Review Reports

Round 1

Reviewer 1 Report

This paper presents a quantitative method for analyzing the stress- strain state and bearing capacity of rigid rectangular foundations. The Boussinesq solution of elastic half space under vertical surface load is established. Additionally, the application of the Hencky’s system of physical equations with non-linear dependencies between mean stress and volumetric strain as well as deviator stress and shear strain, along with the experimental curves, depicts the relationship between bulk modulus and volume stress; shear modulus and shear stress. It is of good reference value to the calculation and design of rigid rectangular foundation. The following points is suggested be improved:

1. The expression of shear strain in abscissa of FIG. 1 on page 2 maybe is wrong, it's should be 2(ε1−ε3)/3?
2. Line54 of Page5 b=1.5.
3. Page5, the source of parameters is unknown and only one example is not enough to show that shear strain plays a leading role.
4. Page6, Figure 4 and Figure 5 are not mentioned in the article.
5. FIG. 8 and FIG. 10 are not clear enough.
6. Page7, Formula 31 should be obtained by "Putting equations(24) and (29) into procured expression (30) above"?
7. The numbering format of each line is not uniform.

Author Response

Thank you very much for your comments on this article. They helped to make corrections and improve the quality of the publication.

1. The expression of shear strain in abscissa of FIG. 1 on page 2 maybe is wrong, it's should be 2(ε1−ε3)/3?

Respond: The expression of shear strain in abscissa of FIG. 1 has already been corrected as recommended.

2. Line54 of Page5 b=1.5.

Respond: The dot has already been turned into a comma.

3. Page5, the source of parameters is unknown and only one example is not enough to show that shear strain plays a leading role.

Respond: The authors added two more groups of parameters to confirm that shear strain plays a leading role.

4. Page6, Figure 4 and Figure 5 are not mentioned in the article.

Respond: The clarification for figures 4 and 5 has been made before them.

5. FIG. 8 and FIG. 10 are not clear enough.

Respond: Please check the text before figure 8 and 10 for making them clearer. Figure 8 shows the dependency curve of total strain on load q with various values of stiffness, and figure 10 indicates the dependency curve of the total settlement on load q with various values of pre-overburden pressure and foundation depth. The purposes of the authors are to show the different curvatures (decaying and persistent) of the curves so that the roles of shear and volumetric components are clearly described.

6. Page7, Formula 31 should be obtained by "Putting equations(24) and (29) into procured expression (30) above"?

Respond: The recommendation has been adopted

7. The numbering format of each line is not uniform.

Respond: The numbering format of each line is followed by the standard templates when formalizing the article by overleaf. We understand that the numbering is applied for some empty lines in some places is mentioned point.

Author Response File: Author Response.docx

Reviewer 2 Report

• Please, recheck the substitute R in Eq. 7?
• In Fig. 4 and 5: Can you explain somewhere under the figure that why the shear strain and Deviatoric strain decreased as the depth increased?
• Page 7, line77: please correct the equation numbers (7 and 7) to (7 and 8)
• In the line under Eq 30: change Eq 29 to Eq 30.

Author Response

Thank you very much for your comments on this article. They helped to make corrections and improve the quality of the publication.

1. Please, recheck the substitute R in Eq. 7?

Respond: Eq. 7 has been rechecked and corrected.

2. In Fig. 4 and 5: Can you explain somewhere under the figure that why the shear strain and Deviatoric strain decreased as the depth increased?

Respond: The explanation for the question has already added after figure 4 and 5

3. Page 7, line77: please correct the equation numbers (7 and 7) to (7 and 8)

Respond: The recommendation has been adopted

4. In the line under Eq 30: change Eq 29 to Eq 30.

Respond: The recommendation has been adopted

Author Response File: Author Response.docx

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.