Design of Conical Foundations with Increased Bearing Capacity in Areas of Undermined Soils

NN

Reviewer’s comments

Authors response

1.

The figures need to be reasonably improved. For example, figures 8, 9, 10, and 11 are vague and the words are too small.

The graphs were constructed by the Plaxis modeling program, and the signatures are not customized for a special font or other signatures. The colour column contains a decoding of deformations in mm, so they were left in case someone wants to repeat the simulation with the same initial parameters. The captions could be removed since the explanation is already in the title of the figure, but the original font of the results further confirms the Plaxis interface.

2.

There are many graphical mismatches in the text. For example, "5" is repeated in Fig. 4b. The labeling of cone height in Fig. 7b does not match with the description. The labeling of Fig. 11 should be the result of numerical simulation of columnar foundation. And the description in 269 rows does not match with Table 4. Therefore, the authors are advised to check and revise the full text

Thank you very much for your comments. We corrected these mismatches and tried to review the text for such flaws.

3.

The word "1" appears in line 10. The line style of the table and the labeling of the letters in formulas should be uniform throughout the text

Thank you very much for your comments. We corrected these mismatches and tried to review the text for such flaws.

4.

During the loading in the experiment in section 2.1, are eccentric loads due to human factors considered? Is the conical foundation pressed directly into the soil or placed into a pre-excavated pit?

The cones are installed on prepared holes in a pre-excavated pit. Next, a roller connection is installed to protect the building from horizontal ground movements, then a base beam is installed, and then the building (usually low-rise) is built up.

5.

In this paper, the aperture angles of 80° and 90° are taken, and it is recommended to take more aperture angles to investigate the effect of the aperture angle on bearing capacity.

Based on previous studies [24,25], the opening angle of the cones α was taken as the average value from the previously considered modeling methods, and also based on the results of preliminary laboratory tests, in this study the operation of cones with an opening angle of 80°-90° was considered.  Lines 163-165, 192-195.

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model in the laboratory and at the test site for the purpose of further research for use in civil engineering as the foundations of buildings and structures.

At the moment, the test results for these angles and shapes are ready. In the next works it is planned to consider cones with a pile stand.

6.

It is suggested to merge figures 12(a) and Fig.12(b) to get a clearer visualization of the effect of the aperture angle on the bearing capacity;

Trial merging showed that it’s a bit busy, curves 5 and 6 overlap curves 7 and 8 (at the publisher's choice figure might be merged). Please see the attached file.

7.

In section 3, only the influence of the aperture angle on the bearing capacity is described, and no underlying mechanism was analysed. So, it is suggested that the authors analyse the mechanism.

Thank you very much. Additional references have been added regarding this issue. The stress-strain state of a conical foundation was described by Houlsby and Martin [26], Chakraborty and Kumar [27] by theoretical analysis and numerical simulation of cone shape with different angle of aperture. 

8.

In this paper, how to divide the mesh for numerical simulation? What constitutive relation is used? It is suggested that the authors provide a detailed introduction.

Creation and division of meshes using the Plaxis 2D program was generated automatically. The average element size and the number of generated triangular elements depended on the global coarseness setting. The global coarseness setting was set to medium, with 328 triangular elements. Lines 311-314.

9.

What is the basis for selecting a conical foundation burial depth as three-quarters of the top radius?

Models of a conical foundation with aperture angle of the cones 90° and 80° were buried into the soil at 0.75 of its height, in order to provide a safety margin under further loading due to an increase in the bearing area when the cone is immersed deeper into the ground. This is approximately 3/4 of the radius but not necessary. The cross-sectional area increases in proportion to the settlement with further loading.

10.

Is the conical foundation proposed in this paper applicable to other soil conditions?

Based on studies [23-25] conical foundations are used as a single piece foundation in offshore and onshore construction for supporting wind turbines on the fine-grained soils like clays. It is assumed that in civil engineering, foundation soils would also be fine-grained, with particles tightly packed together at the contact with the soil.

NN

Reviewer’s comments

Authors response

1.

- The main highlights of the research should clearly discussed point by point.

In discussion part Lines 383-398 highlighted the peculiarity of this work from previously performed ones, most of which considered the conical model of the foundation only as an integral single foundation block for hydraulic structures and wind turbines. Or meant only numerical simulation implied only numerical simulation to determine the bearing capacity of conical foundation models and sensitivity to the type of factors.

p.1. of the Conclusion, this is a general statement giving conclusion on all of the above research methods where conical and columnar foundation models were considered. Also, it was discussed in Lines 412-415.

p.2. of the Conclusion is discussed in Lines 383-386, 392-406.

p.3. of the Conclusion is discussed in Lines 399-406, 412-420, Figure 15.

p.4. of the Conclusion is discussed in Lines 412-415. Figure 16.

p.5. of the Conclusion is discussed in Lines 424-438.

p.6. of the Conclusion is a further research suggestion.

- The abstract can be improved by focusing on the new findings and the main novelty of the research.

Thank you very much. The abstract has been revised to reflect the content of applied research in the geotechnical field. The main outcomes are presented in Lines 22-25, representing the results of tests on load-bearing capacity under the simultaneous influence of horizontal tensile forces on the foundations.

- The article lacks clarity in describing the methodology used for the three-dimensional expandable box and the manufacturing process. A more detailed and explicit explanation of the experimental setup, including materials used and construction process, would enhance the reproducibility and understanding of the study.

Performing a static load test is the main criterion for determining load-bearing capacity for building construction. Since in the undermined area there may be horizontal movements (insignificant values, up to 9 mm per 1 meter of length), an expandable stand was developed where, by unscrewing the bolts between C-sections, the length of the stand increases by the required increment in mm.

- While the article mentions a comparison between conical and columnar foundations, the scope of the comparison appears limited. The study could benefit from a more comprehensive comparison.

A number of authors have conducted theoretical studies of conical foundation models using finite element limit analysis, machine learning regression approach and considered various parameters like apex angles from 0 to 180 degrees, embedded depth to height ratio, strength gradient ratio, anisotropic ratio, angle of internal friction etc. (Lines 130-154).

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model for use in civil engineering as the foundations of buildings and structures in areas with subsidence trough and horizontal tensile strains. The main purpose of foundations is the bearing capacity to withstand the resulting loads and deformations. The cone-shaped foundations are used for offshore structures or wind turbine basement as a single-piece module.

In this work, laboratory and field tests of conical foundation models with an opening angle of 80 and 90 degrees were carried out with the aim of further use for civil engineering purposes in undermined areas. Due to the labor-intensive laboratory and costly field-testing methods, in this work we limited only 2 types of conical models.

- The literature review of article should be improved. Referring to following researches is suggested:

Hygro-thermo-elastic nonlinear analysis of functionally graded porous composite thin and moderately thick shallow panels

Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method

Vibrational behavior of exponentially graded joined conical-conical shells

Thank you for suggesting interesting articles. These articles are devoted to predicting the natural frequencies of connected conical shell structures made of functionally graded material. While the presented study examines a purely geotechnical problem of determining the bearing capacity of conical foundation models for specific deformation in the zone of convex curvature and, as a consequence, horizontal tensile forces of the top layer of soil (Figure 2).

Referring to theoretical studies [23-28], we decided to carry out an experimental study so far of only 2 types of conical models (next we want to try a conical model with a stand pile) and compare them with traditionally used types of foundations.

- The article doesn't address the sensitivity of the results to key parameters. A sensitivity analysis would provide valuable insights into the robustness of the proposed conical foundation design under different soil conditions and loading scenarios.

Nguyen Van et al [24] using machine learning regression approach analyzed the sensitivity of the bearing capacity of conical foundations according to the following dimensionless parameters under study: cone apex angle, embedment depth to height ratio, strength gradient coefficient, anisotropy coefficient, cone shape.

Chouhan et al. [25] investigated the dependence of the vertical load-bearing capacity of a conical foundation on the base roughness, soil friction angle and various apex angles by performing two-dimensional finite element limit analysis (FELA). Theoretical analysis was also carried out by Houlsby and Martin [26] and Chakraborty and Kumar [27].

Due to the labor-intensive laboratory and costly field-testing methods, in this work we limited only 2 types of conical models. In the future there will be more tests, we plan to consider other models, including pile-rack as well as statistical analyses.

- The use of numerical modeling with the Plaxis 2D program is mentioned, but there is a lack of information regarding the verification process of these models. Providing details on how the numerical models were validated against experimental results would strengthen the reliability of the numerical simulations.

Due to the axisymmetric nature of the problem, a two–dimensional (2D) axisymmetric finite element (FE) formulation is used to model the soil domain and conical footing. When modeling using the Plaxis 2D program, the initial parameters of the physical and mechanical properties of soils, namely the type of soil, density deformation modulus, material of foundation models, etc., as well as the geometric characteristics of conical models, were taken identically to those used in the laboratory tests.

The discrepancies between calculations during laboratory tests and numerical modeling were no more than 9%. Line 450-453.

- A more in-depth discussion on potential failure modes and failure mechanisms for both conical and columnar foundations would contribute to a better understanding of the structural behavior.

Bearing capacity, including failure mechanisms were examined with a machine learning technique of multivariate adaptive regression splines (MARS) mode by Nguyen Van et al. [24] depending on cone apex angle, embedded depth ratio, the anisotropic ratio, and the strength gradient ratio.

Collapse loads were also calculated with numerical method using program FIELDS by Cassidy and Houlsby [28]. Lines 154-158. In this work conical foundations did not reach their ultimate load-bearing capacity while loaded identically to columnar foundations.

- The study primarily focuses on immediate bearing capacity and deformation under specific loads. Including a discussion on the long-term performance and durability of conical foundations, especially in the context of settlement over time and cyclic loading, would add depth to the analysis.

In the Introduction part of the article, references were presented to the authors who studied the patterns of rock displacement and deformation as a result of underground mining (Lines 35-105). This work examines the bases and foundations of buildings located near point A of zone I of Figure 1, which is characterized by positive curvature (convexity) and horizontal deformations. The long term performance of the inverted cone is achieved by increasing the cross-sectional area under increasing loads. The stress-strain state of a conical foundation was described by Houlsby and Martin [26], Chakraborty and Kumar [27] by theoretical analysis and numerical simulation of cone shape with different angle of aperture.

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model in the laboratory and at the test site for the purpose of further research for use in civil engineering as the foundations of buildings and structures specifically in zone near the subsidence trough. Cyclic loading would not be applicable here. While regarding the settlement over time the purpose of this study is to minimize the settlements and uneven deformations of the structure bases.

- The article lacks information on statistical significance in the experimental and numerical results. Including statistical analyses, such as confidence intervals or variance assessments, would provide a clearer indication of the reliability and significance of the observed differences between conical and columnar foundations.

Statistical analysis using machine learning regression approach to analyze the sensitivity of the bearing capacity of conical foundations according to the following dimensionless parameters under study: cone apex angle, embedment depth to height ratio, strength gradient coefficient, anisotropy coefficient, cone shape is presented by Nguyen Van et al [24]. Chouhan et al. [25] investigated the dependence of the vertical load-bearing capacity of a conical foundation on the base roughness, soil friction angle and various apex angles by performing two-dimensional finite element limit analysis (FELA). Theoretical analysis was also carried out by Houlsby and Martin [26] and Chakraborty and Kumar [27].

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model in the laboratory and at the test site for the purpose of further research for use in civil engineering as the foundations of buildings and structures.

Due to the labor-intensive laboratory and costly field-testing methods, in this work we limited only 2 types of conical models. In the future there will be more tests, we plan to consider other models, including pile-rack as well as statistical analyses.

NN

Reviewer’s comments

Authors’ response

1.

Introduction; starts with…The problem of stability of foundations in areas with increased horizontal tensile 28 strains, namely in undermined areas, is important for the preservation of buildings and 29 structures, as well as for reducing destruction and cracks of buildings [1,2]… . In this case, it will be necessary to indicate the influence of the tunnel opening on the massif and the importance of knowing this variation in displacements. Surface deformations depend on the convergence displacements of the tunnel and/or cave and the type of massif (soil or rock), depth, structural geology, water table, etc. If the bearing element is the surrounding land itself? Topics that must be presented.

Thank you for your comment. Introduction part has been rewritten and revised. Additional information is provided about the study area, the features of the formation of various deformation zones near underground mine workings. The stress-strain state in the area in close proximity to the underwork is considered, and the idea of ​​using conical foundations is substantiated. References are provided to studies describing the deformations of the subsidence trough in more detail.

A cone or pyramidal prism of failure develops below the flat base foundation. This has to be understood in order to interpret the study of a foundation itself shaped like a cone. And what changes in terms of the bearing-capacity factors for the equations. The type of failure when a load is applied to a foundation is also important.

The drained bearing capacity of a circular foundation on the surface of frictional material, loaded by a central vertical load, is described by Terzaghi (1943):

V=  

where R is the footing radius and  is the effective unit weight of the soil, dimensionless bearing capacity, .

Several authors have investigated the bearing capacity of soil beneath conical footings through numerical methodologies.

Chouhan et al. [25] investigated the dependence of the vertical load-bearing capacity of a conical foundation on the base roughness, soil friction angle and various apex angles by performing two-dimensional finite element limit analysis (FELA). Theoretical analysis was also carried out by Houlsby and Martin [26] and Chakraborty and Kumar [27].

Bearing capacity, including failure mechanisms were examined with a machine learning technique of multivariate adaptive regression splines (MARS) mode by Nguyen Van et al. [24] depending on cone apex angle, embedded depth ratio, the anisotropic ratio, and the strength gradient ratio.

Collapse loads were also calculated with numerical method using program FIELDS by Cassidy and Houlsby [28]. Lines 154-158. In this work conical foundations did not reach their ultimate load-bearing capacity while loaded identically to columnar foundations.

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model in the laboratory and at the test site for the purpose of further research for use in civil engineering as the foundations of buildings and structures. Due to the labor-intensive laboratory and costly field-testing methods, in this work we limited only 2 types of conical models.

 qult=Qult/(BxL), BxL=A if the cross-sectional area is a columnar foundation. The use of Eq 1 A=F/R (1) does not seem to be well written or explained; in line 113 where it says R - ultimate soil resistance it should read bearing-capacity or ultimate strength. (Is columnar foundation the same as superficial or direct foundation?)

Thank you very much. Corrected to ultimate bearing capacity of soil. 

Explain line 96 … was proposed as 3/4 of the radiu… why?

Models of a conical foundation with aperture angle of the cones 90° and 80° were buried into the soil at 0.75 of its height, in order to provide a safety margin under further loading due to an increase in the bearing area when the cone is immersed deeper into the ground. This is approximately 3/4 of the radius but not necessary. The cross-sectional area increases in proportion to the settlement with further loading.

Fig. 13 on the xx axis presents the variable F, kN - I propose F (kN); but in Fig. 12 a) and b) variables F, H (?). In these figures, the results do not seem to present appreciable differences between the two cones used with Qult=140 kN or Fult=140 kN; Fig.3 on the xx axis should explain R0 and F1.

Thank you very much. The load unit was corrected to Newton in laboratory test graph.

Fig. 3 removed - This was a hypothetical graph that we used before conducting laboratory and field studies and in this case, it is not needed.

Eq.2, 3 and 4 require explanation and validation by peers;

The maximum depth of cracks z_max is explained in Lines 81-102.

The dependence of settlement during undermining or tensile deformations in the soil is according to [18,20].

The modelling scale formula is explained below.

Table 1 – N/cm3 should be kN/m3. The natural soil appears to be clay and the material equivalent appears to be granular soil. The mechanical behaviors are different…

In this case, we used the approach of selecting an equivalent material that corresponds to the scale of modeling specifically for strength and deformation characteristics of soils (angle of internal friction, cohesion, deformation modulus of soils). The main focus was on cohesion.

The modelling scale was ml = l/L = Сm/ Сn · ɣm/ɣn= 1/40. This means that the cohesion of equivalent soil is 40 times less than the real one on the site. Same scale and ratio of geometric dimensions for foundation models were used. Lines 231-237.

References to the equiv. material method - Kuznetsov.G.N. Study of the effects of rock pressure on models made of equivalent materials. 1959, Moscow Publishing house Ugletekhizdat, 162 p.

Table 3, 4 and 5 - Horizontal stress strains of soil, mm/m (?), should be Horizontal stress strains of soil, mm/m

Thank you for your comment. Here we mean horizontal strains of soil due to tensile stresses in zone 1 (Figure 2). Corrected as «horizontal tensile strains of soil», measured in mm per meter of length

Figs 9 to 11 deserve the following comments:

1) what is the color and intensity legend and what are the variables of the two-dimensional axes;

Colour and intensity legend is given for deformations in mm.

2) on the assumption that the yy axis must represent the depth below the foundation: the distribution of loads induced in depth or laterally in relation to the axial axis of the application, dissipate due to the action of work, and therefore decrease. Variations in depth can be estimated analytically and/or based on the theory of elasticity. Variations in depth can also be estimated using solutions based on the real behavior of the soil, including isobarics (lines that join points of equal load) - stress bulb. The vertical stress increments under the strip axis for uniformly loaded infinite strip is practically zero for H >= 3 to 4 B.

Yes, vertical axis “Y” is for depth, “X” axis is for horizontal dimensions. 

Here the external influence is the vertical load on the foundation model, as well as the effect of horizontal tensile deformations in the soil.

The vertical deformation is “0” at the depth of 28-30 cm in the expandable box before horizontal tensile displacement of soil (ɛ=0) in Fig 10d.

After horizontal tensile displacement of soil (ɛ=3 mm), the vertical deformation is “0” at the depth of 55 cm, simulating soil sliding in undermined areas, in Fig 11d and 12d.

The bibliography is correct, but it lacks articles or books on foundations.

Thank you very much for your comments. Corrected.

Figure 3, 7, 10, 12 – legend and figure on the same page

Corrected

Delete “please” …(please see Figure 5). … line 151

Corrected

Fig. 6 - Change location

Corrected

Fig. 7 b) – caption does not conform to the figure

Corrected

Fig. 8 – on the same page

Corrected

NN

Reviewer’s comments

Authors response

1.

The 'Introduction' part MUST be revised to ensure the cited references are related to the research topics in this manuscript. The current edition is logically chaotic and confusing. 

Introduction part has been rewritten and revised. The authors tried to give the most detailed overview of the research area and the prerequisites of the problem under study.

2.

The research gap and research significance are not clear.

The research gap is presented in Lines 154 – 158.

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model in the laboratory and at the test site for the purpose of further research for use in civil engineering as the foundations of buildings and structures.

3.

In line 96, why '3/4 of the radius' was chosen, not others?

Models of a conical foundation with aperture angle of the cones 90° and 80° were buried into the soil at 0.75 of its height, in order to provide a safety margin under further loading due to an increase in the bearing area when the cone is immersed deeper into the ground. This is approximately 3/4 of the radius but not necessary. The cross-sectional area increases in proportion to the settlement with further loading.

4.

In line 104, why only '80 and 90 degrees' were considered? 

Based on previous studies [24,25], the opening angle of the cones α was taken as the average value from the previously considered modeling methods, and also based on the results of preliminary laboratory tests, in this study the operation of cones with an opening angle of 80°-90° was considered.  Lines 163-165, 192-195.

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model in the laboratory and at the test site for the purpose of further research for use in civil engineering as the foundations of buildings and structures.

At the moment, the test results for these angles and shapes are ready. In the next works it is planned to consider cones with a pile stand.

5.

Are the 'R's in line 105 and line 113 the same?

Thank you very much. Corrected.

R is for - ultimate bearing capacity of soil,

r is for radius.

6.

All the symbols used in the manuscript should be defined clearly.

Symbols and label were carefully checked for duplication and markings.

7.

In Figure 4, the unit/legend should be presented.

Thank you very much. There is a description/legend below the figure title. 

8.

In Figure 1, the conicals are all under the base of the building, while in the laboratory test in Figure 6, all the conicals are all on the top of the soil, can the authors explain the rationales?

In Fig. 1 there is a pit. The cones are installed on pre-prepared holes in a pre-excavated pit. Next, a roller connection is installed to protect the building from horizontal ground movements, then a base beam is installed, and then the building (usually low-rise) is built up.

9.

The laboratory tests and field tests were conducted in 3-D, while the numerical modelling analysis was conducted in 2D, is 2D enough to represent the physical tests?

Due to the axisymmetric nature of the problem, a two–dimensional (2D) axisymmetric finite element (FE) formulation is used to model the soil domain and conical footing. More information about the numerical simulation is found in Lines 311–318.

NN

Reviewer’s comments

Authors’ response

1.

the process of designing foundations, the necessary strength of the foundation and settlements compatible with the structure must be ensured. The strength mobilized in the mass depends on the geometry of the foundation, which will influence the distribution of stresses in depth. TERZAGHI (1943) developed a theory for calculating load capacity, based on studies by PRANDTL (1920) for metals. To this end, he admitted, in addition to some simplifying assumptions, that the shear strength of the soil is defined in terms of the cohesion c and the friction angle ∅;

Thank you very much for your comment. We do not claim to change these fundamental theories or the previously developed classical foundations of soil mechanics and geotechnics in this article.

For our case, it was important to determine the settlement of a conical foundation under the influence of horizontal tensile deformations of soil bases in undermined areas. The load-bearing capacity only increases with increasing area of contact with the ground. Therefore, the focus is on the settlements of a conical foundation, which is important when designing this type of foundation in undermined areas.

It is considered that the failure occurs along a edge, just below the footing, followed by a logarithmic spiral curve, which continues to the ground surface. One must understand the geometry of the general footing-soil interaction for bearing-capacity equations for strip footing. Terzaghi (1943), Hansen (1970) and Meyerhof (1951) verified that the bearing capacity equations were for shallow foundations where D <= B. A cone or pyramidal prism of failure develops below the flat base foundation. This has to be understood in order to interpret the study of a foundation itself shaped like a cone. And what changes in terms of the bearing-capacity factors for the equations.

The drained bearing capacity of a circular foundation on the surface of frictional material, loaded by a central vertical load, is described by Terzaghi (1943):

V=  

where R is the footing radius and  is the effective unit weight of the soil, dimensionless bearing capacity, .

Several authors have investigated the bearing capacity of soil beneath conical footings through numerical methodologies.

Collapse loads were also calculated with numerical method using program FIELDS by Cassidy and Houlsby [28]. Lines 154-158.

Cassidy, M. J. and Houlsby, G. T. Vertical bearing capacity factors for conical footings on sand, Géotechnique 2002, 52:9, 687-692.

doi:10.1680/geot.2002.52.9.687.

The vertical force exerted by the cone on the soil is V and the properties of the sand are given by the constant friction angle φ, and the effective unit weight, ϒ´. For a homogeneous soil, the method of characteristics has been applied to find a lower bound value of V, and this is then normalised by ϒ´ and R to evaluate a non-dimensional N_ϒ by a rearrangement of equation (1):

N_ϒ =V/ ϒ´πR²

Theoretical analysis carried out by Houlsby and Martin [26] mentioned that the soil is taken to be isotropic but non-homogeneous, with the undrained strength defined as varying linearly with depth:

s_u=s_um + pz (1)

where s_um is the undrained strength at the ground surface, z is the depth below the surface, and r is the rate of increase of strength with depth. It is convenient to define the strength at the level of the footing as s_u0=s_um + ph, as shown in Fig. 1(b). The average bearing pressure q (for weightless soil) is then expressed in terms of this strength:

q= N_c0s_u0 (2)

The dimensionless factor N_c0 is a function of the cone angle, cone roughness, depth of embedment and the rate of increase of strength with depth of the clay. Each of these variables is expressed through a dimensionless parameter, and a parametric study has been made of the problem in which the following cases were examined:

For more details please see: Houlsby, G. T. & Martin, C. M. (2003). Undrained bearing capacity factors for conical footings on clay. Geotechnique 53, No. 5, 513–520. DOI:10.1680/geot.53.5.513.37507.

 Bearing capacity, including failure mechanisms were examined with a machine learning technique of multivariate adaptive regression splines (MARS) mode by Nguyen Van et al. [24] depending on cone apex angle, embedded depth ratio, the anisotropic ratio, and the strength gradient ratio. Bearing capacity of the conical foundation

embedded in anisotropic and heterogenous clays was found as:

Nguyen Van, C.; Keawsawasvong, S.; Nguyen, D.K.; Lai, V.Q. Machine Learning Regression Approach for Analysis of Bearing Capacity of Conical Foundations in Heterogenous and Anisotropic Clays. Neural Comput & Applic 2023, 35, 3955–3976, doi:10.1007/s00521-022-07893-z

Chouhan et al. [25] investigated the dependence of the vertical load-bearing capacity of a conical foundation on the base roughness, soil friction angle and various apex angles by performing two-dimensional finite element limit analysis (FELA).

Chouhan, Kritesh; Lai, Van Qui; Chavda, Jitesh; Yoonirundorn, Kittiphan; Keawsawasvong, Suraparb. Evaluation of vertical bearing capacity factors for conical footing with varying base roughness using FELA and MARS model. Ships and Offshore Structures, 2023. doi:10.1080/17445302.2023.2177030

According to Chakraborty and Kumar [27] the collapse load (Qu) in terms of the bearing capacity factors Nc, Nq, and N_ϒ because of the components of soil cohesion (c), surcharge pressure (q), and soil unit weight (ϒ), respectively, is defined by the following equation:

Chakraborty, M and Kumar, M. Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis. Canadian Geotechnical Journal 2015, 52(12), 2134-2140. doi:10.1139/cgj-2014-0507.

In this work conical foundations did not reach their ultimate load-bearing capacity while loaded identically to isolated shallow foundations.

Since the previous authors limited themselves to only theoretical analysis and modeling, it was decided to test the conical foundation model in the laboratory and at the test site for the purpose of further research for use in civil engineering as the foundations of buildings and structures. Due to the labor-intensive laboratory and costly field-testing methods, in this work we limited only 2 types of conical models.

Figs 11 to 12 deserve the following comments:1) what is the color and intensity legend and what are the variables of the two-dimensional axes; Improve and increase the size of axis labels (Fig. 11 and 12).

Corrected. Figured 10, 11, 12 were supplemented with the color and intensity legend, axes and dimensions of the expandable box: heights and lengths.

2) on the assumption that the yy axis must represent the depth below the foundation: the distribution of loads induced in depth or laterally in relation to the axial axis of the application, dissipate due to the action of work, and therefore decreases. Variations in depth can be estimated analytically and/or based on the theory of elasticity. Variations in depth can also be estimated using solutions based on the real behavior of the soil, including isobarics (lines that join points of equal load) - stress bulb. The vertical stress increments under the strip axis for uniformly loaded infinite strip is practically zero for H > 3 to 4 B.

Figures 11 and 12 show displacements in mm and not stresses in the soil. So vertical displacement is a settlement in mm. For us it was important to determine the settlement of a conical foundation under the influence of horizontal tensile deformations of soil bases (earth surface). The load-bearing capacity only increases with increasing area of contact with the ground. Therefore, the focus is on the settlements of a conical foundation, which is important when designing this type of foundation in undermined areas. Variations of the displacements in depth were calculated with Plaxis 2D modelling.

You must change … maximum permissible deformations (e.g. line 92)… for allowable deformations;

Corrected.

Where do you write … columnar foundation write: Shallow fundations;

Corrected to «isolated shallow foundation».

Change the symbol … angle of internal friction φ for ∅;

Thank you. All of our previous works have been published with the angle of internal friction denoted as φ, both types of symbols are widely used to represent the angle of internal friction.

Always use units in kN (e.g … The columnar (Shallow ) foundations lost their bearing capacity after 150N in laboratory tests and after 75kN in the field tests… (and explain this discrepancy in the found values)

Corrected.

Use kN/m³ (eg Table 2 and 3)

Corrected.

Use kN/m² (e.g line 300)

Corrected.

Use modulus of elasticity (e.g.Table 3)

Thank you for your comment. In our case it was a modulus of deformation obtained from stamp tests.

The modulus of elasticity is determined from tests of soil samples during their elastic behavior, which occurs during unloading, and the modulus of total deformation, which characterizes the behavior of soil in the presence of both elastic and residual deformations.

…slabs weighing 1.25 10⁴ N. (line 329) (is not understandable)

Corrected to surcharges, weighing 12.5 kN.

Use m² (e.g. 340)

Corrected.

Line 496 to 312 before figure 16

The positioning of Figure 16 is next to the discussion paragraph of the Figure 16.

Delete in 5. Conclusions: 6. The horizontal tensile strains caused by horizontal displacement of the soil mass 540 in undermined or seismic areas can be eliminated by installing a special rolling joint lo-541 cated between the conical foundations and the plinth structure. (line 541) (is not evident at work)

Thank you very much. We have omitted the numbering of this statement as a point of conclusion.

However, this paragraph was left behind as a further research suggestion. In fact, further testing is now being carried out as a group of conical foundations under the building with installment of a special rolling joint between the conical foundations and the plinth structure.

The bibliography is correct, but it lacks articles or books on foundations. What happened to bibliography number 24 (line 627)?

The downloadable Word version of the article contains all bibliography numbers.

Editorial comments        

Format line185;

Thank you, though I do not see anything wrong with formatting of Line 185.

Units of D, H, …line 288 and 289

Corrected. Thank you.