# Influence of Layered Angle on Dynamic Characteristics of Backfill under Impact Loading

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}, depending on the filling slurry ability—inevitably cause the phenomenon of solidified filling body stratification. Therefore, in this paper, the influences of the filling surface angle, the cement–sand ratio and different strain rates on the dynamic characteristics and failure mode of layered backfill were studied using an SHPB test system and LS-DYNA simulation software.

## 2. Experiment

#### 2.1. Specimen Preparation

#### 2.1.1. Experimental Materials

#### 2.1.2. Experimental Protocol

#### 2.1.3. Experimental Method

#### 2.2. SHPB Device

^{3}, elastic modulus of 210 GPa and Poisson’s ratio of 0.25~0.3. The strain signal was collected and recorded by the foil strain gauge. The sensitivity coefficient of the strain gauge was 2.08 and its resistance was 120 Ω; the model was BFH120-5AA-D-D150 and the accuracy grade was A. The impact pressure was set to 0.20, 0.21, 0.23, 0.25 and 0.27 MPa. Before the beginning of the experiment, the normal connection of each circuit was checked, and an air-impact experiment was used to determine whether the system was in a normal working state. The experimental device is shown in Figure 5.

## 3. Outcome and Discussion

#### 3.1. Voltage Signal Curve of Layered Filling Body

^{−1}, the cement–sand ratio is 1:4, the number of layers is two and the angle of the layers is 5°. The incident wave and the reflected wave of the filling body are basically equal to the transmitted wave. Therefore, the stresses on both ends of the specimen before impact crushing are basically the same, thus meeting the macroscopic equilibrium conditions.

#### 3.2. Dynamic Stress–Strain Curves of Layered Filling Body

^{−1}, the AB section in Figure 7 indicates the linear elastic deformation stage. There were no micro-pores or micro-cracks in the filling body, and the specimen had high integrity. The value range of σ in this stage was 0 < σ < σ

_{t}; σ

_{t}is the crack initiation value, which can also be regarded as the starting point of the plastic deformation stage of the filling body. The value is generally about 70% of the dynamic peak strength of the filling body. The BC section indicates the plastic deformation stage, when the micro-pores and micro-cracks in the filling body develop rapidly and it is penetrated with new cracks. With the extension of the action time, the degree of damage to the filling body gradually intensified, with a value range of σ between σ

_{t}< σ < σ

_{p}; σ

_{p}is the dynamic peak strength of the filling body. The section CD indicates that when σ

_{p}< σ, the specimen entered the post-peak failure stage and the primary cracks and new cracks rapidly intersected and penetrated to form a macro-failure surface, while the specimen basically lost its bearing capacity [27].

#### 3.3. Influence of Average Strain Rate on Dynamic Characteristics of Layered Filling Body

#### 3.4. Influence of Angle of Filling Surface on Dynamic Characteristics of Filling Body

^{−1}(as the accurate strain rate of the filling body was uncontrollable, the approximate strain rate was adopted), the dynamic peak strength of the layered filling body with the cement–sand ratio of 1:4 decreased from 7.39 MPa to 4.96 MPa with the increase in the filling surface angle. The dynamic peak strength of the layered filling body with the cement–sand ratio of 1:6 decreased from 3.95 MPa to 3.17 MPa, and the dynamic peak strength of the layered filling body with the cement–sand ratio of 1:8 decreased from 1.86 MPa to 1.54 MPa. Therefore, with the increase in the stratification angle, the dynamic peak strength of the filling body gradually decreased. The main reason was that the micro-cracks in the filling surface were greater than the micro-cracks in the complete filling body because the bonding of the filling surface of the layered filling body was far lower than that of the complete filling body. When the angle of the filling surface increases to a certain extent, it is easy for the micro-cracks in the filling body to expand along the tip, which may produce stress concentration resulting in the failure of the layered filling body along the filling surface. Therefore, the dynamic peak strength of the layered filling body decreased gradually with the increase in the angle of the filling surface.

## 4. Failure Mode Analysis of Layered Filling Body

^{−1}, the cement-tailing ratio was 1:4 and the angle of the filling surface was 0°, there was no obvious damage in the upper and lower layers of the filling body but fractures occurred along the middle of the specimen. Due to the existence of the filling body’s filling surface, the stress wave transmitted into the filling body continued to reflect and transmit in the stratification of the specimen, which intensified the dynamic process in the stratification. This resulted in the splitting failure of the specimen under the action of tension along the filling surface. When the angle of the filling was 5°, the layered filling body was slightly damaged along the middle filling surface and many through cracks were produced along the axial direction, but the specimen still had a high bearing capacity. When the angle of the filling surface was 13°, the failure mode of the layered filling body was quite different from the filling bodies with 0° and 5°. The failures of 0° and 5° filling bodies were mainly related to splitting failures along the filling surface of the specimen, while the failure of the 13° filling body mainly concerned shear failure along the filling surface of the specimen. Therefore, under the impact load, with the increase in the angle of the filling surface, it was easy for the layered filling body to slip along the filling surface, resulting in the loss of the bearing capacity of the filling body.

^{−1}and the cement-tailing ratio was 1:4, the degree of damage to the filling body gradually intensified when the angle of the filling surface was 0°, and the upper and lower layers were seriously damaged along the axial direction. The main reason was that when the stress wave acts on the interface of a filling body, the Poisson effect leads to a large tensile stress along the transverse direction of the impacted specimen. Therefore, the filling body specimen was seriously damaged along the axial direction. When the angle of filling surface was 5°, the layered filling body was seriously damaged along the circumferential direction, but the specimen still had a certain bearing capacity. When the angle of the filling surface was 13°, the layered filling body was fractured along the axial direction, and more filling body blocks were produced.

^{−1}and a cement-tailing ratio of 1:4, the 0°, 5° and 13° filling bodies were completely broken and lost their bearing capacities.

## 5. Numerical Simulation of Dynamic Mechanical Properties of Filling Body

#### 5.1. Finite Element Model

#### 5.2. Contact Definition and Boundary Conditions

#### 5.3. Material Model

_{crush}and elastic modulus ${k}_{e}={P}_{c}/{\mu}_{c}$, where P is the hydrostatic pressure, P

_{crush}is the actual pressure and $\mu $ is the volume strain of the specimen, and there is no obvious change in the micro-cracks and micro-pores in the concrete at this stage.

_{crush}≤ P ≤ P

_{lock}, and the internal micro-cracks and micro-pores of the concrete are gradually compacted, resulting in irreversible plastic deformation.

_{lock}, and the micro-cracks and micro-pores in the concrete are completely compacted.

#### 5.4. Selection of Material Parameters

_{1}and D

_{2}and the pressure constants K

_{1}, K

_{2}and K

_{3}. Therefore, in this paper, individual adjustment calculations were carried out on the basis of the parameters determined in a previous study [30], as shown in Table 3.

#### 5.5. Simulation Analysis

#### 5.5.1. Failure Mode Analysis of Layered Filling Body

#### 5.5.2. Analysis of Simulated Stress–Strain Curve of Layered Filling Body

## 6. Conclusions

- (1)
- With the increase of the average strain rate, the dynamic peak strength and dynamic strength growth factor of the layered filling body increased gradually, and the dynamic strength growth factor of the layered filling body with the cement–sand ratio of 1:6 was greater than that of the filling bodies with the cement–sand ratios of 1:4 and 1:8.
- (2)
- With the increase of the stratification angle, the static and dynamic peak strength of the layered filling body decreased gradually, and the higher the cement–sand ratio, the higher the peak strength of the filling body was. There was no obvious change relating to the dynamic strength growth factor and the angle of the filling surface.
- (3)
- According to the failure mode analysis and the LS-DYNA numerical simulation results for the layered filling body, with the increase in the stratification angle the failure mode of the layered filling body changed from splitting failure under tension to shear failure, and the dynamic peak strength of the filling body obtained in the experiment was similar to the dynamic peak strength of the filling body obtained in the simulation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Voltage signal curve and stress balance test of a layered filling body: (

**a**) stress balance test; (

**b**) voltage signal curve.

**Figure 13.**Relationship between the angle of the filling face and the dynamic strength growth factor.

**Figure 14.**Influence of different filling surface angles on the failure mode of a layered filling body: (

**a**) failure mode of layered filling body with approximate strain rate of 16 s

^{−1}; (

**b**) failure mode of layered filling body with approximate strain rate of 27 s

^{−1}; (

**c**) failure mode of layered filling body with approximate strain rate of 40 s

^{−1}.

**Figure 17.**Stress distribution nephogram of 0° layered filling body: (

**a**) failure time of 0.4 ms; (

**b**) failure time of 2.1 ms; (

**c**) failure time of 10 ms.

**Figure 18.**Stress distribution nephogram of 13° layered filling body: (

**a**) failure time of 0.6 ms; (

**b**) failure time of 1.1 ms; (

**c**) failure time of 9.4 ms.

**Figure 19.**Stress–strain curves from the numerical simulation of the filling body at different angles.

Component | CaO | MgO | SiO_{2} | Al_{2}O_{3} | S | Cu | Zn | TFe |
---|---|---|---|---|---|---|---|---|

Content/% | 5.96 | 2.08 | 45.89 | 12.32 | 0.5 | 0.035 | 0.067 | 11.06 |

Layer Number | Mass Concentration/% | Cement–Sand Ratio | Angle/° | Impact Pressure/MPa |
---|---|---|---|---|

2 | 68 | 1:4/1:4 | 0 | 0.20; 0.21; 0.23; 0.25; 0.27 |

1:4/1:4 | 5 | |||

1:4/1:4 | 13 | |||

1:6/1:6 | 0 | |||

1:6/1:6 | 5 | |||

1:6/1:6 | 13 | |||

1:8/1:8 | 0 | |||

1:8/1:8 | 5 | |||

1:8/1:8 | 13 |

ρ (kg·m^{−3}) | G/Pa | A/Pa | B/Pa | f_{c}/Pa | C/Pa | N/Pa | S_{max} |

2000 | 5.57 × 10^{7} | 0.35 | 0.85 | 3.00 × 10^{6} | 0.01 | 0.61 | 7 |

T/pa | D_{1} | D_{2} | Ɛ_{f, min} | P_{c}/pa | μ_{c} | P_{l}/pa | μ_{l} |

1.07 × 10^{3} | 0.04 | 1 | 0.01 | 1.00 × 10^{6} | 1.40 × 10^{2} | 1.00 × 10^{8} | 0.14 |

ε_{0} | FS | K_{1}/Pa | K_{2}/Pa | K_{3}/Pa | |||

1 × 10^{−6} | 0.004 | 8.50 × 10^{9} | −1.7 × 10^{10} | 2.08 × 10^{10} |

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## Share and Cite

**MDPI and ACS Style**

Li, J.; Sun, W.; Li, Q.; Chen, S.; Yuan, M.; Xia, H.
Influence of Layered Angle on Dynamic Characteristics of Backfill under Impact Loading. *Minerals* **2022**, *12*, 511.
https://doi.org/10.3390/min12050511

**AMA Style**

Li J, Sun W, Li Q, Chen S, Yuan M, Xia H.
Influence of Layered Angle on Dynamic Characteristics of Backfill under Impact Loading. *Minerals*. 2022; 12(5):511.
https://doi.org/10.3390/min12050511

**Chicago/Turabian Style**

Li, Jinxin, Wei Sun, Qiqi Li, Shuo Chen, Mingli Yuan, and Hui Xia.
2022. "Influence of Layered Angle on Dynamic Characteristics of Backfill under Impact Loading" *Minerals* 12, no. 5: 511.
https://doi.org/10.3390/min12050511