Upper Bound Solution Analysis of the Ultimate Bearing Capacity of Two–Layered Strip Foundation Based on Improved Radial Movement Optimization
Round 1
Reviewer 1 Report
The manuscript by the authors describes an upper bound solution in conjunction with a planar kinematically permissible multi-block failure mechanism for determining the maximum load capacity of a two-layered strip foundation. The work is interesting, I just have some notes concerning clarity of the method and results, it would be very nice if a Nomenclature illustrating all the parameters appeared in the manuscript is added, for papers focusing on theory. The results can be better presented if all the result figures and font size can be arranged more or less in the same level. Some of the figures are very similar to what has already been published by the same author, for example, Fig. 10 is very similar to Fig. 4 in the paper ‘Research on Horizontal Directional Drilling (HDD) Trajectory Design and Optimization Using Improved Radial Movement Optimization’, a reference is needed for the figure to avoid plagiarism. Also, it would make the novelty more clear if the authors can state in the introduction about the difference of this paper and other published paper by the same author, i.e. the author’s previous work concerned with upper bound method. Overall, it is a good study on this subject, the text is clear and easy to read, the conclusions consistent with the evidence and arguments presented, this work reminded me of some published articles on application of upper bound with more or less approach on the maximum load capacity. In case authors are interested. and for possible citation: https://doi.org/10.1016/j.ijmecsci.2018.02.028;https://doi.org/10.1016/j.ijmecsci.2013.03.010.
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Reviewer 2 Report
The author deals with the planar kinematically permissible multi-block failure mechanism based on the upper bound limit analysis theorem. The authors applied The improved radial movement optimisation (IRMO) algorithm to find a critical slip surface and to calculate a two-layered strip foundation's ultimate bearing capacity while optimizing both processes.
The author has compared the results with previous research, but there are few; it would be better if there are more validation examples.
The author should improve the introduction, the author should clarify the existing studies to show the motivation of this study.
The manuscript has a slightly high duplicate rate, the author should try to correct it to reduce the duplicate rate
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Reviewer 3 Report
This paper presents a kinematically permissible planar multi-block failure mechanism, based on the upper-bound limit analysis theorem, for estimation of the maximum load-bearing capacity of a two-layered strip foundation. The IRMO optimisation algorithm is adopted for identifying the critical slip surface and determining the ultimate bearing capacity of a two-layered strip foundation.
The topic of the study is interesting and will be of interest to the readership of the journal. The methodology is presented with adequate details. The proposed methodology is then verified through two examples. The paper is generally well written and structured. I only have a few minor comments on this work:
- One of the assumptions of the proposed method is the selection of the Mohr-Coulomb constitute model along with associativity. However, it is known that associated Mohr-Coulomb model over estimates the dilatancy of the soil. What are the implications of this? A discussion is needed in this regard.
- The methodology is only discussed for dry soils. What happens is the soil is saturated? How the pore water pressure effects can be incorporated into the proposed method?
- The problem of foundation on layered soil is in general complicated, hence in practice, it is often solved using numerical techniques such as the finite element method (FEM), finite difference method (FDM) or meshfree methods (MM). However, using numerical methods for obtaining the bearing capacity has not been mentioned in the introduction of the paper. For the completeness of the introduction, the authors need to add at least a sentence to the introduction to mention different numerical methods (FEM, FDM and MM) and cite a few references in this regard. I suggest citing at least the following references:
- Lee, J. K., et al. (2016). "Undrained bearing capacity of ring foundations on two-layered clays." Ocean Engineering 119: 47-57.
- Tootoonchi, A. and A. Khoshghalb (2021). "A smoothed meshfree method for simulation of frictional embedded discontinuities." Tunnelling and Underground Space Technology 107: 103666.
- Burd, H. J. and S. Frydman (1997). "Bearing capacity of plane-strain footings on layered soils." Canadian Geotechnical Journal 34(2): 241-253.
- Lavasan, A. A., et al. (2018). "Bearing Capacity of Interfering Strip Footings." Journal of Geotechnical and Geoenvironmental Engineering 144(3).
- Shafee, A, A. Khoshghalb, “Augmenting low-order finite element method with partial nodal strain smoothing for flow-deformation analysis of geomechanical problems”. Int J Numer Anal Methods Geomech. 2022; 46: 3178– 3199.
- Salehi Dezfooli, M., A. Khoshghalb and A. Shafee (2022). "An Automatic Adaptive Edge-based Smoothed Point Interpolation Method for Coupled Flow-Deformation Analysis of Saturated Porous Media." Computers and Geotechnics 145: 104672.
- Kalourazi, A. F., et al. (2020). "Bearing Capacity of Strip Footings Adjacent to Anisotropic Slopes Using the Lower Bound Finite Element Method." International Journal of Geomechanics 20(11).
- Shafee, A. and A. Khoshghalb (2021). "An improved node-based smoothed point interpolation method for coupled hydro-mechanical problems in geomechanics." Computers and Geotechnics 139: 104415.
- Liu, P. F., et al. (2018). "Application of semi-analytical finite element method to evaluate asphalt pavement bearing capacity." International Journal of Pavement Engineering 19(6): 479-488.
- Shafee, A. and A. Khoshghalb (2022). "Particle node-based smoothed point interpolation method with stress regularisation for large deformation problems in geomechanics." Computers and Geotechnics 141: 104494.
I also noticed a few typos/poor sentences in the text (e.g., lines 15-16, 280, etc.), so I suggest the author read the whole text one more time to remove all the typos.
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Reviewer 4 Report
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