Influence of Bearing on Pier Failure Considering the Separation Condition under Near-Fault Earthquake

Round 1

Reviewer 1 Report

The authors present the results of the study the influence of the near-fault vertical earthquake in case of the double span continuous beam bridge. The transient wave function expansion method and the indirect mode function method are used to calculate the seismic response of the bridge. The theoretical solutions of the contact force and displacement response of the bridge under vertical earthquake excitation near-fault are considered in this paper. The influence of stiffness and damping of bearing on pier failure under three different pier heights were considered. The results of the numerical analysis are presented on conclusions.

There are several formal errors in this article :

• The number of references in this paper is 25. But the article cites the paper under number 28 (page 7). Such this publication is not included in the list of references.
• Authors : on page 8, row¯ 5 -  “…The positive and negative signs in Eq. 26 denote the relationship between force and displacement direction….”

      Reviewer comments: The negative signs are not written in (26) but in (27).

• Authors : on page11, row­ 8  - “…eccentric vertical collision is ?? = ???? × ? × ∆?; ...

Reviewer comments: The parameter ?  is not defined.

• Authors : The first letter in the description of figures (Fig.3, 4 5, 7, 8, 9, 11 and 12) start as lowercase letter. name must be an uppercase letter

Reviewer comments: The figure description has to start with the uppercase letter.

Author Response

Thanks for the reviewer's comments. I have revised all the comments mentioned by the reviewer.

Author Response File: Author Response.pdf

Reviewer 2 Report

1. I'm not convinced the term 'the influence of vertical separation on pier bending failure' is the best description of your research. The separation may increase the forces in the pier, but it does not change bearing capacity of the pier (see Fig. 5). Besides when analyzing the failure of a specimen, is is not possible to carry forces 'outside' the failure envelope (it is not physical). In your paper the material is linear elastic (without any limits).
2. Is the assumption about prestressed box girder is important (page 8)? Where do you use this assumption?
3. Why different values of stifnesses and damping factors are given in pages 3 and 9?
4. What is the length of a span?
5. In your model there is no penalty stiffness to prevent penetration of the girder and pier (see Fig. 3). Am I right? This penetration (The relative displacement) can be approximately equal to 20 mm. Is is physical? Can you reduce it (penalty stiffness)? Can you comment it? What is the influence of this assumption on all results? When these both elements are separated what is about the horizontal force? It is set to zero also?
6. In conclusions you state: When T_v > T_s and T_v ≈ T_s , the vertical earthquake causes the separation of the girder and the pier - is it true for all geometries? Excitations? Only one case was studies here.
7. Minor remarks:
   1. page 1: using three height piers -> using piers with three different heigths
   2. page 1: As a transportation hub, under the action of the earthquake, the destruction of the bridge not
   3. only destroyed the transportation counterparts, but also affected the subsequent post-disaster rescue - why the simple past tense is used here?
   4. page 1: In the above study of- which one? or maybe 'studies'?
   5. page 2: Unlike most building structures, the span of the bridge is large ... / Unlike most building structures, the span of a bridge is usually long .. - This sentence (and the next one) are almost the same. Why they are repeated?
   6. page 2: n addition -> In addition
   7. page 3: The calculation model is shown in Figure 1 - this information was provided earlier (at the bottom of the page 2)
   8. page 4: is the axial pressure of the initial girder - what is an initial girder? Do you mean initial pressure?
   9. page 5: Eqn 13 - symbol A is used, to you mean A_b (check also other equations)?
   10. page 5: Can solve for M_n and A_n -> one can solve
   11. page 8: In the stage of impact contact, the displacements of the girder and the pier are different - Its too general sentence. Where?
   12. Page 10. Fig. 2: horizontal axis: times -> time, legend: not separation -> no separation
   13. Page 12: bending moment damage - how is it defined?       
   14. Page 16: (c) -> (b)

 

Author Response

Please see the attachment

Author Response File: Author Response.docx