Numerical simulation of the triaxial test of coal measure expansive soil distributed along the highways in Pingxiang District, Jiangxi, was carried out by means of discrete particle flow, during which the macromechanical properties and the formation and developmental patterns of shear displacement field of the coal measure expansive soil were studied from a mesoscopic perspective. The result showed that the macroscopic stress and strain of test specimens can be significantly influenced by the interparticle friction coefficient of the coal measure expansive soil. Peak value of the deviatoric stress of test specimens increased with increasing friction coefficient, and before reaching the deviatoric stress peak value, the stress-strain relationship of the soil body basically presented a linear variation trend; the soil interparticle contact stiffness varied hyperbolically with the deviatoric stress peak value of test specimens, and the increasing contact stiffness ratio led to a gradual decrease of the deviatoric stress peak value but had only a small impact on the residual strength of test specimens; confining pressure was found to have remarkable influence on both the deviatoric stress peak value and the residual strength of test specimens; when the experimental confining pressure increased from 0.2 MPa to 1.2 MPa, the deviatoric stress peak value and the residual strength of test specimens increased by 2.14 times and 5.11 times, respectively. This paper reveals the macroinstability and failure mechanism of coal measure expansive soil from a microperspective.

Coal measure soil mostly appears ash black in appearance, while the soil mass exposed is greyish with weak interlayer bonding and loose structure. Since coal measure soil is easily weathered and disintegrated with poor water stability after excavation, large gullies are likely to be caused by water and soil loss during heavy rain. Therefore, an urgent problem which should be solved currently is how to handle and utilize engineering with coal measure soil. Some researchers at home and abroad have researched problems and reinforcement measures for engineering with coal measure soil [

In 1979, Cundall and Strack [

A large amount of coal measure strata containing montmorillonite and illite are distributed along the Pingxiang-Lianhua expressway in Jiangxi. As a result, expansive soil can be found in coal measures. Nonetheless, few researches on mechanical properties of the expansive coal measure soil have been reported currently. In this paper, the discrete element method (DEM) is employed to have a 3D numerical simulation of the triaxial test on the expansive coal measure soil, to probe into the influencing rule of parameter changes of the micromechanic structure of the soil mass particles on macromechanical characteristics of the expansive coal measure soil, and to discuss the formation and development law of the shear displacement field of the expansive coal measure soil. The research findings can provide theoretical references for the protective slope design and construction of the expansive coal measure soil.

The discrete element method (DEM) is to consider objects of research as an integral whole consisting of a finite number of discrete particles, in which each particle is idealized as a rigid body and deemed as a discrete calculating unit. The particles are independent of each other with contact and friction. Assuming that the normal contact forces

The tangential contact force between granular particles is defined as the shear force whose size is closely related to the movement track of the particles and their loading history. In this paper, the shear force between granular particles is expressed in the form of increment. When a contact is formed between granular particles, the total tangential contact force

Based on equation (

Since many coal particles are contained in expansive coal measure soil, especially that in the weathering layer of the slope is loose, it results in weak cohesive force between the soils. The shear strength is formed primarily by the internal friction between soil particles. Therefore, a contact sliding model can be utilized to describe the constitutive relationship between the normal force and the tangential shear force interacting between particles. The normal tension between particles is neglected in the contact sliding model. The sliding motion between particles only occurs under set conditions, that is, the shearing force actually generated between particles should be greater than the preset threshold; also, the sliding between particles must be performed within a certain range of shear strength. Assuming that the displacement overlapping between two particles is less than or equal to zero, it can be considered that the two particles have no contact or their contact force is zero. In this way, their constitutive behavior can be described as

A particle flow calculation model is firstly established in this paper according to the actual particle size range of the soil mass by assuming that particles of the soil mass are rigid materials. Meanwhile, the above contact sliding model is used to indicate the particle interaction. After simulating the stress-strain relationship of test pieces in the triaxial test by changing microscomic parameters of particles, the results obtained are compared with those from the laboratory triaxial test. Finally, microscomic parameters of the soil particles that can reflect macromechanical properties of the soil mass are determined through numerous trial calculations and analyses. Furthermore, the calculation model is taken as a basic model for analyzing the influencing law of changes of particle microscopic parameters on macroscopic characteristics of the expansive coal measure soil.

The key to the calculation principle of numerical simulation in the triaxial test is to calculate the stress state of the test piece in the loading process along with stress control. While the test piece is loaded by controlling the movement velocity of the bottom plate and the top plate of the model constraint boundary in the triaxial test that is simulated with the discrete particle flow program [

Servo functions can be called in the cycle of calculating the time steps to reduce the difference between the monitoring stress and the preset stress in the calculation of numerical simulation. The numerical servo functions are adopted to adjust the velocity of conducting lateral restraint against the wall of the test piece, so that the restraint stress can be inclined to a certain constant. The numerical servo functions are achieved by the following algorithms; the velocity of boundary restraint can be expressed as follows:

Assuming that the increment of the binding force generated in the movement of lateral wall restraining within a calculated step can be expressed as follows:

Eliminate

The following equation can be obtained by transposing the inequation:

Therefore, the increment can be determined by the following equation:

In general,

The test soil samples source from the slope of original coal measures at K12 + 110 in A2 section of Wanzai-Yichun expressway in Jiangxi. Natural physical and mechanical indexes of the samples are as follows: the average density of soil particles is 2230 kg/m^{3}; the average natural density is 1680 kg/m^{3}; the natural porosity is 0.32; and the moisture content _{10} = 0.129, _{30} = 0.58, and _{60} = 1.27; the nonuniform coefficient _{u} is 9.84; and the curvature coefficient _{c} is 2.08. The SLB-1 triaxial shear permeameter manufactured by the Nanjing Soil Instrument Factory is used in the test which takes unconsolidated-undrained (UU) shearing. The test pieces are 40 mm in diameter and 80 mm in height. The triaxial shear test is conducted under the ambient pressure of 0.1 MPa, 0.3 MPa, and 0.6 MPa, respectively.

Test results of particle size distribution of coal measure expansive soils.

Test material | Particle size (mm) | Content (%) |
---|---|---|

Coal measure expansive soil | >20 | 2.26 |

10∼20 | 7.73 | |

5∼10 | 14.63 | |

2∼5 | 36.31 | |

0.5∼2 | 24.3 | |

0.25∼0.5 | 10.17 | |

0.075∼0.25 | 3.02 | |

>0.075 | 1.58 |

Sizes of numerical modeling and particle simulation are magnified to save time for calculation and improve the efficiency of analysis. The numerical model of the triaxial test is 2 meters in height and 0.8 meters in diameter. As can be known from the results of the laboratory particle grading test for expansive coal measure soil in Table

Computational model for triaxial numerical experiments. (a) Boundary wall. (b) Particle set.

The walls on the top and at the bottom of the particle flow soil samples are driven to conduct relative movement via the numerical servo system under consolidated and ambient pressure of 0.1 MPa, 0.3 MPa, and 0.6 MPa, so as to unload the test pieces. At the same time, the ambient pressure of the test pieces can be guaranteed unchanged through adjustment of the side wall displacement before the end of loading. Numerical calculation results are approximated to the results of the laboratory triaxial test via repeated trial calculation by changing microscopic parameters of the particles. The final calibrated results of microscopic parameters of the particles are obtained, as shown in Table

Microscopic parameters used in the discrete element method simulations.

Particle density | 2230 kg/m^{3} |

Porosity | 0.32 |

Model particle diameter | 20 mm∼200 mm |

Friction coefficient | 0.3 |

Normal stiffness of particle contact | 1 × 10^{9} N/m |

Tangential stiffness of particle contact | 1 × 10^{7} N/m |

The results of deviation stress and strain of the triaxial test are compared with those of numerical simulation.

The friction coefficient

Graph showing the relationship between bias stress and axial strain with different friction coefficients: (a) bias stress and axial strain; (b) peak deviating stress and friction coefficient.

According to the deviatoric stress-axial strain curve in Figure

Figure

Graph showing the relationship between volumetric strain and axial strain with different friction coefficients.

Based on the original calculation model, the ambient pressure is 0.3 MPa; and the contact stiffness

Graph showing the relationship between different tangential contact stiffness and stress-strain: (a) deviation stress and axial strain; (b) peak deviating stress and tangential contact stiffness.

Graph showing the relationship between volumetric strain and axial strain with different tangential contact stiffness.

As can be seen from Figure

It can be observed from Figure

As can be seen from Figure

Graph showing the relationship between stress and strain with different contact stiffness ratios of particles: (a) deviation stress and axial strain; (b) volumetric strain and axial strain.

The stress state around the test piece in the triaxial test is changed to explore the changing law of deviatoric stress and axial strain under different ambient pressures. Ambient pressures calculated are valued as 0.2 MPa, 0.4 MPa, 0.6 MPa, 0.8 MPa, 1.0 MPa, and 1.2 MPa, while other microscopic parameters remain constant. The calculation results are shown in Figures

Graph showing the relationship between stress and strain with different confining pressures: (a) deviation stress and axial strain; (b) peak deviating stress and confining pressure.

Graph showing the relationship between volumetric strain and axial strain with different confining pressures.

From Figure

The relationship curve of the volumetric strain and the axial strain under different ambient pressures of the test piece is shown in Figure

Based on the original calculation model, the ambient pressure is set as 0.8 MPa; and the porosity of the test piece is set as 0.3, 0.35, 0.4, 0.45, and, 0.5, respectively, while other parameters maintain constant, thus to analyze the stress-strain relationships of the test piece under different porosity conditions. The simulated calculation results are shown in Figure

Graph showing the relationship between stress and strain with different porosity: (a) deviation stress and axial strain; (b) volumetric strain and axial strain.

The relationship curve of volumetric strain and axial strain under different porosity conditions of the test piece is shown in Figure

The displacement and velocity change paths of particles in the test piece can be monitored and tracked in real time in the loading process of numerically simulating the triaxial test with the particle flow code. Moreover, the formation of the shear displacement field and the change law of the stress field of the test piece can be analyzed through elaboration of the displacement vector. Figure

Graph showing the formation and variation of shear displacement field of specimen particles during loading (the confining pressure is 0.6 MPa): (a)

Distribution of the shear displacement field of the test piece under different ambient pressures is presented in Figure

Graph showing the distribution of shear displacement field of specimens with different confining pressures: (a)

Cundall and Strack [^{−3}, and the natural porosity was 0.32. The values of mesoscopic parameters of the test samples were in accordance with the calibrated values in Table

The results of deviator stress and volumetric strain of the test samples simulated by the triaxial test are shown in Figure _{v} = −1.8% while the system achieved its highest density and maximum volume fraction. When the axial strain was

Simulated results of the triaxial test for specimens: the relation curve between (a) deviating stress and axial strain and (b) volumetric strain and axial strain.

Figure

The curve of relationship between volume fraction and axial strain: (a) the relationship between volume fraction and axial strain at the measuring sphere 1 (outside shear band); (b) the relationship between volume fraction and axial strain at the measuring sphere 2 (in shear band).

Figure

Relation between coordination number and axial strain: (a) the relationship between coordination number and axial strain at the measuring sphere 1 (outside shear band); (b) the relationship between coordination number and axial strain at the measuring sphere 2 (in shear band).

Based on the theory of discrete element method (DEM), this paper performed numerical calculations on the triaxial test of expansive coal measure soil as well as simulated the macromechanical properties of the coal measure soil as well as the formation and development of the shear displacement field from the perspective of particle microscopic parameters, from which, results similar to the laboratory test can be obtained. By analyzing microscopic parameters of the particles and the influencing law of the macroscopic stress-strain curve of the expansive coal measure soil, the following conclusions can be made.

The friction coefficient between soil particles exerts a significant influence on the macroscopic stress and strain of the test piece. As the friction coefficient

The contact stiffness between particles increases, whereas the deviatoric stress peak of the test piece decreases, basically presenting a hyperbolic change. When the contact stiffness ratio

The deviatoric stress peak and the residual strength are significantly affected by the ambient pressure in the test. By analyzing from the microscopic mechanism, it is mainly a result of the resistance increase of particle motion in the restrained test piece with the ambient pressure of the test piece. That is to say, the difficulty of displacing the relative sliding of the particle has also increased, which is further manifested by the enhanced deviatoric stress peak of the test piece from the macroperspective.

The monitoring of volume fraction and coordination number in shear band shows that the volume fraction in shear band of coal measure soil decreased with the increase of axial strain when the granular system was in the softening stage, which indicated that the dilatancy behavior of the granular system was basically caused by the loose distribution of particles in the shear band. At the same time, the coordination number began to decrease significantly, indicating that the porosity in the central region of the particle system began to increase, and the dilatancy failure behavior of the particles included not only the slip between the particles but also the angular displacement caused by the rotation of the particles.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This study was supported by the National Natural Science Foundation of China (Grant no. 51609114), the Science and Technology Project of Jiangxi Education Department (Grant no. GJ161101), and the Superiority Science and Technology Innovation Team Project of Nanchang City (Grant no. 2017CXTD012).