Impact of High Energy Mining-Induced Seismic Shocks from Different Mining Activity Regions on a Multiple-Support Road Viaduct

Round 1

Reviewer 1 Report

I have added my comments in the attached report.

Comments for author File: Comments.pdf

Author Response

The authors would like to thank the Reviewer for his general assessment of the manuscript and all valuable specific comments. Point-by-point replies to the comments are provided below.

Specific comments

1. Reliance on responses at specific elements within the finite element models implicitly assumes point wise convergence of the results which is not guaranteed. One should use aggregate measures such as norms (even localised over a region) instead.

DONE. The authors would like to thank the Reviewer for this valid remark. Indeed, the adoption of the linear FEM model for the time history analysis (assumed for the purpose of comparison with RS and MSRS analyses, which are based on the superpositions of modal responses and as such, are limited to linear problems) doesn’t guarantee the point-wise solution convergence.  Taking the average (over the region) response for the detailed analysis is an excellent idea, and we would use it in our future works. In this study, the time-histories of stresses were recorded and primarily assessed in over 200 elements localized in different structure zones. The most representative six elements were chosen for the detailed analysis presented in the study. Considering the remark of the Reviewer,  the following sentence was added in the revised version of the manuscript (lines 511-512) “The response histories were recorded and  assessed in over 200 elements.”

2. Partially related to the previous comment: Here the seismic measurements are used as inputs. It would be more realistic to consider statistical models with for instance the measurements taken as expected values. There have been studies on frequency responses on shells under material uncertainties (collocation SFEM) showing that (not surprisingly) the responses have a statistical nature as well with maximal displacements occurring at different locations and frequencies depending on the variations in materials. With this as background, I wonder if the final conclusions reflect this fact that if the seismic data (shocks etc.) are assumed to be realisations of some stochastic model, then the observed responses can indeed vary quite significantly.

The authors would like to thank the Reviewer for this valuable comment. This issue will be for sure one of the most important topics of our further studies. Indeed, for the THA method (with both uniform and nonuniform variants of excitation) the seismic measurements were used as inputs. However, the authors would like to kindly remark that the RSA and the MSRS methods have a statistical nature, since they are based on response spectral curves. It is worth mentioning that the applied response spectrum functions were developed based on many years of research on mining-induced seismicity, and they correlate with the representative tremors and local soil conditions occurring in the USBC and LGCD regions. Hence, the dynamic response of the bridge to the mining-induced shocks was obtained on the basis of both, deterministic and stochastic, methods. The comparison showed good agreement of all received results.

3. In Figures 16-20 the extremal principal stresses obtained from different calculation methods are compared using graphs. Using THA (both variants) there is oscillation, of course. It appears that this modulation has practically the same frequencies. If you do a Fourier analysis on the THA graphs, do you actually see a difference? Or, if there is a difference, perhaps that gives a more precise way to quantify the differences?

The authors would like to explain, that no significant differences between response frequencies in both variants of THA have been noticed. The subtle observed discrepancies haven’t shown any clear trend which would allow for general conclusions, so this analysis hasn’t been included in the study.

The whole cover letter (with responses to all reviewers)  is included in the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors present an interesting paper, using seismic data + different algorithms to assess the performance of identical engineering structures in the presence of shocks with differing frequency content. Given the importance of this topic to robust engineering, I would suggest that this paper is published after some minor comments are addressed.   Minor comments:

196-197: "For the purposes of this study, all registered data was scaled up proportionally, so that PGA in the horizontal direction WE was raised to 1.7 m/s2." 

   - What effect does this (scalar?) multiplication have on the following? I have the same question about the scaling at 214-215.   Figure 1-2: Was any bandpass applied? Maybe the typical frequency response of the sensors could be mentioned in the caption of Figure 2?   For THA, RSA, and MSRS, perhaps the authors would consider creating a table summarizing algorithmic assumptions, strengths, and weaknesses? The text explains these well, but it would be nice to have a simple place to quickly evaluate this.   "The following response spectrum functions [10,41] were applied (Figure 6):" - While the citations elsewhere is appreciated, it would be nice if the authors would provide just enough context to motivate these.   Should Table II not have error bars for both the finite element and experimental analyses? I would assume based on the measurements in the spectra, the peak frequency measurement should have error bars of around 10%, explaining that level of difference.   "Having the experimentally determined velocity v = 243 m/s"  -> also should error bars be assigned here?  

"Figure 13. The horizontal (WE) acceleration-time histories of subsequent viaduct supports obtained based on the model of non-uniform mining-induced kinematic excitation for: (a) the USCB region; (b) the LGCD region." -> At this point, maybe the authors could remind the readers of the source of the clear difference in frequency content in the two traces?

Author Response

The authors would like to thank the Reviewer for all valuable comments. Having considered the specific comments, the authors revised the text and drawings according to the suggestions. Point-by-point replies to the comments are provided below.

 Specific comments

• 196-197: "For the purposes of this study, all registered data was scaled up proportionally, so that PGA in the horizontal direction WE was raised to 1.7 m/s²." 

 - What effect does this (scalar?) multiplication have on the following? I have the same question about the scaling at 214-215.  

 DONE. The authors would like to kindly explain that the multiplication - scaling up of the maximum PGA of the tremors to 1.7 m/s² - caused only the increase in the dynamic responses of the bridge to the tremors. As the whole analysis was assumed to be a linear one the increases are proportional to the scale factors. However, we would like to indicate that this multiplication, mentioned in lines 196-197 and 214-215,  was introduced for the following two reasons.

       Firstly, we would like to have the same maximum values of PGA for both analyzed regions. It enabled us to focus on the discrepancies in the frequency spectra only, not taking into consideration discrepancies in maximum amplitudes of accelerations. The maximum PGA of the shocks in the horizontal direction WE was scaled up as this was assumed to be the direction of the wave propagation. Vibrations in this directions usually matter mostly as far as the dynamic response of a bridge is studied.

       Secondly, the value of 1.7 m/s² corresponds to maximal PGA of mining tremors recorded in both regions in the last two decades [4]. Hence, the dynamic responses of the bridge to the tremors with such a large value of maximum PGA may be considered as substantial and crucial results for the assessment of the mining tremors impact on the structure. The following sentence was added in the revised version of the manuscript to clarify the abovementioned problem (lines 218-223):

"Scaling up the maximum values of PGA to the same value for both analyzed regions enabled focusing on the discrepancies in the frequency spectra only, and not taking into consideration differences in the shock intensities. It is also worth noticing that the value of 1.7 m/s² corresponds to maximal recorded PGA of mining tremors in both regions in the last two decades [4]. The dynamic responses of the bridge to the tremors with such a large value of maximum PGA may be considered as substantial and crucial results for the assessment of the mining tremors impact on the structure."

• Figure 1-2: Was any bandpass applied? Maybe the typical frequency response of the sensors could be mentioned in the caption of Figure 2?  

DONE. The authors would like to kindly explain that the bandpass of 30 Hz was applied to the registered signals. The frequency range from up to 30 Hz is usually used for the assessment of the dynamic behavior of civil engineering structures located in mining-induced seismic regions. Higher frequencies of mining shocks do not play an important role in the dynamic performance of structures as their fundamental natural frequencies are usually much lower than 30 Hz. Considering this remark of the Reviewer, the range of registered frequencies is mentioned in the caption of Figure 2 and 4 in the new version of the manuscript  (lines 205 and 228).  Also, the clarification on the typical range of frequency registration is added in the revised version of the manuscript (lines 231-232):

       "Typically mining-induced shocks are registered with sensors covering the frequency range up to 30 Hz."

• For THA, RSA, and MSRS, perhaps the authors would consider creating a table summarizing algorithmic assumptions, strengths, and weaknesses? The text explains these well, but it would be nice to have a simple place to quickly evaluate this.  

DONE. Considering the suggestion of the Reviewer, additional subsection 3.2.4 was added to the new version of the text (lines 328-343):

"2.3.4. Comparison of the introduced calculational methods of the dynamic behavior of structures

The general comparison of the calculational methods presented in this section can be summarized as follows:

• The THA is more precise than methods based on the modal analysis (RSA and MSRS). It allows for finding the time-histories of structure response measures (stresses, strains, displacements) at any element. It also enables incorporating different problem nonlinearities like complex material behavior, large displacements or strains, or unilateral contact conditions.
• The methods based on system eigenmodes are much more cost-effective than direct time integration of all the degrees of freedom of the system in the dynamic analysis performed with THA.
• Taking into account the non-uniformity of ground motion, both in THA or by adopting MSRS method may play an important role in the analysis of the dynamic response of large-scale structures to seismic shocks. However one should bear in mind that the correct definition of the non-uniform kinematic excitation model requires the knowledge of local soil conditions and in-situ Such a model for the current analysis is presented in section 3.2."
• "The following response spectrum functions [10,41] were applied (Figure 6):" - While the citations elsewhere is appreciated, it would be nice if the authors would provide just enough context to motivate these.

DONE. Considering the remark of the Reviewer, the following explanation is provided in the new version of the text (lines 294-296):

      " It is worth mentioning that the applied response spectrum curves were developed on the basis of many years of research on mining-induced seismicity, and they correlate with the representative tremors and local soil conditions occurring in the USBC and LGCD regions."

• Should Table II not have error bars for both the finite element and experimental analyses? I would assume based on the measurements in the spectra, the peak frequency measurement should have error bars of around 10%, explaining that level of difference. "Having the experimentally determined velocity v = 243 m/s"  -> also should error bars be assigned here?  

We would like to kindly explain that for the measurements of the natural frequencies of the bridge as well as the wave propagation velocity, the equipment at the disposal of the Laboratory of Building Deformation and Vibration of the Institute of Building Mechanics of the Cracow University of Technology was used to build the measuring track. All measurement points consisted of three piezoelectric high sensitivity (10,000 mV/g) accelerometers 393B12 PCB Piezotronics located in three directions. The frequency range of accelerometers was from 0.15 to 1000 Hz. All sensors were wire connected. Signals were recorded in a synchronous manner. The data sampling of the signal was 1024 Hz. For such a testing scenario, the total measurement uncertainty was estimated at about  8%. It should be emphasized that the calculated measurement uncertainty did not exceed the limit value of 20.00% recommended by the Polish Standards (PN-85/B-02170).

• "Figure 13. The horizontal (WE) acceleration-time histories of subsequent viaduct supports obtained based on the model of non-uniform mining-induced kinematic excitation for: (a) the USCB region; (b) the LGCD region." -> At this point, maybe the authors could remind the readers of the source of the clear difference in frequency content in the two traces?

DONE. Having considered this comment, the authors clarified at this point the source of the difference in frequency contents of the two traces (lines 477-480):

       "It is worth pointing out that two analyzed mining activity areas, i.e. the USCB and the LGCD region, differ significantly in geological structure. This results in differences in parameters characterizing mining-induced tremors, like energy, the lengths of shocks, and, especially, the frequency contents."

The whole cover letter (with responses to all reviewers) is included in the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

No comment from reviewer

Author Response

The authors would like to thank the Reviewer for the review and the assessment of the manuscript.

The whole cover letter (with responses to all reviewers) is included in the attachment.

Author Response File: Author Response.pdf