Impact of Cyclic Loading on Shakedown in Cohesive Soils—Simple Hysteresis Loop Model

Round 1

Reviewer 1 Report

The paper presents a model (SHLM) capable to predict permanent (plastic) strain deformations developed during cyclic loading. The model has been validated with stress controlled cyclic triaxial tests.

The paper is undoubtedly original, fit the scope of the journal and has a valuable practical interest. It is well organized and rigorous in all the steps followed by authors: a comprehensive literature review, a clear background on cyclic behavior of soils, a clear description of tested soil and tests executed. The results are deeply discussed, and the quality of figures is good. The English language and style are good.

I therefore recommend the publication in the journal after a round of minor revisions. I have some suggestions mainly to improve the organization of the manuscript.

Major issues:

Paragraph 4.2 is too long and heavy; some tables can be moved in an Appendix; otherwise, I strongly suggest to insert a paragraph with the main analytical relationships to be used by model users, with a clear indication of the four constants to be specified and the values of “hidden” parameters determined on the basis of the test carried out in the research An short application to a real or idealized case (foundation of vibrating machine ?) should be a valuable improvement

Minor issues:

In the introduction I suggest to define all the parameters in the equations (eps,a is the axial permanent strain, qmax, qmin and so on) Typos: row 224 check “W” Paragraph 4.1 on pore pressure build up seems not relevant for the model application; I suggest to highlight the role of pore pressure in soil stiffness degradation

Author Response

Respond for Review Report 1 for submission of a paper to an Applied Sciences – MDPI journal

 

24.02.2020

 

Dear Reviewer,

We wish to thank You for all the remarks. Below are responses to Comments and Suggestions. 

“Paragraph 4.2 is too long and heavy; some tables can be moved in an Appendix;”

We have moved the statistical analysis of T_x and P_x parameters to Appendix A

“I strongly suggest to insert a paragraph with the main analytical relationships to be used by model users, with a clear indication of the four constants to be specified and the values of “hidden” parameters determined on the basis of the test carried out in the research An short application to a real or idealized case (foundation of vibrating machine ?) should be a valuable improvement”

To fulfill the reviewer's suggestion, we added Appendix B in which we present the idealized case with the algorithm of settlement calculation with SHLM. We have defined the constants in it as well.

“Paragraph 4.1 on pore pressure build up seems not relevant for the model application; I suggest to highlight the role of pore pressure in soil stiffness degradation”

Thank you for this remark. We are going to explore this topic in the next article. We did some additional cyclic triaxial tests with a mid-plane pore pressure transducer.

We checked the manuscript for typos, and complete changes are presented in the manuscript. We present all changes in the red font style.

Thank you for your remarks on this manuscript.

Sincerely,

Andrzej and Wojciech

Author Response File: Author Response.doc

Reviewer 2 Report

The article is well presented and structured. The research is interesting and the conclusions appropriate. However, the comparison of the formulation presented with some of the classic formulas is missed. It is precisely presented in the introduction some of the classic formulations that would allow validating and comparing the capabilities of the model and its advantage over those previous formulations.

Author Response

Respond for Review Report 2 for submission of a paper to an Applied Sciences – MDPI journal

 

24.02.2020

 

Dear Reviewer,

We wish to thank You for all the remarks. Below are responses to Comments and Suggestions. 

 “… However, the comparison of the formulation presented with some of the classic formulas is missed. It is precisely presented in the introduction some of the classic formulations that would allow validating and comparing the capabilities of the model and its advantage over those previous formulations.”

Thank you for this remark. Indeed, the comparison between the models presented in the literature review and between SHLM would show the capability of proposed in this article model the soil deformation in a practical manner. Therefore, we calculated constants and we introduced Figure 13 in which the suggested comparison is presented.

Thank you for your remarks on this manuscript.

Sincerely,

Andrzej and Wojciech

Author Response File: Author Response.doc

Reviewer 3 Report

This manuscript presents a series of cyclic triaxial tests on a clayey material. Based on the experimental observation, an empirical model was proposed. The parameters in this model were calibrated. Using this model, the testing results of the present study were validated, showing a reasonable accuracy. This manuscript is worthwhile for the investigations of the permanent deformation of soils under cyclic loading. However, in the present version, some definitions, demonstrations and organizations are not clear to be published. The English writing should also be double-checked. Thus, significant modifications are needed and I recommend the major revision. My comments are listed as follows.

Lines 44-66. By reviewing the constitutive model of the permanent deformation of soils under cyclic loading, two classic models are missing and should be listed. Gidel et al. (2001) proposed the classic model (Gidel, G., Hornych, P., Chauvin, J. J., Breysse, D., and Denis, A. 2001. A new approach for investigating the permanent deformation behaviour of unbound granular material using the repeated load triaxial apparatus. Bulletin de Liaison des Laboratoires des Ponts et Chaussées, 233, 5–21). Wang et al. (2018a) extended this model by considering the static loading. (Wang, H. L., Chen, R. P., Qi, S., Cheng, W., and Cui, Y. J. 2018a. Long-term performance of pile-supported ballastless track-bed at various water levels. Journal of Geotechnical and Geoenvironmental Engineering, 144 (6): 04018035). Line 86. Where is Fig. 1 (a)? Why the hysteresis loop of N=2 is bigger than that of N=1? In my opinion, opposite trend will be identified, because less energy will be lost after further cycles. This figure does not show clear definitions of the stored and dissipated energies. Please indicate and cite the reference “Wang, H. L., Cui, Y. J., Lamas-Lopez, F., Dupla, J. C., Canou, J., Calon, N., Saussine, G., Aimedieu, P., and Chen, R. P. 2017. Effects of inclusion contents on resilient modulus and damping ratio of unsaturated track-bed materials. Canadian Geotechnical Journal, 54 (12): 1672-1681.” Some demonstrations are also needed in the text for these definitions. The figure caption is not correct. For the soil properties, please add the standard classification (CL or else?) according to the standard, such as ASTM D2487. Table 1. The reason why the authors chose these soil parameters? These were randomly obtained during the sample preparation? Table 2. Same comment as above, why the authors chose these random parameters? How do the authors obtain these testing results? From the testing procedures, these tests do not exist. Line 237. The definitions of N and NL are not clear. Please make some clarifications. Why don’t the authors directly use the cycle as the horizontal axis in Fig. 7? What is the physical meaning of the parameters used in Eqs. (15) and (17)? Line 371. As the physical meaning of bTX,1 and bTX,1000 are not clear, how can the authors make the assumption they are equal? Line 415. This should be Fig. 13. At least, the authors should indicate which figure corresponds to which sample. Table 7. What is the “Error” value in this table? From Fig. 13, some predictions are far different from the testing results. Table 8 corresponds to which sample? Lines 429-436. What is the Theil parameters? And where are the data of these parameters? Except for the three references mentioned above, some other important references related to the soil behavior under cyclic loading should also be cited in the Introduction part, such as: Wang, H. L., Cui, Y. J., Lamas-Lopez, F., Dupla, J. C., Canou, J., Calon, N., Saussine, G., Aimedieu, P., and Chen, R. P. 2018b. Permanent deformation of track-bed materials at various inclusion contents under large number of loading cycles. Journal of Geotechnical and Geoenvironmental Engineering, 144 (8): 04018044. Wang, H. L., Chen, R. P., Cheng, W., Qi, S., and Cui, Y. J. 2019. Full-scale model study on variations of soil stress in the geosynthetic-reinforced pile-supported track-bed with water level change and cyclic loading. Canadian Geotechnical Journal, 56 (1): 60–68.

 

I also recommend five other papers in this topic, about the permanent deformation of soils under cyclic loading.   Abdelkrim, M., Bonnet, G., and de Buhan, P. (2003). “A computational procedure for predicting the long term residual settlement of a plat- form induced by repeated traffic loading.” Comput. Geotech., 30(6), 463–476. Cai, Y., Gu, C., Wang, J., Juang, C. H., Xu, C., & Hu, X. (2013). One-way cyclic triaxial behavior of saturated clay: comparison between constant and variable confining pressure. Journal of Geotechnical and Geoenvironmental Engineering, 139(5), 797-809. Cai, Y., Sun, Q., Guo, L., Juang, C. H., & Wang, J. (2015). Permanent deformation characteristics of saturated sand under cyclic loading. Canadian Geotechnical Journal, 52(6), 795-807. Grabe, P., and C. Clayton. 2009. “Effects of principal stress rotation on permanent deformation in rail track foundations.” J. Geotech. Geoenviron. Eng. 135 (4): 555–565. Trinh, V. N., A. M. Tang, Y. J. Cui, J. C. Dupla, J. Canou, N. Calon, L. Lambert, A. Robinet, and O. Schoen. 2012. “Mechanical characterisation of the fouled ballast in ancient railway track sub-structure by large-scale triaxial tests.” Soils Found. 52 (3): 511–523.

Author Response

Respond for Review Report 3 for submission of a paper to an Applied Sciences – MDPI journal

 

25.02.2020

Dear Reviewer,

We wish to thank You for all remarks. Below are respond to Comments and Suggestions. 

“Lines 44-66. By reviewing the constitutive model of the permanent deformation of soils under cyclic loading, two classic models are missing and should be listed. Gidel et al. (2001) proposed the classic model (Gidel, G., Hornych, P., Chauvin, J. J., Breysse, D., and Denis, A. 2001. A new approach for investigating the permanent deformation behaviour of unbound granular material using the repeated load triaxial apparatus. Bulletin de Liaison des Laboratoires des Ponts et Chaussées, 233, 5–21). Wang et al. (2018a) extended this model by considering the static loading. (Wang, H. L., Chen, R. P., Qi, S., Cheng, W., and Cui, Y. J. 2018a. Long-term performance of pile-supported ballastless track-bed at various water levels. Journal of Geotechnical and Geoenvironmental Engineering, 144 (6): 04018035).”

We extended this paragraph as the reviewer suggested. The changes in the text are highlighted with red font.

“Line 86. Where is Fig. 1 (a)? Why the hysteresis loop of N=2 is bigger than that of N=1? In my opinion, opposite trend will be identified, because less energy will be lost after further cycles. This figure does not show clear definitions of the stored and dissipated energies. Please indicate and cite the reference “Wang, H. L., Cui, Y. J., Lamas-Lopez, F., Dupla, J. C., Canou, J., Calon, N., Saussine, G., Aimedieu, P., and Chen, R. P. 2017. Effects of inclusion contents on resilient modulus and damping ratio of unsaturated track-bed materials. Canadian Geotechnical Journal, 54 (12): 1672-1681.” Some demonstrations are also needed in the text for these definitions. The figure caption is not correct.”

We changed the typos in Fig. 1(a) now is Fig. 1. In Fig. 2, we changed the numeration according to reviewer suggestion. In Fig. 3 the Figure was modified  as well as the figure caption according to the Figure in the given literature. The Article was also added as a reference.

“For the soil properties, please add the standard classification (CL or else?) according to the standard, such as ASTM D2487.”

The according to reviewer suggestion USCS symbol was added.

“Table 1. The reason why the authors chose these soil parameters? These were randomly obtained during the sample preparation? Table 2. Same comment as above, why the authors chose these random parameters? How do the authors obtain these testing results? From the testing procedures, these tests do not exist.”

The soil parameters was obtained by analysis of soil mass and volume during compaction and after consolidation phase. The shear modulus was obtained based on the Bender element tests before cyclic triaxial tests. The parameters of cyclic triaxial test program depends on the initial sample diameters which impacts on the soil stress calculations. The cyclic triaxial test is controlled by the software in which the test program is set in kN units not in kPa.

                “Line 237. The definitions of N and NL are not clear. Please make some clarifications.”

The definition was extended as the reviewer suggested.

                “Why don’t the authors directly use the cycle as the horizontal axis in Fig. 7?”

We decided to use the Seed model to evaluate more general pore pressure characteristics. In the case when we would use the N instead N/N_L values, the pore characteristics would be harder to describe.

“What is the physical meaning of the parameters used in Eqs. (15) and (17)? Line 371. As the physical meaning of bTX,1 and bTX,1000 are not clear, how can the authors make the assumption they are equal?”

Parameters a_TX and b_TX or a_PX and b_PX  controls the total strain normalization parameter and plastic strain normalization parameter. We would say that the a_TX and a_PX parameters gives the information about T_x and P_x value at the beginning of the test and the b_TX and b_PX parameters controls the abation of total and plastic strains. The T_x,1 can be calculated based on the relationship between the b_TX,1 and b_TX,1000 which seems to be constant despite the cycle reference which we have seen during the analysis of the test results so we made the assumption that b_TX,1 = b_TX,1000.

“Line 415. This should be Fig. 13. At least, the authors should indicate which figure corresponds to which sample.”

We placed the information about the sample number on Figures.

                “Table 7. What is the “Error” value in this table?”

The error is the difference between the value from the tests and the prognosis value. We added the appropriate explanation bin Table footer.

“From Fig. 13, some predictions are far different from the testing results.”

We are aware of that but we would like to point the reviewer attention to newly added Fig. 14 in which the comparison between the SHLM prognosis and another model prognosis was conducted. In this comparison, the difference between SHLM prognosis and the model prognosis is far less different.

                “Table 8 corresponds to which sample?”

The data concerns the strain prediction in cycle 10 000 so the calculations are generalized to all samples.

“Lines 429-436. What is the Theil parameters? And where are the data of these parameters?”

The data which we used to calculate the Theil parameter values is in Table 3 (previously in Table 7).

“Except for the three references mentioned above, some other important references related to the soil behavior under cyclic loading should also be cited in the Introduction part, such as: Wang, H. L., Cui, Y. J., Lamas-Lopez, F., Dupla, J. C., Canou, J., Calon, N., Saussine, G., Aimedieu, P., and Chen, R. P. 2018b.. Journal of Geotechnical and Geoenvironmental Engineering, 144 (8): 04018044. Wang, H. L., Chen, R. P., Cheng, W., Qi, S., and Cui, Y. J. 2019. Full-scale model study on variations of soil stress in the geosynthetic-reinforced pile-supported track-bed with water level change and cyclic loading. Canadian Geotechnical Journal, 56 (1): 60–68.”

We included the references in the text.

“I also recommend five other papers in this topic, about the permanent deformation of soils under cyclic loading.   Abdelkrim, M., Bonnet, G., and de Buhan, P. (2003). “A computational procedure for predicting the long term residual settlement of a plat- form induced by repeated traffic loading.” Comput. Geotech., 30(6), 463–476. Cai, Y., Gu, C., Wang, J., Juang, C. H., Xu, C., & Hu, X. (2013). One-way cyclic triaxial behavior of saturated clay: comparison between constant and variable confining pressure. Journal of Geotechnical and Geoenvironmental Engineering, 139(5), 797-809. Cai, Y., Sun, Q., Guo, L., Juang, C. H., & Wang, J. (2015). Permanent deformation characteristics of saturated sand under cyclic loading. Canadian Geotechnical Journal, 52(6), 795-807. Grabe, P., and C. Clayton. 2009. “Effects of principal stress rotation on permanent deformation in rail track foundations.” J. Geotech. Geoenviron. Eng. 135 (4): 555–565. Trinh, V. N., A. M. Tang, Y. J. Cui, J. C. Dupla, J. Canou, N. Calon, L. Lambert, A. Robinet, and O. Schoen. 2012. “Mechanical characterisation of the fouled ballast in ancient railway track sub-structure by large-scale triaxial tests.” Soils Found. 52 (3): 511–523.”

We included the references in the text.

We checked the manuscript for typos and detailed changes are presented in manuscript. All changes are presented in red font style.

Thank you for your remarks to this manuscript.

Sincerely,

Andrzej and Wojciech

Author Response File: Author Response.doc

Round 2

Reviewer 3 Report

The authors have adequately addressed all my comments. This manuscript is appropriate to be accepted as it is.