3.1. Characteristics of Research Area
The method of determining effective geomechanical method parameters for technological and residual pillars for numerical modeling using back-calculation based on the results of numerical simulations, measurement data, and statistical methods are presented in the example of one mining field (D-IE) in Polkowice-Sieroszowice underground copper mine. The Polkowice-Sieroszowice mine belongs to KGHM Polska Miedz SA. It is located in the south-western part of Poland and mines the copper ore deposit which covers the central part of a geological unit known as Sudetic Monocline. Sudetic Monocline falls gently towards the northeast. It is constructed of Permian and Triassic sediments, which have a base made from Proterozoic crystalline rocks and Carboniferous sedimentary rocks. The deposit occurs in Permian formations, contacted by a dolomite limestone series, red sandstone, and Lower Permian limestone. Shaped in the form of a pseudobed of variable thickness (from 0.4 to approx. 20 m) and low gradient (approx. 4°), it lies at great depth (from 600 to 1400 m). The copper ore deposit is formed by an accumulation of sulfides, mainly chalcocite, bornite, and chalcopyrite. Sulfide mineralization occurs at the contact of red sandstone and Permian limestone layers. It includes carbonate rocks (dolomites and limestones), copper-bearing shales in the bottom part of the Permian limestone, and white sandstones. The deposits of the Polkowice-Sieroszowice mine subject to ore mineralization are mainly carbonate rocks and shales. Mining of the deposit is performed using a variety of room and pillar systems, depending on geological and mining conditions in a given mining field [
29].
D-IE mining field was located in the mining area Sieroszowice I, in the Polkowice-Sieroszowice mine. It was a closing field explored since March 2005, where mining works were carried out in the vicinity of gobs. In February 2008, due to problems with maintaining roof stability, the remnant was left behind on the right side of the D-IE mining field (
Figure 2).
In the D-IE mining field, the deposit balance occurs in the lower part of a carbonate series of Permian limestones and the roof part of new red sandstone; it is comprised of grey quartz, fine-grained sandstone, loamy copper-bearing shale, and dolomite loamy shale, as well as streaked, dark grey, crypto-crystalline dolomite. The roof is made of rock layers, being part of a Permian limestone carbonate series, namely of calcareous dolomites with clear divisibility of bed (occurring in intervals of 0–2 m above the excavation roof), of concise calcareous dolomites with quite clear divisibility (occurring in intervals of 2–5 m above the excavation roof), and calcareous dolomites and dolomitic limestones with a bed structure (that occur in intervals of more than 5 m above the excavation roof). The carbonate series is directly covered by anhydrites. The direct floor is built of grey sandstones of red Permian sediment rock. These are fine-grained quartz sandstones with a loamy bond, carbonate-loam bond, and locally anhydrite bond (in the eastern part of the area). The roof part of the sandstones, due to the larger amount of carbonate bond, is harder and more concise. The deposit is oriented towards NW-SE and its decline (2–3°) towards NE. The rock formation has marginal tectonic sensitivity. The height of the mined deposit is 2.0–2.8 m.
Until 2008 mining of the deposit in the discussed area was conducted using a room and pillar system with roof deflection and closing pillar (J-UGR-PS), while in 2008 the closing pillar was liquidated, and further works were performed using a room and pillar system with roof deflection (J-UG-PS). Exploration using the room and pillar system consists in cutting the deposit with rooms and strips with 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 its work in the post-critical state. In the D-IE mining field, the cutting work was carried out using technological pillars situated perpendicular to the mining front, with basic dimensions of 6 × 8 m (J-UGR-PS and J-UG-PS). In the discussed mining systems, the height of excavation in the cutting phase depends on the thickness of the deposit and the requirements of working machines and is not more than 4.5 m. 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. In the D-IE mining field, the width of the opening was 4–5 strips. Along with the progress of the mining front, the technological pillars from the last row before gobs, depending on the degree of their disintegration, are adjusted or cleft into smaller ones. The resultant support pillars are adjusted to residual dimensions in elementary plots and then left in gobs. They work as supports to mitigate the deflection of roof layers. For D-IE field size of residual pillars left in the gobs amounted to approx. 5.2 m
2. In a room and pillar system with roof deflection and a closing pillar, the technological pillars are left in a separated part of the field, creating a gradually lengthening closing pillar. In one of the excavations of this pillar, a conveyor belt is assembled, which successively extends along with the progress of cutting. The width of a closing pillar depends on local geological and mining conditions and is generally 40–120 m [
39]. The work of mining systems J-UGR-PS and J-UG-PS are shown in
Figure 3 and
Figure 4.
3.2. Characteristics of Numerical Modeling
Numerical calculations were performed in a plane strain state by a computer program Phase2 v. 8.0 (Rocscience, Toronto, ON, Canada) [
43]. The computational model was a plate, which comprises the rock layers creating the rock mass (
Figure 5). Construction of the mass resulted from geological recognition conducted in the analyzed field. The upper edge of the model was loaded with vertical pressure, replacing the influence of overlaying rocks. It was assumed that at the upper edge of the plate the stress should be equal to 17.657 MPa, corresponding to the value of the vertical stress set out for the D-IE mining field on the basis of data from the borehole S-294. The calculations considered the deadweight of rock layers. Horizontal stress values were determined on the basis of Poisson’s ratio υ of a given rock layer. For the edges of the plate, the displacement edge conditions were assumed. At the lower edge of the model—lack of vertical displacements while at the side edges—no displacements in directions perpendicular to the surface of the edge. An applied grid of finite elements was composed of three nodal elements of triangular shape. In the central part of the plate, adjacent to the excavations, the grid was densified to improve the accuracy of numerical calculations.
The calculations were performed stepwise, simulating the mining carried out using a room and pillar system with parameters characteristic of an analyzed mining field (64 calculation steps). The first step covered the situation in the rock mass before the creation of mine excavations (
Figure 6a). The second step consisted of the cutting of undisturbed rock into technological pillars (8 m in width) (
Figure 6b). In the next steps, the size of the technological pillars was reduced to residual size (3 m width) and further technological pillars were cut out (
Figure 6c). Cutting of the deposit was carried out with strips having dimensions 6 m width under the roof. Numerical simulations considered the width of the working area opening consisting of 5 strips.
3.4. Determination of Effective Geomechanical Parameters for Technological and Residual Pillars by Numerical Modeling Using Back-Calculation Based on the Results of Numerical Simulations, Measurement Data and Statistical Methods
The parameters of the technological and residual pillars described by an elastic model were determined using the procedure presented in the article. On the basis of in-situ tests carried out in the ZG Polkowice-Sieroszowice mine in 2002–2007, the course of the excavation convergence in time was determined for room and pillar mining systems with roof deflection and closing pillar. The pattern convergence curve, which was adopted as a reference for numerical calculations performed for the D-IE field, is shown in
Figure 7. Each measurement of convergence made on a chosen test post was referred to as the mining step and the position of the working front line on a given day of measurement. This enabled the construction of a model that would fit the actual situation in the field and allow the determination of the effective geomechanical parameters of the technological and residual pillars.
The values of longitudinal elasticity modulus
E were determined for an elastic model, (the parameter having a decisive impact on the numerically calculated values of displacements). Depending on the distance from the face of the mining front, the degree of pillar disintegration is varied. In the first step, the pillars were divided into three groups. Three technological pillars (located close to undisturbed rock) were characterized by longitudinal elasticity modulus
E1, the other two technological pillars with modulus
E2, and the residual pillars with modulus
E3 (
Figure 8). It was assumed that
E1 =
E2 +
a. The following values of
E1, E2, and
E3 were adopted for the matrix of the numerical experiment:
E1 | E2 | E3 |
2000 MPa | 500 MPa | 100 MPa |
6000 MPa | 1500 MPa | 150 MPa |
10,000 MPa | 2500 MPa | 200 MPa |
27 numerical simulations were performed for all combinations of assumed values of Young’s modulus
E. The convergence of the selected excavation in subsequent steps of the executed mining for a few chosen cases is presented in
Figure 9.
Using the method of surface regression with Statistica v. 10 program, the quadratic function parameters of three variables were determined for selected points that are included in a non-linear regression model with dummy variables:
The values of
a,
E2, and
E3 calculated using Statistica v. 10 are shown in
Table 3.
Based on confidence intervals, statistical inference was performed to check whether E1 and E2 are significantly different from each other, namely if the added value of a is different from zero. The assumed level of significance α = 5%.
H0: a = 0
H1: a ≠ 0
The
a = 0 parameter is within 95% of the confidence interval, which indicates that there is no basis to reject the zero hypothesis H
0 (
Figure 10). Therefore, it cannot be stated that at the level of significance α = 5%
E1 ≠
E2. In addition, statistical inference based on test probability of
p-value (
p = 0.893210 > α = 0.05) also indicates that there is no basis to reject H0:
a = 0 hypothesis. In such a situation, it is assumed that
E1 =
E2 and the number of sought parameters of pillars was reduced to two. Technological pillars were characterized by longitudinal elasticity modulus E1, while residual pillars with longitudinal elasticity modulus
E2 (
Figure 11). It was assumed, that
E1 =
E2 +
a and the following values of
E1 and
E2 were applied to the matrix of the numerical experiment:
There were nine numerical simulations. Convergence in the selected excavation is shown in
Figure 12 in subsequent steps.
Using the method of surface regression with Statistica v. 10 program, the quadratic function parameters of two variables were determined for selected points that are included in the non-linear regression model with dummy variables:
The values of
a and
E2 were determined using Statistica v.10 presented in
Table 4.
Statistical inference carried out based on confidence intervals was performed to check whether E1 and E2 are significantly different from each other, namely if the added value of a is different from zero. The assumed level of confidence α = 5%.
H0: a = 0
H1: a ≠ 0
The parameter
a = 0 is located outside the 95% of confidence interval, which leads to rejection of zero hypothesis H
0 (
Figure 13). It can therefore be stated that at significance level α = 5%
E1 ≠
E2. Statistical inference based on test probability of
p-value (
p = 0.010470 < α = 0.05) also suggests rejection of hypothesis H
0:
a = 0.
The final values of
E1 and
E2 parameters determined using Statistica v.10 are shown in
Table 5.
On the basis of
p-values it can be concluded that
E1 and
E2 parameters are statistically significant (
E1: p = 0.0000364562557 < α = 0.05;
E2:
p = 0.0000000000119 < α = 0.05). The effective parameters of pillars
E1 = 311.355 MPa and
E2 = 136.931 MPa are also located in the space defined by the matrix of the numerical experiment. The resulting matching of theoretical values of convergence determined for specified pillar parameters, to in-situ results of convergence measurements is shown in
Figure 14.
Reduced values of elasticity modulus for technological and residual pillars were adopted for further numerical modeling of the geomechanical situation in the D-IE mining field. The final validation of the numerical models was based on the results of convergence measurements of excavations carried out in this field.