# On the Freeze-Thaw Instability of an Open Pit Slope Using Three-Dimensional Laser Scanning and Numerical Simulation

Authors: Juzhou Li; Changhong Li; Guoqing Li; Yongyue Hu; Xuefeng Yi; Yu Wang
Journal: Geofluids
 (2022)

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## Abstract

In order to reveal the instability law of open pit mine slope in high-cold and high-altitude area. Firstly, the slope structural plane is scanned by three-dimensional (3D) laser scanning technology, and the point cloud data is obtained to realize the intelligent identification of rock mass structural plane. The geometric parameters of rock mass are counted, and the physical structure model is established. Then, we carry out freeze-thaw cyclic tests on granite to obtain the corresponding mechanical parameters. Finally, according to the obtained mechanical parameters, we use RS2 finite element software to calculate the shear strength of structural plane and joint by generalized Hoek-Brown criterion and Barton-Bandis criterion, respectively, establish the geomechanical model, and use the finite element strength reduction method to calculate the safety factor of slope and judge the instability of slope. The results show that the physical and mechanical properties of granite deteriorate with the increase of the freeze-thaw cycle. Under the action of the freeze-thaw cycle, the pore water in the rock mass freezes and forms frost heaving force. The expansion of volume leads to the further development of joint fissures. The strength of rock slope decreases gradually with the increase of freeze-thaw cycle times, and the safety factor of slope decreases continuously. It shows that repeated freeze and thaw alternation makes the stability of mine slope worse and worse. The research results are helpful to prevent the occurrence of slope disasters in advance and are of great significance to effectively and safely manage the stability of slope, the treatment of open pit, and environmental treatment.


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## Body

## 1. Introduction

With the development of science and technology, 3D laser scanning technology and finite element software are widely used in the analysis of rock slope stability [1–3]. At the same time, in order to satisfy the growing production demand, China’s mineral resources development has gradually shifted to the northwest region, which is rich in mineral resources but as poor natural environment, with weak infrastructure, poor ecological environment, and extremely cold winter. The temperature variation and seasonal variation caused by the alternation of day and night will have a great impact on the mechanical properties of rock mass. Repeated freeze-thaw cycle will expand and increase the rock fissures, deteriorate the physical and mechanical properties of the rock, and reduce the strength of the slope rock mass, resulting in the sliding of the slope rock mass [4–6]. These issues have become increasingly prominent. Therefore, this paper puts forward the research on the safety and stability evaluation of open pit slope based on 3D laser scanning and numerical simulation.3D laser scanning is the latest development of geological mapping [7], which has been proved to be an effective noncontact tool. It is used to collect rock mass information. Its application fields include surface geological data collection [8, 9], slope stability and displacement monitoring [10, 11], and 3D rock mass model creation [12, 13]. It has the advantages of high density, maneuverability, high precision, and noncontact. At present, many experts and scholars have carried out a series of scanning analysis on rock slope engineering with the help of this technology. Chen et al. [14] compared the difference between 3D laser scanning technology and traditional window mapping technology. The results show that the average dip/dip direction discrepancy between the two methods is 1.5°/16°, which is due to the large amount of data collected by 3D laser scanning technology. It is proved that the 3D laser scanning technology has the advantages of higher efficiency and accuracy in underground mines. Wang et al. [15] used 3D laser scanning technology to scan the fragmentation of blast muck piles and provided high-precision point cloud data for calculating BFMP. They proposed an improved VCCS algorithm based on discrete characteristics. The results show that when the size of crushing block is 0.1 m ~0.5 m, the accuracy of calculation results are about 80%, and when the size of broken block exceeds 0.5 m, almost all bfmp can be calculated correctly. Kromer et al. [16] used a ground-based 3D laser scanning technology to test the Séchiienne landslide in France for six weeks to detect the flow, displacement, and prefailure deformation of discrete collapse events. Then, they proposed an automatic ground laser scanning system with near real-time automatic change detection and processing function. Ma et al. [17] introduced 3D laser scanning technology into the overall deformation monitoring of slope surface in landslide physical model test and comprehensively analyzed the deformation characteristics of landslide in different evolution stages through the example of landslide physical model test. The results show that on the premise of ensuring high-precision feature point monitoring, the overall deformation and displacement of the model slope can be obtained with the help of 3D laser scanning technology.Similarly, RS2 software can carry out fluid structure coupling analysis and dynamic analysis and can automatically generate finite element meshes such as triangles, and material models have the advantages of diversified types. It is also widely used in numerical simulation under cyclic loading [18]. In order to analyze the yield failure of the open pit mine in Minas Gerais, Brazil, Pereira and Lana [19] established many representative slope hypothesis models by using RS2 finite element software, carried out elastic and plastic simulation, and evaluated the yield failure mechanism. Liu et al. [20] used numerical simulation software to study the main causes of coal mine roof accidents. The results show that as the coal seam continues to advance, the maximum settlement displacement remains basically unchanged, and the settlement displacement curve presents an asymmetric flat bottom distribution and the stress concentration in front of the coal wall is the source of the abutment pressure. Silva and Lana [21] used RS2 software to study the failure mechanism of flexural buckling that occurred in Pau Branco Mine, of Vallourec and Mannesman Group, in 2002. Through the back analysis of the failure mechanism, they obtained the representative values of in situ stress state, normal stiffness modulus, and shear stiffness modulus of foliation structure. The results are of great significance to further analyze the stability of phyllite slopes of Pau Branco Mine. Arslan et al. [22] used RS2 finite element software to analyze the stability of marble stope under static and dynamic conditions, built shear strength reduction (SSR) technology into the software to determine the failure mechanism, and put forward suggestions and carried out necessary control to ensure the stability of slope. Adach-Pawelus [23] used RS2 finite element software to conduct numerical simulation in the plane deformation state, combined with seismic activity analysis and numerical simulation methods to illustrate the impact of mine residues on the possibility of seismic events. The results show that undisturbed rock cuttings may have a negative impact on earthquake and rock burst disasters in the mining area.Even though 3D laser scanning technology and RS2 finite element software have made great progress and application, there are few studies on high-cold and high-altitude areas with the help of and combination of these two technologies. In view of this, this paper uses Optech Polaris LR 3D laser scanner to scan the open pit slope in cold area, obtains the point cloud data, realizes the intelligent identification and information extraction of rock mass structural plane, obtains the rock mechanical parameters through the freeze-thaw cycle tests, and establishes the slope mechanical model combined with RS2 finite element software to calculate the safety factor of the slope under different times of freeze-thaw cycle. This has important guiding significance for in-depth understanding of the law of slope instability of open pit mines in high-cold and high-altitude areas and preventing slope disasters and accidents in advance [24].


## 2. Identification and Extraction of Rock Structure Plane

### 2.1. Study Area

The research object of this paper is located in Beizhan iron mine in Hejing County, Korla, Xinjiang, in Northwest China. Permanent Piedmont glaciers are located in the south and west of the mining area, and the altitude of the ore body is 3450-3723 m. The mining area is located in the alpine area with perennial snow, and the climate is extremely cold. The monthly average temperature from January to April and from September to December is lower than zero, and the minimum temperature can reach -40°C. The temperature rises from May to August, generally 5-15°C, and the maximum rise can be 20°C. The temperature at night is usually as low as about -3°C, so the temperature difference between day and night in the mining area is large. The mining area has frequent rain and snow throughout the year. It is the local rainy season from July to August, and it begins to snow in early October. Therefore, it is only suitable to carry out appropriate field operations from May to September every year. The deposit is located in the river valley, and the terrain of the mining area is conducive to natural drainage. The overall strike of the ore body is 97°, and the dip angle is 47°-74°. According to the prediction of landform, meteorology and hydrology, geological structure, human activities, and other conditions in the mining area, the risk of geological disasters such as landslide and debris flow is small, but the risk of collapse geological disasters caused by local high and steep mountains is high. The study area is shown in Figure1.Figure 1
Study area.


### 2.2. 3D Laser Scanning Technique

Optech Polaris LR 3D laser scanner is used to conduct overall scanning and fine scanning of the research area, respectively. The instrument meets the long-distance fine test requirements of the project, as shown in Figure2. The parameters are shown in Table 1.Figure 2
Placement of 3D laser scanner.Table 1
Parameters of 3D laser scanner.
ParametersIndexMaximum measuring distance (m)2000Minimum measuring distance (m)1.5Scanning vision angle (°)360×120Principle of distance measuringPulseLaser head rotation mechanismSwinging mirrorsWorking temperature (°C)-20~50


### 2.3. Rock Structural Plane Geometric Characteristics

In order to have a preliminary understanding of the whole mining area, 11 3D laser scans were carried out, covering the whole mining pit, as shown in Figure3(a). 3D laser scanning was carried out on each point to obtain the point cloud data of each point. After splicing and packaging, a complete 3D geometric model is obtained, as shown in Figure 3(b). At the same time, fine scanning is carried out for the mining area. The scanning point S8 is located on the east side of the pit, including 399020 points. The scanning range is 2044.0957 m2, and the maximum size of the scanning area is 51.2365×61.8522×29.0181 m. Combining the 3D laser scanning technology with the digital camera, the pixel points of the picture are matched with the point cloud, and the gray information or color information of the point cloud data can be obtained. The color information is helpful to display the scanning results, and the results are shown in Figure 3(c).Figure 3
S8 station scanning slope point cloud data.
(a)
Front view(b)
Side view(c)
Triangulation model


#### 2.3.1. Processing of Point Cloud Data

The amount of point cloud data obtained by 3D laser scanning structural plane is large and dense will seriously affect the operation speed. Therefore, in order to realize the programming of the algorithm, it is necessary to divide the point cloud data into space and grid the point cloud data. In this study, for the point cloud data with high scanning accuracy, the 3D difference method is adopted. This method has little impact on the accuracy, and the impact can be ignored. The results are shown in Figure4.Figure 4
Result of grid processing.In order to obtain the optimal threshold, it is necessary to select the discrimination index of structural plane intelligent recognition. In this paper, the point normal vector is used as the discrimination index. The next step is to determine the flatness detection threshold of point cloud. According to the rules, when the value ofξ1 is smaller, the more points are included in the BORDER matrix, which means that more points are regarded as boundary points and do not participate in the next image segmentation algorithm. Conversely, when the value of ξ1 is too large, the number of points in the BORDER matrix decreases, which means that the edge recognition effect is weakened, indicating that some boundary points will not be recognized effectively. So, according to the actual situation of the mining area, the flatness detection threshold ξ1 is set to 20°.


#### 2.3.2. Selection of Optimal Threshold

Make the regional growth thresholdξ2 between 5° and approximately 40°, and the value interval is 5°. The area threshold remains unchanged at 0.5 m2. When the value of regional growth threshold is too small, the growth criteria is relatively severe, and many point cloud data are not identified as structural plane, which makes the regional division too fragmented and the number of structural plane identified is few. When the value of regional growth threshold is too large, the growth criteria is too loose, which leads to a part of the point cloud data located in uneven areas will also be divided into structural plane, and the number of structural plane identified is too large, so it is impossible to distinguish adjacent structural plane. According to visual judgment, when the regional growth threshold is between 20° and 30°, the recognition effect is more realistic. The results of structural plane recognitions are shown in Figures 5(a)–5(c).Figure 5
Intelligent identification results of rock structural plane under different growth and area thresholds.
(a)
ξ2=20°(b)
ξ2=25°(c)
ξ2=30°(d)
W1=0.1m2Similarly, make the area thresholdW1 between 0.1 m2 and approximately 10 m2, and the value interval is 0.1 m2. The regional growth threshold remains unchanged at 20°. When the area threshold W1 is greater than 0.1 m2, the recognition effect is more practical. When the area threshold is too large, more structural plane are eliminated, which leads to too few remaining structural plane and is not conducive to the later structural plane information extraction. The result of structural plane recognition is shown in Figure 5(d). In summary, the growth threshold is 20°, and the area threshold is 0.1 m2.


### 2.4. Extraction of Structural Plane Information of Rock Mass

#### 2.4.1. Acquisition of Structure Plane Occurrence Information

The least square method is used to fit all nodes of each rock mass structural plane obtained before. In this way, the plane equation of quasi plane shape can be obtained. The plane equation is shown in(1)ax+by+c=z.It is assumed that the spatial coordinates ofn points on the structural plane are x1,y1,z1, x2,y2,z2,…,xn,yn,zn, respectively, and the matrix equation can be expressed as
(2)x1y11x2y21⋮⋮⋮xnyn1abc=z1z2⋮zn.Let(3)D=abc,(4)X=x1y11x2y21⋮⋮⋮xnyn1,(5)Z=z1z2⋮zn.So, we need to find vectorD and make ϕD=DX−Z get the minimum value. Finally, the normal vector and plane equation of structural plane are obtained to complete the fitting of the structural plane.This study mainly calculates the dip and dip angle in the occurrence information of structural plane. If the normal vector coordinate of structural plane isx0,y0,z0. According to the working principle of laser emission in 3D laser scanning technology, it can only scan the structural plane with good exposure on the side slope, so z0>0. With the geodetic coordinate system, the due east and due north are defined as the positive directions of the X axis and Y axis, respectively, and the Z axis points to the elevation direction. Therefore, the occurrence information dip θ and dip angle δ of the rock mass structural plane can be expressed by the following equation:
(6)δ=arccosz0ifx0⩾0,y0⩾0,θ=arcsinx0sinδifx0<0,y0>0,θ=360∘−arcsin−x0sinδifx0<0,y0>0,θ=180∘−arcsinx0sinδifx0>0,y0<0,θ=180∘+arcsin−x0sinδ.The occurrence information of point cloud data of rock mass structural plane is shown in Figure6.Figure 6
Distribution characteristics of structural plane and the result of stereographic projection.
(a)
Distribution characteristics of structural plane(b)
The result of stereographic projection


#### 2.4.2. Grouping of Rock Mass Structure Planes Based on Occurrence Information

Then, theK-means cluster analysis method is used to group these occurrence information and is combined with the field investigation of geological information. It is obtained that the structural plane of the slope in the mining area can be divided into three groups, including a group of gently inclined plane and two groups of steeply inclined joints. Intelligent identification mainly finds two groups of steep joints. Finally, the cluster center and average occurrence are calculated. The average occurrence of the two groups of rock mass structural planes is 261°<75° and 307°<77°, respectively. The results are shown in Figure 7.Figure 7
Occurrence distribution characteristics of the rock mass structural plane after clustering and the result of stereographic projection.
(a)
Distribution characteristics of occurrence(b)
The result of stereographic projectionIn this study, the structural plane occurrence modeling method based on empirical probability distribution is adopted to truly reflect the actual structural plane occurrence distribution and then obtain the relative frequency of two groups of rock mass structural plane occurrence. The results are shown in Figure8.Figure 8
3D histogram of the occurrence relative frequency of the structural plane of the two groups of rocks.


#### 2.4.3. Calculation of Spacing between Rock Structural Planes

In order to obtain the spacing between adjacent structural planes, it is calculated according to the method shown in Figure9. The dotted line in the figure is the initial state of the same group of structural planes, the solid line is the ideal state of the structural planes converted according to the above method, and the structural planes are parallel to each other in the same group. The vertical distance calculation equation is used to calculate the distance between adjacent structural planes.
(7)l1:Ax+By+Cz+D1=0,(8)l2:Ax+By+Cz+D2=0,(9)dl1l2=D1−D2A2+B2+C2,Figure 9
Plots of the 7same group of structural surface space distance by calculating.Wherel1 is plane 1 equation, l2 is plane 2 equation, and dl1l2 is the vertical distance between two adjacent structural planes.According to the equation, the distribution characteristics of the spacing information of the two groups of rock mass structural planes are calculated, as shown in Figure10.Figure 10
Histogram of space distance distribution of two groups of the rock mass structure plane.


#### 2.4.4. Calculation of Equivalent Trace Length of Rock Mass Structural Planes

Because the data obtained by the image segmentation method is point cloud data, the method of projection is used to calculate the area of the structural plane, as shown in(10)S=Sxoycosγ,whereγ is the angle between the xoy plane and the structural plane, S is the area of the desired structural plane, and Sxoy is the projected area of the node on the structural plane projected onto the xoy plane.Thus, the exposed area of rock mass structural plane is calculated. For convenience, the structural plane can be replaced by an equivalent circle with equal area. The radius is expressed in(11)S=πr2.The equivalent trace length of the two groups of rock mass structural planes in this paper can be characterized by the equivalent radius obtained by equation (11). The results are shown in Figure 11.Figure 11
Histogram of equivalent trace length distribution of two groups of rock mass structure plane.


#### 2.4.5. Statistics of Structural Plane Information of Rock Mass

Based on the theory of mathematical statistics, according to the point cloud data of S8 rock slope, the probability distribution types and statistical parameters of geometric parameters such as the occurrence of rock mass structural plane calculated above are counted, as shown in Table2.Table 2
Mathematical statistical information of rock mass structural planes.
ParametersDistribution TypeStatistical parametersStructure planeValueTendency (°)Empirical probabilityMeanPlane 1261.000Plane 2309.000Standard deviationPlane 161.942Plane 2103.558Dip angle (°)Empirical probabilityMeanPlane 175.000Plane 277.000Standard deviationPlane 19.266Plane 210.173Space distances (m)Negative exponential distributionMeanPlane 10.355Plane 20.205Standard deviationPlane 10.653Plane 20.256Equivalent trace length (m)Negative exponential distributionMeanPlane 11.081Plane 20.763Standard deviationPlane 10.869Plane 20.576


## 2.1. Study Area

The research object of this paper is located in Beizhan iron mine in Hejing County, Korla, Xinjiang, in Northwest China. Permanent Piedmont glaciers are located in the south and west of the mining area, and the altitude of the ore body is 3450-3723 m. The mining area is located in the alpine area with perennial snow, and the climate is extremely cold. The monthly average temperature from January to April and from September to December is lower than zero, and the minimum temperature can reach -40°C. The temperature rises from May to August, generally 5-15°C, and the maximum rise can be 20°C. The temperature at night is usually as low as about -3°C, so the temperature difference between day and night in the mining area is large. The mining area has frequent rain and snow throughout the year. It is the local rainy season from July to August, and it begins to snow in early October. Therefore, it is only suitable to carry out appropriate field operations from May to September every year. The deposit is located in the river valley, and the terrain of the mining area is conducive to natural drainage. The overall strike of the ore body is 97°, and the dip angle is 47°-74°. According to the prediction of landform, meteorology and hydrology, geological structure, human activities, and other conditions in the mining area, the risk of geological disasters such as landslide and debris flow is small, but the risk of collapse geological disasters caused by local high and steep mountains is high. The study area is shown in Figure1.Figure 1
Study area.


## 2.2. 3D Laser Scanning Technique

Optech Polaris LR 3D laser scanner is used to conduct overall scanning and fine scanning of the research area, respectively. The instrument meets the long-distance fine test requirements of the project, as shown in Figure2. The parameters are shown in Table 1.Figure 2
Placement of 3D laser scanner.Table 1
Parameters of 3D laser scanner.
ParametersIndexMaximum measuring distance (m)2000Minimum measuring distance (m)1.5Scanning vision angle (°)360×120Principle of distance measuringPulseLaser head rotation mechanismSwinging mirrorsWorking temperature (°C)-20~50


## 2.3. Rock Structural Plane Geometric Characteristics

In order to have a preliminary understanding of the whole mining area, 11 3D laser scans were carried out, covering the whole mining pit, as shown in Figure3(a). 3D laser scanning was carried out on each point to obtain the point cloud data of each point. After splicing and packaging, a complete 3D geometric model is obtained, as shown in Figure 3(b). At the same time, fine scanning is carried out for the mining area. The scanning point S8 is located on the east side of the pit, including 399020 points. The scanning range is 2044.0957 m2, and the maximum size of the scanning area is 51.2365×61.8522×29.0181 m. Combining the 3D laser scanning technology with the digital camera, the pixel points of the picture are matched with the point cloud, and the gray information or color information of the point cloud data can be obtained. The color information is helpful to display the scanning results, and the results are shown in Figure 3(c).Figure 3
S8 station scanning slope point cloud data.
(a)
Front view(b)
Side view(c)
Triangulation model


### 2.3.1. Processing of Point Cloud Data

The amount of point cloud data obtained by 3D laser scanning structural plane is large and dense will seriously affect the operation speed. Therefore, in order to realize the programming of the algorithm, it is necessary to divide the point cloud data into space and grid the point cloud data. In this study, for the point cloud data with high scanning accuracy, the 3D difference method is adopted. This method has little impact on the accuracy, and the impact can be ignored. The results are shown in Figure4.Figure 4
Result of grid processing.In order to obtain the optimal threshold, it is necessary to select the discrimination index of structural plane intelligent recognition. In this paper, the point normal vector is used as the discrimination index. The next step is to determine the flatness detection threshold of point cloud. According to the rules, when the value ofξ1 is smaller, the more points are included in the BORDER matrix, which means that more points are regarded as boundary points and do not participate in the next image segmentation algorithm. Conversely, when the value of ξ1 is too large, the number of points in the BORDER matrix decreases, which means that the edge recognition effect is weakened, indicating that some boundary points will not be recognized effectively. So, according to the actual situation of the mining area, the flatness detection threshold ξ1 is set to 20°.


### 2.3.2. Selection of Optimal Threshold

Make the regional growth thresholdξ2 between 5° and approximately 40°, and the value interval is 5°. The area threshold remains unchanged at 0.5 m2. When the value of regional growth threshold is too small, the growth criteria is relatively severe, and many point cloud data are not identified as structural plane, which makes the regional division too fragmented and the number of structural plane identified is few. When the value of regional growth threshold is too large, the growth criteria is too loose, which leads to a part of the point cloud data located in uneven areas will also be divided into structural plane, and the number of structural plane identified is too large, so it is impossible to distinguish adjacent structural plane. According to visual judgment, when the regional growth threshold is between 20° and 30°, the recognition effect is more realistic. The results of structural plane recognitions are shown in Figures 5(a)–5(c).Figure 5
Intelligent identification results of rock structural plane under different growth and area thresholds.
(a)
ξ2=20°(b)
ξ2=25°(c)
ξ2=30°(d)
W1=0.1m2Similarly, make the area thresholdW1 between 0.1 m2 and approximately 10 m2, and the value interval is 0.1 m2. The regional growth threshold remains unchanged at 20°. When the area threshold W1 is greater than 0.1 m2, the recognition effect is more practical. When the area threshold is too large, more structural plane are eliminated, which leads to too few remaining structural plane and is not conducive to the later structural plane information extraction. The result of structural plane recognition is shown in Figure 5(d). In summary, the growth threshold is 20°, and the area threshold is 0.1 m2.


## 2.3.1. Processing of Point Cloud Data

The amount of point cloud data obtained by 3D laser scanning structural plane is large and dense will seriously affect the operation speed. Therefore, in order to realize the programming of the algorithm, it is necessary to divide the point cloud data into space and grid the point cloud data. In this study, for the point cloud data with high scanning accuracy, the 3D difference method is adopted. This method has little impact on the accuracy, and the impact can be ignored. The results are shown in Figure4.Figure 4
Result of grid processing.In order to obtain the optimal threshold, it is necessary to select the discrimination index of structural plane intelligent recognition. In this paper, the point normal vector is used as the discrimination index. The next step is to determine the flatness detection threshold of point cloud. According to the rules, when the value ofξ1 is smaller, the more points are included in the BORDER matrix, which means that more points are regarded as boundary points and do not participate in the next image segmentation algorithm. Conversely, when the value of ξ1 is too large, the number of points in the BORDER matrix decreases, which means that the edge recognition effect is weakened, indicating that some boundary points will not be recognized effectively. So, according to the actual situation of the mining area, the flatness detection threshold ξ1 is set to 20°.


## 2.3.2. Selection of Optimal Threshold

Make the regional growth thresholdξ2 between 5° and approximately 40°, and the value interval is 5°. The area threshold remains unchanged at 0.5 m2. When the value of regional growth threshold is too small, the growth criteria is relatively severe, and many point cloud data are not identified as structural plane, which makes the regional division too fragmented and the number of structural plane identified is few. When the value of regional growth threshold is too large, the growth criteria is too loose, which leads to a part of the point cloud data located in uneven areas will also be divided into structural plane, and the number of structural plane identified is too large, so it is impossible to distinguish adjacent structural plane. According to visual judgment, when the regional growth threshold is between 20° and 30°, the recognition effect is more realistic. The results of structural plane recognitions are shown in Figures 5(a)–5(c).Figure 5
Intelligent identification results of rock structural plane under different growth and area thresholds.
(a)
ξ2=20°(b)
ξ2=25°(c)
ξ2=30°(d)
W1=0.1m2Similarly, make the area thresholdW1 between 0.1 m2 and approximately 10 m2, and the value interval is 0.1 m2. The regional growth threshold remains unchanged at 20°. When the area threshold W1 is greater than 0.1 m2, the recognition effect is more practical. When the area threshold is too large, more structural plane are eliminated, which leads to too few remaining structural plane and is not conducive to the later structural plane information extraction. The result of structural plane recognition is shown in Figure 5(d). In summary, the growth threshold is 20°, and the area threshold is 0.1 m2.


## 2.4. Extraction of Structural Plane Information of Rock Mass

### 2.4.1. Acquisition of Structure Plane Occurrence Information

The least square method is used to fit all nodes of each rock mass structural plane obtained before. In this way, the plane equation of quasi plane shape can be obtained. The plane equation is shown in(1)ax+by+c=z.It is assumed that the spatial coordinates ofn points on the structural plane are x1,y1,z1, x2,y2,z2,…,xn,yn,zn, respectively, and the matrix equation can be expressed as
(2)x1y11x2y21⋮⋮⋮xnyn1abc=z1z2⋮zn.Let(3)D=abc,(4)X=x1y11x2y21⋮⋮⋮xnyn1,(5)Z=z1z2⋮zn.So, we need to find vectorD and make ϕD=DX−Z get the minimum value. Finally, the normal vector and plane equation of structural plane are obtained to complete the fitting of the structural plane.This study mainly calculates the dip and dip angle in the occurrence information of structural plane. If the normal vector coordinate of structural plane isx0,y0,z0. According to the working principle of laser emission in 3D laser scanning technology, it can only scan the structural plane with good exposure on the side slope, so z0>0. With the geodetic coordinate system, the due east and due north are defined as the positive directions of the X axis and Y axis, respectively, and the Z axis points to the elevation direction. Therefore, the occurrence information dip θ and dip angle δ of the rock mass structural plane can be expressed by the following equation:
(6)δ=arccosz0ifx0⩾0,y0⩾0,θ=arcsinx0sinδifx0<0,y0>0,θ=360∘−arcsin−x0sinδifx0<0,y0>0,θ=180∘−arcsinx0sinδifx0>0,y0<0,θ=180∘+arcsin−x0sinδ.The occurrence information of point cloud data of rock mass structural plane is shown in Figure6.Figure 6
Distribution characteristics of structural plane and the result of stereographic projection.
(a)
Distribution characteristics of structural plane(b)
The result of stereographic projection


### 2.4.2. Grouping of Rock Mass Structure Planes Based on Occurrence Information

Then, theK-means cluster analysis method is used to group these occurrence information and is combined with the field investigation of geological information. It is obtained that the structural plane of the slope in the mining area can be divided into three groups, including a group of gently inclined plane and two groups of steeply inclined joints. Intelligent identification mainly finds two groups of steep joints. Finally, the cluster center and average occurrence are calculated. The average occurrence of the two groups of rock mass structural planes is 261°<75° and 307°<77°, respectively. The results are shown in Figure 7.Figure 7
Occurrence distribution characteristics of the rock mass structural plane after clustering and the result of stereographic projection.
(a)
Distribution characteristics of occurrence(b)
The result of stereographic projectionIn this study, the structural plane occurrence modeling method based on empirical probability distribution is adopted to truly reflect the actual structural plane occurrence distribution and then obtain the relative frequency of two groups of rock mass structural plane occurrence. The results are shown in Figure8.Figure 8
3D histogram of the occurrence relative frequency of the structural plane of the two groups of rocks.


### 2.4.3. Calculation of Spacing between Rock Structural Planes

In order to obtain the spacing between adjacent structural planes, it is calculated according to the method shown in Figure9. The dotted line in the figure is the initial state of the same group of structural planes, the solid line is the ideal state of the structural planes converted according to the above method, and the structural planes are parallel to each other in the same group. The vertical distance calculation equation is used to calculate the distance between adjacent structural planes.
(7)l1:Ax+By+Cz+D1=0,(8)l2:Ax+By+Cz+D2=0,(9)dl1l2=D1−D2A2+B2+C2,Figure 9
Plots of the 7same group of structural surface space distance by calculating.Wherel1 is plane 1 equation, l2 is plane 2 equation, and dl1l2 is the vertical distance between two adjacent structural planes.According to the equation, the distribution characteristics of the spacing information of the two groups of rock mass structural planes are calculated, as shown in Figure10.Figure 10
Histogram of space distance distribution of two groups of the rock mass structure plane.


### 2.4.4. Calculation of Equivalent Trace Length of Rock Mass Structural Planes

Because the data obtained by the image segmentation method is point cloud data, the method of projection is used to calculate the area of the structural plane, as shown in(10)S=Sxoycosγ,whereγ is the angle between the xoy plane and the structural plane, S is the area of the desired structural plane, and Sxoy is the projected area of the node on the structural plane projected onto the xoy plane.Thus, the exposed area of rock mass structural plane is calculated. For convenience, the structural plane can be replaced by an equivalent circle with equal area. The radius is expressed in(11)S=πr2.The equivalent trace length of the two groups of rock mass structural planes in this paper can be characterized by the equivalent radius obtained by equation (11). The results are shown in Figure 11.Figure 11
Histogram of equivalent trace length distribution of two groups of rock mass structure plane.


### 2.4.5. Statistics of Structural Plane Information of Rock Mass

Based on the theory of mathematical statistics, according to the point cloud data of S8 rock slope, the probability distribution types and statistical parameters of geometric parameters such as the occurrence of rock mass structural plane calculated above are counted, as shown in Table2.Table 2
Mathematical statistical information of rock mass structural planes.
ParametersDistribution TypeStatistical parametersStructure planeValueTendency (°)Empirical probabilityMeanPlane 1261.000Plane 2309.000Standard deviationPlane 161.942Plane 2103.558Dip angle (°)Empirical probabilityMeanPlane 175.000Plane 277.000Standard deviationPlane 19.266Plane 210.173Space distances (m)Negative exponential distributionMeanPlane 10.355Plane 20.205Standard deviationPlane 10.653Plane 20.256Equivalent trace length (m)Negative exponential distributionMeanPlane 11.081Plane 20.763Standard deviationPlane 10.869Plane 20.576


## 2.4.1. Acquisition of Structure Plane Occurrence Information

The least square method is used to fit all nodes of each rock mass structural plane obtained before. In this way, the plane equation of quasi plane shape can be obtained. The plane equation is shown in(1)ax+by+c=z.It is assumed that the spatial coordinates ofn points on the structural plane are x1,y1,z1, x2,y2,z2,…,xn,yn,zn, respectively, and the matrix equation can be expressed as
(2)x1y11x2y21⋮⋮⋮xnyn1abc=z1z2⋮zn.Let(3)D=abc,(4)X=x1y11x2y21⋮⋮⋮xnyn1,(5)Z=z1z2⋮zn.So, we need to find vectorD and make ϕD=DX−Z get the minimum value. Finally, the normal vector and plane equation of structural plane are obtained to complete the fitting of the structural plane.This study mainly calculates the dip and dip angle in the occurrence information of structural plane. If the normal vector coordinate of structural plane isx0,y0,z0. According to the working principle of laser emission in 3D laser scanning technology, it can only scan the structural plane with good exposure on the side slope, so z0>0. With the geodetic coordinate system, the due east and due north are defined as the positive directions of the X axis and Y axis, respectively, and the Z axis points to the elevation direction. Therefore, the occurrence information dip θ and dip angle δ of the rock mass structural plane can be expressed by the following equation:
(6)δ=arccosz0ifx0⩾0,y0⩾0,θ=arcsinx0sinδifx0<0,y0>0,θ=360∘−arcsin−x0sinδifx0<0,y0>0,θ=180∘−arcsinx0sinδifx0>0,y0<0,θ=180∘+arcsin−x0sinδ.The occurrence information of point cloud data of rock mass structural plane is shown in Figure6.Figure 6
Distribution characteristics of structural plane and the result of stereographic projection.
(a)
Distribution characteristics of structural plane(b)
The result of stereographic projection


## 2.4.2. Grouping of Rock Mass Structure Planes Based on Occurrence Information

Then, theK-means cluster analysis method is used to group these occurrence information and is combined with the field investigation of geological information. It is obtained that the structural plane of the slope in the mining area can be divided into three groups, including a group of gently inclined plane and two groups of steeply inclined joints. Intelligent identification mainly finds two groups of steep joints. Finally, the cluster center and average occurrence are calculated. The average occurrence of the two groups of rock mass structural planes is 261°<75° and 307°<77°, respectively. The results are shown in Figure 7.Figure 7
Occurrence distribution characteristics of the rock mass structural plane after clustering and the result of stereographic projection.
(a)
Distribution characteristics of occurrence(b)
The result of stereographic projectionIn this study, the structural plane occurrence modeling method based on empirical probability distribution is adopted to truly reflect the actual structural plane occurrence distribution and then obtain the relative frequency of two groups of rock mass structural plane occurrence. The results are shown in Figure8.Figure 8
3D histogram of the occurrence relative frequency of the structural plane of the two groups of rocks.


## 2.4.3. Calculation of Spacing between Rock Structural Planes

In order to obtain the spacing between adjacent structural planes, it is calculated according to the method shown in Figure9. The dotted line in the figure is the initial state of the same group of structural planes, the solid line is the ideal state of the structural planes converted according to the above method, and the structural planes are parallel to each other in the same group. The vertical distance calculation equation is used to calculate the distance between adjacent structural planes.
(7)l1:Ax+By+Cz+D1=0,(8)l2:Ax+By+Cz+D2=0,(9)dl1l2=D1−D2A2+B2+C2,Figure 9
Plots of the 7same group of structural surface space distance by calculating.Wherel1 is plane 1 equation, l2 is plane 2 equation, and dl1l2 is the vertical distance between two adjacent structural planes.According to the equation, the distribution characteristics of the spacing information of the two groups of rock mass structural planes are calculated, as shown in Figure10.Figure 10
Histogram of space distance distribution of two groups of the rock mass structure plane.


## 2.4.4. Calculation of Equivalent Trace Length of Rock Mass Structural Planes

Because the data obtained by the image segmentation method is point cloud data, the method of projection is used to calculate the area of the structural plane, as shown in(10)S=Sxoycosγ,whereγ is the angle between the xoy plane and the structural plane, S is the area of the desired structural plane, and Sxoy is the projected area of the node on the structural plane projected onto the xoy plane.Thus, the exposed area of rock mass structural plane is calculated. For convenience, the structural plane can be replaced by an equivalent circle with equal area. The radius is expressed in(11)S=πr2.The equivalent trace length of the two groups of rock mass structural planes in this paper can be characterized by the equivalent radius obtained by equation (11). The results are shown in Figure 11.Figure 11
Histogram of equivalent trace length distribution of two groups of rock mass structure plane.


## 2.4.5. Statistics of Structural Plane Information of Rock Mass

Based on the theory of mathematical statistics, according to the point cloud data of S8 rock slope, the probability distribution types and statistical parameters of geometric parameters such as the occurrence of rock mass structural plane calculated above are counted, as shown in Table2.Table 2
Mathematical statistical information of rock mass structural planes.
ParametersDistribution TypeStatistical parametersStructure planeValueTendency (°)Empirical probabilityMeanPlane 1261.000Plane 2309.000Standard deviationPlane 161.942Plane 2103.558Dip angle (°)Empirical probabilityMeanPlane 175.000Plane 277.000Standard deviationPlane 19.266Plane 210.173Space distances (m)Negative exponential distributionMeanPlane 10.355Plane 20.205Standard deviationPlane 10.653Plane 20.256Equivalent trace length (m)Negative exponential distributionMeanPlane 11.081Plane 20.763Standard deviationPlane 10.869Plane 20.576


## 3. Numerical Simulation Analysis

In this paper, RS2 elastic-plastic finite element software is used for numerical simulation analysis. An important function of RS2 is to calculate the safety factor of slope stability based on the finite element strength reduction method. By using the Hoek-Brown strength criterion, the system can automatically reduce the strength and obtain the safety factor of the slope. In this software, the constitutive model of rock mass includes the generalized Hoek-Brown model, Mohr-Coulomb model, and Cam-Clay model. At the same time, based on the statistical model, users can input relevant joint parameters according to the actual situation when building the slope model, and the system will automatically generate the joint fracture network.


### 3.1. Establishment of Model and Selection of Parameters

In order to obtain the relevant mechanical parameters of rock slope and establish a complete geomechanical model, samples were taken from the site and divided into 6 groups with 2 samples in each group. The samples of each group were subjected to 0, 20, 40, 60, 80, and 100 times of freeze-thaw cycle, respectively, and physical and mechanical tests were carried out. Finally, the parameters shown in Table3 are counted.Table 3
Basic mechanical and physical parameters of freeze-thaw-treated granite samples.
Sample numberLength×width (mm×mm)Mass (kg)Density (g/cm3)Peak strength (MPa)Elasticity modulus (MPa)P-wave velocity (m/s)S-wave velocity (m/s)y0-1100.07×49.46541.42.863172.3858.6543023577y0-2100.01×49.62540.52.796182.4560.0844123456y20-199.58×49.30543.12.859168.7356.3141313391y20-2100.01×50.21540.22.729167.2455.4642653325y40-199.85×50.05542.62.763163.9852.7840123101y40-2100.12×49.63544.92.815158.3553.4440003210y60-1100.22×49.85547.52.800158.7850.8939062984y60-2100.06×49.19544.62.865155.6649.6538943015y80-199.90×49.88548.92.813152.3947.3638262883y80-2100.11×49.76543.52.793149.2345.2338562913y100-1100.12×49.29547.22.866146.6542.9436902664y100-2100.08×49.34546.62.858142.3343.8935462703We intercepted a section line on the west slope of the mining area to automatically generate the section map of the west slope, import it into RS2 software, and generate the model boundary. The structural plane of rock mass is based on the generalized Hoek-Brown criterion, and the joint is a constitutive model based on Barton-Bandis criterion. According to the previous research, the slope is mainly affected by two sets of joint surfaces. The above physical and mechanical parameters were input into RS2 software, and the three node triangular element was used to generate the finite element grid. The model contained 17207 nodes and 29427 elements. We considered the actual boundary conditions on site and get the final result, as shown in Figure12. Finally, five monitoring points were arranged for subsequent research.Figure 12
Contour map of Beizhan iron mine and slope calculation model.


### 3.2. Numerical Simulation Results

#### 3.2.1. Analysis of Maximum Principal Stress and Maximum Shear Strain of Slope Model

According to the definition of principal stress, under the same external force, the principal stress increases with the increase of buried depth. In order to study the variation of the maximum principal stress under different times of freeze-thaw cycle, the cloud chart of the maximum principal stress is obtained as shown in Figure13. It can be found from the figure that the maximum principal stress at the bottom of the slope model is greater than that in other areas, while the top is the smallest. At the same time, the value range of the maximum principal stress does not change with the increase of the times of the freeze-thaw cycle and generally shows a slight upward trend, but it is between -0.75 MPa and 14.25 MPa. This shows that the increase of times of freeze-thaw cycle has little effect on the maximum principal stress of the slope.Figure 13
Cloud chart of maximum and minimum principal stress for different times of the freeze-thaw cycle.
(a)
Cloud chart of maximum principal stress for 0 times of the freeze-thaw cycle(b)
Cloud chart of minimum principal stress for 20 times of the freeze-thaw cycle(c)
Cloud chart of maximum principal stress for 40 times of the freeze-thaw cycle(d)
Cloud chart of maximum principal stress for 60 times of the freeze-thaw cycle(e)
Cloud chart of maximum principal stress for 80 times of the freeze-thaw cycle(f)
Cloud chart of maximum principal stress for 100 times of the freeze-thaw cycleIn order to reflect the influence of different times of the freeze-thaw cycle on slope failure and instability, the cloud chart of corresponding maximum shear strain is obtained by numerical simulation, as shown in Figure14. It can be seen from the figure that the safety factor decreases with the increasing times of the freeze-thaw cycle. At the same time, the maximum shear strain reflects the relative deformation of slope failure. The figure also shows that the relative deformation of failure gradually increases with the increase of the times of the freeze-thaw cycle. Because this paper studies the rock slope, it will not form a complete sliding zone like the soil slope. However, local rock mass spalling and instability failure will occur within the freeze-thaw shear area of the slope. The results show that the times of the freeze-thaw cycle has a great impact on the strength and stability of slope rock mass. The more times of the freeze-thaw cycle, the more serious the deterioration of internal performance of rock mass and the lower the stability of slope.Figure 14
Cloud chart of maximum shear strain for different times of the freeze-thaw cycle.
(a)
Cloud chart of maximum shear strain for 0 times of the freeze-thaw cycle(b)
Cloud chart of maximum shear strain for 20 times of the freeze-thaw cycle(c)
Cloud chart of maximum shear strain for 40 times of the freeze-thaw cycle(d)
Cloud chart of maximum shear strain for 60 times of the freeze-thaw cycle(e)
Cloud chart of maximum shear strain for 80 times of the freeze-thaw cycle(f)
Cloud chart of maximum shear strain for 100 times of the freeze-thaw cycle


#### 3.2.2. Analysis of Total Displacement of Slope Model

Figure15 shows the change of total displacement nephogram of slope rock mass under different times of the freeze-thaw cycle. It can also be found from the figure that the safety factor decreases gradually with the increase of the times of the freeze-thaw cycle. At the same time, due to the self-weight of the overlying rock mass and mechanical excavation, the total displacement reaches the maximum in the first two steps.Figure 15
Cloud chart of total displacement for different times of the freeze-thaw cycle.
(a)
Cloud chart of total displacement for 0 times of the freeze-thaw cycle(b)
Cloud chart of total displacement for 20 times of the freeze-thaw cycle(c)
Cloud chart of total displacement for 40 times of the freeze-thaw cycle(d)
Cloud chart of total displacement for 60 times of the freeze-thaw cycle(e)
Cloud chart of total displacement for 80 times of the freeze-thaw cycle(f)
Cloud chart of total displacement for 100 times of the freeze-thaw cycleAccording to the numerical simulation results, the strength reduction factor decreases with the increasing times of the freeze-thaw cycle. In order to further reflect the relationship between the strength reduction factor and the total displacement of the slope, the curve shown in Figure16 is drawn. It can be clearly seen from the figure that under the same times of the freeze-thaw cycle, the initial increase of the maximum total displacement of the slope is not obvious, and then with the continuous increase of the strength reduction factor, the maximum total displacement changes abruptly and increases significantly. This shows that the slope is obviously damaged when the strength reduction factor reaches this value. When the times of the freeze-thaw cycle increases, the strength reduction factor decreases gradually, and the decreasing range is larger and larger. It shows that the freeze-thaw cycle has a great weakening effect on the mechanical properties of slope rock mass.Figure 16
Relationship between strength reduction factor and maximum total displacement of slope under different times of the freeze-thaw cycle.


#### 3.2.3. Analysis of Yield Elements and Yield Joints of Slope Model

The number of yield elements, yield joints, and their distribution can well show the specific failure degree and failure area of rock. According to the previous test results, the physical and mechanical properties of slope rock mass deteriorate due to freeze-thaw damage, and the strength of rock mass decreases. From the numerical simulation results, it can be found that with the increase of the times of the freeze-thaw cycle, the yield elements of the slope are increasing, and their distribution is spreading from the weathered steps above to the steps below. The distribution of yield joints is becoming more and more dense, and they are mainly distributed on the slope surface like the yield elements. In order to clearly reflect the changes of the number of yield elements and yield joints, the curves of the number of yield elements and yield joints of the slope with the times of the freeze-thaw cycle are drawn, as shown in Figure17. They all increase gradually with the increase of the times of the freeze-thaw cycle, and the increasing rate increases first and then decreases.Figure 17
Number of yield elements and yield joints of slope surface.


#### 3.2.4. Analysis of Horizontal Displacement and Strength Reduction Times of Nodes

Figure12 shows the positions of the five selected nodes in the slope model. By analyzing the relationship between the horizontal displacement and the reduction times of each node under different times of the freeze-thaw cycle, we can further understand the instability and failure of the slope. It can be seen from Figure 18 that the horizontal displacement of the node changes slightly at the beginning, and then, the displacement changes abruptly, indicating that the slope has undergone obvious instability and failure. From node 5 to node 1, the height of the node decreases, and the horizontal displacement of the node also decreases gradually. In addition, the total displacement change of each node and the number of stages corresponding to the mutation decrease gradually with the increase of the times of the freeze-thaw cycle. This result shows that the failure occurs gradually in advance and the slope stability becomes worse.Figure 18
Horizontal displacement curve of each point under different times of the freeze-thaw cycle ((a–f) The times of the freeze-thaw cycle are 0, 20, 40, 60, 80, and 100, respectively).
(a)(b)(c)(d)(e)(f)


#### 3.2.5. Analysis of Safety Factor of Slope Model

According to the above analysis, when the times of the freeze-thaw cycle are 0, 20, 40, 60, 80, and 100, the safety factors of the slope are 1.86, 1.79, 1.7, 1.57, 1.42, and 1.18, respectively, and the safety factors are getting smaller and smaller. At the same time, it is found that the reduction ranges of the safety factor are 3.76%, 5.03%, 7.65%, 9.55%, and 16.9%, respectively. The gradually increasing reduction range further shows that the more freeze-thaw cycle, the worse the slope stability. This law can also be found from the trend of the curve in Figure19. This is because the pore water in the rock mass freezes to form frost heaving force, and the volume expansion leads to the further development of joint fissures. With the increase of the freeze-thaw cycle, the strength of rock slope decreases gradually. Freeze-thaw fatigue damage reduces the physical and mechanical properties of rock, and rock and joints are more prone to yield instability. Therefore, we can understand the freeze-thaw mechanism of rock slope as the cumulative process of rock freeze-thaw damage.Figure 19
Relationship between safety factor and times of the freeze-thaw cycle.


## 3.1. Establishment of Model and Selection of Parameters

In order to obtain the relevant mechanical parameters of rock slope and establish a complete geomechanical model, samples were taken from the site and divided into 6 groups with 2 samples in each group. The samples of each group were subjected to 0, 20, 40, 60, 80, and 100 times of freeze-thaw cycle, respectively, and physical and mechanical tests were carried out. Finally, the parameters shown in Table3 are counted.Table 3
Basic mechanical and physical parameters of freeze-thaw-treated granite samples.
Sample numberLength×width (mm×mm)Mass (kg)Density (g/cm3)Peak strength (MPa)Elasticity modulus (MPa)P-wave velocity (m/s)S-wave velocity (m/s)y0-1100.07×49.46541.42.863172.3858.6543023577y0-2100.01×49.62540.52.796182.4560.0844123456y20-199.58×49.30543.12.859168.7356.3141313391y20-2100.01×50.21540.22.729167.2455.4642653325y40-199.85×50.05542.62.763163.9852.7840123101y40-2100.12×49.63544.92.815158.3553.4440003210y60-1100.22×49.85547.52.800158.7850.8939062984y60-2100.06×49.19544.62.865155.6649.6538943015y80-199.90×49.88548.92.813152.3947.3638262883y80-2100.11×49.76543.52.793149.2345.2338562913y100-1100.12×49.29547.22.866146.6542.9436902664y100-2100.08×49.34546.62.858142.3343.8935462703We intercepted a section line on the west slope of the mining area to automatically generate the section map of the west slope, import it into RS2 software, and generate the model boundary. The structural plane of rock mass is based on the generalized Hoek-Brown criterion, and the joint is a constitutive model based on Barton-Bandis criterion. According to the previous research, the slope is mainly affected by two sets of joint surfaces. The above physical and mechanical parameters were input into RS2 software, and the three node triangular element was used to generate the finite element grid. The model contained 17207 nodes and 29427 elements. We considered the actual boundary conditions on site and get the final result, as shown in Figure12. Finally, five monitoring points were arranged for subsequent research.Figure 12
Contour map of Beizhan iron mine and slope calculation model.


## 3.2. Numerical Simulation Results

### 3.2.1. Analysis of Maximum Principal Stress and Maximum Shear Strain of Slope Model

According to the definition of principal stress, under the same external force, the principal stress increases with the increase of buried depth. In order to study the variation of the maximum principal stress under different times of freeze-thaw cycle, the cloud chart of the maximum principal stress is obtained as shown in Figure13. It can be found from the figure that the maximum principal stress at the bottom of the slope model is greater than that in other areas, while the top is the smallest. At the same time, the value range of the maximum principal stress does not change with the increase of the times of the freeze-thaw cycle and generally shows a slight upward trend, but it is between -0.75 MPa and 14.25 MPa. This shows that the increase of times of freeze-thaw cycle has little effect on the maximum principal stress of the slope.Figure 13
Cloud chart of maximum and minimum principal stress for different times of the freeze-thaw cycle.
(a)
Cloud chart of maximum principal stress for 0 times of the freeze-thaw cycle(b)
Cloud chart of minimum principal stress for 20 times of the freeze-thaw cycle(c)
Cloud chart of maximum principal stress for 40 times of the freeze-thaw cycle(d)
Cloud chart of maximum principal stress for 60 times of the freeze-thaw cycle(e)
Cloud chart of maximum principal stress for 80 times of the freeze-thaw cycle(f)
Cloud chart of maximum principal stress for 100 times of the freeze-thaw cycleIn order to reflect the influence of different times of the freeze-thaw cycle on slope failure and instability, the cloud chart of corresponding maximum shear strain is obtained by numerical simulation, as shown in Figure14. It can be seen from the figure that the safety factor decreases with the increasing times of the freeze-thaw cycle. At the same time, the maximum shear strain reflects the relative deformation of slope failure. The figure also shows that the relative deformation of failure gradually increases with the increase of the times of the freeze-thaw cycle. Because this paper studies the rock slope, it will not form a complete sliding zone like the soil slope. However, local rock mass spalling and instability failure will occur within the freeze-thaw shear area of the slope. The results show that the times of the freeze-thaw cycle has a great impact on the strength and stability of slope rock mass. The more times of the freeze-thaw cycle, the more serious the deterioration of internal performance of rock mass and the lower the stability of slope.Figure 14
Cloud chart of maximum shear strain for different times of the freeze-thaw cycle.
(a)
Cloud chart of maximum shear strain for 0 times of the freeze-thaw cycle(b)
Cloud chart of maximum shear strain for 20 times of the freeze-thaw cycle(c)
Cloud chart of maximum shear strain for 40 times of the freeze-thaw cycle(d)
Cloud chart of maximum shear strain for 60 times of the freeze-thaw cycle(e)
Cloud chart of maximum shear strain for 80 times of the freeze-thaw cycle(f)
Cloud chart of maximum shear strain for 100 times of the freeze-thaw cycle


### 3.2.2. Analysis of Total Displacement of Slope Model

Figure15 shows the change of total displacement nephogram of slope rock mass under different times of the freeze-thaw cycle. It can also be found from the figure that the safety factor decreases gradually with the increase of the times of the freeze-thaw cycle. At the same time, due to the self-weight of the overlying rock mass and mechanical excavation, the total displacement reaches the maximum in the first two steps.Figure 15
Cloud chart of total displacement for different times of the freeze-thaw cycle.
(a)
Cloud chart of total displacement for 0 times of the freeze-thaw cycle(b)
Cloud chart of total displacement for 20 times of the freeze-thaw cycle(c)
Cloud chart of total displacement for 40 times of the freeze-thaw cycle(d)
Cloud chart of total displacement for 60 times of the freeze-thaw cycle(e)
Cloud chart of total displacement for 80 times of the freeze-thaw cycle(f)
Cloud chart of total displacement for 100 times of the freeze-thaw cycleAccording to the numerical simulation results, the strength reduction factor decreases with the increasing times of the freeze-thaw cycle. In order to further reflect the relationship between the strength reduction factor and the total displacement of the slope, the curve shown in Figure16 is drawn. It can be clearly seen from the figure that under the same times of the freeze-thaw cycle, the initial increase of the maximum total displacement of the slope is not obvious, and then with the continuous increase of the strength reduction factor, the maximum total displacement changes abruptly and increases significantly. This shows that the slope is obviously damaged when the strength reduction factor reaches this value. When the times of the freeze-thaw cycle increases, the strength reduction factor decreases gradually, and the decreasing range is larger and larger. It shows that the freeze-thaw cycle has a great weakening effect on the mechanical properties of slope rock mass.Figure 16
Relationship between strength reduction factor and maximum total displacement of slope under different times of the freeze-thaw cycle.


### 3.2.3. Analysis of Yield Elements and Yield Joints of Slope Model

The number of yield elements, yield joints, and their distribution can well show the specific failure degree and failure area of rock. According to the previous test results, the physical and mechanical properties of slope rock mass deteriorate due to freeze-thaw damage, and the strength of rock mass decreases. From the numerical simulation results, it can be found that with the increase of the times of the freeze-thaw cycle, the yield elements of the slope are increasing, and their distribution is spreading from the weathered steps above to the steps below. The distribution of yield joints is becoming more and more dense, and they are mainly distributed on the slope surface like the yield elements. In order to clearly reflect the changes of the number of yield elements and yield joints, the curves of the number of yield elements and yield joints of the slope with the times of the freeze-thaw cycle are drawn, as shown in Figure17. They all increase gradually with the increase of the times of the freeze-thaw cycle, and the increasing rate increases first and then decreases.Figure 17
Number of yield elements and yield joints of slope surface.


### 3.2.4. Analysis of Horizontal Displacement and Strength Reduction Times of Nodes

Figure12 shows the positions of the five selected nodes in the slope model. By analyzing the relationship between the horizontal displacement and the reduction times of each node under different times of the freeze-thaw cycle, we can further understand the instability and failure of the slope. It can be seen from Figure 18 that the horizontal displacement of the node changes slightly at the beginning, and then, the displacement changes abruptly, indicating that the slope has undergone obvious instability and failure. From node 5 to node 1, the height of the node decreases, and the horizontal displacement of the node also decreases gradually. In addition, the total displacement change of each node and the number of stages corresponding to the mutation decrease gradually with the increase of the times of the freeze-thaw cycle. This result shows that the failure occurs gradually in advance and the slope stability becomes worse.Figure 18
Horizontal displacement curve of each point under different times of the freeze-thaw cycle ((a–f) The times of the freeze-thaw cycle are 0, 20, 40, 60, 80, and 100, respectively).
(a)(b)(c)(d)(e)(f)


### 3.2.5. Analysis of Safety Factor of Slope Model

According to the above analysis, when the times of the freeze-thaw cycle are 0, 20, 40, 60, 80, and 100, the safety factors of the slope are 1.86, 1.79, 1.7, 1.57, 1.42, and 1.18, respectively, and the safety factors are getting smaller and smaller. At the same time, it is found that the reduction ranges of the safety factor are 3.76%, 5.03%, 7.65%, 9.55%, and 16.9%, respectively. The gradually increasing reduction range further shows that the more freeze-thaw cycle, the worse the slope stability. This law can also be found from the trend of the curve in Figure19. This is because the pore water in the rock mass freezes to form frost heaving force, and the volume expansion leads to the further development of joint fissures. With the increase of the freeze-thaw cycle, the strength of rock slope decreases gradually. Freeze-thaw fatigue damage reduces the physical and mechanical properties of rock, and rock and joints are more prone to yield instability. Therefore, we can understand the freeze-thaw mechanism of rock slope as the cumulative process of rock freeze-thaw damage.Figure 19
Relationship between safety factor and times of the freeze-thaw cycle.


## 3.2.1. Analysis of Maximum Principal Stress and Maximum Shear Strain of Slope Model

According to the definition of principal stress, under the same external force, the principal stress increases with the increase of buried depth. In order to study the variation of the maximum principal stress under different times of freeze-thaw cycle, the cloud chart of the maximum principal stress is obtained as shown in Figure13. It can be found from the figure that the maximum principal stress at the bottom of the slope model is greater than that in other areas, while the top is the smallest. At the same time, the value range of the maximum principal stress does not change with the increase of the times of the freeze-thaw cycle and generally shows a slight upward trend, but it is between -0.75 MPa and 14.25 MPa. This shows that the increase of times of freeze-thaw cycle has little effect on the maximum principal stress of the slope.Figure 13
Cloud chart of maximum and minimum principal stress for different times of the freeze-thaw cycle.
(a)
Cloud chart of maximum principal stress for 0 times of the freeze-thaw cycle(b)
Cloud chart of minimum principal stress for 20 times of the freeze-thaw cycle(c)
Cloud chart of maximum principal stress for 40 times of the freeze-thaw cycle(d)
Cloud chart of maximum principal stress for 60 times of the freeze-thaw cycle(e)
Cloud chart of maximum principal stress for 80 times of the freeze-thaw cycle(f)
Cloud chart of maximum principal stress for 100 times of the freeze-thaw cycleIn order to reflect the influence of different times of the freeze-thaw cycle on slope failure and instability, the cloud chart of corresponding maximum shear strain is obtained by numerical simulation, as shown in Figure14. It can be seen from the figure that the safety factor decreases with the increasing times of the freeze-thaw cycle. At the same time, the maximum shear strain reflects the relative deformation of slope failure. The figure also shows that the relative deformation of failure gradually increases with the increase of the times of the freeze-thaw cycle. Because this paper studies the rock slope, it will not form a complete sliding zone like the soil slope. However, local rock mass spalling and instability failure will occur within the freeze-thaw shear area of the slope. The results show that the times of the freeze-thaw cycle has a great impact on the strength and stability of slope rock mass. The more times of the freeze-thaw cycle, the more serious the deterioration of internal performance of rock mass and the lower the stability of slope.Figure 14
Cloud chart of maximum shear strain for different times of the freeze-thaw cycle.
(a)
Cloud chart of maximum shear strain for 0 times of the freeze-thaw cycle(b)
Cloud chart of maximum shear strain for 20 times of the freeze-thaw cycle(c)
Cloud chart of maximum shear strain for 40 times of the freeze-thaw cycle(d)
Cloud chart of maximum shear strain for 60 times of the freeze-thaw cycle(e)
Cloud chart of maximum shear strain for 80 times of the freeze-thaw cycle(f)
Cloud chart of maximum shear strain for 100 times of the freeze-thaw cycle


## 3.2.2. Analysis of Total Displacement of Slope Model

Figure15 shows the change of total displacement nephogram of slope rock mass under different times of the freeze-thaw cycle. It can also be found from the figure that the safety factor decreases gradually with the increase of the times of the freeze-thaw cycle. At the same time, due to the self-weight of the overlying rock mass and mechanical excavation, the total displacement reaches the maximum in the first two steps.Figure 15
Cloud chart of total displacement for different times of the freeze-thaw cycle.
(a)
Cloud chart of total displacement for 0 times of the freeze-thaw cycle(b)
Cloud chart of total displacement for 20 times of the freeze-thaw cycle(c)
Cloud chart of total displacement for 40 times of the freeze-thaw cycle(d)
Cloud chart of total displacement for 60 times of the freeze-thaw cycle(e)
Cloud chart of total displacement for 80 times of the freeze-thaw cycle(f)
Cloud chart of total displacement for 100 times of the freeze-thaw cycleAccording to the numerical simulation results, the strength reduction factor decreases with the increasing times of the freeze-thaw cycle. In order to further reflect the relationship between the strength reduction factor and the total displacement of the slope, the curve shown in Figure16 is drawn. It can be clearly seen from the figure that under the same times of the freeze-thaw cycle, the initial increase of the maximum total displacement of the slope is not obvious, and then with the continuous increase of the strength reduction factor, the maximum total displacement changes abruptly and increases significantly. This shows that the slope is obviously damaged when the strength reduction factor reaches this value. When the times of the freeze-thaw cycle increases, the strength reduction factor decreases gradually, and the decreasing range is larger and larger. It shows that the freeze-thaw cycle has a great weakening effect on the mechanical properties of slope rock mass.Figure 16
Relationship between strength reduction factor and maximum total displacement of slope under different times of the freeze-thaw cycle.


## 3.2.3. Analysis of Yield Elements and Yield Joints of Slope Model

The number of yield elements, yield joints, and their distribution can well show the specific failure degree and failure area of rock. According to the previous test results, the physical and mechanical properties of slope rock mass deteriorate due to freeze-thaw damage, and the strength of rock mass decreases. From the numerical simulation results, it can be found that with the increase of the times of the freeze-thaw cycle, the yield elements of the slope are increasing, and their distribution is spreading from the weathered steps above to the steps below. The distribution of yield joints is becoming more and more dense, and they are mainly distributed on the slope surface like the yield elements. In order to clearly reflect the changes of the number of yield elements and yield joints, the curves of the number of yield elements and yield joints of the slope with the times of the freeze-thaw cycle are drawn, as shown in Figure17. They all increase gradually with the increase of the times of the freeze-thaw cycle, and the increasing rate increases first and then decreases.Figure 17
Number of yield elements and yield joints of slope surface.


## 3.2.4. Analysis of Horizontal Displacement and Strength Reduction Times of Nodes

Figure12 shows the positions of the five selected nodes in the slope model. By analyzing the relationship between the horizontal displacement and the reduction times of each node under different times of the freeze-thaw cycle, we can further understand the instability and failure of the slope. It can be seen from Figure 18 that the horizontal displacement of the node changes slightly at the beginning, and then, the displacement changes abruptly, indicating that the slope has undergone obvious instability and failure. From node 5 to node 1, the height of the node decreases, and the horizontal displacement of the node also decreases gradually. In addition, the total displacement change of each node and the number of stages corresponding to the mutation decrease gradually with the increase of the times of the freeze-thaw cycle. This result shows that the failure occurs gradually in advance and the slope stability becomes worse.Figure 18
Horizontal displacement curve of each point under different times of the freeze-thaw cycle ((a–f) The times of the freeze-thaw cycle are 0, 20, 40, 60, 80, and 100, respectively).
(a)(b)(c)(d)(e)(f)


## 3.2.5. Analysis of Safety Factor of Slope Model

According to the above analysis, when the times of the freeze-thaw cycle are 0, 20, 40, 60, 80, and 100, the safety factors of the slope are 1.86, 1.79, 1.7, 1.57, 1.42, and 1.18, respectively, and the safety factors are getting smaller and smaller. At the same time, it is found that the reduction ranges of the safety factor are 3.76%, 5.03%, 7.65%, 9.55%, and 16.9%, respectively. The gradually increasing reduction range further shows that the more freeze-thaw cycle, the worse the slope stability. This law can also be found from the trend of the curve in Figure19. This is because the pore water in the rock mass freezes to form frost heaving force, and the volume expansion leads to the further development of joint fissures. With the increase of the freeze-thaw cycle, the strength of rock slope decreases gradually. Freeze-thaw fatigue damage reduces the physical and mechanical properties of rock, and rock and joints are more prone to yield instability. Therefore, we can understand the freeze-thaw mechanism of rock slope as the cumulative process of rock freeze-thaw damage.Figure 19
Relationship between safety factor and times of the freeze-thaw cycle.


## 4. Conclusions

In this paper, the influence of the freeze-thaw cycle on the slope stability of an open pit mine is studied with the help of 3D laser scanning technology and RS2 finite element software. The following three conclusions are obtained:(1)
For the point cloud data obtained by 3D laser scanning, firstly, the 3D difference method is used for grid processing. After selecting the discrimination index, all nodes are scanned for flatness detection. After the data is simplified, the improved image segmentation algorithm is used to complete the regional division of the structural plane, and the reasonable flatness detection threshold, regional growth threshold, and area threshold are selected to complete the intelligent recognition of rock mass structural plane(2)
The geometric parameters and other information of rock mass discontinuity are extracted, the plane equation of rock mass discontinuity is fitted by the least square method, and the dip angle of rock mass discontinuity is calculated. The structural plane is divided byK-means cluster analysis method based on occurrence information, and the spacing and equivalent trace length of structural plane are calculated. The calculation results are basically consistent with the actual investigation of the mining area(3)
According to the mechanical parameters obtained from the freeze-thaw cyclic test and the distribution of joint surfaces measured by 3D laser scanning technology, the slope mechanical model is established. The finite element strength reduction method is used to numerically simulate and analyze the slope structural plane, and the safety factor of the slope under different times of the freeze-thaw cycle is calculated. The results show that with the increase of the freeze-thaw cycle, the principal stress, volume strain, and displacement gradually increase. The number of yield elements and yield joints increases gradually, the safety factor decreases continuously, and the stability of the slope becomes worse, which shows that the rocks in high-altitude mining areas are in a freeze-thaw cycle all year round. The freeze-thaw fatigue damage degrades the physical and mechanical properties of rocks, and the rocks and joints are more prone to yield instability



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*Source: 1705985-2022-07-31.xml*