Near-Fault Seismic Response Analysis of Bridges Considering Girder Impact and Pier Size

Round 1

Reviewer 1 Report

The paper titled “The Influence of Bridge Pier Size on Structural Failure Under the

Condition of Separation” deals with a T-shaped frame structure simulating typical highway bridges in China. The structure is supported by two hinged and one fixed support. The horizontal and the vertical element are connected with a two-direction spring. The constitutive law applied to the bridge’s material is Hooke’s law of linear elasticity. An analysis is made of the mechanical behavior of the structure under harmonic dynamic loading, for which purpose complex analytical solutions have been developed for different stages of the structure’s dynamic response. Results of varying input parameters are analyzed too.

Critical comments about the content of the paper:

• The title of the paper does not fully correspond with the content of the paper.
• The harmonic dynamic loading incorrectly is identified with a seismic loading.
• The solutions for the stage of cyclic separation between the main horizontal beam and the middle pier have only theoretical contributions. These solutions are not applicable to real bridge structures.
• It is not clear how the values of the natural periods are obtained: T_s = 0,5s, T_v = 0,22s and the values of T_s in Table 2 and Table 3.

Critical comments about the style in the paper:

• There are many cases where the same text or symbol is used in both regular font and italics in different parts of the text. For example: T, T; V,V; H, H; n, n;

AB, AB; CD, CD; q, q; k, k; α, α; β, β ……

• There are many undefined symbols. For example: ρ, φ_mb1, φ_mb2, φ_mn, k_bn, k_rn,

    q_n(t), ς, t⁺, t^-, ω_b1, ω_r1, ω_bn, ω_bd, ω_rd, h_nb, h_nr, M_t, M_r, OA, OB, CD…..

• There are cases where a different letter size is used in the text.

Lines 110, 119, 359.

• There are figures where the size of symbols is very small and it is difficult to read them.

Figures 1, 7-11,13, 14.

• There is a figure where the vertical axis is not denoted correctly: Figure 6.

Critical comments about the English in the paper:

• The level of the English is low: there are many wrong or incorrect terms and phrases and grammar mistakes. Some examples include:

Lines 65, 105, 108, 113, 118, 135, 136, 141, 142, 146, 150, 165, 175, 176, 183, 184, 215, 217, 223, 248, 249, 259, 261, 270, 280, 283, 285, 297, 425, 427,455,

459, 462, 463, 464, 496 … 

I recommend that:

• The content should be revised according to the above mentioned critical comments 1.1-1.4;

The style and language should be corrected according to the above mentioned critical comments 1.5-1.10.

Author Response

1. Attached is the revised manuscript. An explanation of each comment is provided at the end of the article               

2. Because my English level is not high, I asked the magazine to polish my English about the author's service.

3. Because my English level is not high, I asked the magazine to polish my English about the author's service.

Author Response File: Author Response.docx

Reviewer 2 Report

Explain better why the separation significantly changes the longitudinal response of the bridge (the mechanism by which the significant change happens).

line 66, 67: I am not sure about China, but it is generally good practice in bridge design to tie the deck to the abutments and piers, so that separation is precluded.

Overall proofreading is needed. Sentences that require particular attention are the following:

start line 26, end line 28; start line 68, end line 70; start line 90, end line 91; start line 109, end line 111; start line 120, end line 121; start line 131, end line 133; start line 305, end line 306; start line 323, end line 325; start line 366, end line 369; start line 393, end line 395; start line 441, end line 443; start line 531, end line 532; start line 533, end line 535; start line 566, end line 566.

line 45: which exactly is the “above study”?

line 52, 53: This is not true for all records from the Kobe earthquake. Either specify which record, or say “for some records”.

line 99: you say “Both ends of the bridge girder are simply supported”, but it is not clear are they free to move horizontally or not. The symbol you use for these bearings in Fig. 1 implies they are not free to move horizontally (look like pin supports). On the other hand, common sense says they must move horizontally, since otherwise the rubber bearing in the middle will be largely meaningless. Good practice for such bridges is that all bearings, pier and abutments alike, are rubber ones. You must say explicitly in the paper whether these are rollers or pins (hinges) or rubber bearings.

line 104: the description of D(t) and B(t) does not match what is shown in Fig. 1.

line 128 to 133: What you say there is not true since separation introduces nonlinearity and the superposition method is not applicable.

line 303 to 305: say explicitly whether the bearing properties are for a single bearing or a total for the pair of bearings in Fig. 2. I assume it is for a single bearing.

It is not exactly clear what is the amplitude and period of the input motion you use in the analyses. For example, when you use “earthquake excitation period T=0.5” does it mean that you use it for the horizontal shaking only while for the vertical shaking you use “earthquake excitation period T=0.22s”. In other words, within a single analysis do you use the same excitation period for the horizontal and vertical excitation or different periods?

line 335, 336: What you say there implies that the longitudinal natural period of the bridge is around 0.5 s. What is the corresponding vibration mode for this period? If the horizontal natural period of the beam considered as a rigid body sitting on the rubber bearings is computed with the data from Table 1 the natural period is 2.5 s for two rubber bearings (pier only) and 1.4 s for six rubber bearings (pier and abutments). And this is lower bound, since the flexibility of the pier is not included.

Vertical axis title of Fig. 6 wrong.

line 376: η (eta) not defined.

line 380: Figure 8, not 7.

Table 2: Not clear what mode of vibration the listed natural periods correspond to. The longitudinal period is governed by the stiffness of the rubber bearing and the stiffness of the pier has only minor effect on it. See comment for line 335 above.

Figure 9. Seem to me that the results shown make sense only if the abutment supports cannot move horizontally, so effectively the beam acts as a horizontal support to the pier and not the other way around. Same impression for Fig. 10, Fig. 7

Table 3. Pier diameter, not height. Not clear what mode of vibration the listed natural periods correspond to. The longitudinal period is governed by the stiffness of the rubber bearing and the stiffness of the pier has only minor effect on it. See comment for line 335 above. If we assume as mode shape the first mode shape of a cantilever (separated condition) the natural period of the 15 m high, 1.2 m diameter pier would be 0.16 s., very different from the value 0.491 listed in Table 3.

Figure 13. I suggest mentioning in the text that the increase of M_z is due to the increase of mass, and to delete the sentence between lines 503 and 505.

General comment about the parametric study: Instead of using the pier height and the pier diameter as parameter is would have been better combining them into a single parameter, ideally a dimensionless one. The parameter related to the flexural stiffness would have been a good one.

Author Response

1. Attached is the revised manuscript. An explanation of each comment is provided at the end of the article

2. Because my English level is not high, I asked the magazine to polish my English about the author's service.

3. Because my English level is not high, I asked the magazine to polish my English about the author's service.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper deals with the seismic failure of bridges due to separation and the influence of pier size on it. The paper seems well written to this reviewer and could be of interest for readers. However, some improvements are needed.

Comments:

The isolation solution that is considered in the paper should be better emphasized from the beginning: title, abstract, introduction, etc.

Page 2 row 65 a typo occurred. Please check the manuscript.

The description on the way the authors employed to model the isolation devices should be improved. Is it hysteretic? Or equivalent linearization approach has been used? Please give details.

Authors should give more and accurate details on the numerical modelling of the device they are using and the way it may affect the numerical approach and conclusions.

The state of the art on the isolation topic should be also improved. There are a number of literature contributions on the limit state of deformation and fragility analysis of base isolated structures, in particular on how isolators become the critical components in terms of ensuring adequate protection for base isolated structures. Moreover, contributions could be also mentioned on the developments of innovative isolation devices with respect to the vertical earthquake component and the limitation of the maximum horizontal displacement across the device. The following ones among others could be mentioned in the literature review.

“Three-Dimensional base isolation using vertical negative stiffness devices”, Journal of Earthquake Engineering. 2020, 24(12), pp. 2004-2032.

“Reduced-order coupled bidirectional modeling of the Roll-N-Cage isolator with application to the updated bridge benchmark”, Acta Mechanica 2015, 226(10), 3533-3553.

 

Author Response

1. Attached is the revised manuscript. An explanation of each comment is provided at the end of the article

2. Because my English level is not high, I asked the magazine to polish my English about the author's service.

3. Because my English level is not high, I asked the magazine to polish my English about the author's service.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Thank you for the clarifications!

The natural periods are now correct. I also made a mistake in my first review.

I still don’t think what you say about superposition on lines 127-130 is correct. If you run your model with two separate sine waves and add together the responses, you will not get the same response if you run a single analysis with the two sine waves added together (if separation occurs). I suggest you try this and then decide whether to keep the sentence on lines 127-130 or to delete it.

Author Response

I agree with you that my paragraph is misrepresented. Now deleted

 

Author Response File: Author Response.docx

Reviewer 3 Report

The Authors modified the manuscript according to the reviewer's comments and, in the opinion of this reviewer, it could be accepted for publication in the present form.

Author Response

Thank you very much for your review comments

Author Response File: Author Response.docx