Fractional Order Viscoelastic Model for Stress Relaxation of Polyvinyl Chloride Geomembranes

Round 1

Reviewer 1 Report

Although the experimental and simulated results are interesting, the reviewer has concerns, which are needed to be addressed/revised by the authors. The details are as below.

1. Test method: How was a stress relaxation test performed? Was it done by temporarily stopping the tensile loading machine?

2. Why viscoelastic model was chosen when the viscoplastic behavior of such material was reported by others?

3. Please check whether small tau and small gamma in Equation 4, perhaps with other parameters appeared in different places, are explicitly explained.

4. The reviewer would recommend addressing the limitations on that Equation 12 is unit-dependent and can be applicable when t > 1. 

5. The reviewer would like to know whether the relationships between tensile load and tensile strain obtained from the experiments since the start of loading to the start of load relaxation until the end of load relaxation among different specimens are comparable.

6. The following sentence (Line 245) refers to manufacturing stress in one direction. Can it be due to anisotropy in the material property?.

7. In a related matter, the authors have not discussed previous experimental stress relaxation results in general, and results on PVC geomebranes in particular. If such results exist, the authors need to acknowledge them. If such results are scarce, then this should also be noted.

8. Some of the pictures in the paper are not very clear，such as Fig. 4 ~ Fig. 10.

9. Some of the English language can be proofread. 

Author Response

See attachment

Author Response File: Author Response.docx

Reviewer 2 Report

1. Please explain the chemical composition of PVC GMB in detail in page 2.

2. Explain the reason and validity of analyzing the stress relaxation behavior of PVC GMB by fractional order viscoelastic model (FOVM) compared to creep behavior analysis.

3. The stress relaxation behavior of PVC GMB is to analyze the stress change over time by predicting the deformation of PVC GMB. If so, please explain quantitatively how to apply the reduction factor due to this stress relaxation phenomenon to the long-term performance evaluation of PVC GMB.

4. Please change the resolution of Figure 4, 5, 6, 7, 8, 9, 11 to be clearer.

5. Please explain why there is no Figure 10.

6. Please explain the physical meaning of each of the model parameters in Table 2 in relation to the physical properties of PVC GMB.

7. If this paper is focused on the stress relaxation behavior of PVC GMB in a single direction that cannot represent actual deformation, please add a corresponding explanation in the stress relaxation test results.

8. Please arrange the references appropriately in the citation section.

9. Please organize the contents of "Abstract" in accordance with the contents of 6. Conclusion.

Author Response

See attachment.

Author Response File: Author Response.docx