the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Dynamic Fragility of a Slender Rock Pillar in a Sedimentary Rock Mass – from rock mechanics to seismic hazard
Abstract. Fragile geological features (FGF) are the only empirical data to validate seismic hazard analysis over prehistoric timescales. Precariously balanced rocks (PBR) are the most common FGF in practice, with fragility analysis based on rigid body rocking dynamics. FGFs evolved from sedimentary rock masses cannot be treated as rigid blocks, and rock mass properties should be considered in their fragility analysis. Contrary to PBRs, sedimentary FGFs received limited attention from the geological and engineering communities. This paper presents a comprehensive dynamic fragility analysis of a 42-meter-high pillar – the Ramon Pillar (Negev Desert, Israel). The pillar is comprised of a sedimentary rock mass with various discontinuities. An accurate finite elements (FE) model of the pillar (1.25.106 elements) was developed based on high-resolution aerial LiDAR scanning and in-situ measurements of rock elastic modulus along its entire height. The model was validated by comparing computational modal analysis with in-situ measurements of natural vibrations. The first mode of 1.3 Hz was precisely predicted. The second mode was predicted with a 10 % difference: 2.7 Hz calculated compared to 3 Hz measured. An a-priory assumption of rock elastic modulus (or back-calculation) or simplified geometries yielded unsatisfactory results. Following the successful validation, a fully dynamic fragility analysis of the pillar was performed, using recorded ground motions, to study the basal tensile stresses. Located in a region with two seismic sources, the Sinai Negev Shear Zone (SNSZ) and the Dead Sea Transform (DST), the pillar's fragility analysis was used to test regional seismic hazard estimates. It was found that an M 6 earthquake on the SNSZ will probably lead to breakage of the pillar at its base due to stresses exceeding its basal strength. Given a fragility age of 11.4 ky, our analysis challenges the assumption that the SNSZ can produce an M 6 event.
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RC1: 'Comment on nhess-2024-150', Anonymous Referee #1, 26 Nov 2024
This manuscript provided a comprehensive analysis of the dynamic fragility of a slender rock pillar (Ramon, Israel) based on accurate LiDAR scanning of its geometry, in-situ rock elastic modulus determination, and FEM modal and dynamic analysis. Nonetheless, the details of model construction are unclear, and there is a lack of corresponding theoretical equations and measured data, so I do have some comments which I believe will improve the impact of the work. Anyway, it is recommended for publication in NHESS after the following major revision to improve its quality before publication:
- The abstract is not enough to summarize the research results of the manuscript, please revise the abstract again.
- In the Introduction, the significance and innovation of the research in this paper are not clearly explained, and the current research results of dynamic brittleness in the slender rock pillar are not explained, to reflect the research significance and innovation of the manuscript, please revise the introduction.
- In section 3.1, there is a lack of measurement point layout method and measurement error for the elastic modulus of the Ramon Pillar, please supplement the measurement point layout scheme and on-site real picture.
- In section 3.2, only the test data of elastic modulus are given during the construction of the numerical model, but other parameters of lithology are not given, such as Poisson's ratio, please add.
- In section 3.2, the details of model construction are not clear, such as the boundary condition setting method, the load application method, and the related mathematics and mathematical models of the model.
- The manuscript only uses LiDAR to scan the outer surface of the Ramon Pillar, but the trend of the internal fractures and bedding planes of the rock has a great influence on the tensile strength of the rock. Does the numerical model construction process consider the influence of the trend of the internal fractures and bedding planes of the Ramon Pillar, and how is it realized?
- In the 4. Result analysis part, the display and analysis of the simulation results of the model are not in-depth, and there is a lack of stress, strain and plastic zone data, pictures and corresponding correlation analysis after the model is calculated. Dig into the model calculations and analyze them in depth to argue the arguments of the manuscript.
- In the discussion section, there is also a lack of relevant model calculation data and cloud maps, which need to be supplemented.
- The references are too outdated, with papers from 10 years ago accounting for as high as 46.34% of the total. Please update to the latest references.
- The manuscript could benefit from a refinement in writing style. For instance, it is advisable to minimize the use of first-person pronouns like "we" and active expressions such as "We studied" or "We defined." Employing the passive voice consistently across the paper would be more appropriate.
In conclusion, I trust my feedback will be beneficial, and I anticipate the opportunity to assess the refined and enhanced manuscript.
Citation: https://doi.org/10.5194/nhess-2024-150-RC1 -
RC2: 'Comment on nhess-2024-150', Anonymous Referee #2, 10 Dec 2024
Summary:
The manuscript of Jbara and Tsesarsky presents the fragility analysis of a fragile geologic feature (FGF), specifically a 42 m rock pillar that is located in the Negev Desert, for the purpose for making inferences about the maximum magnitude of ancient earthquakes on the nearby Sinai Negev Shear Zone. The authors combined high-resolution LiDAR with measurements of rock elastic modulus along the height of the pillar to produce a finite element model of the pillar. Importantly, they showed that both a simplified geometry or a simplified assumption of rock elastic modulus yielded inaccurate results. A dynamic fragility analysis of the rock pillar was then performed using ground-motion time histories of magnitudes and distance of relevant to their rock pillar. Their primary result is the inconsistency of a M6 earthquake on the Sinai Negev Shear Zone and the observed survival of the feature over its 11.4 ky fragility age. This publication will be a valuable addition to the actively growing research into using FGFs to test seismic hazard models and their components, particularly as this manuscript focuses on expanding the use of the FGF class of rock pillars.
Reviewer Comments:
Regarding the title, seismic hazard is the rate or probability of exceeding a level of ground-motion intensity at a site. While the author’s do make comparisons to a ground-motion model and comment on a relevant seismic source to the site, the claim of “to seismic hazard” is not accurate. I would suggest rewording, as this work tests the magnitude of potential earthquakes on local active faults.
My major comments relate to the need for several key concepts to be corrected or reworded to avoid reader confusion.
First, FGFs do not “validate seismic hazard analysis”, it is not the framework that is validated but a given PSHA model/results/estimates that are validated. Second, rewording is required in a couple of places to make it clearer that it's not the case the PBRs are geomorphically the most common class of FGFs to form, but that precariously balanced rocks (PBRs) are the class of FGFs that have been investigated the most for the purpose of putting constraints on seismic hazard estimates. Third, it is correct to say that the PBR fragility methods cannot be directly applied to other FGF classes that have different failure modes, i.e., beam breaking. However, the PBR fragility methods can be applied to PBRs of any lithology (metamorphic: e.g., Stirling et al., 2012, igneous: e.g., Rood et al., 2024, and sedimentary: e.g., Rood et al., 2020) and for PBRs formed in any geographical location. It is the geometry and mechanics of the rock pillars that requires breaking fragilities (rather than rocking and toppling fragilities) to be determined. Importantly, it is not due to them being composed of sedimentary rocks (the rock pillars could be composed of any rock type, but their mode of failure would be the same). Please correct this throughout.
Based on Figure 3, 17 rebound hammer readings were taken over the 42 m height and the readings were not regularly spaced. Please include a description of the criteria used for the selection of measurement locations, as well as whether an increased density of samples (for example every meter, or sub-meter spacing) would be expected to improve or change the results in a significant way. Also, can you please provide a couple of examples of the “geological judgment” that were used to divide one region from another, as the differences between the divisions are not super obvious based on the data in Figure 3 alone.
For the “Simplified Fragility Analysis” what is the justification for using the Abrahamson, Silva, and Kamai (2014) ground-motion model, rather than: Chiou and Youngs (2014) global ground-motion model or the Akkar, Sandıkkaya, and Bommer (2014) Europe/Middle East ground-motion model (these would seem to be the more obvious choices). Please clarify the choice. Additionally, if there is the truncation of ground-motion models in probabilistic seismic hazard analysis, it is likely at 3 or 5 sigma. Showing 1, 2, and 3 sigma with different shading/line pattern would be helpful on the Figure A2 plots to show the uncertainty included in these models. Or this point should at least be included in the text. Finally, it also needs mentioning somewhere this is an ergodic ground-motion model, and FGFs should be compared to non-ergodic ground-motion estimates to account for the source, path, and site effects specific to the FGF.
For the time histories used for the finite element analysis, it is important to point out that earthquakes of those magnitudes and distances have not been recorded for your specific faults and sites of interest, and that even in the global PEER database there are limited recordings of the relevant large magnitudes at short distances. Therefore, it is necessary to make the assumption that the recordings that you selected for your analysis are appropriate to be applied for your source, path, and site combination. Also, related to the finite element analysis, was the cliff face that can be seen in Figure 2 along one side of the rock pillar included in the modelling? Please clarify this in the manuscript, as well as explain what the effect of this cliff face is (if any) is on the fragility of the pillar. For example, I wonder whether the bending of the pillar as a cantilever beam before breaking would result in there being a collision with the cliff, dampening the response?
Regarding the conclusions about a M6 earthquake event on the Ramon and Nafha-Sa'ad faults not occurring over the past ~11,000 years, what is the rate of occurrence of a M6 earthquake from the magnitude-frequency distribution of these faults? Either from literature or hazard model seismic sources? Specifically, of interest is whether the magnitude-frequency distribution estimates a M6 event more or less frequently than ~11,000 years, as that would make the model inconsistent or consistent with your FGF analysis. Also, given that the magnitude of a rupture and the ground-motion at a distant site are linked but separate, please add some discussion around the fact that the magnitude may be consistent with the survival of the rock pillar. For example, it is possible that the ground-motions from a M6 SNSZ rupture are lower at the rock pillar site than those of the small number of recordings in the PEER database or of the ergodic ground-motion model. Non-ergodic ground-motion models or physics-based simulations would help rule out this possibility.
Finally, a detailed review of the manuscript focusing of consistent word choices and paragraph structure (there are lots of 2 sentence paragraphs!) would greatly benefit the readability. I believe that the clarifications and additional information requested in my review are minor revisions, and I would be happy to review the manuscript again after the necessary revisions have been made and prior to publication.
Figure Comments:
Figure 1: Need to provide a link or reference for the access to the Israel Seismic Catalog plotted. Also, scaling the size and/or colour of the catalog circle symbols with the magnitude of the earthquake event would be helpful for understanding the historical seismicity of the region.
Figure 2: The look direction of the photos would be helpful in understanding the failure direction of the features relative to the orientation of the local faults.
Figure A1 needs a colour bar scale.
Citation: https://doi.org/10.5194/nhess-2024-150-RC2
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