Numerical Analysis for the Caving Characteristics of Rock Mass with Inclined Joints in Caving Mining

In caving mining, the successful initiation and propagation of caving require one low-dip joint set. However, not every mine has a low-dip joint set. (e Hemushan Iron Mine in China was taken as the engineering background, and the caving characteristics of rock mass with inclined joints were analyzed based on the synthetic rock mass (SRM) model. First, the inclined joints were investigated in the Hemushan Iron Mine. Second, model parameters were determined based on the geological conditions of the mine, and seven models were established.(ird, the caving process was simulated, and caving characteristics were monitored. For rock mass with inclined joints after undercutting, the research showed that the crack zone was significant, and the crack zone existed not only around the undercut area but also further away in the model. (e stress concentration areas dispersed in the model except for the top of the undercut area. (e caving line was not a standard arch, and the highest point of the caving line was biased towards the direction of the undercut. Under the same undercut width, with the decrease of joint length in the joint system, the number of cracks decreased, the degree of stress concentration became weaker, and the height of the caving line decreased.


Introduction
Caving mining is a mining method used for underground mines. It refers to all mining operations in which the orebody caves naturally after undercutting [1]. us, the mining costs of caving mining are smaller than those of other mining methods.
is method is of growing interest to companies concerned with the exploitation of massive orebodies because of its low cost [2]. However, theoretical and practical knowledge of caving characteristics, particularly in complex jointed rock masses, is also limited. e caving characteristics affect the mining design and even affect whether caving mining is suitable for a particular mine.
According to Brown [2], any unsupported rock mass will cave if it is undercut to a sufficient extent. Caving occurs as a result of gravity and induced stresses; the induced stresses are caused by undercut engineering or caving of rock mass. e process of caving depends on the relationships between the induced stresses, the strength of the rock mass, and the geometry and strengths of discontinuities in the rock mass. Kendorski [3] contended that the successful initiation and propagation of caving requires the presence of a well-developed, low-dip discontinuity set. e most ideal rock mass conditions for caving are at least two steep-dip discontinuity sets and one low-dip discontinuity set [2]. e steep-dip discontinuity sets provide the vertical displacement for caving. Duplancic and Brady [4] used a seismic monitoring system to study the early stages of caving and developed a conceptual model of caving. e model contains five regions: the caved zone, air gap, zone of discontinuous deformation, seismogenic zone, and surrounding rock mass. ey also found that a flat-lying discontinuity set is required to act as a release mechanism for caving. Based on physical models and field observations, Cumming-Potvin et al. [5] also pointed out that the Duplancic model needs to be extended to include fracture banding. Jiang and Yang [6] performed a numerical simulation of caving characteristics and found that the stress balance arch formed in the orebody and stress concentration appeared at the arch foot. Song et al. [7] used boreholes to monitor the caving mechanism and determined that the caving height of rock strata is closely related to the rock mass quality and is seriously affected by the contact zone of rock strata. Zhang and Zhao [8] used RFPA software to study stope roof caving and concluded that the profile of the caved rock mass under high geostress changes gradually from a parabolic shape to a stratiform shape, while that with horizontal and vertical joints changes to a saddle shape and tower shape, respectively. In summary, the caving characteristics of jointed rock mass are complex, especially for different joint conditions. One of the conditions for caving is the existence of one low-dip discontinuity set; this condition is not found in many mines. erefore, the caving characteristics with no discontinuity set with a low dip, such as those of inclined joints, also need to be studied.
At present, there are three main methods of studying caving characteristics. e first method is field tests in mining, such as seismic monitoring [4,5,9,10]. is method is not suitable for mines at the feasibility study stage or design stage, but it is suitable for monitoring the process of caving. e second method is the use of a physical model [5,[11][12][13][14] in the laboratory. is method has difficulty realizing the conditions of complex jointed rock mass, and it usually assumes that the rock mass is intact or simple (such as a coal seam). e third method is the numerical method, which is mainly based on the discrete-element method and finite-element method. Numerical methods have rapidly developed and been applied in recent years because they can ensure the consistency of mechanical properties and simulate the complex conditions of a rock mass. Hassen et al. [15] analyzed an attentive caving phenomenon incorporating main geotechnical parameters based on the discrete-element method and finite-element method. Vyazmensky et al. [16] analyzed the interaction between block cave mining and a large overlying open pit by finite-element modeling/discrete-element modeling. Vakili and Hebblewhite [17] developed a new cavability assessment criterion for top-coal, and the discrete-element method was employed as the main analytical tool. Li et al. [18] investigated strata movement during the caving process based on a finite-element technique that incorporates an elasto-brittle fracture mechanics constitutive criterion. Cao et al. [19] simulated the ground settlement process caused by mining activity by the universal distinct-element code (UDEC). Paluszny and Zimmerman [20] simulated the growth of fractures around an undercut during caving by a finite-element-based method. Rafiee et al. [21] studied the influence parameters on the cavability of rock mass in block caving mines by using PFC3D software. Ren et al. [22] analyzed the damage evolution of a rock mass during caving and the surface subsidence mechanism based on RFPA2D. Eremin et al. [23] applied the finite-difference method and the continuum damage mechanics approach to simulate the stress-strain evolution of a rock mass on the underground opening during coal extraction. Each of the methods mentioned above has its own advantages and applicable conditions. However, the caving process of a rock mass is a dynamic and continuous process after undercutting. e crack distribution, stress distribution, and caving line are important components for the study of caving characteristics. erefore, the numerical method is a good approach for studying the caving characteristics of jointed rock mass.
In this paper, taking the Hemushan Iron Mine in China as the engineering background, the caving characteristics of rock mass with inclined joints are investigated based on synthetic rock mass (SRM) models. A series of numerical models are compared and analyzed, and the characteristics of the crack distribution, stress distribution, and caving line are determined for a rock mass with inclined joints.

Inclined Joints
e Hemushan Iron Mine is an underground mine in China, located in Maanshan, Anhui Province. e orebody of the Hemushan Iron Mine is located in diorite and limestone, and its shape is lenticular and layered. As shown in Figure 1(a), the dip angle of the orebody is generally 45°to 60°, the horizontal thickness is generally 10 to 85 m, and the length is 130 to 335 m along the strike. In addition, the ore is mainly magnetic ore. At the −150 m level, the strength of ore is low, and the stability of the orebody is poor. In this situation, it is difficult to form the ore drawing conditions and the bottom structure based on the original design of the sublevel open stope mining method, and this situation is suitable for caving mining. e conditions of low ore strength and unstable orebody are advantageous for caving [1,2,24]. However, the occurrences of joints in the mine are investigated and analyzed. As shown in Figure 1(b), there are few low-dip joints in the mine, and the dominant joints are inclined. erefore, it is necessary to study the caving characteristics of the inclined jointed rock mass and prevent potential safety hazards or ore loss and dilution in the mine.

Methodology
e initiation and propagation of caving may be caused by the following three reasons: rock blocks become free to fall under the influence of gravity, large rocks are broken and become free to fall under induced stresses and gravity, or rock blocks become free to slide on the joint under induced stresses and gravity. erefore, the numerical method of the particle flow code was selected since it could be used to study intact rock, jointed rock mass, and large displacements of rock blocks. e particle flow code provides an embodiment of the distinct-element method [25]. It consists of bodies (particles, clumps, and walls) and mechanical contacts (contact models). A body is composed of one or more constituent pieces that make up the body surface. e particles are rigid bodies with finite mass that move independently of one another and can both translate and rotate. e interaction between particles occurs through internal forces and moments. Contact mechanics is embodied in particle-interaction laws (referred to as contact models) that update the internal forces and moments. e time evolution of the system is computed via Newton's laws of motion. e particle flow code provides a synthetic material consisting of an assembly of rigid particles that interact at contacts, such as intact rock, jointed rock mass, and granular materials. 2 Advances in Civil Engineering

Synthetic Rock Mass (SRM).
e particle flow code has been successfully used to study the mechanical properties or mechanical behavior of jointed rock mass [26][27][28][29][30] due to the development of the smooth-joint contact model [31]. e method has been termed the synthetic rock mass (SRM) methodology [25]. As shown in Figure 2, the modeling approach consists of joints (or discontinuities) information (discrete fracture network) in a bonded-particle model [32].
e bonded-particle model is used to represent the intact rock, and the mechanical behavior of the joint is introduced by modifying the contact models at the joint position.
In SRM modeling, two contact models need to be determined. One is the smooth-joint contact model used to represent the properties of joints, and the other is the bonded-particle model representing the properties of intact rock. First, the smooth-joint model simulates the behavior of a planar interface regardless of the local particle contact orientations along with the interface. As shown in Figure 2, the joint geometry consists of a planar interface separating two surfaces (surface 1 and surface 2). e behavior of a frictional or bonded joint can be modeled by assigning smooth-joint models to all contacts between particles that lie on opposite sides of the joint. Second, the flat-joint model is selected in the bonded-particle model. Because it can be applied to hard rock, and larger ratio of uniaxial compression strength to tensile strength can be obtained [33]. As shown in Figure 2, the flat-joint contact simulates the behavior of an interface between two notional surfaces (called faces), each of which is rigidly connected to a piece of a body [32]. In the flat-jointed model, the basic element is referred to as faced grains, each of which is depicted as a circular core and a number of skirted faces. us, faced grains can provide grain interlocking and rotational resistance even after the interface breaks [34]. An interface exists between each set of adjoining faces and is discretized into elements, with each element being either bonded or unbonded. e breakage of each bonded element contributes partial damage to the interface, and each breakage event is denoted as a crack [32].

Parameters of the Model.
e microscopic parameters of a flat-jointed model could not be directly obtained from rock properties. e parameters needed to be calibrated by numerical tests, so that the numerical simulation results were consistent with the actual results. e calibration process for flat-jointed models was systematically introduced by several researchers [25,34,35]. In this paper, a large number of uniaxial compression and tensile numerical tests were carried out, and the calibration objectives of ore properties included the uniaxial compressive strength, tensile strength, Young's elastic modulus, and Poisson's ratio. e numerical tests performed for calibration are shown in Figure 3, and the microscopic parameters of the flat-jointed model are listed in Table 1. e results show that rock properties are very close for those of the numerical model and those of magnetic ore.
e flat-jointed model is appropriate, especially for a larger ratio of uniaxial compression strength to tensile strength. e parameters of the joints also needed to be determined. rough field investigation in mine, the properties of joints were "FAIR" (smooth, moderately weathered, and altered surfaces) based on the chart for GSI estimates (modified by Cai et al. [36]). Under such conditions, Poulsen et al. [28] suggested that the joint friction coefficient was 0.5 and cohesive and tensile strengths were equal to 0. ese parameters were also suggested by Zhang et al. [37].

Model Design.
In underground mining, the rock mass was subjected to vertical compressive stress and confining pressure. erefore, the servo control method was used to exert pressure on the model. As shown in Figure 4, the vertical compressive stress is 4.96 MPa and the confining pressure is 1.98 MPa according to the in-situ stress of the    Another design involved adding joints in the model. According to the conditions of the Hemushan Iron Mine and the requirements for analysis and comparison, seven models were established based on the SRM model. e seven models are shown in Figure 5, and the parameters of each model are shown in Table 2. e average density of the joint system is 3 per meter in model (e). Models (b), (c), and (d) are established by deleting the joint set in model (e). Models (f ) and (g) are established by shortening the length of the joints in model (e). Models (a) to (d) are used to study the caving characteristics of rock mass with no joints and joint sets, models (b) to (e) are used to study the caving characteristics of rock mass with joint sets and joint systems, and models (e) to (g) are used to study the caving characteristics of rock mass with different joint lengths in the joint system.

Numerical Simulation Results
To determine the caving characteristics of a rock mass with inclined joints, the crack distribution, stress distribution, and caving line were monitored during the process of numerical simulation (undercut engineering).

Crack Distribution and Propagation.
e SRM model was composed of bonded particles and joints, and the caving of the rock mass occurred as a result of undercutting. During the caving process, failure occurred in selected bonded contacts, and cracks were generated in the model. erefore, the cracks were monitored during the different widths of the undercut, the results are shown in Figure 6, and red represents cracks.
In the model with no joints, as shown in Figure 6(a), cracks initially appear at the top of the undercut area and extend vertically. With the increase in the undercut width, the direction of crack propagation appears inclined, and then, they connect with each other and lead to the caving of the rock mass. Cracks mainly appear at the top of the undercut area. e joint set models are shown in Figures 6(b)-6(d), and cracks initially appear around the undercut area. With the increase in the undercut width, the direction of crack propagation appears almost perpendicular or inclined to the joint direction, and then, they connect with each other or joints and lead to the caving of the rock mass. Cracks appear at the top of the undercut area, and the heights of the cracks are the highest at the top of the undercut area in the 98°joint set model, but cracks also appear at the upper inclined ends on both sides of the undercut area in the 24°and 124°joint set model. Compared with a model with no joints, the joint set is favorable for the formation of cracks, and the 124°joint set is obvious for the Hemushan Iron Mine.
Joint system models are shown in Figures 6(e)-6(g), and cracks initially appear around the undercut area. With the increase in the undercut width, the direction of crack propagation is inclined to the joint direction, and then, they connect with each other or joints and lead to the caving of the rock mass. With decreasing joint length, the number of cracks decreases under the same width of the undercut. Cracks appear at the top of the undercut area and the upper inclined ends on both sides of the undercut area.

Stress Distribution.
e contact force between particles could be determined by the particle flow code, and the stress distribution and stress concentration area could be determined by the contact force. In the process of numerical simulation, the contact forces were determined during the different widths of the undercut. e results are shown in Figure 7.
e model with no joints is shown in Figure 7(a). e stress concentration areas are mainly distributed in the upper two corners of the rectangular undercut area. With the increase in the undercut width, stress concentration areas also appear on the sides of the undercut area, especially when      e stress concentration areas are distributed in the upper two corners of the rectangular undercut area, but they also appear in other areas in the models except for the top of the undercut area. With the increase in the undercut width, the stress concentration areas on both sides of the undercut area are significant. e joint system models are shown in Figures 7(e)-7(g), and the stress concentration areas are similar to those of the joint set models. With decreasing joint length, the degree of stress concentration becomes weaker under the same width of the undercut.

Caving Line.
e caving line is also known as the caving arch because the shape of the caving line is usually considered to be an arch. In the process of numerical simulation, caving lines are drawn for the different widths of the undercut, and the results are shown in Figure 8.
In the no joints model, as shown in Figure 8(a), the highest point of the caving line is basically located in the middle of the undercut width, and the angle between the caving line and the horizontal direction is small. e joint set models are shown in Figures 8(b)-8(d). e highest point of the caving line is biased towards the direction of the undercut, and the angle between the caving line and the horizontal direction is larger than that of the model with no joints. e joint system models are shown in Figures 8(e)-8(g). e highest point of the caving line is also biased towards the direction of the undercut, and the angle between the caving line and the horizontal direction is larger than that of the model with no joints and that of the joint set models. With decreasing joint length, the height of the caving line decreases under the same width of the undercut.

Discussion
Based on the simulation results of seven numerical models, the caving characteristics of the model with no jointed rock mass and the model with an inclined rock mass can be analyzed. e caving characteristics of rock masses with no joints were simple, but caving mining was difficult. e crack zone mainly appeared at the top of the undercut area, the stress concentration areas were mainly distributed in the upper two corners of the rectangular undercut area, and the caving line could be simplified as an arch. It could be concluded that joints had an important influence on the caving characteristics.
e caving characteristics of rock mass with joint sets or joint systems are complicated, but they are beneficial for caving mining. e caving characteristics were as follows: (1) Crack zone and propagation: an obvious crack zone existed in the inclined jointed rock mass after undercutting. e distribution of the crack zone was related to the undercut width, the dip angle of the joint set, and the joint length in the joint system.
With the increase in the undercut width, the crack zone not only existed around the undercut area but also existed further away in the model (such as in the upper inclined ends on both sides of the undercut area). e direction of crack propagation was inclined to the joint direction, and then, the cracks connected with each other or the joints, which led to the caving of the rock mass. With the decrease in the joint length in the joint system, the number of cracks decreased under the same undercut width.
(2) Stress distribution: with the increase in the undercut width in the inclined jointed rock mass, the stress concentration areas were not only distributed in the upper two corners of the rectangular undercut area but also distributed in other areas in the models except the top of the undercut area. With decreasing joint length, the degree of stress concentration became weaker under the same width of the undercut.  and the angle between the caving line and the horizontal direction was related to the conditions of the joint. For the rock mass of the joint system in this paper, one side of the caving line was very steep (Figures 8(e)-8(g)), and the angle between the caving line and the horizontal direction reached more than 80°. In actual mining, the monitoring tunnel was set up to monitor the caving process (Figure 9), and the results showed that the angle between the caving line and the horizontal direction reached 85°. With the decrease in joint length, the height of the caving line decreased under the same width of the undercut.
It should be noted that the caving of a rock mass with a steeply dipping joint set (such as the 98°joint set in this paper) was difficult in the early stage of mining. However, a large number of cracks existed above the undercut area ( Figure 6(d)). With the continuous increase in the undercut width, the number of cracks also increased, and then, they connected with each other or joints, which led to the caving of the rock mass. In this situation, the amount of rock mass that caved was very large, which would threaten miners, mining equipment, mining facilities, etc. Protection or treatment measures, such as increasing the height of the blasted orebody during undercut engineering and using the blasting ore as the overburden or using hydraulic fracturing to promote caving of the rock mass in the early stage of mining, are necessary for the safety mining of mine.

Conclusions
In this study, the caving characteristics of rock mass with inclined joints in caving mining were investigated. For this purpose, seven numerical models were established based on the SRM model and the conditions of the Hemushan Iron Mine. e crack distribution, stress distribution, and caving line were determined for rock mass with different joint conditions, and the joint conditions included no joints, joint sets, and joint systems. e main conclusions for the caving characteristics of rock mass with inclined joints were as follows: (1) In the caving process, the crack zone was significant, and it not only existed around the undercut area but also existed further away in the model. e distribution of the crack zone was related to the undercut width, the dip angle of the joint set, and the joint length in the joint system. (2) e stress concentration areas not only existed in the upper two corners of the rectangular undercut area (or arch corner) but also dispersed elsewhere in the model except for the top of the undercut area. (3) e caving line was not a standard arch, and the highest point of the caving line was biased towards the direction of the undercut. (4) e joint length had an influence on the caving characteristics of rock mass with inclined joints. Under the same undercut width, with the decrease in the joint length in the joint system, the number of cracks decreased, the degree of stress concentration became weaker, and the height of the caving line decreased.

Data Availability
e data used to support the findings of this study are included within the article.  10 Advances in Civil Engineering