# Numerical Analysis for Shear Behavior of Binary Interfaces under Different Bonded Conditions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3D}, Tang and Lin [20] found that the shear strength, residual strength, peak strength displacement and strain softening degree of sawtooth rock–mortar interfaces were closely related to the internal friction angle of mortar. From the perspective of microscopic parameters, the influence of the parallel bond modulus ratio on the failure mode and failure development of binary interfaces was subsequently explored [21]. Furthermore, the constitutive modeling of binary interfaces is also an important direction [22]. For example, Yu, Liu [23] conducted triaxial compression tests on half-penetrated mudstone joints and suggested a constitutive model. In addition, Wang, Sun [24] observed the bond-slip behavior describing the seismic mechanism at the mortar–rock interface and established a micromechanical model of the bond-slip at the mortar–rock interface, which theoretically establishes the mechanism of the bond-slip behavior. Dong, Yuan [25] proposed an energy fracture criterion for crack initiation at the rock–concrete interface considering viscoelastic properties.

^{2D}to study the effect of the bonded state of the binary interface on the shear stress–shear displacement curves, strength parameters, crack development and damage modes.

## 2. Numerical Modeling of Binary Interfaces with Different Bonded Conditions

^{2D}need to be introduced. In PFC

^{2D}, models can be built to simulate the motion and interaction between various physical components and display the state and result of the motion and interaction. Basic assumptions include:

- (1)
- Modeling

^{2D}to constitute the shear box for the direct shear test, with dimensions of 100 mm × 100 mm, consisting of eight walls. Particles with a reasonable size ratio are generated in the shear box, and loads are applied to these randomly distributed and partially overlapping particles until a static equilibrium state. Also, specific shapes of walls are generated between the upper and lower shear boxes as needed, and the particles inside the shear boxes are divided into two parts, which can be grouped together to simulate different rocks in the subsequent parameter assignments.

- (2)
- Parameter assignment

- (3)
- Shear loading

## 3. Shear Mechanical Behavior under Different Bonded Conditions

#### 3.1. Influence of Bonded Conditions on Shear Stress–Shear Displacement Curve

#### 3.2. Influence of Bonded Conditions on Strength Parameters

_{p}is the partially bonded binary interface shear strength; τ

_{u}is the unbonded binary interface shear strength; τ

_{b}is the fully bonded binary interface shear strength. The strength factor of the unbonded binary interface is 0, and the strength factor of fully bonded binary interface is 1.

#### 3.3. Influence of Bonded Conditions on Crack Development

#### 3.4. Influence of Bonded Conditions on Stress Distribution

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Particle modeling of binary interface in PFC. (

**a**) Shear model of binary interface; (

**b**) 0% bonded ratio; (

**c**) 25% bonded ratio; (

**d**) 50% bonded ratio; (

**e**) 75% bonded ratio; (

**f**) 100% bonded ratio. (# indicates the number of different shear box blocks. The red region means the degree of bonded ratio, other colors represent different locations of the cut box).

**Figure 2.**The shear stress–shear displacement curves of binary interfaces under different bonded conditions. (

**a**) Bonded ratio = 0%; (

**b**) bonded ratio = 25%; (

**c**) bonded ratio = 50%; (

**d**) bonded ratio = 75%; (

**e**) bonded ratio = 100%.

**Figure 6.**Crack development in binary interfaces under different bonded states. (

**a**) Unbonded binary interfaces; (

**b**) 25% bonded binary interfaces; (

**c**) 50% bonded binary interfaces; (

**d**) 75% bonded binary interfaces; (

**e**) 100% bonded binary interfaces.

**Figure 7.**Crack development of interface in unbonded condition (the red region means the distribution of cracks).

**Figure 8.**Crack development of interface in 50% bonded condition (the red region means the distribution of cracks).

**Figure 9.**Crack development of interface in fully bonded condition (the red region means the distribution of cracks).

**Table 1.**Rock physical parameters and parameter calibration results [8].

Rocks | Results | Poisson Ratio | Tangent Modulus/GPa | Uniaxial Compressive Strength/MPa |
---|---|---|---|---|

Mudstone | Test | 0.320 | 4.7 | 11.50 |

Simulation | 0.321 | 4.7 | 11.39 | |

Limestone | Test | 0.114 | 42.6 | 51.80 |

Simulation | 0.114 | 42.8 | 51.50 |

Rocks | Rigidity Ratio | Bonded Modulus/GPa | Strength Parameters/MPa | Max Particle Size/mm | Particle Size Ratio |
---|---|---|---|---|---|

Mudstone | 8 | 0.455 | 4.9 | 0.9 | 1.5 |

Limestone | 1.5 | 3.30 | 17.8 | 0.9 | 1.5 |

Model | Normal Stiffness/GPa | Tangential Stiffness/GPa | Friction Coefficient |
---|---|---|---|

Smooth joint | 100 | 0.8 | 0.54 |

Shear Strength Parameters | Bonded Conditions of Binary Interfaces | ||||
---|---|---|---|---|---|

0% | 25% | 50% | 75% | 100% | |

Cohesion/MPa | 0 | 1.56 | 1.69 | 2.25 | 4.25 |

Friction coefficient | 0.53 | 0.66 | 0.69 | 0.69 | 0.69 |

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**MDPI and ACS Style**

Lv, H.; Han, L.; Zhang, X.; Lin, H.
Numerical Analysis for Shear Behavior of Binary Interfaces under Different Bonded Conditions. *Appl. Sci.* **2024**, *14*, 3686.
https://doi.org/10.3390/app14093686

**AMA Style**

Lv H, Han L, Zhang X, Lin H.
Numerical Analysis for Shear Behavior of Binary Interfaces under Different Bonded Conditions. *Applied Sciences*. 2024; 14(9):3686.
https://doi.org/10.3390/app14093686

**Chicago/Turabian Style**

Lv, Haijun, Lu Han, Xing Zhang, and Hang Lin.
2024. "Numerical Analysis for Shear Behavior of Binary Interfaces under Different Bonded Conditions" *Applied Sciences* 14, no. 9: 3686.
https://doi.org/10.3390/app14093686