Modelling the Structure and Anisotropy of London Clay Using the SA_BRICK Model

Round 1

Reviewer 1 Report

Synopsis:  The constitutive model SA_BRICK developed by the authors is an improvement to the previous BRICK model for capturing the anisotropy and the structure of stiff clay.  Modeling of soil structure is accounted for by model parameters alpha and omega.  Modeling of anisotropy is accounted for by the transformation matrix [M] that incorporates the Young's modulus ratio, shear modulus ratio, and the Poisson's ratio in the horizontal plane.  The SA_BRICK constitutive model was verified using single element model against laboratory test data.  Validation of SA_BRICK as implemented in finite element program PLAXIS was evaluated against the surface settlement due to the excavation of Jubilee Line tunnels at St James's Park in London, UK.  In general, agreements were observed between the calculated results and the field data. 

 

Editorial comments from the manuscript are included in the attached PDF.

 

Reviewer's general comments are listed as follows:

 

1.  When performing verification of anisotropy, why can't the stress paths of the single element model match those of the actual laboratory tests (i.e., q-p' space in Fig. 7a)?  Weren't loads controlled in the laboratory tests?

 

2.  The calibrated value of nu_hh/nu_vh in Table 3 is zero.  Is this value realistic?

 

3.  For comparison purpose, it would be helpful to also provide input parameters of M2-SKH and M3-SKH needed for the finite element program ICFEP.

 

4.  It would be helpful to also provide the comparison of the normalized surface settlements for the East tube.

 

5.  "Class A" in Line 635 does not seem appropriate for this study.  The validation exercise, in reviewer's opinion, is at best a type C1 prediction according to Lambe's classification (1973), in which this was an after-event prediction and results at the time of prediction were known.  The prediction classification should be revised.

 

Comments for author File: Comments.pdf

Author Response

Ljubljana, 23.12.2022

 

Subject: Reply to the comments of Reviewer 1

Dear Editor,

We would like to thank the reviewer on his/her valuable comments, which helped us to clarify and  better formulate our manuscript. The changes in the document are marked red.

We accepted all the comments of Reviewer 1 and made due changes as appropriate, which were added to the text. In the continuation we give detailed itemised answer to reviewer´s comments, as follows.  

Comment 1

Comment 2

The laboratory test 10.1UC was undrained so that the effective stress paths were driven by the changes in the pore pressures. This change was underestimated by both A_BRICK and SA_BRICK model so there was no possibility to model the stress path exactly. In drained test 10.2DE this was not the issue, so the stress path was matched exactly. Appropriate explanation was added in the text.

Comment 3

Although theoretically debatable, the value of parameter nυ_hh = zero, was taken by [1] and by other researchers [2], [3] as the best fit for the observed anisotropic behaviour of London Clay. Appropriate explanation was added to the text, including the references.

Comment 4

This is now provided in the text. The readers are directed to Grammatikopoulou [4] and Jurečič [5] for the full meaning of parameters.

Comment 5

We would like to thank the reviewer for this insightful comment. This data were interpreted in Figure 17 and appropriate comment was added to the text.

We agree with the reviewer. Appropriate change was added to the text including the reference of Lambe[6].

References

[1]         K. C. Ellison, Constitutive Modelling of a Heavily Overconsolidated Clay. PhD thesis, University of Cambridge. 2012.

[2]         J. Wongsaroj, K. Soga, S. Yimsiri, and R. J. Mair, “Stiffness anisotropy of London Clay and its modelling: Laboratory and Field,” in Advances in geotechnical engineering: The Skempton conference, pp. 1205–1216.

[3]         J. Burland and J. Kalra, “Queen Elizabeth II Conference Centre: Goetechnical Aspects,” Proc. Inst. Civ. Eng., vol. 80, no. 6, pp. 1479–1503, Dec. 1986, doi: 10.1680/iicep.1986.527.

[4]         A. Grammatikopoulou, L. Zdravkovic, and D. M. Potts, “The effect of the yield and plastic potential deviatoric surfaces on the failure height of an embankment,” Géotechnique, vol. 57, no. 10, pp. 795–806, Dec. 2007, doi: 10.1680/geot.2007.57.10.795.

[5]         N. Jurečič, L. Zdravković, and V. Jovičić, “Predicting ground movements in London Clay,” Proc. Inst. Civ. Eng. Geotech. Eng., vol. 166, no. 5, 2013, doi: 10.1680/geng.11.00079.

[6]         T. W. Lambe, “Predictions in soil engineering,” Géotechnique, vol. 23, no. 2, pp. 151–202, 1973, doi: 10.1680/geot.1973.23.2.151.

 

Author Response File: Author Response.docx

Reviewer 2 Report

London Clay as the London chalk is a very tricky strata. From this point of view the article is quite interesting.

Critical remarks:

[103] if the paragraph 2 has subparagraph 2.1. it should have also at least subparagraph 2.2 in other case the paragraph should has the title like subparagraph 2.1. Continuous developments ..., because the content is about it.

[153] the paragraph 3 should has different title for example Development of the SA_BRICK model, or Differences between BRICK model and SA_BRICK model or Presentation of the SA_BRICK model and its development, because the content is about it.

[215] Word Table 2 should be in the line 211

[220-222] Table 2: in the last line of the BRICK column (Stiffness parameter) is equation: ψ_ε = ε_ν - ε_ν0 – λ ln (p’/p’₀), but there should be the equation: l_curr = 1/ (1 + β^G ψ_ε)

[231-232] What does that mean the sentences: ... same original shape and form as in the original BRICK model (see Table 1). ... like in the Table 1 we can see only ... BRICK model input parameters for modelling of London Clay (Simpson, [8]) ... Where is these original shape and form in Table 1?

[376-378] Why on Figure 7 is only validation of the SA_BRICK against A_BRICK? Where is the validation of the SA_BRICK against BRICK? For me on the same figures should be also validation of BRICK model based on laboratory test. This will be the full information needed for the discussion.

[667-669] Why the SA_BRICK model was not calibrated in the same way that M3-SKH model, but on different “new data”? What are the “new data” and which are the “old data”?

Paragraph 6. Discussion should be end answers for the questions: What gives this? and What of it results for calculations?

Paragraph 7. Conclusions should be end with some advantages and disadvantages of SA_BRICK model.

Author Response

Ljubljana, 28.12.2022

 

Subject: Reply to the comments of Reviewer 2

Dear Editor,

We would like to thank the reviewer on his/her valuable comments, which helped us to clarify and  better formulate our manuscript. The changes in the document are marked red.

We accepted all the comments of Reviewer 2 and made due changes as appropriate, which were added to the text. In the continuation we give detailed itemised answer to reviewer´s comments, as follows.  

London Clay as the London chalk is a very tricky strata. From this point of view the article is quite interesting.

Critical remarks:

 

Comment 1

[103] if the paragraph 2 has subparagraph 2.1. it should have also at least subparagraph 2.2 in other case the paragraph should has the title like subparagraph 2.1. Continuous developments ..., because the content is about it.

We agree with the reviewer, this is now corrected in the text so that the Section 2 is more comprehensive. Section 2 was renamed: Development of the BRICK model.

Comment 2

[153] the paragraph 3 should has different title for example Development of the SA_BRICK model, or Differences between BRICK model and SA_BRICK model or Presentation of the SA_BRICK model and its development, because the content is about it.

We agree with the reviewer, this is now corrected in the text so that the Section 3 is more comprehensive. Section 3 was renamed: Development of the SA_BRICK model. The structure of the manuscript is clearer, we would like to thank reviewer for this valuable comments.

[215] Word Table 2 should be in the line 211

 

Table 2 is now aligned with the text.

[220-222] Table 2: in the last line of the BRICK column (Stiffness parameter) is equation: ψ_ε = ε_ν - ε_ν0 – λ ln (p’/p’₀), but there should be the equation: l_curr = 1/ (1 + β^G ψ_ε)

Thank you for this correction. Table 2 is now corrected and updated.

[231-232] What does that mean the sentences: ... same original shape and form as in the original BRICK model (see Table 1). ... like in the Table 1 we can see only ... BRICK model input parameters for modelling of London Clay (Simpson, [8]) ... Where is these original shape and form in Table 1?

We agree that this was a cumbersome explanation; what was meant was that the S shaped curve was defined in Table 1 by the columns of string lengths and normalised stiffness G/Gmax. The text was changed appropriately. 

 

[376-378] Why on Figure 7 is only validation of the SA_BRICK against A_BRICK? Where is the validation of the SA_BRICK against BRICK? For me on the same figures should be also validation of BRICK model based on laboratory test. This will be the full information needed for the discussion.

In this case SA_BRICK was validated only against A_BRICK with an aim to get identical results so that mathematical formulation was correctly transferred to different computational environment (e.g. to NAOgeo). Validation of A_BRICK against BRICK was carried out by Ellison [1] and was not subject of this research.

[667-669] Why the SA_BRICK model was not calibrated in the same way that M3-SKH model, but on different “new data”? What are the “new data” and which are the “old data”?

This is explained in full detail in Jurečič at al.[2], which is referenced in the manuscript. The ˝old data˝ are actually ˝previous soft˝ but we did not want to change the name to avoid confusion with the original reference. The reason for the use of both sets of data are for the sake of the comparison due to differences in stiffness measurements that were encountered as a result of the advances made in the laboratory by Gasparre [3] at the time of the research. We decided to keep this to show the range of possible dispersion of the results but the ˝new data˝ should be regarded as much more accurate, as indicated in the text.  

Paragraph 6. Discussion should be end answers for the questions: What gives this? and What of it results for calculations?

Appropriate answers to this comment are added in the text, as follows.

This confirms that kinematic hardening models can provide comparable and compatible results based on the same sound theoretical background regardless of the mathematical formulation (e.g. BRICK versus M3-SKH model) and numerical tools used, if they are based on correct formulation of the parameters derived from the high quality laboratory testing. In that sense the improvement made by SA_BRICK by accounting for anisotropy and structure versus M3-SKH model is notable. 

Paragraph 7. Conclusions should be end with some advantages and disadvantages of SA_BRICK model.

 

This is now commented in the text, as follows.

The obvious advantage of the SA_BRICK model is completeness of the phenomena that can be accounted for to model the behavior of natural clays using a single formulation. As a superposition of BRICK, A_BRICK and S_BRICK, the SA_BRICK model contains all the previous phases of the BRICK development and can be used for modelling a wide area of soils. As for the other kinematic hardening models, the precondition for the appropriate use of the SA_BRICK model are high quality laboratory data for the selection of input parameters. this can be regarded as a disadvantage for a routine use of numerical analyses but also highlights a necessity for the further improvement in laboratory and in-situ testing to advance soil characterization.        

 

[1]         K. C. Ellison, Constitutive Modelling of a Heavily Overconsolidated Clay. PhD thesis, University of Cambridge. 2012.

[2]         N. Jurečič, L. Zdravković, and V. Jovičić, “Predicting ground movements in London Clay,” Proc. Inst. Civ. Eng. Geotech. Eng., vol. 166, no. 5, 2013, doi: 10.1680/geng.11.00079.

[3]         A. Gasparre, Advanced laboratory characterisation of London Clay. Ph.D Thesis, Imperial College, London. 2005.

 

Author Response File: Author Response.docx

Reviewer 3 Report

Please find the attached file. 

Comments for author File: Comments.pdf

Author Response

Ljubljana, 28.12.2022

Subject: Reply to the comments of Reviewer 3

Dear Editor,

We would like to thank all reviewers on their valuable comments, which helped us to better formulate our contribution and focus on general applicability of our research. The changes in the text are marked red.

The authors would like particularly to thank Reviewer 3 for his insightful and instrumental comments. We accepted all the comments and made due changes, which were added to the text. In the continuation we give detailed itemised answer to reviewer´s comments, as follows.  

Comment No.1

The following sentence has been added at the end of Abstract:

Advanced predictions of ground deformations caused by tunnel excavations can be effectively used to mitigate possible damage of existing structures affected by tunnelling in an urban environment.

Also in the conclusions the following text was added to improve the focus of the manuscript in terms of the relevance to structural/geotechnical industry:

With further development of built environment, the accurate numerical prediction of the deformation field around tunnel excavation becomes more important as more the traffic routs require use of underground space. Predictions of ground deformations caused by tunnel excavations with increased accuracy are important to assess, prevent, and mitigate possible damage of existing structures caused by tunnelling. It was demonstrated in the paper that the SA_BRICK model can be used to advance numerical modelling of such boundary value problems with increased accuracy.

 

Comment No. 2

We would like to thank the reviewer for this insightful comment. We understood the need to present the relevance of our research in more contemporary context to highlight the significance of the study. An assessment of recent publication related to the topic of the research has been made. In total 14 recently published and other relevant works were added to the text, including all the references mentioned by the Reviewer.

Comment No. 3

 

This is now added to the references including PLAXIS 3D to show the copyright.

Comment No. 4

This is corrected in all places of occurrence in the document.

Comment No. 5

Quality of Figure 1 was improved.

Comment No. 6

This is now corrected in Table 1 so that there is a consistent annotation with the text.

Comment No. 7

The following sentence was added to the text:

The string lengths are defined against normalised shear modulus (G/G_max) to cover the full range of shear strains.

Comment No. 8

This is now corrected, in the bracket are given Eqs. 1 and 2.

Comment No. 9

 

The text was checked so that mathematical parameters were supported by their respective unit, as appropriate.

Comment No. 10

 

This is added in the text. Additional information about the cross-anisotropy was also included including the reference [1] so that the readers can follow equations more easily.

Comment No. 11

 

Comment No. 12

We would like to thank reviewer for this insightful comment. A following addition was added in the text including the new relevant references:

A comprehensive overview of the geological history, geotechnical and geomechanical characteristics of London Clay is given by Hight et al.[2]. Their work was based on the data obtained from ground investigations for the Terminal 5 at London’s Heathrow Airport, which is also the lithological unit used in this research. London Clay is a typical heavily overconsolidated marine clay of mineral composition comprising poorly crystal-line kaolinite, illite, chlorite, smectite and montmorillonite. At Terminal 5 site the clay was of high to very high plasticity, in which the plasticity index PI averaged around 40%, (minimum of 33% and maximum of 49%) while the liquid limit LL was between 65 and 70%. The same lithological unit at St James’s Park had similar index properties with average water content of 20% to 25% and unit weight varying between 20 kN/m3 to 22 kN/m3 [3]. Coefficient of permeability of London clay typically varies between k=1*10-9 m/sec to k=1*10-10 m/sec, while in terms of strength effective stress parameters the apparent cohesion is characteristically taken as c´= 0, while the angle of shear resistance ranges from peak of Φ´=25^o to large strain of Φ´=20^o and residual values of Φ´=12^o [25].     

 

Comment No. 13

An addition to the text was carried to refer and explain Figure 7 properly:

The SA_BRICK model results are given in Figure 7 together with the prediction of the A_BRICK model and the laboratory results (labelled LAB). The results are shown for samples 10.1UC (undrained shear in compression – upper part in all diagrams except 7d) and 10,2DE (drained shear in extension – lower part in all diagrams) showing: (a) q-p´ diagram, (b) q-εy diagram, (c) u- εy diagram and (d) εy -εvol diagram (only for drained sample 10.2DE). Verification data of the A_BRICK model on London clay samples do not allow comparison of stiffness, as they are not given in Ellison's work. It can be seen in the figure that the model-ling of anisotropy in SA_BRICK is fully comparable with the results [43] as in both cases, SA_BRICK gives practically the same results as the A_BRICK model. A partial deviation is visible only in the case of volume deformation prediction (Figure 7d). It should be noted that the laboratory test 10.1UC (upper part in diagrams) was undrained so that the effective stress paths in the laboratory were driven by the changes in pore pressures. As it can be seen in Figure 7c this change was underestimated by both A_BRICK and SA_BRICK model so there was no possibility to model the stress path exactly. In drained test 10.2DE this was not the issue, so the stress path was fully matched. Certain minor deviations can also be attributed to the different steps for the load steps, the position or placement of the initial bricks and cords, and the accuracy of the given geological history and sampling.

Comment No. 14

The following quantitative information was added to the text:

Generally, in undrained tests effective stress paths in the laboratory were driven by the changes in pore pressures. This change was slightly underestimated by SA_BRICK model so there was no possibility to model the stress path exactly (e.g Figures 9a, 10a), which was reflected at large strains so that the absolute vale of maximum deviator stress q_max was almost exactly matched but at twice as large axial strain ea (e.g Figures 9b, 10b). The sample 27UC (Figure 11) was sheared along pre-existing fissures which was reflected again at large strains so that the prediction of q_max was some 50% larger that the measured value.

 Comment No. 15

This is now changed; both comments are appreciated by the authors as changes give more clarity to Section 5 of the manuscript.

 

Table 4 was corrected (it is now Table 5, to conform with the comments of the other Reviewer)

Comment No. 16

 

This measured date are referred only for the east side of the settlement trough. The discrepancies for the west side of the settlement trough is explained in the paragraph bellow. Appropriate comment is added to the text to clarify this.

[1]         A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, Cambridge, Cambridge. 1927.

[2]         D. W. Hight, F. McMillan, J. J. M. Powell, R. J. Jardine, and C. P. Allenou, “Some characteristics of London Clay,” in Characterisation and Engineering Properties of Natural Soils – Tan et al. (eds.), 2003, pp. 851–907.

[3]         J. R. Standing and J. B. Burland, “Unexpected tunnelling volume losses in the Westminster area, London,” Géotechnique, vol. 56, no. 1, pp. 11–26, Feb. 2006, doi: 10.1680/geot.2006.56.1.11.

 

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Please refer to the attached file.

Comments for author File: Comments.pdf

Author Response

Ljubljana, 31.12.2022

Subject: Reply to the comments of Reviewer 3

Dear Editor,

The authors would like to thank Reviewer 3 for his insightful and instrumental comments. We accepted all the comments and made due changes, which were added to the text and figures. In the continuation we give detailed itemised answer to reviewer´s comments, as follows.  The changes in the text are in red.

Comment No.1

 

We checked all the figures for the resolution. Figures 4, 5, 13, 15 and 17 have been improved and replaced. We suppose now that all the figures are within the required qualities. If the production team have some additional requests we will further upgrade the resolution of the required figures.

Comment No. 2

 

Corrected, general is out.

Comment No. 3

 

Corrected.

Comment No. 4

 

Corrected.

Comment No. 5

 

Corrected.

Comment No. 6

 

It is a mass water content, the text was corrected.

Comment No. 7

 

Corrected.

Comment No. 8

 

Corrected.

Comment No. 9

 

Corrected.

Comment No. 10

 

Corrected.

Comment No. 11

 

Table 3 is now reorganised so that anisotropy and structure parameters are separated. It is also  reformatted to be at the same page.

Comment No. 12

 

Corrected.

Comment No. 13

 

Corrected. Both figures 15 and 17 were updated.

Author Response File: Author Response.docx