Mining exploitation influence range
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Abstract
Mining exploitation has a negative impact on the natural environment. Voids created in the rockmass result in displacements and deformations of land surface. During planning and conducting the exploitation, the range of exploitation influence in the form of linear deformations is being determined. On the basis of mininggeological parameters of exploitation, the exploitation range of influences is calculated. According to the literature, many different ranges of exploitation influences can be determined depending on what has been the purpose of it. Different types of exploitation influence ranges can be distinguished, such as theoretical, damage or measurable. In the paper, the matters connected with determining those three types of the influence range are taken under consideration. The comparison of magnitudes of determined influence ranges is illustrated with two practical examples.
Keywords
Deformation measurements Deformation prediction Mining damage1 Introduction
The mining exploitation is causing the occurrence of voids in the rockmass. The void, moving towards the land surface, results in the occurrence of linear deformations—subsidence as well as nonlinear ones—e.g., craters, cracks (Lee and Abel 1983). Due to the fact that the mining exploitation is conducted on a big area and for a long time, it is challenging to monitor exploitation effects as well as to determine its influence range (Peng 1986; Sroka et al. 2011).
The term ‘mining exploitation influence range’ is not easily and unambiguously definable one. This issue can be treated as the philosophical one. In the literature on the one hand, there are many different definitions of exploitation influence range (Darling 2011; Sinclair Knight Merz Pty Ltd. 2014); on the other hand, the determination of fixed range borders seems to be questionable. If dynamical influences are taken into account (paraseismic mining shakings of the ground, rock bursts), the effects of such a phenomenon could be registered tens of kilometres from the epicentre, where no other influences are not registered.
 1.
The theoretical (model) influence range r_{t}
 2.
The damage influence range r_{d}
 3.
The measurable influence range r_{m}
According to some of modelling theories, the range of linear deformations is neverending just like the probability in accordance with the normal distribution theory. On the basis of the most popular theories of deformations forecasting (geometricintegral theories), the border of theoretical range of exploitation linear deformations influences can be determined. In accordance with the Budryk–Knothe theory (Knothe 1984; Kratzsch 1983), one of the parameters is the angle of the main influences range, what has an impact on the radius of the main influences range, but this parameter is not directly the theoretical influence range (r_{t}).
The mining exploitation has a negative impact on the natural environment. The exploitation is a threat to the safety of people and objects located within its influence range. The construction works specialists determine the resistance of buildings to mining exploitation influence on the basis of states of the bearing capacity and of the serviceability. Those border states determine the state of object’s deformation and possibility of its usage. From this point of view, it is crucial to determine the harmfulness of the exploitation influence for construction objects. Therefore, the next border value can be determined, which is the damage influence range (r_{d}).
Significantly different is the approach of the land surveyors to this issue. When measuring on the land surface the results of ongoing mining exploitation, they highlight limitations of accuracy of conducted measurements of displacements and deformations. From this point of view, a deformation or a displacement is registered only when the magnitude of this parameter is higher than the error occurring during its determination, this is that the displacement is significant from the measuring point of view or it can be treated as the measurement error. In this situation, there can be distinguished the measurable influence range (r_{m}).
In the paper, there is presented the analysis of rules for determining the mining exploitation influence range in accordance with theoretical considerations. There is also suggested the definition of a theoretical influence range.
2 Theoretical models
The theoretical models, which are used to forecast deformations caused by the underground mining exploitation, allow to determine the spatial distribution of deformations caused by the underground mining exploitation. In the literature, different theoretical solutions based on different foundations can be found (Chugh et al. 1989; Darling 2011). Those models are using the group of parameters which allow to connect mininggeological conditions of the exploitation with deformations caused by this exploitation (Ambrožič and Turk 2003). Among many other theoretical solutions, the geometricintegral methods are the most popular in Europe and two of such models are used in the paper.
2.1 Knothe’s theory
This theory is a basic solution that is being used in Polish mining (Knothe 1984). This is due to the fact that with this theory the results of calculations are highly accurate in comparison with the measurements, and still this theory remains very simple and the physical meaning has been given to the parameters of this theory (Hejmanowski and Malinowska 2009). The theory is used to forecast deformations caused by the underground exploitation of different useful minerals (Hejmanowski 1993). Currently, this model functions accurately enough for mining practice aims in many different variants of computer software.
In the Knothe’s theory, as it can be seen above, a radius of the main influence range is unambiguously defined. On the other hand, an angle of the main influence range (β) is one of two basic parameters of the Knothe’s theory. An angle of the main influence range is connected with physical–mechanical properties of the rock mass, and it allows to describe in the very simple way really complex structure and properties of the rock mass. A radius of the main influence radius is linearly related to the depth of exploitation. As a result of the parameterisation of the Gauss function, the influence reaches further than the magnitude of radius of the main influence range. In many publications, the extent of the influence range angle on the basis of the Knothe’s theory has been indicated for different geological layers in Poland. As an example for the bituminous coal exploitation in Upper Silesian Coal Basin (Polish: Górnośląskie Zagłębie Węglowe—GZW), this parameter can be assumed to have a value of 67.6 grad. A maximum final subsidence that is present in Eq. (3) also depends on one of the parameters, which is the way in which the afterexploitation void has been filled as well as the introduced methods of exploitation. Regarding the Polish mining in GZW for the longwall exploitation, this parameter is being calculated between 0.7 and 0.9 (on average 0.8). What has to be taken into account is the fact that the parameters for certain conditions of conducting the exploitation are the most accurately calculated on the basis the empirical data (conducted exploitation supervised with geodetic measurements). When the dependency (3) is put into Eq. (1), vertical displacements can be determined and afterwards the rest of deformation indicators can also be determined. The theory is simple, but to receive accurate results, it is needed to have some experience in calculating as well as to have the set of parameters adequate to conditions of conducted exploitation (Kwinta 2011).
2.2 Ruhrkohle’s theory
In the Ruhrkohl’s theory similarly to the Knothe’s theory, the Aviershin’s formula can be used to determine the indicators in the horizontal plane.
3 Theoretical influence range
With those assumptions, the magnitude of the theoretical influence range can be determined for underground mining exploitation.
Magnitudes of variability coefficients of indicators in the function of the distance from the verge of exploitation in the Knothe’s and the Ruhrkohle’s theories
η_{K,R}  δ_{S} (%)  δ_{T_U} (%)  δ_{K_E} (%) 

1.0  0.61  4.32  17.86 
1.1  0.29  2.23  10.16 
1.2  0.13  1.08  5.38 
1.3  0.06  0.49  2.66 
1.4  0.02  0.21  1.23 
1.5  0.01  0.09  0.53 
1.6  0.00  0.03  0.21 
1.7  0.00  0.01  0.08 
1.8  0.00  0.00  0.03 
1.9  0.00  0.00  0.01 
2.0  0.00  0.00  0.00 
As it can be seen in Fig. 4 and in Table 1 for the distance from the exploitation levelling with the radius of the main influence range, the magnitudes of indicators can be significant. For subsidences, this indicator equals about 0.6% of the maximum value; for gradients of subsidence profile and horizontal displacements, the magnitude of the variability indicator equals about 4% of the maximum value; and for the curvatures of the subsidence profile and horizontal deformations, the variability coefficient equals about 18% of the maximum magnitude of those indicators. Obviously the relative magnitudes depend to large extend on the intensity of the exploitation. For exploitations which causes big magnitudes of deformations indicators, within the distance of the main influence radius the magnitudes of deformations indicators can be significant. In general, for practical solutions it can be assumed with appropriate accuracy that the influence range in accordance with both the Knothe’s and the Ruhrkohle’s theories equals 1.5 of the radius of the main influence range in that particular theory.
4 The damage influence range
This formula picks the biggest influence range from all deformations indicators which are taken into consideration.
In order to determine the distance from the exploitation in which the damage influences occur, the theories presented in the previous part of the paper are being used. As previously, the flat state of deformations (Fig. 3) is taken into considerations. In this case, the formulas to calculate the distance from the edge of the exploitation to the place where border deformations values occur can be formulated.
Unfortunately the simple transformation is not possible with regard to the curvature and displacement radius, and the determination of the damage influence radius is connected with conducting iterative calculations.
In this equation, x_{0} is the approximate magnitude of the damage influence range and in next iteration steps the magnitude used for calculations is the one computed in the previous iteration step. As the initial magnitude for this variable, the radius of the main influence range in the theory r_{K} is adopted.
In this case, as the initial magnitude x_{0}, the radius of the main influence range r_{R} is also adopted.
Using the above formulas, the damage influence range can be determined, when the basic geometric parameters of the exploitation, the exploitation system and the parameters of the calculations model are known.
5 The measurable influence range
The last analysed type of the influence range is the measurable influence type that is the distance from edge of the exploitation to the place where deformations indicators can be determined on the basis of the conducted geodetic measurements (Darling 2011; Kratzsch 1983; Unlu et al. 2013).
Primarily the states of the deformation process had been characterised only descriptively. Along with the development of the geodetic instruments and of the calculations methods, more and more modern geodetic methods of measurements were used. One of the most important developments was the introduction of the digital rangefinder, which allowed to obtain more accurate measurements results. Next significant improvement in the measurements methods was the usage of the GPS satellite system (Liu et al. 2012). The emergence of the GNSS satellite systems (Havasi 2012) has allowed to obtain the results of completely new quality along with limiting the time consumption and the costs of conducting the observations (lack of the need of the longtime reference of measurements to fixed points). The development of the satellite technologies, particularly of the spacebased radars, causes the next approach revolution in the area of measuring the deformations on the land surface. It has become possible to determine even small deformation magnitudes for huge areas. Therefore, the SAR technology is going to be used more and more often when the exploitation influence range is determined (Cheng et al. 2016; Milczarek et al. 2017).
Unfortunately the results of the deformations measurements, which allows to describe the state of the process, contain also the probabilistic information. The geodetic measurements due to the technological reasons are burdened with different factors which results in occurrence of the random, systematic errors and outliers. Also the medium (the rock mass) is very changing and heterogeneous, what causes the occurrence of significant disturbances in the deformation picture. As a result of all those reasons, it is impossible to unambiguously determine the border of the influence range on the basis of measurements. By using the statistical methods, the border of the range with the analysis of the accuracy can be determined.
Depending on the measurement methodology used to determine the deformations in the mining areas, the different accuracies of the determination of displacements and deformations are obtained. To be able to talk about the displacement determined on the basis of measurements, the magnitude of the displacement has to be bigger than the magnitude of the error with which this value has been obtained. Therefore, the influence range border obtained on the basis of measurements depends on the applied measurements methodology.
On the basis of abovementioned formulas and assuming the standard magnitudes of measurement errors, the measurable influence range for the most popular measuring methods equals (with the average distance between measuring points d = 20 m): for the satellite visualizations (SAR), it can be assumed that m_{S}= 3 mm.
Obviously the higher accuracy is expected, and the costs and time consumption of the measurements are growing significantly.
Taking into considerations only measurements errors connected with accidental errors of the measuring methods, the magnitudes of measurable influence range which are obtained are exaggerated. Due to the fact that the random dispersion is occurring in connection with the deformation process, the level of trustfulness has to be increased (e.g., p = 2); then, the measurable influence range is significantly shorter.
6 Examples of influence ranges calculation
For the curvature radius, it is impossible to determine the damage influence range, because the minimum curvature radius that has been calculated is bigger that the border damage magnitude (40 km).
Levelling measurements
Subsidence  m_{H} (mm)  m_{S} (mm)  m_{T} (mm/m) 

Geometric  1.0  1.4  0.1 
Trigonometric  3.0  4.2  0.3 
GNSS satellite  5.0  7.1  0.5 
Distance measurements (determining of deformations)
Measurement name  m_{d} (mm)  m_{ε} (mm/m) 

Direct  1.0  0.07 
Geodetic networks (angularlinear)  2.0  0.14 
GNSS  5.0  0.35 
Integrated networks  3.0  0.21 
Losses caused by the exploitation limitations
Border of  Surface area (km^{2})  Volume (mln m^{3}) 

Commune  3.45  8.63 
Damage influence range  4.76  11.91 
Measurable influence range  5.04  12.59 
Theoretical influence range  5.44  13.60 
The difference between the exploitation volume in the theoretical range and in the damage range equals almost 1.7 million cubic metres. Therefore, the application of the damage influence range has an economical justification. Of course the most optimal solution is to reach an agreement with the commune and to exploit within the whole field with the protection of individual objects from the mining exploitation impact.
The example 2 concerns the exploitation in the Ruhr region (Busch et al. 2015, 2017; Preusse 1990). The designed exploitations in this case had the borders of influence range determined on the level of 1 mm. It was the theoretical influence range which was causing many problems starting from the big distances from the exploitation to the problems with verification of the exploitation effects on the basis of measurements. Taking the damage influence range as the referential one, the analysis is conducted how the influence range is going to change when the theoretical range (1 mm) is replaced with the damage influence range.
For indicators in the horizontal plane, the Aviershin formula (2a) is adopted.
It can be acknowledged that in this case the damage influence range is going to decrease from about 40% to about 70% of the theoretical influence range.
7 Conclusions

the theoretical influence range—the distance from the exploitation edge to the point in which deformations reach certain magnitude (assumed) or the distance in which it can be assumed that the influences are disappearing in accordance with the theoretical considerations (the model);

the damage influence range—the distance from the exploitation edge to the point in which deformation reaches the defined border magnitudes (damaging) for the objects located on the land surface (e.g., the border magnitude of the damaging deformations for the cubature objects);

the measurable influence range—the distance from the exploitation edge to the point in which the magnitudes of the deformations indicators are bigger than the error of the adopted measuring method with the appropriate level of trustfulness taken.

the theoretical influence range—used mainly in connection with calculating the forecasted deformation indicators in accordance with the adopted calculating method;

the damage influence range—used primarily in designing the mining exploitation and in determining the borders of the mining areas;

the measurable influence range—used for designing the mining measurements dedicated to monitoring the deformation influences.
In accordance with the presented considerations, it has to be stated that the furthest range is the theoretical influence one and the shortest one is the damage influence range. From the perspective of protecting the objects affected by the mining exploitation, the most optimal solution is to use the damage influence range.
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