Numerical Methods as an Aid in the Selection of Roof Bolting Systems for Access Excavations Located at Different Depths in the LGCB Mines

Abstract

The values of primary stresses are not allowed for as a criterion in the selection of roof bolting systems in mining excavations located at various depths in Polish copper ore mines. Therefore, in order to ensure enduring and safe operation of excavations, in particular, those driven in unfavourable geological and mining conditions, this problem has required solutions based on numerical methods. This article presents an example of applying numerical simulations to the evaluation of the stability of headings in Polish copper ore mines. The analyses included mining excavations located at various depths in the rock mass. This issue is of great importance, as safety regulations are prioritised in mining excavations which remain in operation even for several decades. The stability of the headings was evaluated with the use of the RS2 specialist numerical simulation software. This computer program uses the finite element method (FEM) for calculations. The rock parameters used in the numerical models have been determined on the basis of the Hoek–Brown classification. For that purpose, the RocLab 1.0 software was used. The parameters of the stress field were identified from the profile of the GG-1 shaft with the assumed hydrostatic state of stress. The numerical modelling was performed in a triaxial stress state and in a plane strain state. The numerical analyses were based on the Mohr–Coulomb failure criterion. The rock medium was described with the elastic-plastic model with softening (roof and walls) and with the elastic-plastic model (floor). The results of the numerical analyses served to provide an example of the application of a roof bolting system to protect headings located at the depths of 1000 m b.g.l. and 1300 m b.g.l.

1. Introduction

The copper ore deposit mined in Poland by KGHM Polska Miedz S.A. is located in Lower Silesia, between the towns of Lubin and Glogow. The Legnica-Glogow Copper Belt (LGCB) comprises three underground mining plants: Lubin, Polkowice-Sieroszowice and Rudna. The copper-bearing rocks are located at a depth from approx. 370 m b.g.l. (in the Lubin-Malomice mining area) to 1385 m b.g.l. (in the Deep Glogow mining area) [1].

Roof bolting is the most commonly used roof support system in the mines of the LGCB region. The selection of a roof bolt system is preceded by identifying the roof class of a mining excavation (from class 1—the worst—to class 5—the best) in accordance with the “Instructions on determining the geomechanical parameters of roof rocks with respect to roof classes in copper mines, as required in the selection of a roof bolting system design” [2]. Roof rocks are classified on the basis of such parameters as:

• Roof bedding (vertical split);
• Concentration of mineralised cracks;
• Fault concentration;
• Average fault throw;
• Tensile strength of the roof rock beam.

A particular design of the roof bolting system is selected in accordance with the “Regulations on the selection, construction and control of excavation support in the KGHM Polska Miedz S.A. mines” [3]. The roofs in the headings are protected with bolts at least 1.6 m long. The distance between the bolts (the bolting mesh) is adjusted depending on the class of the roof and on the width of the heading below the roof (

Table 1. Selection of a roof bolting system for headings in the LGCB mines [3].

Roof Class	Maximum Excavation Width [m]	Bolting Mesh [m]
I	6.0	1.0 × 1.0
II	7.0	1.0 × 1.0
III	7.0	1.5 × 1.5
IV	7.0	2.0 × 2.0
V	8.0	2.0 × 2.0

).

Support is provided not only to the roof but also to the side walls of the heading in cases where the excavation height is greater than 4.5 m (regardless of the side wall inclination angle) or where the excavation height is not greater than 4.5 m and moving the side walls outwards by approximately 10° is not possible. The roof bolts have a length of at least 1.6 m and are spaced in the side walls at 1.5 × 1.5 m. The lower row of roof bolts is situated at a distance of approximately 1.8 m from the floor [3,4].

The regulations on the selection of roof support systems for the headings and production excavations in the LGCB mines do not allow for the values of primary stresses in the rock mass at the depth of the excavations. As a result, the roof support system may be inappropriately selected and lead to problems with the stability and functionality of the excavations. This fact may be of particular importance in the case of headings (both access and preparatory excavations) which have transport or ventilation functions. Their functionality must be ensured over a time spanning from several years to over a decade.

In recent years, owing to the increase in computing power, numerical methods have become a common tool in solving various problems related to rock mass mechanics. The advantage of such methods lies in their ability to analyse objects of practically any geometry, allowing for different models describing the behaviour of the material under load, spatial changes in rock mass properties, specific field of primary stresses, dynamic loads, etc. They also provide solutions to both two-dimensional and three-dimensional tasks [5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Currently, the most popular numerical calculation methods employed in solving problems related to rock mass mechanics include the finite element method (e.g., PHASE2, RS2, RS3, NASTRAN, ANSYS, MIDAS GTS NX) and the finite difference method (e.g., FLAC software). Other methods include the boundary element method (e.g., EXAMINE) or the distinct element method (e.g., UDEC).

Numerical methods have significantly expanded research possibilities related to the analysis and evaluation of the stability of excavations in underground mines. They are frequently used, both in Poland and abroad, to solve problems related to driving excavations in underground mines in varying or difficult geological and mining conditions [19,20,21,22,23,24,25,26,27,28,29,30]. Numerical modelling allows predictions of the stress concentration zones and the potential locations in which the rock mass may become unstable in the vicinity of a mining excavation. The results of numerical simulations are used to plan and design inter alia access, preparatory, production, and other special-purpose excavations of various shapes and dimensions, as well as to aid the selection of adequate support systems [31,32,33,34,35,36,37,38].

2. Predictions of the Stability of Headings in the LGCB Mines

The decrease or the loss of stability in headings located at different depths (1000 m b.g.l. and 1300 m b.g.l.) in one of the LGCB mines were modelled with the use of numerical simulations. The numerical calculations were performed in the RS2 software, which is based on the finite element method (FEM), i.e., one of the most popular numerical methods.

Table 2. Mean strength and strain rock parameters for the Jm-15/H-173 borehole and the Jm-15-460 borehole.

Location	Rock Type	h [m]	ρ [MPa]	Rc [MPa]	Rr [MPa]	Ei [MPa]	ν [-]
Roof	Anhydrite I	0.70	2.94	132.49	6.43	42,420.00	0.24
	Anhydrite II	1.80	2.94	117.61	5.25	38,240.00	0.24
	Anhydrite III	3.00	2.94	97.88	5.58	40,600.00	0.24
	Anhydrite IV	9.30	2.94	86.93	5.94	38,300.00	0.24
	Dolomite I	1.20	2.81	175.86	7.20	68,400.00	0.26
	Dolomite II	1.70	2.79	156.21	8.03	47,290.00	0.25
	Dolomite III	0.60	2.63	194.22	10.05	89,800.00	0.27
	Dolomite IV	0.70	2.64	186.60	8.98	82,050.00	0.28
	Dolomite V	1.00	2.70	165.69	4.55	65,050.00	0.24
	Dolomite VI	0.70	2.73	126.89	9.59	23,400.00	0.22
	Dolomite VII	0.60	2.65	188.90	10.87	84,400.00	0.27
	Dolomite VIII	0.70	2.80	118.44	5.45	39,150.00	0.23
	Dolomite IX	1.60	2.71	95.00	10.16	27,170.00	0.22
Walls	Dolomitic shale	0.60	2.69	111.49	9.06	28,890.00	0.23
	Sandstone I	1.20	2.40	47.85	2.93	16,940.00	0.17
Floor	Sandstone II	9.50	2.33	36.19	2.78	13,600.00	0.14

The symbols used in the above table are as follows: h—thickness of rock layers, ρ—volume density, R_c—rock sample strength to uniaxial compression, R_r—tensile strength of the rock sample, E_i—longitudinal modulus of elasticity, v—Poisson’s ratio.

lists rock parameters used in the numerical simulations of the stability of headings in the conditions of one of the LGCB mines. The parameters were determined from geomechanical tests of rock samples. The rock samples for the laboratory tests were obtained from two boreholes: Jm-15/H-173 (rock layers in the roof and in the floor) and Jm-15-460 (rock layers in the walls). The rock parameters obtained from the Jm-15/H-173 and Jm-15-460 boreholes show the typical geological structure of the Fore Sudetic Monocline. In this structure, the access and preparatory excavations of the LGCB mines are driven. The immediate roof layers contain very strong carbonate formations (calcareous dolomite), as opposed to the rock layers which form the mined deposit and the floor layers.

Subsequently, the Hoek–Brown failure criterion, which is broadly used in geomechanical analyses of rock mass deformations and effort, was assumed for the rock mass. The generalised Hoek–Brown failure criterion for a fractured rock mass may be described with the following equation [39]:

$${\sigma }_1={\sigma }_3+{\sigma }_{ci}·{\left(m_b·{\displaystyle \frac{{\sigma }_3}{{\sigma }_{ci}}}+s\right)}^a$$

(1)

where:

• σ₁—value of the maximum principal effective stress at failure,
• σ₃—value of the minimum principal effective stress at failure,
• m_b—the Hoek–Brown constant for the rock mass,
• s and a—constants depending on the rock mass properties,
• σ_ci—uniaxial compressive strength of the rock sample.

When rock mass tensile strength σ_tm is exceeded, the equation for a = 0.5 can be formulated as follows:

$${\sigma }_{tm}={\displaystyle \frac{{\sigma }_{ci}}{2}}·\left(m_b-\sqrt{{m_b}^2+4s}\right)$$

(2)

After the failure criterion had been assumed, the RocLab 1.0 software and Hoek–Brown classification [39,40,41,42] were used to determine the rock mass parameters (strength and strain parameters) for each of the rock layers present in the Jm-15/H-173 and Jm-15-460 boreholes (

Table 3. Rock mass parameters determined with the RocLab 1.0 software—the Jm-15/H-173 borehole and the Jm-15-460 borehole.

Location	Rock Type	c [MPa]	φ [°]	σt [MPa]	Erm [MPa]
Roof	Anhydrite I	9.914	38.66	1.061	31,085.97
	Anhydrite II	8.801	38.66	0.942	28,022.81
	Anhydrite III	7.324	38.66	0.784	29,752.25
	Anhydrite IV	6.505	38.66	0.696	28,066.78
	Dolomite I	16.040	39.00	3.893	60,215.79
	Dolomite II	14.248	39.00	3.458	41,631.65
	Dolomite III	17.715	39.00	4.299	79,055.23
	Dolomite IV	17.020	39.00	4.131	72,232.54
	Dolomite V	15.113	39.00	3.668	57,266.63
	Dolomite VI	11.574	39.00	2.809	20,600.14
	Dolomite VII	17.229	39.00	4.182	74,301.36
	Dolomite VIII	10.803	39.00	2.622	34,465.62
	Dolomite IX	7.579	37.69	1.442	22,180.23
Walls	Dolomitic shale	6.447	30.41	1.327	18,250.37
	Sandstone I	3.589	40.54	0.180	10,701.33
Floor	Sandstone II	2.520	39.06	0.093	7072.00

The symbols used in the above table are as follows: c—cohesion, φ—internal friction angle, σ_t—uniaxial tensile strength of the rock mass, E_rm—rock mass modulus of elasticity.

).

The numerical model was constructed in the RS2 application, in a triaxial stress state and in a plane strain state. Numerical calculations were performed for an isotropic and for a uniform medium. The rock medium was described with the elastic-plastic model with softening (layers in the roof and walls) and with the elastic-plastic model (layers in the floor). Table 4 shows the strength and strain parameters of the rocks in the model. The numerical model was developed on the basis of the Mohr–Coulomb failure criterion, which states that rock may reach threshold effort under the following condition:

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

(3)

or

$${\sigma }_3=-{\sigma }_t$$

(4)

where:

• σ₁—effective maximum stress at failure,
• σ₃—effective minimum stress at failure,
• φ—internal friction angle,
• c—cohesion,
• σ_t—uniaxial tensile strength of the rock mass.

Table 4. Rock mass parameters adopted for the numerical modelling in the elastic-plastic medium with softening (the roof and the walls) and in the elastic-plastic medium (the floor), for the Coulomb–Mohr criterion.

Location	Rock Type	h [m]	Es [MPa]	ν [-]	σt [MPa]	φ [°]	c [MPa]	δ [°]	φres [°]	cres [MPa]
	Anhydrite I-III	5.50	29,356.00	0.24	0.871	38.66	8.137	2.00	36.73	1.627
Roof	Anhydrite IV	9.30	28,066.78	0.24	0.696	38.66	6.505	2.00	36.73	1.301
	Dolomite I-VIII	7.20	52,975.30	0.25	3.611	39.00	14.879	2.00	37.05	2.976
Walls	Dolomite—shale—sandstone formations	3.50	17,435.35	0.20	0.976	37.41	5.971	2.00	35.54	1.194
Floor	Sandstone	9.50	7072.00	0.14	0.093	39.06	2.520	2.00	39.06	2.520

The symbols used in the above table are as follows: h—thickness of rock layers, E_s—longitudinal modulus of elasticity, v—Poisson’s ratio, σ_t—tensile strength of the rock mass, φ—internal friction angle, c—cohesion coefficient, δ—dilatancy angle, ϕ_res—residual internal friction angle, c_res—residual cohesion coefficient.

Table 4. Rock mass parameters adopted for the numerical modelling in the elastic-plastic medium with softening (the roof and the walls) and in the elastic-plastic medium (the floor), for the Coulomb–Mohr criterion.

Location	Rock Type	h [m]	Es [MPa]	ν [-]	σt [MPa]	φ [°]	c [MPa]	δ [°]	φres [°]	cres [MPa]
	Anhydrite I-III	5.50	29,356.00	0.24	0.871	38.66	8.137	2.00	36.73	1.627
Roof	Anhydrite IV	9.30	28,066.78	0.24	0.696	38.66	6.505	2.00	36.73	1.301
	Dolomite I-VIII	7.20	52,975.30	0.25	3.611	39.00	14.879	2.00	37.05	2.976
Walls	Dolomite—shale—sandstone formations	3.50	17,435.35	0.20	0.976	37.41	5.971	2.00	35.54	1.194
Floor	Sandstone	9.50	7072.00	0.14	0.093	39.06	2.520	2.00	39.06	2.520

The symbols used in the above table are as follows: h—thickness of rock layers, E_s—longitudinal modulus of elasticity, v—Poisson’s ratio, σ_t—tensile strength of the rock mass, φ—internal friction angle, c—cohesion coefficient, δ—dilatancy angle, ϕ_res—residual internal friction angle, c_res—residual cohesion coefficient.

Numerical analyses were performed for a group of four headings. The excavations have a trapezoidal shape. In the headings, the side walls were inclined at an angle of 10°. The adjacent excavations are separated by pillars 20 m in width.

Table 5. Dimensions of the analysed headings.

Excavation Height hw [m]	Excavation Width Below the Roof dr [m]	Excavation Width at the Floor df [m]	Mean Excavation Width da [m]	Excavation Surface Area Sr [m2]
3.50	7.00	5.80	6.40	22.40

lists the dimensions of headings in their assumed cross-sections. The headings were protected with full-length-grouted rockbolts in a 1.5 m × 1.5 m bolting grid (Figure 1). The parameters of the employed RM-18 1.8 m long bolts are shown in

Table 6. Parameters of the RM-18 grouted rockbolts [43].

Parameter	Value
Bar diameter [mm]	18.2
Bar length [m]	1.8
Bar material	steel
Young’s modulus [MPa]	210,000.0
Real load-capacity [kN]	170.0
Residual load-capacity [kN]	17.0
Pretension [kN]	30.0

.

The stress values were identified from the GG-1 shaft profile as per PN-G-05016:1997 [44]. The calculations included the porosity and water-logging of the rock layers. Table 7 shows the calculated primary stress values for two heading depths: 1000 m b.g.l. and 1300 m b.g.l. Owing to the deposit depth, the hydrostatic state of stress was assumed in the numerical models:

$${\sigma }_z={\sigma }_x={\sigma }_y,$$

(5)

where:

• σ_z—vertical stresses,
• σ_x and σ_y—horizontal stresses.

Table 7. Primary stresses for two depths in the LGCB mines.

Depth H [m]	Vertical Stresses σz [MPa]	Horizontal Stresses σx [MPa]	Horizontal Stresses σy [MPa]
1000	22.11	22.11	22.11
1300	30.12	30.12	30.12

Table 7. Primary stresses for two depths in the LGCB mines.

Depth H [m]	Vertical Stresses σz [MPa]	Horizontal Stresses σx [MPa]	Horizontal Stresses σy [MPa]
1000	22.11	22.11	22.11
1300	30.12	30.12	30.12

Two variants of loads acting on the group of headings were assumed for the numerical calculations. The flat, rectangular plate with openings shaped to correspond to the shapes of the analysed excavations located inside was assumed to be loaded on its edges:

• Load variant 1 (heading depth H = 1000 m b.g.l.):

  –

  side edges: p_x = 22.11 MPa;

  –

  upper edge and bottom edge: p_z = 22.11 MPa;

  –

  direction perpendicular to plate surface: p_y = 22.11 MPa.

• Load variant 2 (heading depth H = 1300 m b.g.l.):

  –

  side edges: p_x = 30.12 MPa;

  –

  upper edge and bottom edge: p_z = 30.12 MPa;

  –

  direction perpendicular to plate surface: p_y = 30.12 MPa.

The edges of the analysed plate were provided with supports which do not slide either in the vertical or in the horizontal direction. The numerical modelling employed finite elements having three nodes and a triangular shape. The plate edges were assumed to be at a 100 m distance from the extreme points on each side of the analysed excavations (the roof, the floor and the side walls). In all numerical models, the plate was 288.0 m × 203.5 m. Owing to the assumed dimensions of the plate, its edges (pillars) were not located excessively close to the excavations and thus had no influence on the results of calculations of the area of the excavations. In order to increase the accuracy of numerical calculations, smaller-size finite elements were used in the middle of the plate, in the area where the headings were driven (region of dense finite elements) (Figure 2). In each numerical model, the calculations were performed in two steps:

• Step 1: original state of the rock mass (no mining excavations present in the analysed plate);
• Step 2: state with the excavations present (four mining excavations present in the rock mass).

In the numerical simulations, it was assumed that the optimal measure of heading stability is the range of the yielded rock mass zone in the roof of the heading.

3. Modelling Results

The numerical modelling of the stability of headings located at different depths in the rock mass (1000 m b.g.l. and 1300 m b.g.l.) in the geological and mining conditions assumed for the LGCB mines confirmed the results in a three-stage work: “Regulations on the selection of support systems for special-purpose room excavations in copper ore mines—Stage 1, Stage 2 and Stage 3” [45,46,47]. The numerical simulations also demonstrated that:

• The maximum range of the yielded rock mass (from 50% to 100%) in the roof (

  Table 8. Yielded rock mass range in the roofs of the analysed excavations (yield between 50% and 100%).

  Excavation	Yield Range in the Roof [m]		Increase in Yield Range in the Roof
  	Load Variant 1	Load Variant 2	[m]	[%]
  1	1.42	2.15	0.73	51.41
  2	1.35	2.33	0.98	72.59
  3	1.36	2.27	0.91	66.91
  4	1.54	1.97	0.43	27.92

  ) of the headings located at the depth of 1000 m b.g.l. (load variant 1) was from 1.35 m to 1.54 m (Figure 3 and Figure 4). For comparison, the maximum range of the yielded rock mass (from 50% to 100%) in the roof of the headings located at the depth of 1300 m b.g.l. (load variant 2) was from 1.97 m to 2.33 m (Figure 5 and Figure 6). A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. has thus caused the range of the yielded rock mass in the heading roof to increase from 0.43 m (heading 4) to 0.98 m (heading 2). The maximum range of the yielded rock mass in the roofs of all headings was greater than the 1.8 m range of the bolted zone. This fact indicates that in the LGCB mines, the heading depth in the rock mass may have a decisive impact on its stability. Problems with heading stability may occur when the yielded rock zone in the roof is larger than the bolted zone.
• The surface of the yielded rock area around a group of headings increases together with an increase in the excavation depth (increase in primary stress in the rock mass); this phenomenon negatively influences the stability of mining excavations and is strictly related to the stress and strain parameters of the rock layers surrounding the excavations.
• The maximum range of the yielded rock mass (from 50% to 100%) in the walls (

  Table 9. Yielded rock mass range in the walls of the analysed excavations (yield between 50% and 100%).

  Excavation	Yield Range in the Wall [m]		Increase in Yield Range in the Wall
  	Load Variant 1	Load Variant 2	[m]	[%]
  1 (left wall)	2.83	3.45	0.62	21.91
  1 (right wall)	2.79	3.26	0.47	16.85
  2 (left wall)	2.87	3.47	0.60	20.91
  2 (right wall)	2.69	3.23	0.54	20.07
  3 (left wall)	2.89	3.32	0.43	14.88
  3 (right wall)	2.78	3.24	0.46	16.55
  4 (left wall)	3.02	3.34	0.32	10.60
  4 (right wall)	2.73	3.25	0.52	19.05

  ) of the headings located at the depth of 1000 m b.g.l. was from 2.69 m to 3.02 m (Figure 3 and Figure 4). For comparison, the maximum range of the yielded rock mass (from 50% to 100%) in the walls of the headings located at the depth of 1300 m b.g.l. was from 3.23 m to 3.47 m (Figure 5 and Figure 6). A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. has thus caused the range of the yielded rock mass in the walls to increase from 0.32 m (heading 4, left wall) to 0.62 m (heading 1, left wall).
• A more complex formation mechanism of yielded rock mass was observed in the floors of the excavations. A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. has caused the vertical range of the yielded rock mass in the floors to increase only to a limited degree in comparison to the change in the horizontal range. The maximum vertical range of the yielded rock mass (from 50% to 100%) in the floors of the headings (

  Table 10. Yielded rock mass range in the floors of the analysed excavations (yield between 50% and 100%).

  Excavation	Yield Range in the Floor [m]		Increase in Yield Range in the Floor
  	Load Variant 1	Load Variant 2	[m]	[%]
  1	2.54	2.92	0.38	14.96
  2	2.58	2.97	0.39	15.12
  3	2.53	3.13	0.60	23.72
  4	2.58	2.96	0.38	14.73

  ) was from 2.53 m to 2.58 m (for the depth of 1000 m b.g.l.) and from 2.92 m to 3.13 m (for the depth of 1300 m b.g.l.) A change in the heading depth caused the vertical range of the yielded rock mass to increase from 0.38 m (heading 1 and heading 4) to 0.60 m (heading 3).
• The horizontal ranges of the yielded rock mass in the floors changed more significantly due to the change in the heading depth (

  Table 11. Horizontal range of yielded rock mass in the floors of the analysed excavations (yield between 50% and 100%).

  Excavation	Horizontal Range of Yielded Rock Mass in the Floor [m]		Increase in Horizontal Yield Range in the Floor
  	Load Variant 1	Load Variant 2	[m]	[%]
  1	5.80	9.52	3.72	64.14
  2	5.80	10.25	4.45	76.72
  3	5.80	9.98	4.18	72.07
  4	5.80	9.71	3.91	67.41

  ). The maximum horizontal range of the yielded rock mass (from 50% to 100%) in the floors of the headings located at the depth of 1000 m b.g.l. was 5.80 m and was equal to the width of the heading at the floor. In the headings located at the depth of 1300 m b.g.l., the horizontal range of the yielded rock mass in the floors increased significantly and was from 9.52 m to 10.25 m. A change in the heading depth has thus caused the horizontal range of the yielded rock mass to increase from 3.72 m (heading 1) to 4.45 m (heading 2).
• The results of the numerical analyses obtained for the plastic-elastic model with rock softening correspond best to the observed cases of stability loss in the mining excavations in the LGBC mines.

4. Discussion

The numerical simulations allowed an optimal selection of the roof bolting design for headings driven at different depths in the rock mass in the conditions of the LGCB mines. For safety reasons, the simulations were based on an assumption that the bolted zone in the roof must be larger by at least 0.25 m than the maximum range of the yielded zone (yield from 50% to 100%). In the case of the headings driven at the depth of 1000 m b.g.l., the selection of 1.8 m long RM-18 grouted bolts in the 1.5 × 1.5 m grid (bolt distance) was proven correct. However, in the case of headings driven at 1300 m b.g.l., the range of the bolting zone should be increased. The selected bolts were 2.6 m long RM-18 grouted bolts in the 1.5 × 1.5 m grid (bolt distance).

The analysis of the results of numerical simulations also confirmed that a change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. caused the range of the yielded rock mass in the walls to increase. In actual mining conditions, the stability of the walls may be thus compromised. Observations in the LGCB mines indicate that in such cases, the walls may be effectively reinforced with the use of bolts not shorter than 1.6 m and installed in the 1.5 m × 1.5 m bolting grid (bolt spacing), with the bottom row of the bolts situated at a distance approximately 1.8 m from the floor. In justified cases, the walls may be reinforced with so-called deep bolts (longer than 2.6 m), e.g., cable bolts.

A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. caused a limited increase in the vertical range and a significant increase in the horizontal range of the yielded rock mass in the floors. In situ observations in the LGCB mines indicate that in the case of deep headings (located more than 1000 m b.g.l.), the floor is uplifted more frequently than in the case of headings located at smaller depths. This phenomenon is also influenced by the low values of strength and deformation parameters of sandstones present in the floors of the headings.

In situ studies performed in the LGCB mines confirm that in the geological and mining conditions of the Polish copper ore mines, the stability of the heading is affected by its depth in the rock mass. In some cases, a loss of stability was observed for headings which were driven in similar geological and mining conditions but at different depths in the rock mass. The roof support system was, in these cases, selected in accordance with the binding regulations in the LGCB mines [3]. However, the regulations do not allow for the depth of the excavation in the rock mass and, thus, for the level of primary stresses in the mined rock mass.

Numerical modelling confirms that the stability of the heading is strictly related to its depth and, thus, to the level of primary stresses in the rock mass. Therefore, the regulations on the selection of roof bolting systems in the LGCB mines seem to require verification based on the results of numerical simulations, and a criterion should be added which would account for the depth of the heading in the selection process of such a roof bolting system.

The stability of the heading is also affected by its shape, height and width, as well as by the strength and strain parameters of the rocks around it. These parameters should be taken into consideration when selecting a roof support system for headings driven in the difficult geological and mining conditions of the LGCB mines.

Increased computing power and improved specialist software has allowed mining excavations and their roof support systems to be designed with the use of numerical methods. They enable broad and extensive analyses of heading stability in any geological and mining conditions. The results of such numerical analyses should be verified for correctness with the help of in situ observations of the stability of mining excavations in the LGCB mines.