Use of machine learning algorithms to assess the state of rockburst hazard in underground coal mine openings

?uksz Wojtecki, Sestin Iwszenko, Derek B. Apel, Miros?w Bukowsk,Jnusz Mkówk

a Central Mining Institute, Katowice, 40-166, Poland

b School of Mining and Petroleum Engineering, University of Alberta, Edmonton, T6G 2R3, Canada

Keywords:Hard coal mining Rockburst hazard Machine learning algorithms

A B S T R A C T

1. Introduction

Rockburst is a dangerous dynamic phenomenon occurring in underground excavations. This phenomenon is associated with a violent energy release,inelastic deformation of rocks,and ejection of rocks into the excavation. As a result of the rockburst, the excavation is destroyed,and the support and equipment inside are damaged. This phenomenon is also dangerous for the miners working in underground excavations. Rockbursts occur in underground mines of various minerals and rocks and during the excavation of tunnels for civil engineering projects.

In most cases, rockburst is caused by a rapid release of the energy stored in the surrounding rocks near the excavation boundaries.This type of rockburst is the most common and can be called stress (or strain) rockburst (Ortlepp and Stacey, 1994). The primary condition for the occurrence of this type of rockburst is a sufficiently high level of stress. Rocks must also be able to accumulate elastic energy and release it rapidly.This type of rockburst is also present in underground hard coal mines.Rockbursts in the coal seams are correlated to the high stresses. This phenomenon is referred to as a coal bump. Underground mining of coal seams occurs at ever greater depths, associated with an increasingly higher level of primary stress.The increase in stress is also related to the more frequent edges and remnants of coal seams extracted earlier and the remaining protective pillars. Also, other mining factors,such as excessive bed cutting,may affect the stress increase in the seam.

In underground hard coal mines,impact-induced rockburst can occur even in less or not stressed coal seams.This type of rockburst is called stroke rockburst.A fracture in the thick layer of competent rocks, e.g. sandstones, causes a high-energy tremor. A tremor is a sudden release of energy accumulated in the rock mass, manifesting in rock mass vibrations, air shock waves, and acoustic phenomena. The dynamic load pulse on the seam may result in the ejection of coal or other rocks into the excavation. This type of rockburst is correlated with the geological structure of the deposit.The thickness of the sandstone layer and its vertical distance from the excavation are significant.

Mixed mechanism rockbursts, i.e. stress-stroke rockbursts, are common in hard coal mines or even dominant (Bara′nski et al.,2012). They are caused by the dynamic load pulse resulting from the fracture of competent rocks, which would affect the partially stressed sidewall of the coal seam.

Technical factors also significantly impact the occurrence of the rockburst hazard.For example,change of longwall mining direction or excavation of the drifts not parallel to the bedding of the coal seam favors rockburst. Therefore, the occurrence of rockburst can be minimized using appropriate preventive measures, such as reinforcement of the excavations,and adoption of destress blasting(Konicek et al., 2013; Wojtecki and Konicek, 2016), water saturation,or large-diameter drilling to destress the coal seam or layers of competent rocks located above or below the excavated coal seam.

However, the distance and time range of such destressing methods are limited.All mentioned factors make the assessment of the rockburst hazard in hard coal mines difficult.Rockbursts in hard coal mines are complex phenomena,and they are still difficult to be predicted and controlled.

The mining of coal seams has been carried out in the Upper Silesian Coal Basin (USCB) for over 200 years. As the mining descends to greater depths, the rockbursts began to occur, accompanied with the mining of deep coal deposits.From the beginning of the 20th century,rockburst became a significant concern in Upper Silesian mines (Bukowska, 2012a). This phenomenon has been investigated for an extended period. It is enough to mention such scientific works,e.g.Konopko(1984),Parysiewicz(1966),Dubi′nski and Konopko(1995,2000),Drzewiecki and Kabiesz(2008),Mutke(2008), Bukowska (2012a, 2013), Dubi′nski (2013), Prusek and Masny (2015), Konicek and Schreiber (2018), Kabiesz (2019), and Konicek et al. (2019). A mining tremor occurs along with each rockburst, but only 1% of mining tremors with energy can cause a rockburst (Dubi′nski and Konopko, 1995). Despite the systematic decline in coal production in the Polish part of the USCB, the number of rockbursts remains similar. This is due to the deteriorating mining conditions as the coal mining is carried out at ever greater depths and complex geological and mining conditions. In the USCB, multi-seam coal mining has been carried out for many years. As a result, many remnants exist close to the currently extracted coal seams.The number of dynamic phenomena in Polish hard coal mines officially classified as a rockburst in the last 15 years ranges from one to five per year (Kabiesz, 2019).

It should be noted that when the excavation completely loses its functionality, it is considered a rockburst. However, smaller-scale dynamic phenomena exist in coal mines in the USCB, which are not classified as rockbursts. As a result of these dynamic phenomena, the rock support systems and underground infrastructure elements are often destroyed.In addition,the floor heave takes place many times. Therefore, in this study, all dynamic phenomena causing any damage to the underground excavations were classified as rockbursts.

Rockbursts in underground mine workings, especially in hard coal mines,are phenomena of a complex nature and not easy to be predicted. However, specific methods for assessing the rockburst hazard have been developed over many years. The prediction of rockbursts in underground excavations can be made in the long term (potential rockburst hazard assessment) or short term (current rockburst hazard assessment).

This article utilizes the machine learning algorithm models for the rockburst hazard assessment. Data on the risk of rockbursts came from one of the hard coal mines in the USCB. The database includes cases with tremors where rockbursts did not cause any damages to the underground excavations. This article is a continuation of a study on the application of machine learning algorithms to the rockbursts presented by Wojtecki et al. (2021).

2. Potential rockburst hazard assessment in hard coal mines

Potential rockburst hazard assessment is usually carried out when the excavation is being planned.The occurrence of rockbursts in underground hard coal mines primarily depends on the nature of the seam and the surrounding rocks. The most critical factors potentially influencing the occurrence of rockbursts are the ability of rocks (including coal) to accumulate the strain energy, the tendency of coal itself and individual waste rocks to burst, and the tendency of entire rock mass, i.e. seam-surrounding rock system,to rockburst. Secondly, the stress that may occur in the vicinity of the excavation is essential. The stress level can be initially estimated, considering geological and mining factors.

2.1. The rock mass bursting tendency index WTG

The ability of rocks (including coal) to accumulate the strain energy, the tendency of coal itself and individual waste rocks to burst,and the tendency of entire rock mass,i.e.seam-surrounding rock system to rockburst, are defined based on the mechanical properties of rocks and structural and geological features of the rock mass.Among others,there are indicators such as the uniaxial compressive strength (UCS)Rc(Konopko,1994), the strain energy storage indexWET(Szecówka,1972), the rheological index of coal tendency to rockburstWRTproposed by M. Borecki (Dubi′nski and Konopko, 2000), the time of dynamic destructionODR(Kidybi′nski and Smo?ka, 1988), the elastic potential energy indexPES(Bukowska,2012a),the rock mass numberLg(Konopko,1994),the rock mass bursting tendency indexWTG, and the rock mass kinetic energy indexWEK(Bukowska,2002; 2012b, 2013). In addition,collective analysis of factors that may affect the occurrence of rockbursts can also be performed, e.g. the indexGEOof the geological-geomechanical system for rock mass bursting tendency assessment (Bukowska, 2012a).

Most of the rockburst tendency indicators used, determined during the compression of sample based on the stress-strain characteristics, are determined only based on its pre-critical phase. For these indicators, the geomechanical and energetic properties of the pre-critical phase are not related to the postcritical properties of rocks or coal seams (Bukowska, 2013). Some of the pre- and post-critical properties of rocks determined in the tests on the testing machine usingWTGwere developed.The theory of post-critical deformation and its influence on the excavation stability,taking into account the pre-and post-critical properties of the damaged rock or coal,were proposed by Petukhow and Linkov(1979). The observations carried out in the USCB showed that, to determine the value ofWTG, the study of the geomechanical properties of the rocks surrounding a given seam should also be carried out at an interval of up to 100 m from the roof and up to 30 m from the floor of the coal seam(excavation).Ninety percent of rockbursts find their source in this depth interval. In order to calculateWTG, it is necessary to obtain the pre-critical Young’s modulusEfor all types of rocks deposited up to 100 m above and 30 m below the coal seam(excavation)and post-critical modulus of coalMcoal.An example of the determination of these moduli based on the stress-strain characteristics is shown in Fig.1.

Fig.1. Determination of pre- and post-critical moduli of selected carboniferous rocks based on the stress-strain characteristics.

The equivalent Young’s modulus of a set of rocks(within 100 m above and 30 m below the coal seam),Erock,is determined based on the Young’s modulusE(MPa) and the thicknessh(m) ofnindividual types of rocks in the set,according to the following formula(Bukowska, 2002):

The rock mass bursting tendency indexWTGis calculated as follows (Bukowska, 2002):

The coal seam-surrounding rock system is prone to rockbursts when theWTGindex is between 1 and 2 (Bukowska, 2005). The Young’s modulus of the surrounding rocks is lower than the postcritical modulus for coal. The coal seam-surrounding rock system behaves like a rock sample when pressed in a soft testing machine.After exceeding the strength of the coal, the dynamic effect is simultaneously enhanced by the discharge of elastic energy accumulated in the surrounding rocks.When theWTGindex is less than 1, the coal seam static destruction occurs. The Young’s modulus of the surrounding rocks is much greater than the post-critical modulus of coal (Mcoal<>Erock). The surrounding rocks are characterized by low mechanical parameter values and thus a poor ability to accumulate elastic energy, and the system loses the ability to transition to a new equilibrium state.

2.2. Theoretical stress value

Stress concentration zones are correlated with a high risk of rockbursts.The state of stress in a specific point of the rock mass is the sum of gravitational and tectonic stresses and the stresses resulting from mining remnants in surrounding coal seams. Stress concentration areas are characterized by the fact that the values of the stress tensor components are greater than they would appear from the depth of deposition. The zones of increased stress are generated mainly by unmined parts of the deposit, such as pillars,edges, and remnants of other coal seams. The type of remainders,their spatial distribution, and the time that has elapsed since they were left are taken into account in determining the theoretical value of the stress.There may also be destressed zones in the rock mass related to the goaf from earlier exploitation and active rockburst prevention. However, the destress effect fades with time. In hard coal mines where long-term multi-seam mining occurs, the determination of theoretical stress distribution is complicated.Several methods have been developed for this purpose, e.g. the analytical methods(Drze?′zla et al.,1988;Ba′nka et al.,2011),and the empirical-analytical method (Kabiesz and Makówka, 2009) based on a series of geophysical measurements (Dubi′nski,1989).

In this article,the disturbed rock mass model was applied.This model was proposed by Bili′nski(1985)and successively developed in the following years(Bili′nski,1992,2005;Bili′nski et al.,1997).As mining continues in sufficiently large areas,the initially compacted rock mass is transformed into a set of sequential settling on the goaf layers. Even though the layers are composed of rocks, i.e. a rigid material, practically not deformed, they show a great ability to deform, mainly due to the bending of a rock layer. Such a deformation becomes possible due to fractures,as a result of which the rock layers lose their physical continuity and only maintain geometric continuity,taking the form of destressed layers.This model was developed based on many years of research in hard coal mines in the USCB (Bili′nski, 2005). The formulae in this model are empirical.

One of the elements of the disturbed rock mass model is the rock mass stress modification coefficient.This coefficient concerns the causes influencing the stress level in the longwall panels. The partial factors reflect the influence of each cause on the stress level.The stress value resulting from the depth was adopted as the initial stress value, precisely the vertical stress componentpz(MPa), and can be calculated as (Sa?ustowicz,1968):

where γ is the unit weight of the rocks(N/m3), andHis the depth below surface level (m). For the USCB rocks, the unit weight is assumed as 25 kN/m3(Sa?ustowicz, 1968). The partial factors increasing or decreasing the stress in the rock mass are presented below.The theoretical value of the vertical stress component in the coal seams where the excavations included in the database were located was calculated by the formulae proposed by Bili′nski(2005).

The rock mass destress factor(a3)was applied among the partial stress reduction factors.As a result,the impact factor of the destress mining of theith adjacent coal seam is calculated according to the following formula:

whereHoiis the vertical distance to theith extracted coal seam(m);zoiis the compression of goaf(m),which is defined as the thickness of theith extracted seam multiplied by 0.4,andzoi=0.9 m;andtis the time that has elapsed since theith adjacent coal seam was extracted (yr).

Partial stress increase factors resulting from the disturbed rock mass model and present in the database from the selected mine are as follows: the remnant impact factor (a4), the fault impact factor(a5), the coal seam edge impact factor (a6), the old goaf impact factor(a7), the heading impact factor(a8), the impact factor of the change in the direction of mining(a9)and the caving longwall startup factor (a11). If a given factor increasing or decreasing the stress was not present,the value of the corresponding impact factor was taken as 1.

It was assumed that the first of the mentioned impact factors increasing the stress in the rock mass(a4)concerns only the remnant left in the same coal seam.The impact factora4ranges from 1.1 to 1.5(Bili′nski, 2005), depending on the width of the pillar. The fault impact factor(a5)may range from 1.1 to 1.3(Bili′nski,2005).

The coal seam edge impact factor (a6) exists because the stress increase in the rock mass occurs in the vicinity of the edge of the adjacent coal seam. In the openings located in the impact zone of the coal seam edge, support deformation or floor heave is often observed. The impact factor of theith edge of the coal seam is as follows:

whereHkiis the vertical distance to theith edge of the coal seam(m); andziis the compression of goaf (m), andzi= 0.4 m. Eqs. (6)and(7)were also used to determine the stress increase ahead of the longwall face due to the mining pressure. The longwall face was found to be the edge of a coal seam at a distance of 0 m.In this case,the timettaken for the calculations was assumed as 0 year. The calculated impact factora6at the longwall face equaled approximately 1.5. The mining pressure range was assumed up to 100 m ahead of the longwall face.A decrease of the impact factora6by 0.1 every 20 m ahead of the longwall face was assumed. The old goaf impact factor (a7) was assumed between 1.1 and 1.3. The heading impact factor (a8) was initially related to the approaching of the longwall face to the heading in or near the same coal seam(Bili′nski,2005).However,this factor was used to describe the excessive bed cutting,which weakens a body of coal and may cause a bump.The heading impact factor(a8)was assumed as 1.2.The impact factor of the change in the direction of mining(a9)was assumed as 1.3.The caving longwall start-up factor (a11) was applied to a part of longwall galleries within the range of the initial 50-m advance of caving longwall, and it was assumed as 1.1. The final value of the vertical stress componentpFwas estimated by multiplying the vertical stress componentpzresulting from the depth by the impact factors described above. However, the vertical stress componentpzis assumed to increase with depth due to the weight of the overburden. In order to take into account the impact of factors other than the weight of the overlying rocks, it was decided to apply an anomaly of the vertical stress component:

The anomalyAdescribes the percentage deviation of the calculated vertical stress component considering all factors from the value obtained by the depth of deposition only.

3. Current rockburst hazard assessment in hard coal mines

In the USCB hard coal mines, constant monitoring of the rockburst hazard is carried out. In the short term, the current assessment of the rockburst hazard is based on several partial methods,e.g. mining seismology, seismoacoustic method, and smalldiameter drilling method, being a part of the complex method(Bara′nski et al., 2012). In the daily assessment of the rockburst hazard of a given excavation by the complex method, the result of the mining hazards assessment(potential risk of rockburst)is taken into account and supplemented with the results of the mentioned partial methods (Bara′nski et al., 2012).

The seismic and rockburst hazards are usually correlated with each other. Seismological observations make it possible to assess the rockburst hazard associated with the processes occurring in the coal seam itself or thick layers of sandstone. Seismic activity is correlated not only with the processes of rock mass destruction as a result of mining,but also with geological and mining factors such as faults, sedimentation disturbances, pillars, remnants and edges of other coal seams.

Based on the tremor base, some seismological parameters can be calculated, e.g. parameterbof Gutenberg-Richter (G-R) distribution, seismic hazardSHAZ, and slope of the line fitted to the cumulative energy versus time plota. These parameters are calculated in a moving time window and can be used as indicators of the current rockburst hazard.

Theb-value of G-R distribution may indicate the possibility of a strong tremor, resulting in a rockburst in the excavation. This parameter can be calculated based on the seismic energy of mining tremors (Lasocki, 1995). The use of this parameter in hard coal mines in the USCB area has been the subject of many studies, e.g.Mutke et al.(2016a)and Wojtecki et al.(2020).On the other hand,a low value of parameterbof G-R distribution may indicate the possibility of strong tremors.

The seismic hazardSHAZis defined as the probability that the energy of at least one tremor will be higher than assumed critical energy during the forecast horizon (Go?da and Kornowski, 2011).The critical energy of the tremor for which the excavation can be considered as threatened by rockburst was assumed as 1 ×104J.

The slope of the line fitted to the cumulative energy versus time plot(a)is not commonly used in mines but seems to be helpful for this purpose(Wojtecki et al.,2020).However,the interpretation of this parameter can be twofold,i.e.if the value of the parameterais high,it means the release of a large amount of energy from the rock mass, and thus a high risk of rockbursts. On the other hand, however,when theavalue is low,the energy is not released,which may be related either to the absence of rockburst hazard or to the accumulation of elastic energy in the rock mass (abrupt release of seismic energy).

The three parameters mentioned above were used for assessing the current rockburst hazard in the selected excavations for a given day.All these parameters were calculated in a moving 2-week time window. Such a narrow time window allowed it to capture the impact of individual geological and mining factors on seismic activity and the risk of rockbursts correlated with it. Exemplary distributions of these parameters for one of the selected openings are shown in Fig. 2. The triangle marks the day on which a strong tremor with the energy of 2 ×107J occurred. This particular case was included in the database.

Fig. 2. Distributions of the b parameter of G-R relation,seismic hazard SHAZ and slope of the line fitted to the cumulative energy versus time plot a for one of the openings in the selected mine (the triangle marks the day when the strongest tremor in the area of the selected opening, included in the database, occurred).

4. Preparation and structure of the database

The database was collected in one of the USCB hard coal mines at risk of rockbursts. These data concerned the last 25 years to ensure similar conditions and technology of mining works and rockburst prevention. In the selected mine, coal seams are exploited in a longwall system with caving.Most of the extracted coals are characterized by strength properties that determine their ability to accumulate elastic energy. Moreover, thick layers of sandstone are also present. The fracturing of these layers generates strong tremors. Many years of exploitation of numerous coal seams have left remnants and pillars, where high-stress level occurs. In addition, complicated geological and mining conditions affect the occurrence of rockbursts. Therefore, rockburst prevention measures are widely used in the selected coal mine, e.g. support reinforcement and destress blasting. Moreover, continuous seismological monitoring is carried out using an underground network of seismometers.

The geological, mining and technical/technological factors that could affect or minimize the risk of rockbursts in excavations were collected in the database.Also,seismic parameters were taken into account. Similar to the standard assessment of the current rockburst hazard (e.g. in the complex method), factors potentially influencing the rockburst hazard were taken into account and supplemented with the three parameters calculated based on current seismic monitoring. Thus, a total of 11 parameters were selected to train the models.

One hundred fifty points located in underground openings of a selected hard coal mine were chosen. Each selected point was correlated with the mining tremor. Among 150 points, 53 points were found where the destruction of the excavation was observed due to the tremor.They were classified as rockbursts and labeled as one. The scale of these effects ranged from minor damage, e.g.destruction of single arches of the steel support,breaking of singleprops,and local floor heave,to complete collapse of the excavation.In the remaining 97 points, the openings were not damaged,despite the occurrence of the tremor.These points were labeled as zero. The input database was unbalanced. The difference between the number of tremors without damage to the openings and rockbursts is even greater. The number of rockbursts is a small fraction of the total number of tremors that can cause a rockburst.

The database included the previously described rock mass bursting tendency indexWTG,expressing the tendency of the entire seam-surrounding rock system to rockbursts. This parameter ranged from 0.24 to 2.53 (mean 1.48). According to the presented scale of rock mass tendency to rockbursts based on theWTGindex,in 88 cases, the rock mass was prone to rockbursts (1 ≤WTG≤2),which corresponded to 58.7% of the database. The second geological parameter considered was the thickness of the seam. It ranged between 1.4 m and 8.25 m (mean 4.74 m).

All mining and other geological factors influencing the stress level in the coal seam have been replaced with a parameter,i.e.the anomaly of the vertical stress componentA. It ranged between-21.72%and 203.54%(mean 54.37%).In 23 points(15.33%of the cases),the anomaly of the vertical stress component equaled 0.No factors caused the stress increase or decrease in the vicinity of these points, or they canceled out each other. Eight points were located in openings excavated in the distressed coal seams(5.33%of the cases).The remaining 119 points were within the geological and mining factors range, causing the coal seam stress to increase. For 54 points, 0% 200%. The statistical parameters of theWTGindex, the seam thickness,and the anomaly of the vertical stress componentAare presented in the box plots collected in Fig. 3.

Fig.3. The statistical parameters of the WTG index, the seam thickness,and the anomaly of the vertical stress component A (box plots with division into rockbursts cases -1 and cases with no damage to the excavation - 0).

Both the coal seam thickness and the other parameters presented below were used previously by Wojtecki et al.(2021).Three factors concerning the workings themselves were included, i.e. the type of excavation, the support reinforcement, and the active rockburst prevention.The first of them characterized some standard features of workings.Three categories were distinguished:drilled headings(46 records), longwall galleries (90 records), and opening-out headings(14 records).In the coal face of drilled heading,the coal is mined,and arch steel support is placed. The coal body is exposed, and it is impossible to strengthen the support, e.g. by props, due to continuous miner, crusher, and scraper chain conveyor. Additional stress related to the mining pressure occurs in longwall galleries(i.e.main gate and tailgate). Longwall mining is commonly used for mining seams at great depths and with high stresses in the rock mass,thus it is unlikely to retreat in the near future.However,the support of these openings is usually additionally reinforced at a certain distance in front of the longwall face, and active rockburst prevention is commonly performed to destress the coal seam and surrounding rocks. The opening-out headings were drilled usually in pillars,

where an uneven stress distribution is expected,and in most cases,these openings were at least a few years old.In these openings,the transport of output was usually conducted.The mined coal is usually transported through these excavations by a belt conveyor series. In older excavations of this type, the steel arch support is often corroded to some extent. The second factor included was the reinforcement of steel arch support. Appropriate rock support can prevent or minimize the effects of rockbursts. The support reinforcement was present in 121 points.This support reinforcement was based on hydraulic props(105),both props and bolts(7),other wooden support (5), additional steel horseheads (2), and a combination of props,additional steel horseheads,and reduced spacing of steel arches (2). In the other 29 cases, the excavation support consisted only of standard steel arches without additional reinforcement. The third factor was active rockburst prevention. This rockburst prevention was performed in 69 points.In a selected mine,blasting is the main form of active rockburst prevention. The longhole destress blasting in the roof rocks embraced 27 points, the destress blasting in the coal seam occurred in 7 points,and both of them executed together in 35 points. In 81 points, active rockburst prevention was not performed.

The input database also contained two seismic parameters, i.e.the tremor energyE(J) and the correlated peak particle velocity(PPV, in m/s). The tremors included in the database had seismic energy between 8×102J(ML=0.58)and 6×108J(ML=3.67).Even a strong tremor, localized at a considerable distance from the mining excavation,cannot destroy the excavation.On the contrary,a tremor of relatively low seismic energy, but close to the excavation, can cause damage. The relationship linking the PPV, the hypocentral distance, and the scalar seismic momentMowas proposed by Mutke et al.(2016b).The calculated PPV values in the database were between 0.006 m/s and 0.77 m/s.For 103 points,the PPV value exceeded 0.05 m/s, so that the excavation could be damaged in most cases.The average PPV value was approximately 0.108 m/s.The focal mechanism and the way of radiation of seismic energy from the source were not considered.

Three seismological parameters for the current assessment of the rockburst hazard were used, i.e.bparameter of G-R distribution, seismic hazardSHAZ, and the slope of the line fitted to the cumulative energy versus time plota.There was seismic activity in 139 points included in the database,which allowed the calculation of these parameters. Concerning thebparameter of the G-R distribution,for 15 points,the seismic catalog was not numerous,and the obtained values deviated significantly from the expected values. However, this type of data is quite common in hard coal mines,therefore,it was decided to keep it in the training database of the machine learning model. For 124 points, the parameterbof the G-R distribution was between 0.24 and 2.18.The seismic hazardSHAZvaried between 0 and 0.97. The slope of the line fitted to the cumulative energy versus time plot ranged from 0(a line parallel to theX-axis) to 2.16 × 106. The values of the parameters described above are commonly found in the selected mine.

The occurrence of rockbursts in the underground excavation has been correlated with the mentioned parameters via Pearson’s correlation coefficient. It is a statistic that measures the linear correlation between two variables, and it varies from +1 (total positive linear correlation)to-1(total negative linear correlation).When the Pearson’s correlation coefficient equals 0, it means that a linear relationship between two variables does not exist.The value of this coefficient for the rock mass bursting tendency indexWTGwas 0.16(Table 1).The Pearson’s correlation coefficient for the anomaly of the vertical stress component equaled 0.081.Such value could be due to how the vertical stress component was computed,i.e.it was a single value for an arbitrarily chosen point,and the distribution map of the vertical stress component was not plotted. Pearson’s correlation coefficients for other factors related to the occurrence of rockbursts were analyzed by Wojtecki et al. (2021). The rockburst occurrence was best correlated with PPV and the thickness of the coal seam(Table 1).Some slight negative correlation concerned only rockburst prevention, which is understandable. As a rule, the application of rockburst prevention should minimize the risk of rockburst. A similar effect was not found in the case of support reinforcement.For this case, and for the rest of the parameters, Pearson’s correlation coefficient was close to 0. Therefore, a robust linear relationship between the occurrence of rockburst and the parameters used in the input database was not confirmed.

Table 1 Pearson’s correlation coefficient between the occurrence of rockburst and the parameters related to this phenomenon.

5. Machine learning algorithms

The use of machine learning algorithms takes place in various areas of life and often in geosciences. These algorithms build a mathematical model from sample data, called training data, to forecast or make decisions without being directly programmed by humans. They learn the mapping function that turns the input single variable or more variables into the output variable. The machine learning algorithms can be classified into four major categories, i.e. supervised, unsupervised, semi-supervised, and reinforcement.Supervised learning uses labeled training data to learn.In this article, we used algorithms based on supervised learning.Each of the 150 points was labeled 0(tremor without damaging the excavation)or 1 (excavation damage or destruction).

5.1. Previous use of machine learning algorithms for rockburst hazard assessment in hard coal mines

The use of machine learning algorithms in geoscience has been the subject of numerous publications(e.g.Wang et al.,2020;Zhang et al.,2020,2021a,b;Rezaee et al.,2021).Numerous studies mainly concerned the phenomenon of rockbursts in non-coal mines and drilled tunnels (e.g. Feng et al.,1998; Su et al., 2009; Zhou et al.,2012, 2016; Pu et al., 2018). In some cases, data from hard coal mines and other mines or tunnels were used to train the rockburst hazard assessment models (e.g. Feng and Wang,1994). The input parameters were mainly the mechanical parameters of the rocks and those related to stresses, e.g. UCS, uniaxial tensile strength,strain energy storage index, and maximum tangential stress(Feng and Wang, 1994; Feng et al., 1998; Su et al., 2009; Zhou et al.,2012, 2016; Pu et al., 2018). Occasionally, other parameters were taken into account, e.g. depth and rock brittleness coefficient, but the core was the parameters mentioned above.

The occurrence of rockbursts in hard coal mines is complex and influenced by many factors.In addition to the factors related to the coal seam itself,i.e.its mechanical properties and stresses occurring in it,the structure and properties of the rock mass surrounding the seam and the technical/technological parameters are also important.

The use of machine learning algorithms only to assess the state of rockburst hazard in hard coal mines was presented in Sun et al.(2009)and Shi et al.(2015). In both cases,backpropagation neural networks were used. Sun et al. (2009) proposed the use of the following 10 parameters related to the occurrence of rockbursts in mining excavations in an underground coal mine:depth,coal seam thickness and its change,dip angle of the coal seam,coal strength,roof strength, complex degree of geological structure, roof management situation,pressure relief situation,and coal noise.In turn,Shi et al. (2015) used 8 input parameters: depth, lithological character of the roof, complexity of the structure, coal seam thickness,dip angle,mining method,pillar,and mining technology.Sun et al.(2009)trained the model on 17 records and tested it with 6 records.This model was a 4-layer neural network, with the sigmoid function as the excitation function. The input layer consisted of 40 nodes, and the output layer consisted of 4 nodes, representing 4 rockburst risk grades (i.e. no threat,weak, moderate,and strong).

On the other hand,Shi et al.(2015)proposed a model trained on 16 records and tested on 10 records. In this case, three levels of rockburst hazard were used, i.e. weak, medium, and strong. This article used artificial neural networks, but other more popular machine learning algorithms were also used to assess the rockburst hazard.

5.2. Machine learning algorithms used to build models

Five supervised machine learning algorithms have been adopted to assess the rockburst hazard in underground excavations taking into account the previously described parameters,i.e.decision tree(DT),random forest(RF),gradient boosting(GB),extreme gradient boosting(XGB),and multilayer perceptron classifier(MLPC),being an example of artificial neural network. The algorithms to be used in this research had been utilized earlier and were proved to be effective compared to other machine learning algorithms(Wojtecki et al., 2021). Similar studies on the effectiveness of using 10 supervised learning methods to classify the rockbursts in underground projects were carried out by Zhou et al. (2016). Among others, the following methods were used (Zhou et al., 2016): classification tree, neural network, RF, GB machine, na?ve Bayes, and support vector machine. A model of RF combined with the GB machine was more reliable than other models, and indicatorWetwas the most relevant predictor of rockburst classification (Zhou et al., 2016). In this article, an attempt to use selected machine learning algorithms to distinguish between rockbursts and nondamaging tremors has been made.

The considered estimation of rockburst hazard can be described in terms of the classification problem.Let us consider the setx?Rn,whereRn=R×R×…×Rdenotesn-dimensional real number space. The setxis called the feature space, and its element,xi, is called the feature vector. Further, we will consider the mappingx→y,wherey?Z.The mapping is a classification,andyrepresents the possible class set.For example,in rockburst hazard assessment,the coordinates of feature vectorxican represent selected parameters,such as the PPV,the seam thickness,WTG,and the anomaly of the vertical stress component. The elements ofyencode the rockburst occurrence, i.e. 1 - rockburst, and 0 - non-destructive tremor. The machine learning algorithms try to find the mapping betweenxandyusing a setxtr?x:For the elementxi,the valueyi?yis known. The selected machine learning algorithms used to assess the rockburst hazard will be described in the sections below.

All parameters affecting the risk of rockbursts were treated as input variables, and the labeled risk of rockbursts (0 or 1) was the output variable.The calculations were made in JupyterLab(https://jupyter.org/; Kluyver et al., 2016), using the Scikit-learn library(Pedregosa et al., 2011). The preprocessing package was used to prepare the dataset for training the models. First, the standardization method, called the mean removal, was applied. In this method,the average value of each characteristic is removed,and a scaling operation takes place. This operation is done by dividing each characteristic by its standard deviation, and as a result, each feature is zero-centered. Next, the set of 150 input data has been randomly split into a training dataset (120 records) and a testing dataset (30 records) using the train-test split method. This technique can be used for supervised learning algorithms.Splitting data ensures that there are independent sets for training and testing.The testing set is to evaluate the model fit independent of the training.

5.2.1. The DT algorithm

DTs perform classification using sequential tests(Quinlan,1986,1993). A tree is a kind of directed acyclic graph. Its structure includes a node called the root,to which none of the edges from the remaining nodes of the tree leads, intermediate nodes with one incoming edge and at least two outcoming edges,and nodes called leaves with one incoming edge but no outcoming edges.The root is the starting node of the tree, and the leaves are its ending nodes.The root and all intermediate nodes represent tests, while the leaves are labeled with the classes.The classification process begins from the root node of the tree.The feature vectorxiis subjected to a test, and depending on its result, it is directed to another test related to the next node in the tree. This process is repeated until the leaf is reached.The class assigned to the leaf is the result of the classification process.The learning algorithm has to determine the tests that should be performed at each tree node so that the DT can give appropriate classification for any given feature vector. The problems that arise are to keep the tree structure reasonably simple and to make the algorithm robust to the noise, which is always present in the actual data.

The proposed algorithm uses an information gain to rate the possible feature tests and their order. The DTs are known for their advantages: the explainability, robustness to missing data, and flexibility according to testing criteria. However, they also tend to overfit, and unique algorithms are usually used to mitigate this disadvantage. Another problem arising is the model instability -the structure of the generated DT can vary significantly with small changes within the training set (Kuhn and Johnson, 2013). When training the models, the quality of a split was measured using the Gini impurity. However, the maximum number of leaf nodes and depth of DTs were not declared.Instead,the balanced class weight was used to split an internal node, and at least two samples were usually obligatory.

5.2.2. The RF algorithm

The RF is an example of ensemble algorithms. This kind of machine learning method uses the power of collective decisionmaking. The RF algorithm is known for its low tendency to overfitting(or good ability to generalize).The RF classifier is composed of a set of DT classifiers. Each of the DT is fed with the input data,and the classification result is determined upon the aggregation of the decision taken by each of the trees.The most crucial part of RF classifier construction is to ensure that the DTs composing it are uncorrelated. The algorithm for RF classifier construction makes use of randomness in two phases. First, the bagging or bootstrapping process is performed. Random sample is taken from the training dataset.Next,a subset of features are selected at random to be used in the other part of the algorithm. Then, the DT is constructed based on the selected sample and feature set. Finally, the DT is remembered, and the process is repeated as long as the assumed number of created DTs is reached(Breiman,2001;Cutler et al.,2012).Ten DTs were usually present in a single forest of the RF models presented in the article.Again,the Gini impurity was taken to measure the quality of a split,and the maximum number of leaf nodes and depth of DTs were not predetermined. The minimum number of samples required to split an internal node equaled 2.

5.2.3. The GB algorithms

Boosting algorithms are another example of ensemble learners(Kuhn and Johnson, 2013). Again, the prediction is made collectively,but the ensemble is composed of so-called week classifiers.A week classifier performs only slightly better than random guessing.One of the first boosting algorithms developed was AdaBoost(Schapire,1999). The algorithm was the inspiration for developing the framework allowing for the adaptation to different kinds of problems (Friedman, 2001). The idea behind the algorithm is to iteratively improve the classifier by adding the week classifiers one by one, each time trying to improve the prediction quality. The quality is determined by the loss function informing of the summary error made so far when classifying the training set. The improvement in prediction is achieved by adding the weak learner minimizing the gradient of the loss function.

The GB algorithm proved its robustness in many applications(Kuhn and Johnson,2013).Though the GB algorithm does not force the week learner, a DT is usually used. The GB algorithm found its further development in the XGB classifier(Chen and He,2015;Chen and Guestrin, 2016). The novelty of the XGB algorithm lies in the proposed regularization term. The regularization prevents the algorithm from developing too complicated tree structures during the learning process, significantly improving its generalization abilities. In addition, the highly efficient implementation of the algorithm is available, increasing its applicability and easiness of use.

5.2.4. The MLPC

The MLPC was inspired by analyzing the brain’s neural tissue structure.The idea of perceptron was first presented by Rosenblatt(1958).The perceptron is a model for the operations performed by a single neuron. It calculates the output as the function of the weighted sum of the inputs:

whereh(xi)is the perceptron response for the input feature vectorxi;xkidenotes thekth coordinate of the vectorxi;fis the activation function,and it is nonlinear and usually takes the form of a sigmoid or hyperbolic function.Multilevel perceptron is composed of many(usually few) layers of neurons. Each neuron of thejth layer is connected with each neuron of the (j+1)th layer. The first layer represents the value of input vectorxi,and the last layer elaborates the output signal for multilayered perceptron.The valuewifor each neuron is determined during the learning process along with the free termb. The architecture of MLPC (the number and size of layers) usually should be relatively straightforward. Too complicated networks tend to overfit, mainly when the training data are moderate (Haykin, 2004). The adaptive learning rate was applied when training MLPC models.The input layers consist of 11 neurons.Then there were two hidden layers with five nodes in each. The function activating the hidden layers was the rectified linear unit function. In the output layers, two nodes represent the condition whether or not the rockburst has occurred. A stochastic gradient descent was the solver for the weight optimization.

The authors of this study have attempted to determine whether or not the models of the selected machine learning algorithms can distinguish between the cases in which a rockburst causing damage to the underground workings has occurred and the cases where there was no damage to the excavation after the tremor.

6. Results

The effectiveness analysis of the models of machine learning algorithms was based on the confusion matrix and related parameters such as accuracy, recall, precision,F1-score, and selectivity.In the analyzed confusion matrices of the tested models,true positives (Tp) mean that the model correctly recognized the rockburst in the test dataset. True negatives (Tn) mean that the model correctly recognized cases where the excavation was not damaged despite the tremor. False positives (Fp) mean overestimation, i.e.the case where the excavation was not damaged has been classified as a rockburst. False negatives (Fn) mean that the rockburst has been classified as an event without damage to the excavation.The phenomenon of rockburst is rare compared to tremors that do not damage the excavation.

For this reason, the correctly classified cases of rockbursts, i.e.true positives and underestimations (false negatives) are critical.The parameter describing the ratio of correctly classified positives,i.e.true positives,to the number of positives(P)in the dataset is the recall (sensitivity). This parameter was included in assessing the effectiveness of the model classification. Selectivity (specificity) is the parameter describing the ratio of correctly classified negatives,i.e.true negatives,to the number of all negatives in the dataset.This parameter determines the effectiveness of the classification of the model’s negative cases (N). Accuracy is the ratio of all correctly classified cases, i.e. true positives and true negatives, to the total number of cases in the dataset.For an unbalanced dataset,accuracy can become an unreliable measure of model performance.Precision is the ratio of correct positive predictions to the total predicted positives, i.e. true positives and false positives.F1-score is the harmonic mean of precision and recall. It performs well on an imbalanced dataset. The performance of the models of five selected machine learning algorithms,i.e.DT,MLPC,RF,GB,and XGB,trained and tested on 10 randomly selected datasets is shown in Tables 2-6, respectively. Training and testing models on 10 randomly selected different datasets were performed to check the solution’s stability and effectiveness. The same datasets (numbered 1, 2, …,10)were used for training and testing the models of each machine learning algorithm.

Table 2 Efficiency of DT models.

Table 3 Efficiency of MLPC models.

Table 4 Efficiency of RF models.

Table 5 Efficiency of GB models.

Table 6 Efficiency of XGB models.

7. Conclusions

The relationship between the occurrence of rockbursts and the factors causing them is not linear. Therefore, the use of machine learning algorithms seemed to be a promising solution.Compared to the previous solutions,a number of machine learning algorithms were used to assess the risk of rockbursts in hard coal mines,and an attempt was made to apply factors related to the occurrence of rockbursts and parameters related to tremors and their distribution. In hard coal mines, the number of factors contributing to rockbursts is significant.However,the article attempts to limit the number of parameters and replace the geological and mining parameters with the rock mass bursting tendency indexWTGand the anomaly of the vertical stress component in coal seams.A total of 11 parameters were considered while creating the input dataset. The models of machine learning algorithms were trained with the used parameters to assess the potential rockburst hazard and parameters obtained from seismological observations. The purpose of the investigations was to identify cases when, under given conditions and the results of current seismological monitoring,a tremor with a given energy and PPV will lead to a rockburst in the excavation.Binary labeling was applied in the dataset,i.e.whether there was a rockburst or not.

Correct classification of rockbursts and the smallest possible number of false negatives (underestimations) is essential. The number of false alarms is also essential, as each is associated with taking preventive measures associated with expenses and interruptions in the technological process.However,in assessing the effectiveness of the models, the recall parameter should be considered first.

Concerning the average value of the recall parameter,the DT and MLPC models proved to assess the rockburst hazard effectively. It equaled 0.81 and 0.76,respectively.The average recall value for the models of the other algorithms did not exceed 0.7.However,the DT and MLPC models had the lowest average values of the specificity,which determined the correctness of classification of tremors that did not damage the openings, as 0.8 and 0.81, respectively. The models of the other algorithms had higher average specificity values, i.e. it was 0.92 for GB models, 0.88 for RF models, and 0.85 for XGB models.

DT and MLPC models built on an 11-parameter database classified the rockburst cases most accurately,similar to the models of these algorithms built on a 25-parameter database(Wojtecki et al.,2021). Reducing the number of parameters affecting the risk of rockbursts in the input database resulted in a deterioration of the recall parameter for the DT and MLPC models presented in this article.When more parameters in the input database were present,the average recall value was 0.83 for DT models and 0.84 for MLPC models (Wojtecki et al., 2021). Thus, reducing the number of parameters did not significantly change the efficiency of model classification.

On average,approximate 80%of rockbursts have been correctly identified by DT and MLPC models. The joint application of parameters potentially influencing the risk of rockbursts and parameters related to tremors and their distribution allowed us to train machine learning models to correctly classify historical rockbursts in the selected hard coal mine in the USCB,Poland.In mining practice, it is important to determine whether or not, in the given geological, mining and technological conditions, there will be a rockburst in the opening as a result of the tremor, i.e. damage or destruction of the opening. Assuming the forecast maximum energy of tremors generated in the thick sandstone layer and the correlated PPV value, the developed models could be applied for this purpose.However,the application of the proposed solutions in mining practice requires further research.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the Ministry of Science and Higher Education, Republic of Poland (Statutory Activity of the Central Mining Institute, Grant No. 11133010). The authors would like to thank the Polish Mining Group for providing the data used for the calculations and discussing the results.