An Explicit Finite Element Method for Saturated Soil Dynamic Problems and Its Application to Seismic Liquefaction Analysis
Round 1
Reviewer 1 Report
I appreciate the invitation to review the manuscript entitled “An explicit finite element method for saturated soil dynamic problems and its application to seismic liquefaction analysis”, whose proposal presented contributes to the improvement of computational models.
The work itself presents an introduction with the main studies related to the theme, followed by the objective of the work. It then describes the proposed formulations to achieve the objectives. Finally, the work ends with a comparative analysis of the proposed model in relation to known models in the literature, indicating that the suggested model has results similar to models present in the literature, but with reduced computational cost.
On line 156 there is a typo, it's equations (6) and (6), I imagine it's equations (6) and (7). Check legend some figures.
Author Response
Reply to #1 reviewer
I appreciate the invitation to review the manuscript entitled “An explicit finite element method for saturated soil dynamic problems and its application to seismic liquefaction analysis”, whose proposal presented contributes to the improvement of computational models.
The work itself presents an introduction with the main studies related to the theme, followed by the objective of the work. It then describes the proposed formulations to achieve the objectives. Finally, the work ends with a comparative analysis of the proposed model in relation to known models in the literature, indicating that the suggested model has results similar to models present in the literature, but with reduced computational cost.
Comments 1:
On line 156 there is a typo, it's equations (6) and (6), I imagine it's equations (6) and (7). Check legend some figures.
Reply:
Many thanks for the referee’s kind reminding.
According to the reviewer’s advice, we have corrected the content in the revised manuscript.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This paper needs to be revised via follows:
* [4-11] these papers should be written clearly.
* Eq.(2) needs to be ended with COMMA.
*Line 108 needs to be ended with POINT.
*At the end of all equations must be putted "COMMA" or "POINT" according to the typing rules. Therefore, they need to pre-check all the paper.
*Figure 2. needs to be explained a little more.
* The results and findings should be compared to and discussed in the context of earlier work in the literature such as; Calculating university education model based on finite element fractional differential equations and macro-control analysis; Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design; Calculation of tourism development income index based on finite element ordinary differential mathematical equation; Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model; Response model for the psychological education of college students based on non-linear finite element equations; Children’s cognitive function and mental health based on finite element nonlinear mathematical model; Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory; Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation;
*They need to explain what is the menaings of figures.
* The authors are requested to add more details regarding their original contributions in this manuscript.
Author Response
Reply to #2 reviewer
This paper needs to be revised via follows:
Comments 1:
[4-11] these papers should be written clearly.
Reply:
Many thanks for the referee’s kind comments.
The main object of this paper is a new numerical computational method. Literatures 4-11 describe the damages to the structure due to the large deformation caused by the liquefaction. Therefore, we focus on numerical analysis methods based on different saturated formulations rather than the damage of structures.
Comments 2:
Eq. (2) needs to be ended with COMMA.
Line 108 needs to be ended with POINT.
At the end of all equations must be putted "COMMA" or "POINT" according to the typing rules. Therefore, they need to pre-check all the paper.
Reply:
Many thanks for the referee’s kind reminding.
According to the reviewer’s advice, we have corrected partially the content in the revised manuscript.
Comments 3:
Figure 2. needs to be explained a little more.
Reply:
Thanks for your valuable comments.
According to the reviewer’s advice, we add corresponding explanations for Fig. 2.
Comments 4:
The results and findings should be compared to and discussed in the context of earlier work in the literature such as; Calculating university education model based on finite element fractional differential equations and macro-control analysis; Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design; Calculation of tourism development income index based on finite element ordinary differential mathematical equation; Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model; Response model for the psychological education of college students based on non-linear finite element equations; Children’s cognitive function and mental health based on finite element nonlinear mathematical model; Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory; Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation;
Reply:
Thanks for your valuable comments.
As the reviewer considered, we verified the proposed method by comparing with other method, such Newmark Implicit method and Xu’s method in example 2 and 3.
Comments 5:
They need to explain what is the meanings of figures. The authors are requested to add more details regarding their original contributions in this manuscript.
Reply:
Thanks for your valuable comments.
The main contents in figures are described in the manuscript.
Author Response File: Author Response.docx
Reviewer 3 Report
The present manuscript proposes an explicit finite element method for saturated soil dynamic problems and demonstrates its application to seismic liquefaction analysis. The research topic is very interesting, the presentation is in general easy to follow and the importance of the manuscript to computational mechanics and computational geomechanics is relatively high. I recommend it for publication. Recommendations of minor revision are following
R1 In the introduction there should be a sentence to portray the porous media theory importance in practical applications in Geotechnics. So, in line 24 after the first text sentence should be entered the following text
«The porous media theory and computational schemes have an important influence in geomechanics. Specifically, porous media analyses govern the physical behaviour of cohesive soils consolidation and failure[citations1-4] and cohesionless soils [citations 5-6] response when subjected to static and dynamic loading.»
Where [citations] are
1 Houmadi Y, Benmoussa MYC, Cherifi WNEH, Rahal DD (2020) Probabilistic analysis of consolidation problems using subset simulation. Comput Geotech 124:103612.
2 Savvides AA, Papadrakakis M (2020) A probabilistic assessment for porous consolidation of clays. SN App. Sci. 2(12):2115.
3 Ashraf A, Soubra AH (2012) Probabilistic analysis of strip footings resting on a spatially random soil using subset simulation approach. Georisk Assess Manage Risk Eng Syst Geohazards 6(3):188–201
4 Savvides, A.A., Papadrakakis, M. A computational study on the uncertainty quantification of failure of clays with a modified Cam-Clay yield criterion. SN Appl. Sci. 3, 659 (2021). https://doi.org/10.1007/s42452-021-04631-3
5 Uncertainty quantification and propagation in the modeling of liquefiable
Sands Vicente MercadoFelipe Ochoa-CornejoRodrigo AstrozaWaleed El-SekellyTarek AbdounCesar PasténFrancisco Hernández Soil dynamics and Earthquake engineering 123 2019 p 217-229
6 Quantification of Model Uncertainty in Shear Strength Predictions for Fiber-Reinforced Sand Shadi S. Najjar, A.M.ASCE; Salah Sadek, M.ASCE; and Alexander Alcovero Journal of Geotechnical and Geoenvironmental Engineering Volume 139 Issue 1 - January 2013
R2 It would be convenient to write down the equations for the 3D problem or equivalently to clearly depict the differences between 2D and 3D cases. It would also strengthen the importance and the computational efficiency of the proposed algorithm to present a small example in 3D case. It is more important to provide the equations of the algorithm in the 3D case.
R3 What is Parameter 1, Parameter 2, Parameter 3 in Table 3? Please make them clear because the reader may not be very familiar with Opensees and the references pointed out for the material constitutive modelling do not write it clearly. Also in equation 16 what is ?
R4 In Conclusion it is nice to propose the best computational strategy for using the proposed algorithm. Please refer to your results in Fig 7 but add the statement that the generality of the strategy proposed needs to be confirmed for various types of analyses
Author Response
Reply to #3 reviewer
The present manuscript proposes an explicit finite element method for saturated soil dynamic problems and demonstrates its application to seismic liquefaction analysis. The research topic is very interesting, the presentation is in general easy to follow and the importance of the manuscript to computational mechanics and computational geomechanics is relatively high. I recommend it for publication. Recommendations of minor revision are following
Comments 1:
R1 In the introduction there should be a sentence to portray the porous media theory importance in practical applications in Geotechnics. So, in line 24 after the first text sentence should be entered the following text.
«The porous media theory and computational schemes have an important influence in geomechanics. Specifically, porous media analyses govern the physical behaviour of cohesive soils consolidation and failure[citations1-4] and cohesionless soils [citations 5-6] response when subjected to static and dynamic loading.»
Where [citations] are
1 Houmadi Y, Benmoussa MYC, Cherifi WNEH, Rahal DD (2020) Probabilistic analysis of consolidation problems using subset simulation. Comput Geotech 124:103612.
2 Savvides AA, Papadrakakis M (2020) A probabilistic assessment for porous consolidation of clays. SN App. Sci. 2(12):2115.
3 Ashraf A, Soubra AH (2012) Probabilistic analysis of strip footings resting on a spatially random soil using subset simulation approach. Georisk Assess Manage Risk Eng Syst Geohazards 6(3):188–201
4 Savvides, A.A., Papadrakakis, M. A computational study on the uncertainty quantification of failure of clays with a modified Cam-Clay yield criterion. SN Appl. Sci. 3, 659 (2021). https://doi.org/10.1007/s42452-021-04631-3
5 Uncertainty quantification and propagation in the modeling of liquefiable Sands Vicente MercadoFelipe Ochoa-CornejoRodrigo AstrozaWaleed El-SekellyTarek AbdounCesar PasténFrancisco Hernández Soil dynamics and Earthquake engineering 123 2019 p 217-229
6 Quantification of Model Uncertainty in Shear Strength Predictions for Fiber-Reinforced Sand Shadi S. Najjar, A.M.ASCE; Salah Sadek, M.ASCE; and Alexander Alcovero Journal of Geotechnical and Geoenvironmental Engineering Volume 139 Issue 1 - January 2013
Reply:
Thanks for your valuable comments.
According to the reviewer’s advice, we have added the content in the revised manuscript.
Comments 2:
It would be convenient to write down the equations for the 3D problem or equivalently to clearly depict the differences between 2D and 3D cases. It would also strengthen the importance and the computational efficiency of the proposed algorithm to present a small example in 3D case. It is more important to provide the equations of the algorithm in the 3D case.
Reply:
Thanks for your valuable comments.
The relevant work will be given in future papers.
Comments 3:
What is Parameter 1, Parameter 2, Parameter 3 in Table 3? Please make them clear because the reader may not be very familiar with Opensees and the references pointed out for the material constitutive modelling do not write it clearly. Also in equation 16 what is ?
Reply:
Thanks for your valuable comments.
Cs1-Cs3 are the parameters defining a straight critical-state line ec in e-p’ space[1]. According to the reviewer’s advice, we have added the content in the revised manuscript.
[1] YANG ZH, LU J, ELGAMAL A. OpenSees soil models and solid-fluid fully coupled elements[J]. User’s Manual. 2008.
Comments 4:
In Conclusion it is nice to propose the best computational strategy for using the proposed algorithm. Please refer to your results in Fig 7 but add the statement that the generality of the strategy proposed needs to be confirmed for various types of analyses.
Reply:
Thanks for your valuable comments.
According to the reviewer’s advice, we add corresponding explanations in conclusion.
Author Response File: Author Response.docx
