Influence of a Type of Rock Mass on the Stability of Headings in Polish Underground Copper Mines Based on Boundary Element Method

Abstract

This paper presents the results of a numerical analysis of the impact of rock mass geomechanical parameters on the stability of preparatory headings located within the Legnica-Glogow Copper District. The paper shows the results of numerical calculations prepared for headings driven in two rock mass types with different strength and deformation parameters, which allow illustrating their influence on the safety of mining performed in underground copper ore mines. Numerical modeling was performed using the Examine2D 7.0 software, in the plane strain state. Numerical simulations were performed for an isotropic and for a homogenous medium. The rock medium was described with an elastic model. The parameters of the rock mass for numerical modeling were calculated using the Hoek–Brown classification. The Coulomb–Mohr strength criterion was adopted as a measure for assessing the rock mass effort. Numerical simulations confirmed the dependance between the stability of the analyzed excavations and rock mass geomechanical parameters.

1. Introduction

Along with the development of deep underground mines appears an increasing difficulty in understanding the failure mechanism of a rock mass surrounding roadways and introducing deformational control. The geological surroundings of shallowly located headings are often simpler, e.g., lower values of the primary stress and less influenced by geological faults, while deep mining faces complicated problems such as in situ stress increase, a varied geological environment, and combinations of multi-type rock masses. Due to these factors, the instability mechanism of deep rock structures and the mechanical properties of underground rock masses are becoming more complex. It is difficult to precisely estimate the deformation of rock masses surrounding the headings located at a great depth, which makes the prevention of keeping their structural stability increasingly difficult. Unpredicted loss of rock stability may cause dynamic disasters such as roof collapse, rock bursts, gas and coal outbursts, or large-scale subsidence [1]. Owing to a large excavation dimension and heading height, any dynamic event can have a ruinous effect when it occurs [2]. In Poland, copper ore mining has exceeded 1200 m below the ground level and is strongly affected by difficult geology and mining conditions. Due to the extraction depth, copper ore mining is influenced by a growing number of problems connected with the rock mass stability and the occurrence of dynamic events. Therefore, there is a need to perform further research on the prediction and prevention of the potential stability loss in the future [3].

The deflection of the overlaying strata or block disintegration is related to the rock mass parameters. The most important factors playing a substantial role in forming subsidence and ground shifts are the strength and deformational characteristics of the rock mass [4]. For example, the strength and stiffness properties of the rock mass impact the angle of draw, being one of the key parameters in subsidence analysis and prediction [5]. As the rock mass increases, the angle of draw decreases. In contrast, weak rocks extend the scope of subsidence at the surface. A strong rock layer tends to decrease the extent of subsidence, and a weak layer increases the area of deformation. Moreover, the weak strata could impact the scope of subsidences significantly more than the strong layer could [4].

The proper design of the rock headings demands an accurate understanding of the rock mass mechanical properties. There have been numerous attempts to find a way to correctly estimate the rock material parameters being used as the input for analytical and numerical simulations [6,7,8,9]. The results of these simulations are strongly influenced by the entered values. An undue trust in the simulation output without controlling the accuracy of the input parameters may cause devastating disasters in rock engineering ventures [4]. The parameters defining the rock mass material properties are mainly cohesion, tensile strength, internal friction angle, vertical stress, and the lateral pressure coefficient of the deeply located headings’ surroundings [1]. Deformation of rock material is expressed, among others, through Poisson’s ratio ν and the longitudinal modulus of elasticity E [3].

Understanding rock mass parameters enables the use of numerical analysis methods. Numerical simulations meaningfully expand the scope of research related to the evaluation of the rock mass stability [10,11]. Numerical modeling gives the possibility to define the stress concentration locations and potential regions endangered by the stability loss [12]. The numerical analysis approaches can be divided into the conventional and advanced data processing methods. Unlike the analytical approaches, numerical simulation can be applied to assess the stability of both the room and pillar or longwall mining methods. Numerical methods can be classified into one of three main groups. The first one, the continuous method, includes the Finite Element Method (FEM), the Boundary Element Method (BEM), and the Finite Difference Method (FDM). The second and third groups consist of more complicated and complex numerical methods, such as the Distinct Element Method (DEM) or the coupled Finite Element-Discrete Element Method (FEM-DEM), being recently introduced to the excavation stability analysis. Numerical methods allow the accurate assessment of mining subsidences and the magnitude of ground movements and preventing dynamic events. Numerical analysis considers the nonlinear behaviors of the pillars and rock floor materials. Moreover, numerical modeling enables the design of the complex deposit geometry and boundary conditions [4]. Numerical simulations and stability assessment performed may lead to further development of more efficient mining technologies and solutions designed to improve safety in underground mine plants [13].

This article aims to research the influence of the rock mass geological structure on the headings’ stability and deep underground copper mining safety with the use of numerical analysis based on the boundary element method.

2. Geological Conditions of the Legnica-Glogow Copper District Mines

Copper deposits mined by KGHM Polska Miedz S.A. within the Legnica-Glogow Copper District are a fragment of the Fore-Sudetic monocline. The Fore-Sudetic monocline is a geological unit in southwest Poland, bordering the Zar pericline to the west, the Silesian-Krakow monocline to the east, the Fore-Sudetic block to the southwest, and the Szczecin-Lodz synclinorium to the northeast [14].

The Fore-Sudetic monocline consists of sedimentary rocks that cover a substrate made of Proterozoic crystalline rocks. The results of dating the copper-laden rock layers indicate that the balance reserves of this ore originated in the Permian. The top of the deposit is made of dolomite-limestone rocks of the Lower Zechstein, and the bottom is made of Rotliegend sandstones. The balance thickness of the deposit varies locally and ranges from several dozen centimeters to several meters. The rock layers that make up the monocline are inclined at an angle of 3–5°, and the depth at which they are located increases to the northeast [14].

As a result of geological and exploratory work around copper deposits in today’s Legnica-Glogow Copper District, the presence of 1,403,467,000 balance tons of copper ore resources was confirmed with an average thickness of 3.45 m and a copper content of 2.09%. The presence of 29,362,000 tons of copper has also been documented [15].

The area of the deposit is located between Legnica and Glogow. The deck has the shape of an elongated polygon 30–35 km long and 7–10 km wide, and its area is approximately 300 km². Copper mineralization includes Lower Zechstein limestones, dolomites and shales, and Weissliegend or Rotliegend sandstones. The copper content in the deposit rocks is heterogeneous. In practice, only those parts of the seam in which the copper-bearing series meets the balance criteria of at least 0.9% copper content are considered a deposit [16]. Copper shale has the highest content of copper. Sandstone mineralization is significant in the area of operation of the Rudna mine and irregular in the area of Polkowice. In some areas, the dolomites show little mineralization, and in others, they are the main carrier of copper (e.g., in the area of Polkowice) [17].

Violation of the original state of stress and deformation of the rock mass leading to the loss of stability are greater the more anisotropic the rock mass is. This type of rock mass occurs within the Legnica-Głogow Copper District mine. The anisotropy of the rock headings in this area results not only from the lithological variability of the rocks (the rock mass is made up of carbonate rocks, sandstones, and shales with different geomechanical properties), but also from the presence of tectonic geological disturbances. Roof rocks of established headings in the Lower Silesian Copper District have a layered structure, in which the spaces between the layers are filled with rock material with reduced strength parameters, composed of gypsum, calcite, or slate. The sandstones that make up the bottom part of the exploitation door contain binders of different compositions, which translates into the variability of the physical factors and strength properties of the bottom rocks [16].

Today, three copper ore mines of KGHM Polska Miedz S.A. operate in the area of the Legnica-Glogow Copper District. These include the mines “Lubin”, “Polkowice-Sieroszowice”, and “Rudna”. The “Lubin” mine exploits the “Lubin-Malomnice” field. This deposit is dominated by sandstone rocks, which constitute about 67% of all rocks in this area. Eighteen percent of the resources are Zechstein limestone carbonate rocks and 15% Zechstein copper shales. The average thickness of the deposit is 2.33 m, and the depth of deposition varies from 368 to 1006 m. This part of the seam shows a high tectonic involvement of the deposit rocks. The deposit is shallow, not much deeper than the loose Cenozoic sediments. As a result of dislocation, the rock series building this fragment of the deck was divided into blocks of various shapes, which then moved relative to each other vertically and horizontally, creating ditches, frameworks, and stair systems. There are no clear discontinuous dislocation lines in the deposit area, only fault zones, the discharges of which range from a few centimeters to several dozen meters. The width of the faults ranges from 250 to 1500 m [18].

The “Polkowice-Sieroszowice” mine extracts the ore in the “Polkowice”, “Sieroszowice”, and “Radwanice-Wschód” deposits. Mining is carried out at a depth of 676 to 1084 m. In addition to copper, rock salt is present in the deposit rocks. The rock salt seam is the largest in the central and northern part of “Sieroszowice”. The copper-bearing carbonate rocks of the Zechstein limestone dominate in the mine and account for 80%, 55%, and 93% of the deposit rocks of individual deposits, respectively. The resources of the Zechstein copper shale amount to 12%, 14%, and 7% of the total deposits, respectively. Weissliegend sandstone is found only in the “Polkowice” and “Sieroszowice” deposits, and its content is 8% and 31%, respectively. The series of copper-bearing shale located in the mining area contains large amounts of copper and silver, but the seam thickness does not usually exceed 1 m. The “Polkowice” and “Sieroszowice” deposits are located in the areas with developed tectonics. In zones deformed by faults or folds of the layers, the collapse of the series of rocks that make up the seam increases or decreases in relation to the usual inclination of the layers at an angle of 3–6°. The deviation from the general course of the layers varies locally, and the changes can be as high as 90°. There are numerous discontinuous dislocations in the “Polkowice” and “Sieroszowice” deposits. The range of shifts in the “Polkowice” area usually does not exceed 1 m, and the sum of shifts may reach a value of several dozen meters. Apart from discontinuous dislocations, there are fold–fault structures around “Sieroszowice” [18].

The “Rudna” mine extracts from the “Rudna” and “Sieroszowice” deposits. The exploitation depth ranges from 920 to 1170 m. The average thickness of the seam within the “Rudna” deposit is 4.26 m. The deposit rocks are composed of Zechstein carbonate rocks and clay-dolomite shales, as well as Weissliegend sandstones. The presence of depression zones influenced the lithological development of the deposit rock layers. In depression zones, copper is found in sandstones, copper-bearing shales, as well as clay and dolomites. Carbonate ore constitutes 11%, shale ore 6%, and sandstone ore 83% of all ore resources of the Rudna deposit. The deposit layers fall at an average angle of 1–6°, but locally, the fall of the layers can even reach 45°. There are discontinuous dislocations in the deposit, which together form a system of numerous block structures [18].

3. Numerical Analysis of Headings’ Stability in the Legnica-Glogow Copper District Mines

Numerical modeling in this article was performed with Examine2D 7.0, using the boundary element method. The boundary element method is a numerical modeling method that divides a given area into finite elements. In the connecting nodes of these elements, differential calculations are performed, the results of which allow modeling, e.g., the stress distribution around the analyzed element [19].

After a few decades of development, the Boundary Element Method (BEM) has found its place around numerical methods for differential equations. While more popular methods such as the Finite Element Method (FEM) or Finite Difference Method (FDM) can be classified as the domain method, the BEM differs in terms of the numerical discretization being conducted at a reduced spatial dimension. For three spatial dimensions, the discretization is only performed on the boundary surface of the analyzed element. For two spatial dimension problems, the discretization is performed only on the boundary contours. This solution leads to linear systems and computer memory requirement reduction, which makes the calculations more efficient. This effect is most visible when the domain is unbounded. Such domains need to be truncated and approximated in domain methods. The BEM automatically models the behavior of the element’s surroundings without the need to construct a mesh to estimate it. Since mesh preparation seems to be the most labor intensive and cost consuming in numerical modeling, especially for the FEM, the BEM is more effective in terms of mesh deploying. When the problem includes moving boundaries, it is easier to adjust the mesh using the BEM, which makes the method preferably used. The advantages of the BEM are essential for choosing the right method to solve numerical problems [20]. The are several publications regarding the BEM, describing the characteristics of the method and the equations used during the calculations. Additional information on the method can be found in the studies performed by Beskos, Kythe, Balaš, and others [21,22,23].

3.1. Problem Geometry

In the Polish copper mines, the room and pillar mining system is used. Mining the ore using the room and pillar system consists of cutting the deposit with rooms and strips with the separation of technological pillars of a certain geometry, which protect the roof over the working area. The size of the pillars is chosen to provide the work in the post-critical state. In the discussed mining system, the shape of the excavation is an inverted trapezoid. The height of excavation in the cutting phase depends on the thickness of the deposit and the requirements of the working machines. The width of excavations does not exceed 7 m. The minimum size of the opening face of the mining front is equal to the sum of two strips and the length of two rows of pillars into undisturbed rock. Along with the progress of the mining front, the size of the technological pillars from the last row before gobs, depending on the degree of their disintegration, is reduced and remnant pillars are created. The remnant pillars are left in the gobs. They work as supports to mitigate the deflection of roof layers [24]. The currently used mining system allows obtaining from 75% to even 90% of the deposit ore [17].

Mining the minerals in the KGHM mines includes the preparatory works, consisting of contouring the deposit with a network of underground roadways [18]. Preparatory excavations are protected with rock bolt support, which is the primary support for all excavations in the mines [17].

In this paper, preparatory excavations mined for the use of the room–pillar with roof deflection (J-UG-PS) mining system are analyzed. In the J-UG-PS system, the copper ore deposit is mined with rooms and strips up to 7 m wide, excavated to the full thickness of the deposit. During the work, technological pillars with the basic geometry of 6–9 m × 8–16 m are separated and located with the axis perpendicular to the mining front line [24]. Figure 1 shows a scheme of the J-UG-PS mining system.

The geometry of the excavations analyzed in this study was determined based on two different cross-sections of the preparatory excavations driven around one of the mining fields located in the Legnica-Glogow Copper District, where ore was mined using the J-UG-PS system. The first cross-section runs through the ramps, the second through the entries. The geometrical data of the cross sections are presented in

Table 1. Geometric cross-section data.

Parameter	Value (m)
Excavation height	4.30
Excavation roof length	7.00

.

In the Legnica-Glogow Copper District mines, the headings have the characteristic shape of an inverted trapezoid. Figure 2 presents ca ross-section through an analyzed single heading; Figure 3 shows cross-sections through ramps and entries.

3.2. Geological Conditions and Rock Mass Parameters

The analysis was performed for representative rock layers occurring in the Legnica-Glogow Copper District mines. Two different rock layer systems were analyzed, the parameters of which are presented in

Table 2. Rock mass parameters for the excavation drilled in sandstone.

Rock Layers	Rock Layer Thickness (m)	Rock Layer Density (g/cm3)	Rock Layer Poisson Ratio (-)
Overburden	500	ρ = 2.70	v = 0.20
Anhydrite	250	ρ = 2.95	v = 0.25
Dolomite	100	ρ = 2.80	v = 0.25
Sandstone I	100	ρ = 2.40	v = 0.20
Sandstone II	50	ρ = 2.30	v = 0.15

and

Table 3. Rock mass parameters for the excavation drilled in dolomite.

Rock Layers	Rock Layer Thickness (m)	Rock Layer Density (g/cm3)	Rock Layer Poisson Ratio (-)
Overburden	500	ρ = 2.70	v = 0.20
Anhydrite	250	ρ = 2.95	v = 0.25
Dolomite	100	ρ = 2.80	v = 0.25
Dolomite	100	ρ = 2.80	v = 0.25
Dolomite	50	ρ = 2.80	v = 0.25

. The headings are located at a depth of 1000 m, respectively in sandstone (Table 2) and in dolomite (Table 3).

Numerical modelling was performed using the Examine2D 7.0 software, in the plane strain state. Numerical simulations were performed for an isotropic and for a homogenous medium. The rock medium was described with an elastic model. The parameters of the rock mass for numerical modeling were calculated using the Hoek–Brown classification. The Coulomb–Mohr strength criterion was adopted as a measure for assessing the rock mass effort [25]:

$${\sigma }_1={\sigma }_3·\frac{1+\sin \phi }{1-\sin \phi }+\frac{2c·\cos \phi }{1-\sin \phi },$$

(1)

where:

${\sigma }_1, {\sigma }_3$—maximum and minimum stress at failure;

$\phi$—angle of internal friction;

$c$—cohesion.

The cohesion and the angle of internal friction were calculated based on the Hoek–Brown classification from the formulas [26,27,28,29]:

$$c=\frac{{\sigma }_{ci}·\left[\left(1+2a\right)·s+\left(1-a\right)·m_b·\frac{{\sigma }_{3max}}{{\sigma }_{ci}}\right]·{\left(s+m_b·\frac{{\sigma }_{3max}}{{\sigma }_{ci}}\right)}^{a-1}}{\left(1+a\right)·\left(2+a\right)·\sqrt{1+\frac{6·a·m_b·{\left(s+m_b·\frac{{\sigma }_{3max}}{{\sigma }_{ci}}\right)}^{a-1}}{\left(1+a\right)·\left(2+a\right)}},},$$

(2)

$$\phi =\arcsin \left[\frac{6·a·m_b·{\left(s+m_b·\frac{{\sigma }_{3max}}{{\sigma }_{ci}}\right)}^{a-1}}{2·\left(1+a\right)·\left(2+a\right)+6·a·m_b·{\left(s+m_b·\frac{{\sigma }_{3max}}{{\sigma }_{ci}}\right)}^{a-1}}\right],$$

(3)

where:

$${\sigma }_{3max}=\frac{{\sigma }_{ci}}{4}.$$

(4)

Performing these calculations allowed determining the parameters then adopted as assumptions for numerical modeling in Examine2D 7.0. The calculated parameters are shown in

Table 4. The results of calculations based on the Coulomb–Mohr strength criterion.

Rock Type	h (m)	${\mathit{\sigma }}_{3\mathit{m}\mathit{a}\mathit{x}} \left(\mathbf{MPa}\right)$	σt (MPa)	c (MPa)	φ (o)
Sandstone	1000.0	3.75	−0.04	1.04	39.06
Dolomite	1000.0	37.50	−3.32	13.68	39.00

.

The numerical model was based on the values of primary stresses calculated according to the Therzagi formula, taking into account the weight of the overlying rock layers. The calculated vertical and horizontal stresses are included in

Table 5. Primary stresses.

Rock Type	Thickness h (m)	Unit Weight of Rock $\mathit{\gamma }$ (g/cm3)	Vertical Stress σz (MPa)	Horizontal Stress σx (MPa)
Sandstone	50.0	2.30	26.71	4.71
Dolomite	50.0	2.80	27.22	9.07

.

The numerical model was a plate where boundary contours were discretized. The plate edges were assumed to be at a 150.0 m distance from the extreme points on each side of the analyzed headings (the roof, the floor, and the side walls). Based on the numerical calculations of the headings’ stability for each model, the following parameters were determined:

-

Distribution of principal stresses σ₁;

-

Distribution of principal stresses σ₃;

-

Horizontal stress distribution σ_XX;

-

Vertical stress distribution σ_YY;

-

Total displacements;

-

Strength factor.

The analysis of the results indicated that the optimal measure of the stability of the headings is the range of the strength factor zone. The strength factor is calculated by dividing the rock strength (based on defined failure criteria) by the induced stress.

4. Discussion of Numerical Modeling Results

The distribution of the σ_YY stresses in the ramps and entries is shown in Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8. The conducted analysis showed that for both types of analyzed rock masses in which the excavations were established, the distribution of the σ_YY stresses in the vicinity of excavation was similar. Numerical simulations showed that the tensile stresses are concentrated in the roof and, to a lesser extent, in the bottom of the heading. Compressive stresses arise in the excavation’s ribs, particularly in the corners. σ_YY stresses between the excavations obtain values like the ones within the primary stress field, which proves the correct design of the protective pillars. The proper selection of the pillar sizes is conducive in terms of maintaining the stability of the headings located in their vicinity. In the cross-section of the ramps and entries, it is shown that σ_YY stresses acting on the protective pillars located between the ramps have a shorter range than the stresses acting on the protective pillars between the entries. In the central zone of the protective pillars located between the sandstone entries, the stresses are lower than in the case of dolomite pillars.

The location of roof stress measurement is presented in Figure 9. Graphs illustrating the dependence of distance to the excavation boundaries on the σ_YY values show that the tensile stresses acting on the heading roof in dolomite, having better strength and deformation parameters, reach slightly higher amounts than those occurring in sandstone (Figure 10).

The protective pillars’ stress measurement location is shown in Figure 11. The stress values affecting the external part of the protective pillar in cross-section through the entries are bigger than the ones acting on the internal part of the pillar. The stresses affecting the protective pillars located between the ramps have similar values on both sides of the pillar. The stresses’ distribution in the excavation ribs of the ramps and entries, drawn based on σ_YY distribution models in individual sections, prove that the compressive stresses reach similar values both in the internal and external ribs (Figure 12 and Figure 13), comparable for sandstone and dolomite.

The stability of the analyzed headings was assessed based on the numerically defined distributions of the strength factor. The strength factor is calculated by dividing the rock strength (based on the failure criteria) by the induced stress. The strength factor allows recognizing areas of potential rock mass instability, and its limit value is 1. Places where the index value falls below the limit are places of potential rock mass stability loss.

The strength factor value is related to the rock geomechanical parameter. The lower the strength and deformation parameters of the rock material in which the excavation is located, the greater the probability of losing the excavation stability is. A lower risk of instability occurs in the headings driven in dolomite and is greater in the headings created in sandstone (Figure 14).

Figure 15 and Figure 16 show close-up views of a single excavation with the extent of stability loss zone measured. The results of the strength factor distribution calculated using the numerical methods for headings located in sandstone show that the greatest risk of loss of stability occurs in the roof and floor of the excavation. The extent of the destruction zone is greater in the ribs than in the central part of the excavation, which may indicate the need to cover the area with longer bolts to protect the side fragments of the headings. As we move away from the boundaries, the strength factor reaches higher values, which is related to the rock mass returning to its primary stress field.

In the excavations driven in dolomite, being a material with high strength and deformation parameters, the risk associated with instability covers mainly the roof and floor of the excavation. The range of zones threatened by stability loss is greater within the roof and smaller within the floor, which is related to the intensification of the tensile stresses affecting the indicated heading fragments. In the immediate ribs’ vicinity, the strength factor values are higher than in the roof and floor area, but remain lower than 1. The extent of the zones at risk of instability is noticeably smaller for dolomite than for sandstones. Directly after the zones at risk of stability loss within the roof and floor of the excavation, there are zones with a very high strength factor. Most of the area analyzed in the numerical simulations is covered by safe values of the strength factor, indicating the ability to maintain the rock mass stability. Distribution of strength factor values in the cross-section through entries drilled in sandstone and dolomite is presented in Figure 17.

5. Conclusions

The performed numerical modeling confirmed the dependence of the heading stability on the strength parameters of the rock mass. Having a lesser impact on the values of stresses affecting the driven heading, different geomechanical parameters of the rock mass determine its stability, as well as the size of emerging displacements. Rock material displacements create heading deformation, being a direct symptom of stability loss, and increase the probability of sudden roof collapses or (under appropriate conditions) even dynamic stress relief phenomena. Detailed analysis of the strength and deformation parameters of the rock mass type and the strength factor distribution will allow the optimal selection of the excavations’ lining, creating less of a threat to miners’ health and lives.

Numerical methods allow a broad analysis of mining excavations’ stability. Accurate recognition of stresses affecting the excavation and modeling the effects of their impact enable the development of appropriate prevention methods and excavation conditions’ monitoring. Analysis of the models created for the needs of the article showed that having knowledge of the geomechanical parameters forming the rock mass is important in the context of ensuring safe and effective exploitation of copper ores in the conditions of the Legnica-Glogow Copper District. The results of the numerical modeling gave much crucial information about rock mass behavior in the vicinity of excavations. The innovativeness of the simulations performed is based on the possibility to predict the behavior of the rock mass in advance, without the need to perform labor-intensive and costly in situ experiments. This in turn allows the development of appropriate guidelines and new mining technologies designed to solve the problems of rock mass stability. Numerical modeling simulation results may enhance the deployment of the improved ongoing monitoring system of rock mass parameters, enabling the prediction of dynamic phenomena affecting the rocks. The future research will contain an analysis of the complex geological situation and different types of excavations located in Polish mines.