Simulation of Triaxial Tests for Unsaturated Soils under a Tension–Shear State by the Discrete Element Method

Round 1

Reviewer 1 Report

The topic of this article is very attractive. The structure and the obtained results are good. It can be accepted after a few revisions:

1. The topic of this paper is related to unsaturated soil. I wonder why no references from Antonio Gens, Eduardo Alonso, Sebastia Olivella, Jean Vaunat and Alfonso Rodriguez-Dono since they are famous scientists in unsaturated soil mechanics who developed the famous Barcelona Basic Model (BBM), BEXM as well as developed the famous software for unsaturated soil (CODE_BRIGHT)?

2. Detailed information related to the used MatDEM and the used version should be explained.

Comments for author File: Comments.pdf

Author Response

Reply Q1: The introduction related to unsaturated soil is added as follows.

‘Compared with saturated soil, the existence of gas phase leads to the complexity of mechanical properties for unsaturated soil. Alonso et al. [13] established the first constitutive model of unsaturated soil, i.e., Barcelona basic model (BBM). Subsequently, in order to accurately describe the coupling relationship between mechanics and water retention behaviors of unsaturated soil, many scholars (e.g., Wheeler et al. [14], Gallipoli et al. [15], Li [16], Sun et al.[17] and so on) proposed a series of elastoplastic coupled constitutive model. With the development of computer technology, it has become a trending to study geotechnical engineering by numerical method. Many scholars have developed finite element programs to solve unsaturated soil problems, such as LAGAMINE [18], CODE-BRIGHT [19], THYMER3D [20], U-DYSAC2 [21], etc. These studies pay more attention to the macro-mechanical behavior of unsaturated soil.’

[13] Alonso E E, Gens A, Josa A. A constitutive model for partially saturated soils[J]. Géotechnique, 1990, 40(3): 405-430.

[14] Wheeler S. J.，Sharma R. S.，Buisson M. S. R. Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils. Géotechnique. 2003, 53(1): 41-54.

[15] Gallipoli D.，Gens A.，Sharma R.，et al. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique. 2003, 53(1): 123-135.

[16] Li X. S. Thermodynamics-based constitutive framework for unsaturated soils 2: a basic triaxial model. Géotechnique. 2007, 57(5): 423-435.

[17] Sun De'an，Sheng Daichao，Xiang Li，et al. Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions. Computers and Geotechnics. 2008, 35(6): 845-852.

[18] Charlier R. Approche unifiée de quelques problèmes non linéaires de mécanique des milieux continus par la méthode des éléments finis, Doctoral Thesis, Université de Liège, 1987.

[19] Olivella S., Carrera J., Gens A. & Alonso E. E. Nonisothermal multiphase flow of brine and gas through saline media, Transport in Porous Media, 1994, 15(3): 271–293

[20] Chen Y , Zhou C , Jing L . Modeling coupled THM processes of geological porous media with multiphase flow: Theory and validation against laboratory and field scale experiments[J]. Computers & Geotechnics, 2009, 36(8): 1308-1329.

[21] Wei C F. Static and dynamic behavior of multiphase porous media: Governing equations and finite element implementation[D] (PhD thesis). Norman, Oklahoma: University of Oklahoma, 2001.

 

Reply Q2:

The related content is added as follows.

‘MatDEM is a general discrete element software for geotechnical materials developed by Nanjing University. Based on the MATLAB calculation method, it adopts the innovative GPU matrix algorithm to realize the discrete element simulation of millions of particles. Its calculated number of units and efficiency are more than dozens of times that of other commercial software. On the basis of reaching the standard of hardware, it can complete the large-scale three-dimensional discrete element numerical simulation in a few hours. The software can realize the automatic modeling of discrete element materials and the calculation of energy conservation of discrete element systems. The software integrates pre-processing, calculation, post-processing and powerful secondary development, provides a perfect function interface and efficient calculation engine, and completes complex multi-field coupling simulation through secondary development. MatDEM 1.32 version is adopted for this research.’

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is thematically interestingly written, but the authors should have made an effort and written it literally according to the template for this Sustainability journal.
For example, citing references is not considered at all in the text! The introduction states, "In the text, reference numbers should be placed in square brackets [ ] and placed before the punctuation; for example, [1], [1-3], or [1,3]. For embedded citations in the text with pagination, use both parentheses and brackets to indicate the reference number and page numbers; for example, [5] (p. 10) or [6] (pp. 101-105)."....
Therefore, I cannot suggest the publication of this paper. I can only advise the authors to write and resubmit it according to the template.
In addition, if the authors wish, they can correct the following deficiencies:
Extension of the introduction, extension for what the discrete element method can be used, maybe you can list some papers that are available for open access, for example: https://doi.org/10.17794/rgn.2021.4.12
You should also check the topics in this journal https://www.mdpi.com/search?q=discrete+element+method&journal=sustainability
Instead of Fig. 2 and Fig. 3, it should be Fig. 2a and 2b.
Line 386. the title of the figure and the figure must be on the same page.

The conclusion should state more clearly what new knowledge has been gained in this paper compared to previous findings.

Kind regards.

Author Response

• The format of references has been modified according to the template.
• Relevant references have been added as follows.

[35] Li, T.; Xiao, J. Discrete Element Simulation Analysis of Biaxial Mechanical Properties of Concrete with Large-Size Recycled Aggregate. Sustainability 2021, 13, 7498. https://doi.org/10.3390/su13137498

[36] Qi, Y.; Indraratna, B.; Ngo, T.; Ferreira, F.B. Advancements in Geo-Inclusions for Ballasted Track: Constitutive Modelling and Numerical Analysis. Sustainability 2021, 13, 9048. https://doi.org/10.3390/su13169048

[37] An, H.; Wu, S.; Liu, H.; Wang, X. Hybrid Finite-Discrete Element Modelling of Various Rock Fracture Modes during Three Conventional Bending Tests. Sustainability 2022, 14, 592. https://doi.org/10.3390/su14020592

[38] Wang, Y.; Li, X.; Li, J.; Xu, J. Numerical Simulation of Impact Rockburst of Elliptical Caverns with Different Axial Ratios. Sustainability 2022, 14, 241. https://doi.org/10.3390/su14010241

• The picture number has been modified.
• The conclusion has been modified as follows.

‘In this paper, a relationship between tensile strength and water content was obtained by comprehensive comparison between the results of complex uniaxial tensile test and numerical simulation test. Besides, the discrete element simulation of triaxial tension shear test for unsaturated soils was carried out. The simulation results demonstrate that (1) the water content affects the peak deviatoric stress, dilatancy behavior and failure modes. (2) The strength increases with the decreasing of water content and the increasing of confining pressure. (3) The dilatancy phenomena is obvious for the situations with low confining pressure range and water content. (4) The samples occur pure tensile failure under small confining pressure condition, occur shear elongation and tensile failure under middle confining pressure condition, and occur shear failure under large confining pressure condition.’

Author Response File: Author Response.docx

Reviewer 3 Report

1.      The paper is interesting and presents the application of the discrete elements method in the simulation of triaxial tests for unsaturated soils under tension - shear state. A relationship between moisture content and uniaxial tensile strength with different void ratio is obtained, which is applied for uniaxial tensile discrete element simulations to establish a relationship between grain-scale parameters and water content from back analysis. Discrete element method is used to get the relationship between deviating stress and axial displacement under different water content, and also to study the effects of water content on the peak strength and dilatancy with different confining pressure.

2.      The choice of a continuous or discrete method depends on the specifics of the studied problem and, mainly, on the scale and geometry of the fracturing system. The discrete element method has been adapted to represent the behavior of discrete media, from weakly fractured media using the dihedral method to strongly fractured media. The blocks can be modeled in rigid or deformable form, and their assembly is done along the discontinuities represented by contacts. This method of discrete elements allows the consideration of large deformations, rotations and instabilities in an advanced stage, the contacts being able to open, then disappear and other contacts appear. Modeling of underground structures and, in particular, three-dimensional modeling is a useful tool, which offers engineers the opportunity to make certain decisions. Three-dimensional modeling offers a unique solution in solving the problems of soil mechanics and geotechnics, the engineer having the possibility to obtain a better representation of the real behavior of the soil, foundation ground and constructions with which they interact. The hydrocolloidal cohesion has a reversible character and gives plasticity to the rocks. Its value is strongly influenced by humidity and causes certain rocks to change their consistency from a flowing state to a hard, solid state, as the humidity decreases. Starting from such a finding, it can be explained the increase of the shear strength with the increase of s, not only by the increase of the friction forces (when j> 0), but also by the increase of the hydrocolloidal cohesion component, as a result of an increased compactness, and reduced humidity. As a result, especially in the case of very low-strength clay rocks, it is necessary to determine a conventional friction angle, which expresses both the friction process and the hydrocolloid bonds. Experimentally, it was found that if the shearing of the specimen occurs immediately after the application of normal force, then the coefficient of friction has values ​​close to zero. In fact, this behavior of clay rocks is also manifested in the case of unsaturated soils, which leads us to consider that the distribution of water pressure in the pores during consolidation is not an explanation for obtaining a low shear strength by performing the tests, without waiting the consolidation of the rock specimen. The increase in shear strength of clay rocks is due to the intensification of the number of contact points between fine particles, surrounded by water bound by molecular forces (adsorbed - absorbed) and over time, due to the processes of concentration and deposition of salts solubilized in water. Increasing the number of contacts between the areas of adsorbed water of the clay particles can be obtained only by compaction, i.e. by reducing the porosity. As a result, the true parameters on which the shear strength depends are: compaction, compactness and humidity; they are modified by the value of the normal stress applied during shearing.

3.      The dilatancy phenomenon is obvious for the situations with low confining pressure range and water content. The dilatancy phenomenon could be also studied rheological!

Author Response

Reply：In this paper, discrete element method is used to simulate triaxial tests of unsaturated soil under tension-shear state. Discrete element method is used to study the effects of water content on the peak strength and dilatancy with different confining pressure. The displacement field of the numerical sample are analyzed qualitatively, and the mechanism and process of the failure are analyzed from the prospective of energy and dissipation.

Round 2

Reviewer 2 Report

The authors have taken most of my advice into account, and probably that of other reviewers, and the paper now looks much better.
However, a good editorial review of the graphic design and appearance of the pages will be needed when comments and editorial marks are removed.
Line 450 after the word "that" should be ":".
Line 450 to 453 The four major points in the conclusion should be below each other. The numbers can be replaced with bullets.
Best regards!

Author Response

Reply:

• The conclusion has been modified according to the suggestions on revision.
• The format of the manuscript has been further adjusted according to the template.

Author Response File: Author Response.pdf