# Space-Time Evolution Characteristics of Deformation and Failure of Surrounding Rock in Deep Soft Rock Roadway

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## Abstract

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^{3D}software is used to establish a three-dimensional numerical model of surrounding rock damage under load, and to study the displacement, stress, and plastic expansion process of damage and failure evolution in the surrounding rock of the roadway. The mechanical response mechanism of deep soft rock roadway surrounding rock bending deformation, elastoplastic transformation, and unloading failure is verified by MATLAB numerical analysis, and the space-time evolution characteristics of soft rock deformation and failure are revealed. The results show that the surrounding rock of deep soft rock roadway has many failure modes, such as obvious displacement and deformation, high stress concentration, and intensified plastic transformation in the surrounding rock. The vertical stress in the surrounding rock is concentrated at the direct top and bottom, and the horizontal stress is concentrated at the roadway side and bottom; plastic deformation and failure first appeared at the roadway side, and then extended to other parts. The research conclusion provides an important reference for surrounding rock control and roof management of high-stress soft rock roadway under deep excavation disturbance.

## 1. Introduction

## 2. Deformation and Failure Mode of Deep Soft Rock Roadway

#### 2.1. Mechanical Model Criterion

_{e}is the bending moment of the top beam section in the elastic limit state, β is the ratio of the ultimate tensile strength and ultimate compressive strength of the roof plate surrounding rock, β = 1/25. Therefore, it can be obtained that the maximum bending moment in the mid-span of the roof plate surrounding rock is as follows:

#### 2.2. Significant Deformation of the Roadway Envelope

#### 2.3. Surrounding Rock Stress Concentration Appears

#### 2.4. Internal Elastic-Plastic Failure Transition of the Surrounding Rock

_{3}is the maximum principal stress, σ

_{1}is the minimum principal stress, c is the cohesive force, and φ is the angle of internal friction.

_{p}. Then, combine the M-C yield criterion and the stress balance principle with a micro-element of plastic zone for analysis and calculation, we can derive the plastic zone width calculation formula [24]:

_{0}is the cohesive force of the rock formation, φ

_{0}is the angle of internal friction at the interface between the roof and coal seam, φ is the internal friction angle of the rock body, p is the vertical primary rock pressure, $N=\frac{2{c}_{0}\mathrm{cos}{\phi}_{0}}{1+\mathrm{sin}{\phi}_{0}}$, $A=\frac{1+\mathrm{sin}\phi}{1-\mathrm{sin}\phi}$, A is the ratio of the peak vertical stress to the horizontal stress in the ultimate equilibrium state, h is the micro-element height of the plastic zone of the roof plate, l is the length of the roof plate, and m is the depth-span ratio of the roof beam, which is m = h/l in this case.

## 3. Deformation and Failure Characteristics of Deep Soft Rock Roadways

#### 3.1. Numerical Model Building

^{3D}software, setting parameters, and constraints to obtain the model under the original rock stress state, and solving again after excavation. A series of cloud diagrams that can characterize the deformation of the surrounding rock can be obtained, and the specific process can be represented by the flowchart in Figure 5.

#### 3.2. Deformation and Displacement Distribution Characteristics of the Surrounding Rock

#### 3.3. Characteristics of Surrounding Rock Stress Distribution

#### 3.4. Failure Characteristics of the Plastic Zone of the Surrounding Rock

_{3}is the maximum principal stress, σ

_{1}is the minimum principal stress, c is the angle of internal friction, and φ is the cohesion. Figure 12 shows the cloud map of the plastic zone distribution of the surrounding rock in the roadway model after excavation. The area divided by the green dashed line in Figure 12 is the fracture zone, and the stress curve of the rock in this range gradually tends to the Mohr’s envelope and then reaches the yield point, at which the rock is compressed beyond its yield strength and forms a broken zone in this range. The rock adjacent to the broken zone is in a plastic state, whereas the stress curve of the rock in the deeper part does not reach the Mohr’s envelope and is still in an elastic state.

## 4. Engineering Simulation Validation

#### 4.1. Engineering Model Building

#### 4.2. Analysis of Simulation Result

- Roof plate deformation is obvious

- 2.
- High stress concentration inside the roof plate

_{x}and M

_{y}are obtained using the above method of drawing deflection clouds, as shown in Figure 18. The distribution and trend of the bending moment in Figure 18 show that M

_{x}gradually decreases along the inclination length from negative to positive. Then, it gradually increases after changing from positive to negative and achieves the maximum value at the center of the simply supported edge, which is opposite to the built-in supported edge. The trend of M

_{y}is similar to that of M

_{x}, but the maximum value is obtained in the ellipse range adjacent to the opposite simply supported edge, and the overall numerical size of M

_{y}is higher than that of M

_{x}.

_{x}is higher at the four corners, and the absolute values of shear at the two corners of the built-in supported side and simply supported side are slightly lower than the two simply supported side corners. The shear values at the same side corners are equal, and the signs are opposite. V

_{y}gains the maximum positive value at the center, and the absolute values of shear at the two corners of the lower side are the highest, with a negative direction.

- 3.
- The roof plate rapidly transforms from elastic deformation to plastic deformation

_{1j}and σ

_{3j}denote the calculated value of the major and minor principal stresses in the limit equilibrium state of the stress body, c is the cohesive force, and φ is the internal friction angle.

_{1}and σ

_{3}are substituted into Equation (7) to obtain the calculated values of major and minor principal stresses. Then, we can obtain the difference between σ

_{1}, σ

_{3}, σ

_{1j}and σ

_{3j}, using which to derive a set of surfaces of stress difference in three-dimensional space, and the iso-surfaces of stress difference are projected in the xoy plane. Thus, we can analyze the relative high and low relationship between maximum and minimum principal stresses and their calculated values in different parts of the thin plate, as well as analyze the distribution of plastic zone and the degree of plastic failure of the roof surrounding rock to a certain extent.

## 5. Conclusions

- The simplified mechanical model analysis of the roof beam of the deep soft rock roadway shows that it has the characteristics of the maximum deflection in the middle of the roof beam, the concentration of shear stress at both ends of the roof beam, and the bending moment of the beam in the plastic state is obviously higher than the elastic limit bending moment. The deformation of the surrounding rock in the deep soft rock roadway has the features, such as significant displacement deformation, significant stress concentration, and sudden elastic-plastic failure, of the surrounding rock.
- Through FLAC
^{3D}numerical simulation analysis, it is found that the deformation of the surrounding rock in the displacement, stress, and plastic zone distribution of the deep soft rock roadway presents the following characteristics: the surrounding rock produces an overall inward extrusion deformation; the vertical stress in the surrounding rock is concentrated at the immediate roof and the immediate bottom; the horizontal stress is concentrated at the roadway gangs and the floor; the plastic deformation damage occurs at the roadway gangs first, and then extends to other parts. - Using the simplified mechanical model of thin rectangular plate as an equivalent substitute for the deformation and failure of the roof plate surrounding rock under the setting background. The theoretical equations of deflection, bending moment, and stress of the model deformation are obtained by combining the elastic mechanics and geomechanics theories. The three-dimensional spatial demonstration cloud maps of the surrounding rock are derived and analyzed by Matlab software to reveal the spatial and temporal evolution law of the deformation and failure of the deep weak surrounding rock under the excavation and unloading perturbation. The simulation results above provide strong validation for the theoretical analysis and numerical simulation conclusions in the paper.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Elastic Modulus E/GPa | Poisson Ratio μ | Compressive Strength ${\mathit{\sigma}}_{\mathit{c}}$/MPa | Tensile Strength ${\mathbf{\sigma}}_{\mathbf{t}}$/MPa |
---|---|---|---|

0.85 | 0.21 | 19 | 1.17 |

Rocks | Thickness/m | Density/(kg∙m^{−3}) | Friction Angle/(°) | Modulus of Shear /GPa | Poisson’s Ratio | Tensile Strength/MPa | Cohesive Force/MPa |
---|---|---|---|---|---|---|---|

siltstone | 10.00 | 2400 | 36 | 3.73 | 0.25 | 1.78 | 1.75 |

Fine Sandstone | 6.00 | 2580 | 33 | 3.25 | 0.16 | 3.48 | 3.46 |

Coal | 6.00 | 1350 | 27 | 0.35 | 0.21 | 1.17 | 1.19 |

Sandy mudstone | 5.00 | 2370 | 31 | 1.43 | 0.26 | 1.81 | 1.96 |

Mudstone | 10.00 | 1750 | 32 | 1.21 | 0.26 | 1.71 | 2.05 |

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**MDPI and ACS Style**

Wang, X.; Zhang, Y.; Zhang, Q.; Wei, Y.; Liu, W.; Jiang, T. Space-Time Evolution Characteristics of Deformation and Failure of Surrounding Rock in Deep Soft Rock Roadway. *Sustainability* **2022**, *14*, 12587.
https://doi.org/10.3390/su141912587

**AMA Style**

Wang X, Zhang Y, Zhang Q, Wei Y, Liu W, Jiang T. Space-Time Evolution Characteristics of Deformation and Failure of Surrounding Rock in Deep Soft Rock Roadway. *Sustainability*. 2022; 14(19):12587.
https://doi.org/10.3390/su141912587

**Chicago/Turabian Style**

Wang, Xinfeng, Yiying Zhang, Qiao Zhang, Youyu Wei, Wengang Liu, and Tian Jiang. 2022. "Space-Time Evolution Characteristics of Deformation and Failure of Surrounding Rock in Deep Soft Rock Roadway" *Sustainability* 14, no. 19: 12587.
https://doi.org/10.3390/su141912587