New Cadanav Methodology for Rock Fall Hazard Zoning Based on 3D Trajectory Modelling

Round 1

Reviewer 1 Report

The article is quite good.

The work will be greatly improved if the authors write a new version of the abstract.

The new summary should be more concrete. You have to detail the achievements. And it is convenient to present the weaknesses indicating that they are the subject of ongoing investigations.

Author Response

1) The work will be greatly improved if the authors write a new version of the abstract.

The new summary should be more concrete. You have to detail the achievements. And it is convenient to present the weaknesses indicating that they are the subject of ongoing investigations.

 

Authors’ response

Thank you very much indeed for your feedback and suggestion. The abstract has been modified/restructured as follows (please see attached version of the revised manuscript):

“Most rock fall hazard zoning methodologies are currently based on trajectory modelling, usually performed along 2D slope profiles. For many topographic configurations, this approach can not provide a realistic description of the way rock fall trajectories and, ultimately, hazard are spatially distributed all over a slope. This paper presents a new methodology for rock fall hazard zoning, directly applicable to 3D topographies, starting from 3D trajectory simulation results. The procedure is an extension of the Cadanav methodology introduced for hazard zoning along 2D slope profiles. As such, it is fully quantitative and attempts at reducing as much as possible uncertainties and subjective elements affecting current methods for rock fall hazard analysis and zoning. It is also among the first to introduce a “fully-coupled” rock fall intensity-frequency approach. Hazard is estimated by means of “hazard curves”, described at each point of the slope by rock fall intensity-return period couples. These curves may be superimposed on any intensity-return period diagram prescribed in national or regional land use planning regulations, in order to determine which hazardous condition prevails at each point of the slope. The application of the new Cadanav methodology is illustrated for both a theoretical case of simple topography underlying a linear cliff and a real configuration involving a complex topography, characterised by strong three-dimensional features affecting the paths of the blocks. For all topographic models, results obtained for several scenarios involving either localised or diffuse source areas proved that the methodology performs extremely well, providing objective and reproducible results based on a rigorous combination of rock fall energy and return period. Additional tests and real case studies are currently under investigation, for strengthening even further the validation of the approach and extend its applicability to even more complex rock fall scenarios.”   

Author Response File: Author Response.docx

Reviewer 2 Report

I suggest adding data and comments about the differences in the computational time between cases of Cadanav 2d and Cadanav 3D.

Author Response

1) I suggest adding data and comments about the differences in the computational time between cases of Cadanav 2d and Cadanav 3D.

 

Authors’ response

Thank you very much indeed for your feedback and suggestion. Computational times characterising Cadanav 2D and Cadanav 3D were addressed in Section 6.2, lines: 609-628, as follows (please see attached version of the revised manuscript):

“the computational time required for hazard zoning, also for 3D topographies, depends only on the spatial discretisation of the problem and the number of rock fall trajectories processed. In particular:

-  for 1D zoning along 2D slope profiles, the time is proportional to the product of the number of control abscissas x_2D along the slope profile, into which the profile itself is subdivided, and the number of 2D rock fall paths n_tot,2D computed;

- similarly, with regards to 2D zoning for 3D topographies, the computational time is a function of the number of elements constituting the mesh on the horizontal plane (x_3D, y_3D) and the number of 3D trajectory runs n_tot,3D = n_source · n_traj,source performed.

According to the complexity of the problem in the sense specified above, therefore, the difference in the computational times between 1D zoning and 2D zoning, marked as t_1D and t_2D, respectively, can be expressed by the ratio:

 

t_1D/t_2D = (x_2D· n_tot,2D) / [(x_3D·y_3D)·n_tot,2D]                                       (14)

 

In principle, applications to 3D topography involve more elements constituting the spatial domain and require more trajectories to be run (due to their higher variability). Despite this aspect, however, in all the cases tested, the times required for zoning computations remained extremely contained (i.e., a few minutes) - and way shorter, for instance, than those necessary for the performance of the 3D rock fall simulations".   

Author Response File: Author Response.docx

Reviewer 3 Report

Dear Authors,

I really appreciated your paper, particularly the discussion of advantages and possible lacks of this method. You have already addressed all of my possible questions, therefore I only congratulate you for your work.

Best regards

Author Response

Dear Authors,

I really appreciated your paper, particularly the discussion of advantages and possible lacks of this method. You have already addressed all of my possible questions, therefore I only congratulate you for your work.

Best regards

 

 

Authors’ response

Thank you very much indeed for your feedback!