Punch shear tests have been widely used to determine rock shear mechanical properties but without a standard sample geometric dimension suggestion. To investigate the impacts of sample geometric dimensions on shear behaviors in a punch shear test, simulations using Particle Flow Code were carried out. The effects of three geometric dimensions (i.e., disk diameter, ratio of shear surface diameter to disk diameter, and ratio of disk height to shear surface diameter) were discussed. Variations of shear strength, shear stiffness, and shear dilatancy angles were studied, and the fracture processes and patterns of samples were investigated. Then, normal stress on the shear surface during test was analyzed and a suggested disk geometric dimension was given. Simulation results show that when the ratio of the shear surface diameter to the disk diameter and the ratio of disk height to the shear surface diameter is small enough, the shear strength, shear stiffness, and shear dilatancy angles are extremely sensitive to the three geometric parameters. If the ratio of surface diameter to disk diameter is too large or the ratio of disk height to surface diameter is too small, a part of the sample within the shear surface will fail due to macro tensile cracks, which is characterized by break off. Samples with a greater ratio of disk height to shear surface diameter, namely when the sample is relatively thick, crack from one end to the other while others crack from both ends towards the middle. During test, the actual normal stress on the shear surface is greater than the target value because of the extra compressive stress from the part of sample outside shear surface.

Shear fracture is one of the fundamental failure patterns of rocks. At present, Mohr–Coulomb criterion is widely used for the determination of shear strength and the envelope, which intercepts the

In a triaxial compression test, the sample fails under axial and confining stresses. The strength envelope can be obtained by the tangent line of the Mohr’s stress circles based on minimum and maximum principal stresses [

Rock sample dimensions in laboratory tests significantly impact the test result. As shown in _{i}_{i}_{i}_{i}

To investigate the influence of the geometric dimensions of the sample disk on the shear behavior of rocks in the PST, punch shear simulations were carried out under zero normal stress by using Particle Flow Code (PFC). Variations in shear mechanical parameters under various geometries were studied. Then, the failure process and fracture pattern of disks with different disk dimensions were investigated. Finally, the normal stress on the shear surface during the test was analyzed and a suggested disk size was given.

PFC^{3D}, a three-dimensional discrete element modeling framework, has been widely used in rock mechanical simulations. The model framework simplifies rock material into balls and bonds. A ball in the PFC^{3D} is a rigid and the surface of the ball is defined by radius. A ball has a single set of surface properties. Balls can translate and rotate. As linear parallel-bond can transmit both force and moment while contact-bond only transmits force [

where _{c}^{l} and ^{d} is linear force and dashpot force, respectively; _{c}

where _{c}

The force–displacement law for the parallel-bond force and moment consists of the following seven steps.

Update the bond cross-sectional properties. In this step, the radius

Update normal force. The normal force will be recalculated according to the relative normal-displacement increment

Update shear force. Shear force of the parallel-bond will be recalculated in this step:

where _{s}

Update twisting moment:

where

Update bending moment:

where

Update the maximum normal and shear stresses at the parallel-bond periphery:

where

Enforce strength limits. If the tensile strength limit of the parallel-bond is exceeded, then break the bond in tension. If the shear strength limit of the parallel-bond is exceeded, then break the bond in shear.

In PFC^{3D}, stress is applied within the model by moving walls or balls. If the tensile or shear strength of a bond is exceeded, a tensile or shear micro-crack will be formed. The numerical model in this study is composed of five walls (_{i}_{i}_{i}_{i}_{i}

where

As the strength of a parallel-bond conforms to the Mohr–Coulomb criterion. Therefore, the strength of a parallel-bond can be described by the parameters of parallel-bond tensile strength, parallel-bond cohesion and parallel-bond friction angle. The detailed descriptions of the micro-parameters used in the simulations are detailed in _{i}_{d}_{i}_{h}_{i}

Micro-parameter | Value |
---|---|

Parallel-bond tensile strength (MPa) | 4.0 |

Parallel-bond cohesion (MPa) | 4.5 |

Parallel-bond friction angle ( |
42 |

Ratio of maximum to minimum radius of ball | 1.4 |

Ration of normal to shear stiffness of parallel | 1.5 |

Particle friction coefficient | 0.57 |

No. | _{d} |
_{h} |
No. | _{d} |
_{h} |
No. | _{d} |
_{h} |
No. | _{d} |
_{h} |
No. | _{d} |
_{h} |
|||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 30 | 15 | 60 | 26 | 40 | 15 | 60 | 51 | 50 | 15 | 60 | 76 | 60 | 15 | 60 | 101 | 70 | 15 | 60 |

2 | 100 | 27 | 100 | 52 | 100 | 77 | 100 | 102 | 100 | ||||||||||

3 | 140 | 28 | 140 | 53 | 140 | 78 | 140 | 103 | 140 | ||||||||||

4 | 180 | 29 | 180 | 54 | 180 | 79 | 180 | 104 | 180 | ||||||||||

5 | 220 | 30 | 220 | 55 | 220 | 80 | 220 | 105 | 220 | ||||||||||

6 | 30 | 60 | 31 | 30 | 60 | 56 | 30 | 60 | 81 | 30 | 60 | 106 | 30 | 60 | |||||

7 | 100 | 32 | 100 | 57 | 100 | 82 | 100 | 107 | 100 | ||||||||||

8 | 140 | 33 | 140 | 58 | 140 | 83 | 140 | 108 | 140 | ||||||||||

9 | 180 | 34 | 180 | 59 | 180 | 84 | 180 | 109 | 180 | ||||||||||

10 | 220 | 35 | 220 | 60 | 220 | 85 | 220 | 110 | 220 | ||||||||||

11 | 45 | 60 | 36 | 45 | 60 | 61 | 45 | 60 | 86 | 45 | 60 | 111 | 45 | 60 | |||||

12 | 100 | 37 | 100 | 62 | 100 | 87 | 100 | 112 | 100 | ||||||||||

13 | 140 | 38 | 140 | 63 | 140 | 88 | 140 | 113 | 140 | ||||||||||

14 | 180 | 39 | 180 | 64 | 180 | 89 | 180 | 114 | 180 | ||||||||||

15 | 220 | 40 | 220 | 65 | 220 | 90 | 220 | 115 | 220 | ||||||||||

16 | 60 | 60 | 41 | 60 | 60 | 66 | 60 | 60 | 91 | 60 | 60 | 116 | 60 | 60 | |||||

17 | 100 | 42 | 100 | 67 | 100 | 92 | 100 | 117 | 100 | ||||||||||

18 | 140 | 43 | 140 | 68 | 140 | 93 | 140 | 118 | 140 | ||||||||||

19 | 180 | 44 | 180 | 69 | 180 | 94 | 180 | 119 | 180 | ||||||||||

20 | 220 | 45 | 220 | 70 | 220 | 95 | 220 | 120 | 220 | ||||||||||

21 | 75 | 60 | 46 | 75 | 60 | 71 | 75 | 60 | 96 | 75 | 60 | 121 | 75 | 60 | |||||

22 | 100 | 47 | 100 | 72 | 100 | 97 | 100 | 122 | 100 | ||||||||||

23 | 140 | 48 | 140 | 73 | 140 | 98 | 140 | 123 | 140 | ||||||||||

24 | 180 | 49 | 180 | 74 | 180 | 99 | 180 | 124 | 180 | ||||||||||

25 | 220 | 50 | 220 | 75 | 220 | 100 | 220 | 125 | 220 |

Twenty-five of the 125 samples were selected for analysis. _{d}_{h}_{d}_{h}_{h}_{d}_{h}_{d}_{h}_{d}_{h}_{d}_{h}

_{d}_{h}_{d}_{d}_{d}_{h}_{d}_{d}_{h}

In the linear stage, the shear stress increases linearly with the increase of the shear displacement (_{d}_{h}_{d}_{h}_{d}_{h}_{d}_{h}_{d}_{h}_{d}_{h}

The change in normal displacement with shear displacement is shown in

_{i}_{d}_{h}_{d}_{h}_{h}_{d}_{h}_{d}_{h}_{d}_{d}_{h}_{d}_{h}_{d}_{h}_{d}_{h}

_{d}_{h}_{h}_{h}_{h}_{h}_{h}

According to Huang et al. [_{s}_{d}_{s}_{s}_{s}_{s}_{s}

_{sp}_{s}_{d}_{h}_{sp}_{d}_{h}_{sp}_{sp}_{d}_{h}

As shown in _{c}_{c}_{sp}_{c}_{sp}_{d}_{c}_{h}_{c}_{c}_{h}_{c}_{h}_{h}_{c}_{h}_{sp}_{d}_{h}_{sp}_{sp}_{h}_{sp}_{d}_{h}

As shown in

_{d}_{h}_{d}_{h}_{d}_{h}_{d}_{d}_{h}_{h}_{d}_{h}_{d}_{h}

The PST has been used by researchers to determine the shear mechanical parameters of rocks. However, there are no suggested sample geometric dimensions at present. Simulations using PFC3D were carried out to investigate the influences of sample geometric dimensions on shear behaviors in the PST. We found that:

When the ratio between sample _{i}_{i}

In the PST, a cylindrical shear surface will be formed. If the disk height is comparatively small or the diameter of the surface is comparatively larger, the sample can easily produce a tensile fracture within the shear surface. Samples with a small ratio between sample _{i}_{i}

In the PST, the actual normal stress is greater than the set value, which results in larger shear strength. The suggested sample geometric dimensions are given as a _{i}_{i}