Definition of Yield Seismic Coefficient Spectrum Considering the Uncertainty of the Earthquake Motion Phase
Round 1
Reviewer 1 Report
This paper provides a study concerning design response spectra compatible earthquake motion simulations. The used approach is interesting but the manuscript must be improved giving more information on the used data and explaining more in depth the used approach. Among other questions, the dependence of the response spectra with location is not clear.
The manuscript is very well written, and well structured. It only needs, from my point of view, a minimal revision of English by a native. In the attached manuscript, some mistakes are corrected.
Specific comments:
- In general, more references concerning the method and specific calculations should be included in the manuscript.
- line 72. Northwest China-03 1997 earthquake? Please, improve the quote of this earthquake. Some reference concerning this event or accelerograms? What component(s) was(were) used?
- Figure 1. More information about these plots must be given, including used records, due to they are used to justify the work done. Also to refer clearly the used earthquakes. Why authors do not use the same earthquakes/records for figures 1a and 1b? It could be interesting to show all used earthquakes, records and components in a table. Can authors explain clearly how they compute the yield acceleration? Can the authors explain why the variability is period-dependent? Are the figures independent of the used records and its distance to the epicenter?
- line 98 (for the first time). Please, avoid the acronym wrt along the text. It does not look good in a scientific paper.
- lines 114-116. The used requirements of the Chinese code are a tangle. Earthquake (felt) intensity VIII or magnitude 8.0? The Chinese code considers as a rare event who happens with a return period of 475 years? An event with a probability of exceedance of 2-3% in 50 years does not have a return period of 475 years but 2500 years (for a 2%). What means medium firm for the Chinese code? What means a design earthquake group 2?
- Figure 2. Have the authors computed the values included in this figure or are they obtained from a previous paper? If they have computed them, the authors must explain how they do it (used records, ...). If not, authors must include the reference. Have the authors computed the uncertainty of the fitted parameters? Really they can give six accurate decimal digits for the parameter values? And for the computed parameters in lines 133 and 134?
- Line 144. What means Joshua Tree time history? Please, refer correctly the earthquake, the station and the used components.
- Figures 4 and 5. These figures are confusing with relation to the used data. A response spectra depend on the earthquake and the location. The same happens with figure 9.
-Line 180. Can authors explain what is the bias index?
Comments for author File: 
Comments.pdf
Author Response
Response to Reviewer 1 Comments:
We wish to express our appreciation to the Reviewers for their insightful comments and constructive suggestions, which have helped us significantly to improve our manuscript. According to the suggestions, we have thoroughly revised our manuscript and its final version is enclosed. Point-by-point responses to the comments are listed below. Our response follows (the reviewer’s comments are: Reviewer 1 is in “Red” and Reviewer 2 in “Blue”) in our revised manuscript.
Open review: (x) I would not like to sign my review report
( ) I would like to sign my review report
English language and style
( ) Extensive editing of English language and style required
( ) Moderate English changes required
(x) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style
Yes | Can be improved | Must be improved | Not applicable | |
Does the introduction provide sufficient background and include all relevant references? | (x) | ( ) | ( ) | ( ) |
Is the research design appropriate? | (x) | ( ) | ( ) | ( ) |
Are the methods adequately described? | ( ) | ( ) | (x) | ( ) |
Are the results clearly presented? | ( ) | (x) | ( ) | ( ) |
Are the conclusions supported by the results? | ( ) | (x) | ( ) | ( ) |
Response #1:
We greatly appreciate the reviewer’s efforts and comments, which helps us to revise our manuscript and improved the quality. Based on your valuable feedback we carefully revised methods, results and conclusions parts carefully, and language of overall paper is improved in our revised paper change highlighted in (Red).
Comments and Suggestions for Authors:
This paper provides a study concerning design response spectra compatible earthquake motion simulations. The used approach is interesting but the manuscript must be improved giving more information on the used data and explaining more in depth the used approach. Among other questions, the dependence of the response spectra with location is not clear.
Response: Thank you for your comment. Your feedback is highly appreciated; we have carefully considered your comments in more information about the data and explained in depth the used approach. We tried to make the contribution looks better.
Comment: The manuscript is very well written, and well structured. It only needs, from my point of view, a minimal revision of English by a native. In the attached manuscript, some mistakes are corrected.
Response: We appreciate the positive feedback from the reviewer. Based on your suggestion, we revised our manuscript carefully and tried to avoid the mistake in our writing and tried to make our manuscript clearly. In addition, the revised version of the manuscript has been reviewed by a native-English language and the changes are addressed. See our revised manuscript.
Specific comments:
Comment: In general, more references concerning the method and specific calculations should be included in the manuscript.
Response: As you suggested, we added 9 References [6, 12, 13, 14, 15, 25, 29, 30, and 34] and we conducted more calculations. See revised manuscript and references section in page 17 as highlighted in red color.
Comment: line 72. Northwest China-03 1997 earthquake? Please, improve the quote of this earthquake. Some reference concerning this event or accelerograms? What component(s) was (were) used?
Response: We greatly appreciate the valuable suggestions offered. Based on those suggestions, we added Table 1 under Title (Main information of recorded earthquake ground motions used in this study ….), (See Table 1 in page 4). Based on that, we re-written some parts of this section, (see our revised manuscript page 3). These changes have clearly improved the quality of our manuscript
Comment: Figure 1. More information about these plots must be given, including used records, due to they are used to justify the work done. Also to refer clearly the used earthquakes. Why authors do not use the same earthquakes/records for figures 1a and 1b? It could be interesting to show all used earthquakes, records and components in a table. Can authors explain clearly how they compute the yield acceleration? Can the authors explain why the variability is period-dependent? Are the figures independent of the used records and its distance to the epicenter?
Response: Thank you for your valuable questions, according to the reviewer’s suggestions all the information of records ground motion were added in Table 1 (See Table 1 in page 4). In all recorded ground motions, the main (first) component were used except in regression in which we used two components. We used different earthquake events with different magnitude and epicenter distance to investigate the effect of phase on nonlinear response of structure.
To compute the YSC of a target single degree of freedom system (SDOFs) we assign an initial YSC and conduct the nonlinear dynamic response analysis of the target SDFS then obtain the response ductility. If the obtained response ductility is coincided with the assigned ductility factor, the initial YSC is the aimed YSC. If the obtained response ductility differs from the assigned duality factor we modify the initial YSC until the obtained response ductility coincide with the assigned ductility factor. For more details see our revised manuscript page 3 line 84.
The variability is period-dependent. The definition of natural period is given by Equation 20, which were added in our revised manuscript (see page 14 lines 255-257)
DRSCEMs give almost same response spectrum even though the assigned Fourier phases are different but the YSC demand spectra are usually affected strongly by the assigned Fourier phases. Fig.1a emphasizes these effects of the phase on YSC demand spectra. However Fig 1b shows the effect of assigned initial Fourier amplitude on YSC demand spectra that gives a very minor effect comparing with the Fourier phases. Because these effects are well known we do not need to confirm by using many observed records. Our main concern is also not to make clear the effect of epicenter distances.
Comment: line 98 (for the first time). Please, avoid the acronym wrt along the text. It does not look good in a scientific paper.
Response: Thank you for your bright observation. According to your notation, we carefully revised our manuscript and we avoided those acronyms. Please track the revised manuscript.
Comment: lines 114-116. The used requirements of the Chinese code are a tangle. Earthquake (felt) intensity VIII or magnitude 8.0? The Chinese code considers as a rare event who happens with a return period of 475 years? An event with a probability of exceedance of 2-3% in 50 years does not have a return period of 475 years but 2500 years (for a 2%). What means medium firm for the Chinese code? What means a design earthquake group 2?
Response: Thank you for your feedbacks. In the recent seismic design code in China GB50011-2010 the seismic precautionary intensity of buildings shall be expressed by intensity 6, 7, 8 and 9.
Your raised question is reasonable. Of course In the Chinese code the return period is not clearly mentioned but based on the Reference [34] the rare earthquake event with the probability of exceedance 2-3% in 50 years is described as a return period of 1640-2475 years. We just follow this description.
Although the site class in Chinese code is defined by shear wave velocity of rock or equivalent shear wave velocity of soil but the definition of site class II (medium firm) is also taken from Reference [34]. About the design earthquake group the county-level cities in China were divided into three groups (group 1,2 and 3) according to seismic precautionary intensity and design basic acceleration of ground motion (China GB50011-2010-Appendix A). (See our revised manuscript page 5 lines 126-128)
Comment: Figure 2. Have the authors computed the values included in this figure or are they obtained from a previous paper? If they have computed them, the authors must explain how they do it (used records, ...). If not, authors must include the reference. Have the authors computed the uncertainty of the fitted parameters? Really they can give six accurate decimal digits for the parameter values? And for the computed parameters in lines 133 and 134?
Response: We developed a computer program to calculate the Hurst index and variance, because we only use Landers record to obtain Figure 2 but it is also needed to analyze 250 recorded ground motions for developing regression equations that discuss in Chapter 3. The detail process to calculate the result shown in Figure 2 is explained in section 2.2 (see lines 145-146)
According to reason putted in revised manuscript (see page 7 lines 147-149), we changed all the digits in our manuscript to three digits.
Comment: Line 144. What means Joshua Tree time history? Please, refer correctly the earthquake, the station and the used components.
Response: Thank you for good comment. We added all information of this record in Table 1. (See page 4). We revised this part in page 6 in our revised manuscript.
Comment: Figures 4 and 5. These figures are confusing with relation to the used data. A response spectra depend on the earthquake and the location. The same happens with figure 9.
Response: Thank you for your suggestion. To make clear the used data, this section was re-written with providing a clear explanation of all figures. (See revised manuscript paragraph 2.4 and figures 4 and 5 captions)
Furthermore in revised manuscript we explain the reason of reduction of fluctuation in the nonlinear response spectra when we use simulated phases based on fBm process comparing to the case of using observed earthquake motion phases. For the case of Fig.9, we would like to demonstrate that using average Fourier amplitude as the initial Fourier amplitude is better than using the initial Fourier amplitude of only one record. Because the YSC demand spectrum is located within the fluctuation range of those YSC demand spectra and more smoother.
Comment: Line 180. Can authors explain what is the bias index?
Response: Bias index is usually added to the regression equation to reduce the bias effect of used data set. For example in Eq. (16) the bias index is equal to ?6.
Author Response File: Author Response.pdf
Reviewer 2 Report
Authors have presented a method to construct spectrum compatible earthquake motion using fractional Brownian motion. The topic is interesting and definitely structural earthquake engineers are in dire need of this thing. Although the authors claim that their output would be significant to nonlinear dynamic analysis, they did not present a case study. If possible, please include one. The paper is average but does have merits to be accepted once the authors address major comments as follows:
a) Background: -I don't think that synthetic accelerograms can replace recorded time histories. Rather you need to write that they are scarce and cannot fulfill the demand each time.
-Line 31-33: Why such information is needed for a structural engineer?
-LIne 35: Although the argument is true, the uncertainties associated with synthetic accelerogram generation are not graver? Please clarify.
- Line 41: Please include examples.
Line 59: Please, also write about the development of methods, e.g. stochastic method of synthetic accelerogram generation, and so on.
LIne 62: Some of the researchers have also compared with real-time data, please check e.g. https://www.sciencedirect.com/science/article/pii/S1631071317300718
Fig. 2: Please provide the coefficient of determination in the figure.
Conclusion: Please rewrite the conclusion using your results. What is the applicability of the method beyond China, e.g. in very much different seismotectonic setting? Please also discuss the results in comparison with other results and try to justify why your method is unique though superior or relative standing of your method amongst similar approaches.
- Please take care of typos in several locations of the manuscript.
Author Response
Response to Reviewer 2 Comments:
We wish to express our appreciation to the Reviewers for their insightful comments and constructive suggestions, which have helped us significantly to improve our manuscript. According to the suggestions, we have thoroughly revised our manuscript and its final version is enclosed. Point-by-point responses to the comments are listed below. Our response follows (the reviewer’s comments are: Reviewer 1 is in “Red” and Reviewer 2 in “Blue”) in our revised manuscript.
Open review: (x) I would not like to sign my review report
( ) I would like to sign my review report
English language and style:
( ) Extensive editing of English language and style required
(x) Moderate English changes required
( ) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style
Yes | Can be improved | Must be improved | Not applicable | |
Does the introduction provide sufficient background and include all relevant references? | ( ) | ( ) | (x) | ( ) |
Is the research design appropriate? | ( ) | (x) | ( ) | ( ) |
Are the methods adequately described? | (x) | ( ) | ( ) | ( ) |
Are the results clearly presented? | (x) | ( ) | ( ) | ( ) |
Are the conclusions supported by the results? | ( ) | ( ) | (x) | ( ) |
Response #2:
We greatly appreciate the reviewer’s efforts and comments, which helps us to revise our manuscript and improved the quality. Based on your valuable feedback we carefully revised introduction, research objective and conclusion parts carefully, and language of overall paper is improved in our revised paper. Changes are highlighted in (Blue).
Comments and Suggestions for Authors:
Authors have presented a method to construct spectrum compatible earthquake motion using fractional Brownian motion. The topic is interesting and definitely structural earthquake engineers are in dire need of this thing. Although the authors claim that their output would be significant to nonlinear dynamic analysis, they did not present a case study. If possible, please include one. The paper is average but does have merits to be accepted once the authors address major comments as follows:
Response: Thank you for your comment. Your feedback is highly appreciated; we have carefully considered your comments in the introduction section of revised manuscript. For the case study, we apply this method to the reinforced concrete structure (MDOF) in the next paper. It is not included in this paper because it needs large space to explain detail, such as making prototype model, defining cross sections and material properties, conducting pushover analysis, converting the multi-story to the SDOF system for being able to apply the proposed method.
Comment: Background: -I don't think that synthetic accelerograms can replace recorded time histories. Rather you need to write that they are scarce and cannot fulfill the demand each time.
Response: Thank you very much for your suggestion. We consider your opinion in our revised manuscript. (See page 2 lines 33-37). But our opinion is that synthetic accelerograms are needed in engineering field. Why a synthetic accelerogram is necessary for design purpose is very simple. Even for the case of an elastic seismic design of a structural system, it is usually not so easy to obtain a proper recorded accelerogram to be used for design purpose at the design site, which satisfies a target earthquake magnitude and epicenter distance as well as the site condition. Needless to say for the case of nonlinear seismic design of a structural system. Our main concern is to develop an algorithm to generate an earthquake motion phase to be use for simulating DRSCEM, which satisfy the seismic force condition in the code at the design site. Therefore we develop regression equations of Hurst index and its standard deviation as functions of the earthquake magnitude, epicenter distance and site condition.
Comment: Line 31-33: Why such information is needed for a structural engineer?
Response: To design a structure in seismic environments we need a seismic force acting to the structure. The most simple case to define the seismic fierce is to assign a time history of earthquake motion for dynamic analysis of the structural system. Usually this kind of the time history of earthquake motion is defined at the base rock level of the ground and consider the amplification effect of the layered ground as well as the irregular profile of the ground. If there is an earthquake fault that moves during earthquake causes the permanent displacement on the surface and result in structural damage. At lines 28-31 in pages 1and 2, Considering these effects to design a structure is common in seismic engineers.
Comment: Line 35: Although the argument is true, the uncertainties associated with synthetic accelerogram generation are not graver? Please clarify.
Response: Thank you for your remarkable comments. We just mentioned the well-known sources of uncertainty controlling time histories of synthesized earthquake motions. It is a trend in the field of seismic design of structures to take into account these uncertainties as mentioned in Reference [15] to simulate earthquake motions to be used for dynamic analysis of the structural systems. (See page 2 lines 46-49)
[15] Irikura Recipi, Strong ground motion prediction method for earthquakes with specified source faults,
https://www.jishin.go.jp/main/chousa/16_yosokuchizu/recipe.pdf#search=%27%E5%85%A5%E5%80%89%E3%83%AC%E3%82%B7%E3%83%94%27
Comment: Line 41: Please include examples.
Response: Thank you for your suggestions. If you suggested to include an example of seismic design of a structural system, it is not possible because of the space limitation in the current manuscript and we will discuss in our future paper. But if you suggested to show examples of simulated time histories of DRSCEMs it would be unnecessary because the usage of DRSCEM is too common for the nonlinear seismic design of structural system.
Comment: Line 59: Please, also write about the development of methods, e.g. stochastic method of synthetic accelerogram generation, and so on.
Response: Thank you for your feedback. The method to simulate time histories of earthquake motions based on the Gaussian stochastic process has been developed in 1960 but it is not worthwhile to summarize here because our main concern is concentrated on the usage of DRSCEM and also the methods to simulate DRSCEMs. Those are summarized in the INTRODUCTION.
Comment: Line 62: Some of the researchers have also compared with real-time data, please check e.g. https://www.sciencedirect.com/science/article/pii/S1631071317300718
Response: Thank you so much for your valuable information. We added this information and that reference in our revised manuscript. (See page 2 line 37, and reference [6].
Comment: Fig. 2: Please provide the coefficient of determination in the figure.
Response: Thank you for this question. We think that the method to calculate as a function of is well defined through Equations. (6) and (7) in page 6. A simple least square fitting of Equation (8) to those data can be defined the coefficients of the equation in Figure 2. Those processes are explained just above the Equation (8) in page 6. The only changes are the effective digits from 6 digits to 3 digits.
Comment: Conclusion: Please rewrite the conclusion using your results. What is the applicability of the method beyond China, e.g. in very much different seismotectonic setting? Please also discuss the results in comparison with other results and try to justify why your method is unique though superior or relative standing of your method amongst similar approaches.
Response: Thank you very much for your valuable suggest, as you suggested, we revised the section of the conclusion. (See revised paper page 16). The seismic design force is usually defined by the elastic response spectrum after consideration of seismotectonic environment to simplify the design procedure. Because the method to define the design elastic response spectrum is almost same everywhere in the world, we discuss in this manuscript to develop a method to simulate DRSCEM taking into account the phase uncertainty that reflect the uncertainty caused by the complexity of seismotectonic environment.
Comment: Please take care of typos in several locations of the manuscript.
Response: Thank you a lot for your feedback, so we revised our manuscript carefully and tried to avoid the mistake in our writing and tried to make our manuscript clearly. In addition, the revised version of the manuscript has been reviewed by a native-English speaker and the changes are addressed. See our revised manuscript.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The paper can be accepted for publication in current form.
