Seismic,evaluation,of,the,destress,blasting,efficiency

Krzysztof Fułwk,Piotr Mertuszk,Witold Pytel,Mrcin Szumny,Tristn Jones

a Research and Development Centre,KGHM Cuprum Ltd.,Wrocław,53-659,Poland

b Luossavaara-Kiirunavaara AB(LKAB),Malmberget,SE-983 81,Sweden

Keywords:Rockburst hazard Destress blasting Induced seismicity Seismic events Dominant frequency

A B S T R A C T In this paper,selected methods of destress blasting efficiency assessment are presented,and novel quantitative methods based on in situ seismic measurements are proposed.The newly formulated solution combines two different approaches.The first,which is useful mostly for the near-field seismic analyses,is based on the analysis of seismic amplitude characteristics,and the second,relevant for farfield evaluation,is extended by the duration and frequency of the seismic wave.Both approaches are based on the seismic analyses of the waveforms generated by blasting recorded by the local seismic network.The proposed solutions are tested and validated in deep underground mines in Poland in which the room-and-pillar mining method is applied.Based on performed analysis,it is shown that both methods may be used as a rockburst hazard control in underground mines.However,developed methods may also be successfully implemented in other engineering practices,including the assessment of seismic vibrations in open pits and quarries.

Underground mining at great depths is associated with the presence of high stresses in the surrounding workings in many cases(Guha,2000;Li et al.,2007;Abdellah et al.,2014;Mazaira and Konicek,2015).With the progress of mining and ever greater deposit depths,significant changes in stress and strain conditions have been observed.Such phenomena may lead to seismic events and rockburst occurrence(Hoek,2007;Lyle et al.,2014;Fuławka et al.,2018a;Małkowski and Niedbalski,2020).The dynamic nature of such events and their stochastic distribution in space and time negatively affect the safety and continuity of mining operations(Pytel et al.,2020).

One of the mining areas characterized by a high geomechanical risk is the Lower Silesian Copper Basin in Poland,where three very large underground copper mines operate.The room-and-pillar mining method is the dominant technology applied there and is relatively well suited to the flat geometry of the orebody.The dimensions of rooms and pillars are selected according to the local hardness of the rocks.However,the main cause for geomechanical risk occurrence is usually related to the local mining and geologic conditions.The exploitation of the flat copper deposit is currently conducted at depths ranging from 600 m up to 1200 m,on average.The specific geologic structure,mainly within the roof stratum,favours the occurrence of strong seismic events.The high strength and low deformability of the dolomite stratum lead to accumulation of elastic energy within the main roof.The floor stratum in turn consists of sandstone which is much weaker.The average compressive strength of the floor varies between 30 MPa and 100 MPa in most cases,while the compressive strength of roof dolomite may reach 250 MPa.Under such conditions,mining progression tends to cause the strong dolomite layers to fail due to the occurrence of high stresses,resulting in the occurrence of seismic events.Such a situation is currently observed in all mining panels of Polish copper mines,but its intensity is greatest within the regions around tectonic discontinuities such as faults,joints,etc.In the case of such events,the floor yields around the pillar resulting in floor heaving manifested by significant energy release.

According to recent studies,over 2500 mining tremors with the seismic energy exceeding 103J are observed in the area of the Polish copper mines each year(Lasocki,2005;Rudzi′nski and Dineva,2017;Caputa and Rudzi′nski,2019).The strongest high-energy events in the past have reached the energy of 109J(ML=5).Such a high intensity of seismic activity causes frequent dynamic release of the energy accumulated in the rock mass which may lead to rockbursts and roof falls.According to Butra and Kudełko(2011),several rockbursts with significant consequences in the mine workings were observed each year between 1990 and 2010,with 22 events in 2010.Many of them involved casualties and fatalities(Lasocki et al.,2017;Fuławka et al.,2018a).According to the data provided by the Polish State Mining Authority(https://www.wug.gov.pl/),since 2008,there have been more than 59 fatal accidents in Polish copper mines.About 45%of them were related to ground control issues such as roof falls and rockbursts.In the last decade,the most tragic year was 2016 when 14 miners died,two were seriously injured,and 49 were lightly injured due to seismic activity and loss of opening stability(Fuławka et al.,2018b).Besides the human losses,there are also technical and economic losses due to significant damage to the infrastructure.

Thus,to minimise this risk,various preventive actions are practised.Some of them are strictly organisational in nature,but there are also technical measures that allow for a significant rockburst hazard reduction.Among the technical methods,destress blasting seems to be the most effective(Konicek et al.,2011;Saharan and Mitri,2011;Vennes et al.,2020).

Destress blasting may be defined as a source of two phenomena:fractures of rock mass and induced seismic vibrations.These factors may affect the rock mass differently or their effects may be combined.As it was pointed out by Vennes and Mitri(2017)as well as Drover and Villaescusa(2019),the main goal of destress blasting is to generate such seismic energy that will allow fracturing of the rocks within the overloaded area and thus move the stress concentration zone far away from the production panel.Such effects may be observed mostly in the direct vicinity of the blasting site.It may be assumed that a higher energy of detonation allows reaching more distant zones.In turn,Brauner(1994)highlighted that induced seismic vibrations may contribute significantly to decreasing the friction of joint planes and may contribute to expanding the pre-existing network of joints within the rock mass and creating new fractures.This effect may be considered farreaching(Fig.1).It means that regardless of the analysed effect,the main goal of destress blasting is preconditioning the rock mass,preventing energy accumulation in the rock mass and triggering the seismic event if the rock mass in the vicinity of the mining panel is overstressed.

Fig.1.General mechanism of destress blasting in deep mines(based on Roux et al.,1958).

The specific technique of destress blasting,in terms of the construction of explosive charge,location of blastholes and firing sequence,is related to the adopted mining method,and in many cases relies on trial-and-error and historical experience.One such method is called torpedo blasting and is commonly used in longwall mining(Konicek et al.,2012;Wojtecki et al.,2013,2017a,b)as well as in top-coal caving(He et al.,2020).In this method,long blastholes are drilled in the roof strata.Their length,diameter and inclination depend on the local geomechanical conditions.In principle,the explosive column of the torpedo hole should be in the overloaded area where the rock mass accumulates a high amount of strain energy.The use of torpedo blasting is effective from a destressing point of view because a large amount of explosives may be concentrated in several blastholes,helping to maximise the amplitude of the induced seismic wave.However,in most circumstances,this method reveals itself to be too expensive and time-consuming.Moreover,the detonation of a large mass of explosives within the roof strata may result in significant damage to the rock mass,leading to the increased risk of roof failure in the mine excavations(Anderko et al.,2015).This also maximises the magnitude of induced seismicity which,if it is present,can be much easily felt on the surface and at a greater distance.This may cause serious anxiety among the community within the surrounding areas.Therefore,in mines where the drill-and-blast excavation approach is utilised,the multi-face blasting technique seems to be much more suitable,because in this method,explosives are used for both rock mass destressing and the ore extraction purposes.Such a technique is practised in deep copper mines in Poland belonging to KGHM Polska Mied′z S.A.,where room-and-pillar mining method with roof deflection and pillar softening is used.This involves the simultaneous firing of explosives in a number of mining faces within the panel(usually from 10 to 20)in the absence of the crew in the vicinity of blasting site.Due to the exceptionally large scale of mining operations,which may involve approximately 700 mining faces and more than 60 tonnes of explosives detonated each day,this method is treated as the most effective tool for rock mass destressing in the conditions of Polish copper mines.It was also proven that multi-face(or group)blasting allows reaching a high extraction rate with relatively high seismic prevention effectiveness(Mertuszka et al.,2015).The exemplary scheme of destressing with the use of multi-face blasting is presented in Fig.2.

Here is accepted a general assumption that more faces detonated at once will provide a higher amplitude of the seismic wave,and therefore will increase the possibility of rock mass disintegration.In fact,as this analysis has proven,such an assumption is not always correct because in some cases,seismic waves generated by detonation of subsequent faces may tend to damp each other.Due to this uncertainty,the periodic evaluation of destress blasting efficiency is essential for controlling and further improving geomechanical risk mitigation and seems to be the most important task of the contemporary rockburst prevention process.

In this paper,the authors have attempted to develop a novel method of destress blasting efficiency evaluation,essential for the control of rockbursts in underground mines.Selected methods of stress-release blasting are reviewed and a new quantitative method based on the in situ seismic measurements is proposed.For this purpose,methods for determination of factors describing the destressing effectiveness,expressed through the seismic amplitude,duration or dominant frequency of waves,are also presented.

As pointed out by Mertuszka et al.(2020),a reliable assessment of drilling and blasting operations should be based on the measurable parameters which may be effectively compared and verified.In the case of destress blasting,the evaluation methods may be divided into provocation rate-based methods,which rely on the criterion of the triggered tremor occurrence,and more complex methods,wherein various parameters measured in situ are used during the evaluation process.A general description of both methods is presented in this section.

Fig.2.Exemplary scheme of rock mass destressing with use of multi-face blasting.

Fig.3.(a)Energy(in J)and(b)quantitative triggering rates observed in one of the Polish copper mines in 2006-2018.

Over the last 50 years,results of numerous research studies on the provocation rate-based evaluation of destress blasting efficiency have been published(Karwoski et al.,1979;Hakami et al.,1990;Hakami and Taube,1992;Hedley,1992;Lightfoot et al.,1996;Poplawski,1997).As pointed out by Saiang and Nordlund(2005),regardless of the type of blasting and its location,the success rate was defined as triggering a significant seismic event shortly after completion of blasting or within a waiting period.Similarly,in Polish copper mines,the effectiveness of destress blasting is considered in terms of tremor triggering rate(Gogolewska and Bernat,2006;Gogolewska and Bartos,2008;Gogolewska and Kowalczyk,2020).In general,there are two factors used for such assessments.The first one(TR-N)is based on the dependence between the total number of tremors observed in a certain period of time and the number of tremors that occurred in the so-called waiting time.The second factor(TR-E)is energy-based and describes the ratio between the energy of triggered tremors and total energy of all tremors observed in the analysed area.Both factors may be calculated using the following formulas:

where∑itis the total number of triggered tremors within the waiting time,in the analysed area and certain period of time;∑isis the total number of all tremors within the analysed area and certain period of time;∑Etis the total energy of triggered tremors within the waiting time,in the analysed area and certain period of time;and∑Esis the total energy of all tremors within the analysed area and certain period of time.

The above methods are simple to use and have no limitations in term of the time or area subjected to analysis.Therefore,such evaluation is a universal solution that can be adapted in any mining panel.However,according to recent studies,one may conclude that when comparing triggering factors,one may observe that quantitative and energy domains show the opposite results(Butra and Pytel,2010;Gogolewska and Tomczak,2017;Fuławka et al.,2018a;Mertuszka et al.,2018).An analysis of seismic event triggering rates observed in one of the Polish copper mines from 2006 to 2018 using both approaches is presented in Fig.3.According to the adopted mining method,blasting is performed twice a day,i.e.after the second shift(ca.17:30-18:30)and the fourth shift(ca.5:30-6:30)-green areas in Fig.3.In most cases,the waiting period after the group blasting does not exceed 1 h.Based on Eqs.(1)and(2),tremors are considered to be triggered if they occur in the moment of face firing or during the waiting period.Hence,triggering rates may be determined.

When examining the energy triggering rate,one may conclude that only 19% of tremors occurred within the waiting period.In turn,when analysing blasting efficiency in the quantitative domain,a bit higher effectiveness of 25% may be observed.However,it is difficult to directly determine the efficiency of destress blasting in Polish copper mines,especially in the energy domain,where the seismic distribution is characterised by a random occurrence time in the last several years.Furthermore,it should be emphasised that the possibility of tremor triggering depends mainly on the rock mass condition in the vicinity of the analysed area.If the rock mass is prone to instability,a greater number and energy of provoked tremors are observed.Otherwise,both the frequency of triggered tremors and their energy are relatively low.

Based on the above analysis,one may conclude that using provocation rate-based evaluation seems to be too simplistic.According to previous experiences,no significant seismic activity is observed in most of the panels at the beginning of mining.As the mining sequence matures,higher stress conditions develop ahead of the mining front and the overall stress path is difficult to ascertain and evaluate with empirical methods.In such panels,the assessment of blasting in the light of a provocation rate-based approach may give inadequate results.Moreover,one of the main objectives of destress blasting is to generate such a strong seismic effect that it may create some cracks within rocks,and thus reduce the ability to accumulate the elastic energy in the vicinity of panels.In this case,the possibility of mining tremor occurrence should drop significantly and the rate of provocation efficiency will be an insufficient assessment measure.It means that the seismic evaluation of destress blasting should be conducted in parallel to quantitative provocation efficiency assessment.

According to recent research,there are more complex assessment methods,which provide more reliable results due to the inclusion of source vibration data and the mining operations occurring.This section provides a brief description of selected quantitative methods published already,including numerical analyses,estimation of induced energy and analyses of the seismic velocity changes.

2.1.Numerical analyses

Numerical methods have been developed rapidly in the last decades and may currently be treated as an efficient tool for destress blasting development.Application of computer simulations allow predicting,with some approximation,the effect of energy induced by detonation in terms of sequence of firing and the total amount of explosives.The first applications of numerical modelling for the analysis of rock mass response to dynamic blast loading were proposed by Taylor et al.(1986)who developed a continuum-based failure model to describe the characteristic dynamic fracture of rock under tension.Later,numerical methods for examining objects under dynamic loading were developed by Maxwell and Young(1998)who used the continuum method for simulation of the damage zone range.Recently,numerical simulations were utilised to determine the characteristic of seismic wave propagation in the rock mass after the detonation of explosives(Chen and Zhao,1998;Ma et al.,1998)and its effect on crack propagation around the blasthole(Zhu et al.,2007,2013;Ma and An,2008;An et al.,2017;Baranowski et al.,2020).In the field of rock mass preconditioning or destressing after blasting,some advanced simulations were also implemented(Tang and Mitri,2001;Baranowski et al.,2019;Xu et al.,2019).Numerical methods were used as well to analyse the effect of blasting on adjacent underground infrastructure(Zheng et al.,2015;Sainoki et al.,2017;Pytel et al.,2019;Yi et al.,2021).

With the use of numerical simulations,such parameters as the maximum amplitude of the seismic wave,stress-strain characteristic for a given rock mass area or dynamic changes of safety margins may be determined.It should be noted that numerical analyses are cost-effective because they allow comparing different scenarios,and finally indicate the most effective choice for given conditions.However,the reliability of numerical simulations is closely related to the quality of the input data at the stage of model development.Therefore,access to detailed geotechnical data as well as using appropriate boundary conditions confining the model is of crucial importance for obtaining reliable results.

2.2.Estimation of induced energy

In recent years,many studies were aimed at determining the energy generated by blasting,which was treated as a measure of blasting efficiency.One of the first attempts at developing an energy-based evaluation was proposed by Sedlak(1997)who investigated particular components of post-blasting energy balance.The same methodology was later recommended by Hinzen(1998)and Sanchidrián et al.(2007).However,as Konicek et al.(2013)pointed out,the analysis of energy in the source itself does not provide information about the actual seismic effect in a particular site.Thus,the“seismic effect”(SE)parameter for the Ostrava Coal-Field region was proposed for analyses.According to the above studies,SEmay be calculated using the following formula:

whereElocalis the seismic energy calculated based on local seismic monitoring;εEis the heat of explosion;Kis the empirical coefficient representing natural conditions of the rock mass;ψ=Eseis／Elocalis the coefficient considered for the efficiency of seismic monitoring in the analysed region;Klocalis the combined coefficient characterised by local mining and geologic conditions,andKlocal=KεE／ψ;andQis the mass of explosives.

In turn,the seismic energy(Eseis)may be defined using the below relationship:

whereEVTis the total energy of explosives detonation(sum of explosive energy in each blasthole),andEpris the released deformation energy.

The seismic energy is directly proportional to the mass of the explosive,but such an assumption is only correct in the case of seismic wave interference triggered by the detonation of explosives in subsequent faces,as proven by Mertuszka et al.(2018).In other cases,the total induced seismic energy,calculated as the sum of the energy generated by all blastholes may be substantially overestimated.

2.3.Analyses of the seismic velocity changes based on geotomographic methods

The main goal of destress blasting is to reduce the ability of the rock in the immediate vicinity of the excavation to carry stress by fracturing and damaging its structure.In many cases,however,the sources of the tremors are located at a relatively long distance from the mining faces,beyond the zone of the blasting induced cracks.In this case,the proper destress blasting should provide a dynamic impulse with such characteristics that affect the stress conditions in the rock mass prone to instability located away from the firing site.

The effect of such blasting may be evaluated by tracking the velocity/stress changes within the analysed region.For this purpose,the geotomographic method is mostly used.It may be assumed that stress changes correlate with the seismic hazard.Thus,it is desirable to develop such destress blasting that will allow reducing the velocity of seismic wave propagation and the stress values at the forefront of the mining panel(He et al.,2011;Kabiesz et al.,2015;Mutke et al.,2016).Evaluation of destress blasting efficiency based on geotomography is efficient and allows determination of local changes in seismic hazard.On the other hand,it is time-consuming and expensive in comparison to previously mentioned methods.

2.4.Seismic evaluation based on peak particle velocity

As pointed out by Parida and Mishra(2015),the detonation of explosives in the blastholes generates dynamic stress due to rapid gas acceleration towards the blasthole wall.The range and value of these stresses are strictly related to the amplitude of induced vibrations.According to Dowding(1985),it is possible to determine the maximum normal stress(σs)and the shear stress(τs)generated by blasting if the peak particle velocity(PPV)is known.In the case of destress blasting,these dynamic stresses should be as high as possible,since they will more strongly affect the degree of rock mass disturbance and thus its ability to store stress.The dynamic stresses σsand τsmay be determined according to the following formulas(Mutke et al.,2016):

wherePPVis the peak particle velocity(m/s),Eis the Young’s modulus(Pa),ρ is the density(kg/m3),Gis the shear modulus(Pa),v is the Poisson’s ratio,andcvis the seismic wave propagation velocity(m/s).

In turn,as stated by Nicholls et al.(1971),Mohammadnejad et al.(2012),Murmu et al.(2018)and Stankovi′c et al.(2019),PPV generated by blasting is related to the amount of simultaneously detonated explosives in a power way.Therefore,the predicted PPV(PPVp)may be calculated from the following relationship:

wherek,α and β are the constants associated with the given site and blasting procedure;ris the distance between the firing site and measurement point(m);andQis the maximum charge per delay(kg).

Then,the PPV estimation formula can be simplified by introducing the scaled distance(R0)parameter:

wheren=1／β.

Finally,Eq.(7)may be expressed as follows:

However,Eq.(9)describes the predicted PPV after the detonation of explosives with the same delay,and therefore cannot be used to evaluate or predict the result of blasting where more than one delay has been applied.In the case of the firing of multiple holes or even faces,seismic waves may interfere with each other,and depending on local conditions,this may result in damping or amplification of the seismic waves.This approach also lacks the effects of fracture interaction between holes or proximity of holes to one another.Thus,to include the superimposition of seismic waves,Agrawal and Mishra(2019)have proposed modification of Eqs.(7)and(9).They validated the empirical constantsk,α and β by measuring PPV after the detonation of all blastholes and adding the superimposition factor(S)to the formula,which may be positive in case of seismic amplification or negative while seismic attenuation occurs.The PPV for multiple blastholes(PPVMH)may be described from the relationship:

The superimposition factor depends strongly on local mining and geologic conditions and the delay accuracy of detonators.In the case of blasting characterised by the same parameters,the result of prediction must also be the same.Thus,evaluation of seismic effect based on Eq.(10)only(without reference to in situ measurements)may lead to overestimation or underestimation.

An innovative approach to the evaluation of blast-induced vibration was proposed by Lu et al.(2012,2017).The authors focused on the development and propagation of transient release of in situ stress(TRIS).As the authors concluded,PPV of TRIS induced vibration is correlated with strain energy of excavated rock masses,and may be a more reliable parameter for the evaluation of damages in the surrounding of blast holes.However,such approach is very complex,and it is currently challenging to utilise it in the everyday evaluation of blasting efficiency.

Taking into account the above analysis and also based on the authors’previous experiences,it may be stated that the characteristic seismic vibrations in the vicinity of the firing site may be successfully treated as an indicator of destress blasting efficiency.The distribution of seismic wave amplitude in the surrounding of the blasting site may suggest that the dominant frequency of the seismic wave and energy dissipation after each stress release blasting may be very useful parameters for a comparative evaluation of destress blasting efficiency.Methods of obtaining information about amplitude,frequency,and relative power of the seismic signal,which were used to evaluate the efficiency of the destress blasting,are presented in the next section.

The approach presented within this paper is based on continuous in situ seismic measurements using a local seismic network installed underground.The proposed method of destress blasting evaluation is based on seismic analyses of the waveforms generated by blasting in terms of:(i)amplitude of acceleration/velocity/displacement,(ii)frequency characteristic,(iii)duration,and(iv)relative seismic energy distribution.

From the blasting efficiency point of view,the induced seismic wave should be characterised by the highest possible amplitude with the longest possible duration of the seismic excitation.In turn,when examining frequency spectra,a clear dominant frequency,close to the natural frequency of the rock mass,is strongly desirable.The average lower eigenfrequency(natural)of the rock mass in the vicinity of workings in Polish copper mines,according to previous observations,varies from 3 Hz to 10 Hz(Lehmann et al.,1996).However,it depends on many factors such as geology,mainly in terms of rock disintegration level,rock strength parameters,damping factors,etc.

3.1.Trial site

The exploitation level in the area of interest is located 870 m below the surface,on average.The immediate roof consists of a thin dolomite/limestone stratum with the average compressive strength ranging from 137 MPa to 174 MPa.The main roof in turn is formed by medium-strength anhydrite(88 MPa)with an average thickness of 60 m.In the floor stratum,grey sandstone with a relatively low comprehensive strength of 30 MPa is located.The geologic profile over the analysed mining panel is presented in Fig.4.

The applied mining technique is based on a two-phase,almost complete extraction approach with the first phase creating yield pillars after driving rooms,while during the second phase,these pillars are mined out on the retreat.The mining cycle consists of the following operations:drilling and blasting,roof bolting and scaling,transportation of rocks by haulers or loaders to the unit discharge points,then by belt conveyors and skips to the surface,from where by belt conveyors to the ore enrichment plants.

3.2.Seismic monitoring and data processing

All seismic events observed within the considered mining area were collected using a well-developed underground seismic network.In the vicinity of the analysed panel,local seismicity is recorded by 64 uniaxial seismometers with a bandwidth ranging from 0.5 Hz to 100 Hz.The dedicated ELOGOR-C seismic monitoring system was developed for continuous observations of seismicity in the area of Polish copper mines.The sampling frequency of 500 Hz allows for appropriate reflection of the frequency content of ground motion induced by blasting in the near wave field.

The seismic waveforms recorded in underground conditions are continuously disrupted by electrical noise and noise generated by the ventilation system.This kind of noise is characterised by relatively constant frequency.In the analysed conditions,it was characterised by dominant frequencies of 50 Hz for electrical noise and 12.5 Hz for ventilation noise.Prior to analysis,the waveforms were processed to remove unwanted effects and noise from the seismic image.For this purpose,a second-order Butterworth filter with a bandpass corresponding to the seismometer bandwidth was applied.This kind of filter is commonly used for the purpose of high-frequency seismic data processing(Mollova,2007;Douglas and Boore,2011;Li et al.,2020).In order to separate electrical and ventilation noises from the records,additional bandstop filters in the ranges of 12.4-12.6 Hz and 49.9-50.1 Hz have been applied.

For the biased data,a zero-phase procedure was used to eliminate a potential phase displacement.The spectral characteristic of the recorded seismic wave was determined using the fast Fourier transform(FFT)and short-time Fourier transform(STFT).In both cases,the windowing procedure was preceded by a Hanning window,which has a satisfactory frequency resolution and ensures reduced spectral leakage.The efficiency of Hanning window in spectral analyses of blasting-and mining-induced vibration has been proven in recent research(Ainalis et al.,2018;Fan et al.,2020).

Fig.4.Geologic profile over the analysed mining panel.

The STFT is an efficient tool that allows performing the qualitative comparison of different destress blasting by tracking changes in the relative power distribution.The power distribution is“relative”because values shown on thez-axis do not represent the exact amplitude values,but the spectral amplitude,as in the FFT calculations(Mertuszka et al.,2018;Fuławka et al.,2019).Moreover,when combining the time-frequency analyses with statistical methods,i.e.regression analyses,the relationships between parameters such as the amplitude,frequency and seismic load duration may be determined.If the statistical population is sufficient,then the local effect of the abovementioned parameters on seismic energy distribution may also be defined.In such a case,the outcome variable may be defined as the high-intensity area in the spectrogram plot,and parameters such as amplitude,frequency and time are used as the predictors.

3.3.Description of mining system and local geomechanical conditions

A single-level flat copper deposit over the analysed area is excavated with the use of the room-and-pillar mining method with roof deflection.The geometry of underground workings and direction of exploitation are presented in Fig.5.

To determine the stress conditions within considered mining panel,a numerical three-dimensional(3D)finite element method(FEM)-based analysis has been performed with the use of NEi Nastran software.The overall stress state considering principal stresses σ1,σ2and σ3within the immediate roof strata was presented as a von Mises stress contour map.The results of numerical calculations are presented in Fig.6.

It is well known that the local velocity of seismic waves also depends on the degree of surrounding rock mass effort which in turn may be represented numerically by the value of von Mises stress described as follows:

From the above it may be concluded that the shortest route of seismic wave transmission between the mining front and seismic post passes through the dolomitic rock mass where the value of von Mises stress varies from 16 MPa to 18 MPa.It means that the effect of varying stress with respect to wave velocity in this case is rather insignificant.

Fig.5.Geometry of workings in the vicinity of analysed mining panel.

Fig.6.Contour of calculated values of von Mises stress(MPa)in the deposit level.

During the multi-face blasting,explosives are fired with specified delays in several mining faces.An evaluation method based solely on the analysis of the PPV generated by firing in a single face(or single delay)does not reflect the real conditions of simultaneous detonation of several mining faces located at different distances from the seismic post.In such cases,results may be significantly underestimated due to possible amplification of overlapping seismic waves.It means that the overall assessment should refer to all detonated holes/faces.Therefore,the blasting efficiency for a single face(SFE)should be determined for each detonated face according to the formula.:

wherePPVmis the measured PPV for a single face(m/s),andPPVpis predicted using Eq.(7).

Then the efficiency of near-field sequenced multi-face blasting(BEn)may be defined as the ratio of the sum of blasting efficiency factor(SFE)and the number of detonated faces(n):

The multi-face blasting efficiency factor is easy to implement and,at the same time,is an effective tool for blasting effectiveness evaluation in both underground and open-pit sequenced blasting.It should be noted,however,that this method is only suitable for analysis of near-field wave records,where the amplitudes generated by the detonation of successive delays are clearly visible.In this case,due to the proximity from the seismic source,it is expected that the observed frequencies of seismic vibration will be relatively high and will not match the local natural frequency of the rock mass.Therefore,in Eq.(13),both the time and dominant frequencies of a seismic wave are neglected.

The proposed interpretation of the multi-face blasting efficiency factor(BEn)is then as follows:

(1)IfBEn＜0.9,the induced seismic effect is lower than the predicted one,and blasting is ineffective.

(2)IfBEn=0.9-1.1,the induced seismic effect is close to the predicted one,and blasting is moderately effective,

(3)IfBEn＞1.1,the induced seismic effect is higher than the predicted one,and blasting is highly effective.

For simultaneous firing of a group of faces or for evaluation of blasting records from the far-field,where the amplitude distribution generated by the detonation of subsequent faces is significantly scattered and disturbed,a modified destress blasting efficiency factor(BEf)may be used.This type of analysis allows considering the amplitude of vibrations,their frequency characteristic,and the total time of excitation.The general form ofBEfis expressed as follows:

whereESAis the component of seismic effect generated by seismic amplitude distribution,Etis the component of seismic effect related with duration of seismic load,andEfis the component of seismic effect related to the frequency of induced vibrations.

As mentioned by Agrawal and Mishra(2019),the analyses of PPV generated by multiple hole detonation should be corrected by theSfactor,which describes the local tendency of seismic wave superimposition or attenuation.Therefore,ESAin Eq.(14)may be determined according to the following relationship:

wherePPVmaxis the maximum recorded amplitude of seismic velocity/acceleration,generated by the firing of a group of holes/faces;andPPVR0is the estimated PPV generated by the face detonation characterised by a maximumR0determined with Eq.(8).

Due to the high variability of the total amount of explosives used in the blasting works,theSfactor for the total amount of explosives should be determined.The localSfactor was determined based on analysis of PPV distribution from 30 multi-face blasts,performed within the analysed mining panel.

The dependence between theSfactor and the total amount of explosives is presented in Fig.7.

Thus,theSfactor may be determined by the formula:

whereℶand ε are the empirical constants describing local mining and geologic conditions,andQtotalis the total amount of explosives(kg).

At the same time,the effect of the duration of the seismic vibration may be determined from the following equation:

wheretrecis the recorded time of seismic vibrations(s),tmaxis the detonation time of the last blasthole during the firing of a group of faces(s),and θ is the empirical factor determining the effect of vibration duration on the level of seismic load.

The total effective time of seismic vibrations(trec)may be determined from the Husid plot of the acceleration/velocity timeseries showing the increase of Arias intensity(AI)over time(Lee and Green,2008).The AI for horizontal seismic acceleration(IA)is determined using the following formula(Arias,1970;Liu et al.,2016):

wherea2x(t)anda2y(t)are the waveforms of seismic acceleration inx-andy-directions,respectively;tis the variable describing the dependence of intensity on the time;andtAis the total duration of vibration(s).

In general,it may be assumed that the duration of the seismic load corresponds with the time in which the AI remains between 5% and 95%(Afshari and Stewart,2016;Baltay et al.,2019).

The last component of Eq.(14)describes the effect of seismic wave frequency on the local distribution of seismic energy.It may be assumed that with a decrease in the seismic frequency,the observed displacement increases,and therefore,the possibility of rock mass destressing is higher.However,the most effective frequency from the rockburst prevention point of view is equal to the eigenvalue of the rock mass frequency(Uenishi,2017).Therefore,the frequency component(Ef)may be determined according to the following formula:

wherefnis the eigenfrequency of surrounding rock mass(Hz),fdis the dominant frequency of induced seismic waves(Hz),and ϑ is the empirical factor describing the effect of the frequency component of the seismic wave on the overall level of seismic load.

The coefficients θ and ϑ may be determined based on statistical analyses of STFT relative power distribution of seismic signals after blasting.According to the authors’preliminary analyses,the coefficient θ in the conditions of Polish copper mines varies from 0 to 0.5,while ϑ is between 1 and 2.In case of a lack of in situ measurements,ϑ and θ may be determined using statistical regression methods supported by numerical modelling.However,the reliability of such a solution is strongly dependent on the quality of the developed numerical model.The changes of the frequency componentEfwith respect to different values of dominant frequencies are presented in Fig.8.

As a result,the proposed interpretation of the overall blasting efficiency using the modified multi-face blasting efficiency factor(BEf)is as follows:

(1)IfBEf＜1,the induced seismic effect is lower than the predicted one,and blasting is ineffective.

(2)IfBEf=1-1.2,the induced seismic effect is close to the predicted one,and blasting is moderately effective.

(3)IfBEf＞1.2,the induced seismic effect is higher than predicted one,and blasting is highly effective.

From the above interpretation,one may conclude that theBEffactor may be calculated even when theEforEtcomponent is unknown.In such a case,the calculated blasting efficiency is based on amplitude distribution only,and factorsEfandEtshould be assumed as 1.

Fig.8.Distribution of the frequency component Ef for ϑ=1.85 and fn=3.5 Hz.

Both methods of destress blasting efficiency evaluation were tested and validated in one of the mining panels in an underground copper mine in Poland.TheBEnfactor was used for the near-field evaluation of the sequenced firing of 4 faces,i.e.one by one with delays of 4-5 s between each face.Faces differed in the total amount of explosives and delay times.The first two faces were detonated with the use of 6 cut holes,while the third and fourth faces were detonated with drilling and blasting patterns based on 4 cut holes(Fig.9).

All cut holes were filled with 3.5 kg of bulk emulsion explosives.Therefore,the maximum charge per delay was 21 kg for the first and second faces and 14 kg for the third and fourth faces.Knowing the distance from the measurement site and the amount of explosives used in each face,it was possible to determine if the induced seismic effect(Fig.10-blue waveform)of blasting is better or worse than the expected one(Fig.10-red line).The record of induced seismic wave and the distribution of the predicted PPV values are presented in Fig.10.

Spatial location of each face in relation to measuring site has been presented in Fig.11.

Knowing the amplitude distribution generated by detonation of each face,it was possible to determine overall blasting efficiency.The results of calculations for each fired face(SFE)and for the entire group of faces(BEn)are presented in Table 1.

The blasting efficiency factor allows comparison of results of blasting operations differing in parameters such as the total amount of explosives,type of initiation,and the delay time used,and indicates the most effective configuration for local mining and geologic conditions.As shown in Fig.10,in 3 of 4 faces,the detonation of the cut holes,which are fired as the first group of holes,generates amplitudes close to predicted values.Other blastholes,which were characterised by smaller charge per delay,should theoretically induce lower amplitudes.However,delay times that were used during the blasting generated superimposition of the seismic waves which resulted in numerous visible seismic amplifications.In this case,the efficiency of blasting is greater than the expected one.It should also be noted that in the fourth face,the amplitude generated by detonation of cut holes was 50%lower than the expected value.It may be expected that such a situation was strictly related with firing order.Namely,first two faces(faces 1 and 2)pre-fractured rock mass which is located on the way of seismic wave propagation from faces 3 and 4.Therefore,the amplitude generated by detonation of cut holes in faces 3 and 4 was significantly lower than the expected value.Still,due to seismic amplification,PPV generated by detonation of other subsequent holes was greater than the calculated threshold.As a result,the effectiveness of the detonation of single faces ranged between 1.19 and 1.45,while the overall blasting efficiency was 1.31.

Fig.9.Drilling and blasting pattern used during sequenced blasting.

Fig.10.The recorded waveforms of sequenced blasting of 4 faces and predicted PPV values.

Fig.11.Location of subsequently detonated mining faces.

Nevertheless,the sequenced blasting is not a method commonly used in Polish copper mines.The main method of blasting is based on simultaneous firing of explosives in a group of faces to amplify the seismic effect and potentially maximise the probability of rock mass destressing.Thus,theBEffactor has been calculated for a series of 15 destressing blasts carried out in the analysed mining panel.All faces within each group have been detonated with the drilling and blasting pattern presented in Fig.12.

These works were characterised by differing distances of the fired faces from the measuring instruments and different amounts of detonated explosives.The results ofBEfcalculated by Eq.(13)are presented in Table 2.

Table 1Calculated destress blasting efficiency factor for sequenced blasting of 4 faces.

Table 2Calculation of destress blasting efficiency factor.

An analysis indicates that the resulting destress blasting efficiency factors vary significantly and reach values between 0.8 and 4.3.At the same time,the results appear to be highly reliable as theBEffactor is not susceptible to the variability of the total amount of explosives used during blasting.This shows that multi-face blasting with a greater amount of explosives,even if the generated amplitude is higher,may be less effective.The example of the usefulness of the destress blasting effectiveness factor may be noticed when comparing the group blasting No.6,for which theBEffactor was 0.9,and group blasting No.9,for whichBEfamounted to 4.3.In the first case,16 faces and 1432 kg of explosives were detonated,while 5 faces and 576 kg were detonated in the second one.The waveforms generated by both events are presented in Fig.13.

From the analysis of blasting Nos.6 and 9,one may conclude that the amplitudes generated in both cases reached almost the same level.However,in blasting No.6,almost three times more explosives were detonated.In turn,significant difference is visible in terms of seismic load duration and observed frequency.Blasting No.9 generated vibration with the dominant frequency of 3.5 Hz which most likely was close to the natural frequency of rock mass.As a result,the visible resonance occurred in induced ground motion around the measuring site.Such a situation is confirmation that the time and frequency of seismic load also play significant roles in destress blasting efficiency assessment.The evaluation of multi-face blasting efficiency with respect to the amount of explosives is presented in Fig.14.

Fig.12.Drilling and blasting pattern used during multi-face blasting works in analysed mining panel.

Fig.13.Comparison of two destress blasting differing in number of faces and total amount of explosives.

However,when analysing results of all 15 destress blasting,it may be observed that in scope of generated seismic effect,the multiface approach in most cases leads to improvement of blasting efficiency,in comparison to the single-face firing.Still,the assumption that the seismic effect is mostly related to the amount of explosives seems to be inappropriate.According to the presented analysis,parameters such as the spatial location of each face,applied delays and local geomechanical conditions have even stronger impact on seismic effect than the mass of explosives only.A meaningful example of this statement may be observed in the case of two blasts in which over 1000 kg of explosives have been used.According to Fig.13,in both cases,the evaluated efficiency was 0.9,which suggests that detonation of subsequent faces causes wave attenuation instead of its amplification.In turn,there were numerous cases where the mass of explosives varied in the range of 600 kg and 800 kg,but blasting efficiency was twice as that expected.

Fig.14.Changes of the BEf factor with the mass of the explosives.

Thus,using theBEffactor,it is possible to determine which blasting sequences and face locations favour the amplification of the effect,and which approaches should be abandoned.Comparing this method to previous studies presented in Section 2,it may be stated that implementation of factors such as duration of vibrations and their dominant frequency increases the reliability of performed evaluation due to more reasonable description of recorded seismic load.However,it is crucial to accurately determine empirical factors which describe the effect of each component of the seismic wave on the overall level of seismic load.These factors may be evaluated with the use of in situ measurements and statistical methods,or in some cases,with the use of numerical simulations,but only in the case of a properly validated 3D model.If there are doubts about the correctness of determined weights for frequency and time components,then the parametersEtandEfin Eq.(14)should be defined as 1.In such a case,analysis will be based on recorded amplitudes only,which mitigates the possibility of overestimation or underestimation of results.

Within this paper,the novel quantitative methods of destress blasting efficiency were developed and validated based on in situ measurements.The first approach allows determining the multiface blasting efficiency factors and is based solely on the amplitude,taking into account the dynamic parameters of seismic wave.However,in comparison to previous methods described in the literature,a clear improvement in the reliability of efficiency evaluation may be observed.It was proven that the obtained results cover a wide range of parameters,including the distance from the firing point,the total amount of explosives and parameters describing seismic attenuation in local mining and geologic conditions.Moreover,theBEnfactor takes into consideration the total number of faces and/or holes detonated during blasting,which is a novelty compared to recent studies.Still,it must be borne in mind that an effective estimation of the destress blasting efficiency using the proposed factor requires fulfilling the condition of the nearfield measurement.When long distances from the blasting site exist,the waveforms generated by the detonation of successive holes may overlap each other,and thus reduce the applicability of the method.

For simultaneous blasting or blasting recorded from long distances,an improved blasting efficiency factorBEfhas also been developed.This method enhances previous approaches by including the time and frequency components into the blasting efficiency assessment formula.This solution is highly advanced and requires additional seismic analyses to determine the overall duration of seismic load,frequency characteristics and distribution of the relative power of the seismic signal.In this case,additional in situ measurements are required to determine the natural frequencies of the rock mass.At the same time,the information obtained using theBEffactor is more comprehensive compared to other currently available methods of destress blasting evaluation.It can be assumed that its regular implementation fordestress blasting assessment will allow indication of the most suitable parameters of destress blasting for existing local mining and geologic conditions.

It should also be noted that both approaches may be easily applied not only in the conditions of deep copper mines in Poland but also in other underground mines as well as in quarries and open-pits,where the seismic effect of blasting has to be monitored due to safety regulations.

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 paper has been prepared through the Horizon 2020 project funded by the European Union on“Next Generation Carbon Neutral Pilots for Smart Intelligent Mining Systems(NEXGEN-SIMS)”(Grant No.101003591).