Probabilistic Analysis of Floods from Tailings Dam Failures: A Method to Analyze the Impact of Rheological Parameters on the HEC-RAS Bingham and Herschel-Bulkley Models

Round 1

Reviewer 1 Report

This manuscript  explores the sensibility of tailings dam breach flood mapping to rheological parameters in Bingham and Herschel-Bulklev model and the developed method is based on the probabilistic  Latin Hypercube Sampling of rheological parameters. her are my concerns:

1.       In the abstract, please clarify how the presented parameters ranges of developed algorithm may guide other similar studies?

2.       More relevant keywords are needed

3.       Direct citation is not a good practice. For instance, “[25] focused on the examination of uncertainties” in line 59 should be “the authors in [25] focused on the examination of uncertainties”.

4.       The research gaps in the introduction section are unclear.

5.       The authors have stated the aim of the study but the contribution should be explicitly reported

6.       Section 6 should be closing remarks instead of Highlights. Or combine with section 5 as one section.

7.       Please clarify how your results compared to the state of the art and how it results go beyond the state of the art.

8.       The paper needs proofreading, there are many grammatical errors and some sentences hard to understand.

The paper needs proofreading, there are many grammatical errors and some sentences are hard to understand.

Author Response

Dear reviewer, thank you for your attention and contributions. We have great expectation to the consideration of this paper for publication, and certainly, the suggestions made may contribute to improve its quality. Hereby we expect to give you the answers to all the concerns you pointed out:

1. The extensive developed literature review allowed to identify the minimum and maximum values of different parameters used in sensitivity analysis. Differently from the presented paper which aimed to better understand the global influence of these different parameters comparing Bingham and Herschel-Bulkley Models on HEC-RAS, the literature-based defined ranges may serve as a good reference for establishing boundaries for sensitivity tests, that could be performed in other case-studies considering specific tailing materials such as Ore, Iron, Bauxite etc. Once rheological properties of tailings dams are barely in-situ determined, tests using these ranges may provide important feedback related to the level of uncertainty of flood maps an risk analysis for specific case-studies. The developed code could also be used with this purpose (if HEC-RAS is used) or it could be adapted for other hydrodynamic models. Following your suggestion, we’ve added a summary complimentary description of these perspectives in the abstract;
2. In order to be more precise in relation to the content of the research, we’ve included new complementary keywords;
3. Following your suggestion, we’ve made substitutions all over the text in order to eliminate the “direct citations”;
4. In spite that some studies explored uncertainty on rheology and its impacts on natural and debris flows estimations, there are no studies which performed dam-break sensitivity analyses related to rheological parameters. Furthermore, once both Bingham and Herschel-Bulkley models may be suitable for dam-breach flood modelling purposes, it is considered relevant to understand how these models may influence hydrodynamic forecasts in function of the uncertainty level related to the rheological data which may be available for the development of practical analyses. These points are unclear in the scientific literature and is considered by the authors the main gap which is investigated in the article. Therefore, in order to be more clear on that statement and on the specific gaps, as suggested by the reviewers, we adapted and completed the explanation given on the sixth paragraph of the introduction;
5. As suggested, we expanded the initial text in the last paragraph of the introduction by adding a more comprehensive text related to the contributions of the article;
6. We agreed with the suggestion and we considered it by combining the last two sections of the article;
7. In order to give this more detailed view of the obtained results in contrast with the state of the art, we’ve included some paragraphs on the discussion section. Once there are no studies which performed this kind of test in dam-break studies, comparison was mainly done in relation to mudflow studies in relation to the magnitude of parameters and the sensitivity of simulation results. Differently from other studies, the analysis also included the examination of flood wave arrival times, considering the significant importance of this parameter in risk assessments. In addition, some magnitude comparisons related to the specific case study were done to appreciate the sensitivity of dam-breach flood forecasts in relation to other variables already explored in literature (breach parameters and Manning coefficients). These discussions were certainly profitable to improve the paper;
8. As recommended, the first version of the paper was proofreaded in order to eliminate grammatical errors and avoid misunderstanding.

In addition to these considerations, we improved other aspects of the paper, correcting some reference issues and small figures and tables format updates. The new submitted version brings all these modifications.

Kind regards.

Reviewer 2 Report

This manuscript presents a comparison between Bingham and Herschel-Bulkley models as non-Newtonian fluid options in the HEC-RAS software by conducting probabilistic analyses of floods from tailings dam failures. The impact of rheological parameters on flood area, maximum depth and arrival time was analyzed for both the hydrodynamic models and thus the sensitivity of the models to the chosen rheological parameters was compared in terms of hydrodynamic associated probability. The authors collected extensive data of the studied rheological parameters based on a broad literature review. On the basis, they carried out 1,000 simulations aiming at each hydrodynamic model so as to ensure the adequacy of sample capacity. The present work should be beneficial for a reasonable choice of the hydrodynamic models and for further understanding of flood behavior from tailings dam failures. This paper can be a good addition to the Water literature. Thus, the reviewer recommends that it can be considered for publication in this journal. Several minor concerns are listed below.

1.      The authors denoted volumetric concentration of solids and coefficient of variation as C_v and CV, respectively. Such a symbolic notation easily leads to a confusion of different concepts. For example, latter can be denoted as COV or something else. On the other hand, I see that the author did not like using subscripts. For example, some variables such as the yield stress, dynamic viscosity of the mixture and strain rate were not correctly denoted in lines 129 and 130 and elsewhere. The authors adopted μ_m to represent dynamic viscosity of the mixture at the beginning, however, they took away the subscript thereafter without any explanation. In Table 3, the notation of yield stress was changed to Ty.

2.      Lines 465. The maximum average runoff height for each area was defined by equation 5). The authors claimed that j is the cell index; N_wc is the total number of flooded cells (h>0); H_max is the maximum flow depth. First, the notation h did not appear before, what was the meaning? Second, what was the meaning of H_max? Was there a maximum flow depth in each flooded cell or area defined by the authors or anything else?

3.      In Appendix A (PDF page 20), the value of 1.00x10^-07 Pa of parameter a (Machado, 2017) was significantly smaller than the remainder corresponding to the same solids (Iron). Did the authors correctly cite the original data?

4.      Did the authors correctly use the punctuation marks in numbers, e.g., 38.276,34 in Table 2?

Author Response

Dear reviewer, thank you for the contributions and the recommendation for publication. We are glad that the presented topic and content was appreciated and recommended for publication. Hereby we expect to give you the answers to all the minor concerns you pointed out:

1. we followed your recommendation to change notation in order to ease understanding on the different variables. COV was used for coefficient of variation – thank you for the suggestion. We have also updated the whole text in relation to the variables notation and subscripts, in order to get homogeneity, also between text, figures and tables.
2. “H” stands for floodwater height/depth. The maximum flow depth (Hmax) during the simulation period for each cell in the computational mesh is automatically extracted with the algorithm. Thus, with the equation 5 we calculate the maximum average runoff height (Hmean) for each area by summing the maximum flow depth (Hmax) for all the flooded cells within the areas (A1 and A2). It does that considering the summing of heights for all the cells in which the simulated depth (height) is greater than zero (h>0) for any time of simulation, and dividing the sum of them by the total number of flooded cells (NWC). A short version of this description was added in the text before Equation 5 in order to clarify this point in the article.
3. We checked the source and analyzed the data in order to understand this difference. Indeed, the Machado (2017) value is significantly smaller than the remainder corresponding to the same solids (Iron). Machado (2017) study was based on the analysis of iron ore tailings samples along the affected area after the Fundão dam rupture in Minas Gerais, Brazil. The rheological curve of the flow stress defined as most representative in the author's study is, indeed, 10^-7 E^39.278 Cv. The value of the parameter “a” in this curve is small and the value of “b” is large, thus, up to a certain value of “Cv”, the calculated yield stress indicates small values. From the increase of Cv, i.e. the amount of solids present in the mixture, the yield stress increases considerably. The author (Machado, 2017) makes two comments which justifies this behavior (translated from Portuguese): (1) “in the tests carried out, a viscoelastic behavior of the material was observed, since the higher the value of stress was imposed, the faster and greater the deformation of the material was”; (2) “the particular characteristic of the ore processed by Samarco (Mine Company) is that it has low iron content, so it was subjected to very severe grinding steps, generating abrasive materials of very fine granulometry. The tailings deposited in the Germano complex (Specific area related to Fundão Mining activity) are basically composed of fine sands (sandy tailings) and ultrafine sands ('fine' tailings or mud)”. Therefore, the low value of “a” is understandable once it is compensated with the high value of “b” when calculating Cv.
4. Corrections related to punctuation marks in numbers were done all over the article in order to correspond to international standards.

In addition to these considerations, we improved other relevant aspects of the paper, improving English, including more details relative to the results in comparison to other studies and updating format issues on figures and tables. The new submitted version brings all these modifications.

Best regards.

Round 2

Reviewer 1 Report

The authors have addressed my comments. I have no further concern