)^{2} + \cdots$$

(27)

Taking the limit of $\Delta p_{{\text{c}}}^{{\prime }} /\Delta t_{{\text{v}}}$ as $\Delta t_{{\text{v}}} \to 0$ gives:

$$\frac{{\partial p_{{\text{c}}}^{{\prime }} }}{{\partial t_{{\text{v}}} }} = \frac{\psi }{\lambda - \kappa }\frac{{p_{{\text{c}}}^{{\prime }} }}{{t_{{\text{v}}} }}$$

(28)

Therefore, the increment in $p_{{\text{c}}}^{{\prime }}$ due to mechanical creep, ${\text{d}}p_{{\text{c}}}^{{{\prime }2}}$ is expressed as:

$${\text{d}}p_{{\text{c}}}^{{{\prime }2}} = \frac{{\partial p_{{\text{c}}}^{{\prime }} }}{{\partial t_{{\text{v}}} }}|_{{\left( {\varepsilon_{{\text{v}}}^{{\text{p}}} ,V_{{\text{S}}} } \right)}} {\text{d}}t = \frac{{\psi p_{{\text{c}}}^{{\prime }} }}{{\left( {\lambda - \kappa } \right)t_{{\text{v}}} }}{\text{d}}t$$

(29)