Overall summary

The article presents a one-dimensional analytical development to model degradable porous media (DPM). The Case Study and motivation of the research is to model Municipal Solid Waste (MSW) degradation and consolidation. Existing models in the literature take into account hydro mechanical coupled consolidation (Terzaghi consolidation theory) and there are also studies on degradation, i.e. biodegradation of the organic fraction of the waste. For further improvements of MSW modeling a coupling between hydromechanics and degradation is needed, the paper bridges this gap. Results for two representative MSW sets of data are presented. Conclusions highlight the fact that for the initial stages of consolidation, the newly degradation coupled model predicts an increase of excess water pressure due to a prevalent effect of the degradation of mechanical properties compared to the increase of permeability and void coefficient. Finally an appendix presenting the developments to obtain the solution of the partial differential equations is provided.

Overall strengths and impact

The reviewer thanks the authors for the clarity of the presentation, scientific soundness and the potential impact of the publication.

The methods presented in the paper are novel in the sense that no coupling between degradation and hydromechanics in the manner done by the authors were available in the literature at the time of the publication.

The paper presents a purely analytical approach providing the solution of the partial differential equations describing the physics of the problem. This is of great interest because it allows obtaining the solution of boundary value problems with great accuracy and refinement without incurring heavy and computing expensive numerical models.

One of the assumptions made in the present research is that the rate coefficient of secondary compression (c_s) is equal to the classical degradation rate coefficient (c). Which means, as stated in page 5: ‘biodegradation-induced secondary compression develops simultaneously with solid mass loss under a constant load.’ This assumption is important because it explains the occurrence or not of excess pore pressure in the initial stages of consolidation. Therefore, one of the conclusions of the article is a direct result of this assumption; it could be helpful to clarify this in the discussion and conclusions.

A possible future research could be to define the relation between c_s and c and try to validate the results of the model with actual data.

Overall the paper is a well written, scientifically sound and brings an important contribution to the field. The research is not only applicable to the field of MSW but also to a more general framework of saturated porous media with organic content.

Specific comments

In the title it is not mentioned if the research is based in an analytical, numerical or experimental approach, the reader needs to go to the abstract to know.

In the last line of the abstract it is stated: ‘The numerical results are of wider interest, being applicable to other DPM.’ It is not clear to which numerical results this refers to.

Figures 3 and 5 present results for two different sets of cases and consolidation times. In figure 5 results for a time equal to 0,2 days are not displayed, if figures 3 and 5 presented the same time frame they could be more comparable and informative.