A Unified General Resistance Formula for Uniform Coarse Porous Media
Round 1
Reviewer 1 Report
Many previous researchers studied the non-linear relationship between seepage velocity and hydraulic gradient in coarse granular materials. They managed different approaches and variables to define the resistance formula applicable to that type of granular media. Based on the analysis of the different approaches and experimental data obtained by the researchers, The current authors propose a unified general seepage equation applicable to large-sized granular materials. Such an equation gives unity to the main non-linear resistance formulas developed to date. Particularly relevant, are the conclusions regarding the relationship of the linear (α*) and quadratic (β*) dimensionless coefficients of the resistance formula with the representative size of the particle and the geometrical features of the porous materials. The paper is interesting and of extreme scientific value. The authors have done the work in a very diligent and detailed manner. Their findings are supported by experimental work to obtain the material constants α and β. The results are complete and the obtained general seepage equation which allows for different conditions. The work is complete and the authors are commended for the approach and efforts made. Therefore, the paper is recommended for publication as is.
Author Response
Dear reviewer 1
We are grateful for all the comments you had made. It is specially gratifying that we have aroused your interest and have your appretation for the scientific value of the manuscript with a work, in your opinion, carried out in a diligent and detalied manner advising its publication as submited
Kind Regards,
J.C. López
Reviewer 2 Report
There is some algebraic manipulation and data fitting exercise in the present manuscript. I feel that novelty is not enough to warrant publication.
Author Response
Dear reviewer 2
We regret that we were unable to convey the sufficient scientific interest of the manuscript. However, we have modified the sections "Introduction and objetives" and "Conclusions" in order to highlight the importance of the research.
Regards,
J.C. López
Reviewer 3 Report
The authors proposed a unified general seepage equation that can be used for porous media of coarse granular particles. The research topic is not highly innovative but still interesting for academic study. It brings an alternative solution to seepage through granular porous media when seepage velocity strikes the Forchheimer flow regimes. Based on my first impression, this work is recommended to be published in a journal, such as Water of MDPI. However, before any formal acceptance, I would like to leave a few constructive comments to help the authors present this work with better clarity and higher quality in terms of charts and tables.
(1). The introduction is not very well organised in a logical structure. The research gap has not been highlighted with proper expression yet. Half of the content (i.e., Lines 29-40) was occupied by the content of non-Darcy flow at high speed on the textbook level, whereas the research gap and question identification (Lines 41-44) were not delivered in high clarity. The authors should consider improving this portion to raise interest and dazzle readers, i.e., highlighting your research significance.
(2). Equation (4): Reynolds number should be Re instead of Re. Also, Pe was assigned to particle weight, while Pe is often recognised as a Perclet number, a hydrodynamic dimensionless number that quantifies diffusion against advection. The authors may want to avoid any potential confusion in regard to those.
(3). A few works listed below can be reviewed and cited in section 2: state of the art.
Chapter 5 of Bear (1972), Zhu (2023), Mulqueen (2005), Irmay (1958), Yan et al. (2022a) and Yan et al. (2022b)
Bear, J. (1972). Dynamics of fluids in porous media. New York, USA: American Elsevier Publishing Company, Inc.
Irmay, S. (1958). On the theoretical derivation of Darcy and Forchheimer formulas. Eos, Transactions American Geophysical Union 39 (4), 702-707.
Mulqueen, J. (2005). The flow of water through gravels. Irish journal of agricultural and food research, 83-94.
Yan, G., Ma, Y., Scheuermann, A., and Li, L. (2022a). The Hydraulic Properties of Aquabeads Considering Forchheimer Flow and Local Heterogeneity. Geotechnical Testing Journal 45 (4), 891-900.
Yan, G., Shi, H., Ma, Y., Scheuermann, A., and Li, L. (2022b). Intrinsic permeabilities of transparent soil under various aqueous environmental conditions. Géotechnique Letters 12 (3), 1-7.
Zhu, J. (2023). Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media. Hydrology 10 (1), 21.
(4). In section 3, methodology, please concisely present your method and standard for preparing porous media (e.g., ASTM or Spanish standard?) and why you selected those samples. Are there any grain size distribution (GSD), soil classification, fundamental soil testing parameters, maximum and minimum dry densities, uniformity and curvature coefficient, void ratio and porosities?
(5). Figures 1-11 and Figures 17-28 are presented in not very high quality. Please consider adding a black box outside and putting light grey grid lines to assist readers interested in reading and tracking those data for future research. Also, the captions of those figures are relatively inadequate. The captions of figures should attain a meaning that can help readers understand each figure without further searching for too much technical information in nearby content. Besides, the figures' font size is not black and is too small for reading, and the fitting equations inset are not presented properly, e.g., fitting equations overlap each other in Figures 18-20, so they cannot be read. Do remember a golden principle that the manuscript is not only written to be published but also to be read. Please read through your work to see if it is readable or tough to read through from a reader's perspective so that you will improve your work. You can also compare your artwork against the publications recommended in this review comment of any you cited to see if you can improve your chart quality.
(6). Please update all mathematical symbols in italics in all content, equations, and figures.
(7). Please leave a space between any value and unit (e.g., 40mm -> 40 mm) as well as large or less than (3.4<Rp<193) -> (3.4 < Rp < 193) throughout your manuscript.
(8). The citation format is incorrect; all references were cited using author and date but not in MDPI's style: number or author with number. Please check the MDPI citation style.
(9): In section 4, experimental part, have you measured water temperature? Temperature influences the soil water density and dynamic viscosity, i.e., kinematic viscosity. Any measurements of temperature with precision? How did you ensure your piezometers have no bubble clogging? What is your piezometer's measuring precision? What are your experimental criteria for achieving steady-state flow conditions? What is your specimen-preparation procedure, and what range of specimen density, void ratio, and porosity can be well achieved with an acceptable standard deviation? How did you get bubbles out of your samples to ensure fully saturated conditions?
(10). Table 1's caption is located above Table 1, but Table 2's caption is left under Table 2, any consistency in format and typeset?
(11). Figure 28: What is Series1 in the legend of Figure 28? Missing the diameter in the legend? Please read through your paper from a reader's perspective because this manuscript's readability is still off track of publication straightaway.
(12). Please give an English proof editing to your current manuscript with either a native speaker or grammar software, such as Writefull or Grammarly, in a basic version without any AI assistance.
(13). A similarity report is attached to this review comment to reduce similarity further.
(14). Please highlight your scientific contribution and engineering application at the end of your conclusion.
Comments for author File: 
Comments.pdf
Extensive editing of the English language required
Author Response
Dear reviewer 3,
Next, we will try to answer each of your doubts and comments.
Please see the attachment
Kind Regards,
J.C. López
Author Response File: 
Author Response.docx
Round 2
Reviewer 2 Report
Authors have taken care of the comments and improved the manuscript.
