Decreasing Mining Losses for the Room and Pillar Method by Replacing the Inter-Room Pillars by the Construction of Wooden Cribs Filled with Waste Rocks

energies

Article Decreasing Mining Losses for the Room and Pillar Method by Replacing the Inter-Room Pillars by the Construction of Wooden Cribs Filled with Waste Rocks

Krzysztof Skrzypkowski Faculty of Mining and Geoengineering, AGH University of Science and Technology, Mickiewicza 30 av., 30-059 Cracow, Poland; [email protected]

Received: 16 June 2020; Accepted: 7 July 2020; Published: 10 July 2020

Abstract: The article presents methods of securing mining excavations using wooden cribs. For the underground room and pillar method used to excavate zinc and lead ore body in the Olkusz-Pomorzany mine in Poland, model tests for the replacement of rock pillars by wooden cribs are presented. In the first stage of research, the results of laboratory strength tests carried out on models of four-point, six-point and eight-point cribs made of wooden beech beams at a 1:28 scale arranged horizontally were determined. For the first time, a concave round notch connection was used to connect the beams of the wooden cribs. The maximal capacity of cribs consisting only of beams and filled with waste rocks taken from underground mining excavations was determined. In addition, the vertical deformations of the cribs at maximal loading force and their specific deformations are presented. Additionally, on the basis of load-displacement characteristics, the range in variability of the stiffness of empty cribs and those filled with waste rocks was calculated as a function of their compressibility. In the second stage of research, the room and pillar method was designed in the Phase2 numerical program. The aim of the study was to determine the stresses in the inter-room pillars. Based on the results of laboratory and numerical tests, a factor of safety was determined, indicating that it is possible to reduce mining losses while maintaining the safe exploitation conditions of the ore body.

Keywords: wooden cribs; mining losses; room and pillar method; stiﬀness; mining support

1. Introduction The rational management of mineral resources is aimed at combining the efficiency of their extraction, their comprehensive and rational use, and minimizing damage to the human environment. The use of resources is shaped at all stages of geological and mining activity, from the exploration and documentation of deposits, through the design, exploitation and processing of minerals. The main factors affecting the use of resources are, among others, the classification of resources, and mining losses and dilution of the deposit. In underground mining, new support systems are still being sought, whose main task is, among others, to reduce mining losses, while maintaining a high level of safety for the works being carried out. In room and pillar methods, attempts are made to strengthen the excavations or replace the inter-room pillars by wooden or concrete constructions. Barczak and Tastillo [1], Korzeniowski and Skrzypkowski [2], and Korzeniowski et al. [3] studied wooden cribs with beams of rectangular and square section. Daehnke et al. [4], Dison and Smith [5], and Mining Product Developments [6] determined the strength parameters for grout bags in conjunction with timber pack. Skrzypkowski [7] and Strata Worldwide Company [8] determined the load-displacement characteristics for groups of wooden props. Kushwaha et al. [9] tested a steel cog. Strata Worldwide Company [8]

Energies 2020, 13, 3564; doi:10.3390/en13143564 www.mdpi.com/journal/energies Energies 2020, 13, 3564 2 of 20 Energies 2020, 13, x FOR PEER REVIEW 2 of 21

Kushwahaproposed to et secure al. [9] excavationstested a steel in cog. the Strata form ofWorldwide sand props. Company Li et al. [8] [10 ]proposed designed to an secure expandable excavations pillar, inwhich the form uses of a chemicalsand props. mixture Li et al. that [10] expands designed when an expandable water is introduced. pillar, whichLuan uses et al.a chemical[11] created mixture and thattested expands a lightweight when water and high-strength is introduced. foam Luan concrete et al. [11] and created a mortise-and-tenon and tested a structurelightweight hollow-block and high- strengthwall. Hadjigeorgiou foam concrete et al.and [12 a], mortise-and-tenon Kang et al. [13], and st Caoructure et al. hollow-block [14] proposed wall. to replace Hadjigeorgiou rock pillars et al. by [12],artificial Kang pillars et al. based [13], and on cement Cao etbinder. al. [14] Despiteproposed the to significant replace rock technical pillars progress by artificial that haspillars been based made on in cementrecent years, binder. wood Despite is still the used significant to support technical underground progress excavations, that has been especially made in miningrecent years, ones. Woodenwood is stillcrib used support to support is commonly underground used to strengthenexcavations, underground especially mining mine roadway ones. Wooden and room crib excavations. support is commonlyCribs that areused full, to openwork,strengthen empty,underground or filled mine by cement roadway binder and orroom waste excavations. rocks are used.Cribs Thethat woodenare full, openwork,cribs used inempty, underground or filled mining by cement are built binder of old or railwaywaste rocks sleepers, are roundused. The wood wooden or properly cribs prepared used in undergroundrectangular or mining cylindrical are built wooden of old beams. railway The sleeper capacitys, round of the wood crib or support properly depends, prepared among rectangular others, oron cylindrical the geometry wooden and the beams. number The of capacity contact pointsof the joining crib support individual depends, cribs, theamong type others, of wood on used, the geometrythe type of and cut the jams, number and the of methodcontact points of filling joining the empty individual space cribs, [4]. For the example, type of wood a cubic used, crib the made type of ofpine cut wood jams, 1.5 and m longthe method filled by of waste filling rocks the hasempty a capacity space [4]. of 6.75For MNexample, at 25% a compressibilitycubic crib made and of 13.50pine woodMN at 1.5 50% m compressibility. long filled by waste However, rocks for has oak a withcapacity the sameof 6.75 configuration, MN at 25% thecompressibility support is 11.25 and MN 13.50 at MN25% at compressibility 50% compressibility. and 45 MNHowever, at 50% for compressibility oak with the same [15]. Testsconfiguration, on the connection the support configuration is 11.25 MN of atfour-point, 25% compressibility nine-point and 45 full MN contact at 50% beams compress haveibility shown [15]. that Tests the magnitudeon the connection of elastic configuration and plastic ofsti four-point,ffness depends nine-point on the and contact full contact area of beams the beams have and shown height. that Stitheff nessmagnitude increases of elastic linearly and with plastic the stiffnesscontact surfacedepends and on increases the contact exponentially area of the asbeam thes height and height. decreases Stiffness [1]. The increases capacity linearly of the with wooden the contactcrib increases surface with and increasingincreases expone convergence.ntially Foras the example, height cribsdecreases 1.6 m [1].1.1 The m capacity with a height of the of wooden 1.45 m, × cribmade increases of round with timber increasing from pine convergence. wood, have For an exam averageple, capacity cribs 1.6 of: m 140× 1.1 kN m withwith aa compressibility height of 1.45 m, of made10%; 220 of round kN at atimber compressibility from pine of wood, 20%; andhave 270 an kN average at 30% capacity compressibility of: 140 kN [16 ].with In undergrounda compressibility hard ofcoal 10%; mines, 220 woodenkN at a compressibility cribs are an alternative of 20%; toand the 270 possible kN at costly30% compressibility necessity of driving [16]. anotherIn underground roadway. hardWooden coal cribs mines, are wooden used to cribs maintain are an roadways, alternative which to the means possible that costly there necessity is no need of todriving make another roadway.roadway forWooden the next cribs longwall. are used The to same maintain roadway roadways, has a transport which means function that for there the is first no longwall need to make and a another roadway for the next longwall. The same roadway has a transport function for the first ventilation function for the second longwall (Figure1a,b). longwall and a ventilation function for the second longwall (Figure 1a,b).

(a) (b)

Figure 1. Application of wooden cribs to maintain the roadway for the next longwall: (a) Arrangement Figureof wooden 1. Application cribs in a maingate;of wooden (b cribs) General to maintain view of the the roadway wooden for crib. the next longwall: (a) Arrangement of wooden cribs in a maingate; (b) General view of the wooden crib. In underground ore mining, rock bolt support is the basic way to support excavations [17,18]. Often,In however,underground the rock ore boltmining, support rock is bolt additionally support is strengthened the basic way by to means support of a excavations wooden support [17,18]. in Often,the form however, of individual the rock props bolt orsupport rows of is propsadditional as wellly strengthened as by means ofby wooden means of cribs. a wooden The primary support task in theof the form wooden of individual support props is the or fencing rows of and props strengthening as well as ofby placesmeans threatened of wooden with cribs. a The roof primary fall [19]. task In a ofroom the andwooden pillar support method is with the fencing roof sag and in copper strengthenin ore miningg of places in the threatened Legnicko-Głog withó wa roof Copper fall District[19]. In ain room Poland, and woodenpillar method cribs arewith used roof during sag in copper the last-phase ore mining liquidation in the Legnicko-G of post-miningłogów spaces. Copper Wooden District in Poland, wooden cribs are used during the last-phase liquidation of post-mining spaces. Wooden

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Energies 2020, 13, x FOR PEER REVIEW 3 of 21 cribs are built between residual pillars (Figure2a,b). The cribs built in the middle of the excavation constitutecribs are built an element between that residual strengthens pillars the(Figure rock 2a,b). bolt support The cribs and built at thein the same middle time actof the as anexcavation element separatingconstitute an access element to the that section strengthens endangered the rock by the bolt roof support fall. In and zinc at and the lead same ore time mining act as in an the element Olkusz regionseparating in Poland, access to the the cribs section next enda to thengered side by walls, the roof mainly fall. inIn zinc the cornersand lead of ore the mining widened in the crossings, Olkusz constituteregion in Poland, a support the reducing cribs next the to width the side of the walls, excavation mainly roof in the (Figure corners2c–e). of the widened crossings, constitute a support reducing the width of the excavation roof (Figure 2c–e).

(b)

(d) (e)

Figure 2. Cribs in Polish ore mining: (a) Support of the widened room in the room and pillar method withFigure roof 2. sagCribs in in the Polish Legnicko-Głog ore mining:ów ( Coppera) Support District of the in widened Poland (the room use in of the cribs room in the and phase pillar of method cutting technologicalwith roof sag pillars);in the Legnicko-G (b) Residualłogów pillar; Copper (c) General District view in of Poland crib; (d )(the Support use of of cribs the widened in the phase room inof zinccutting and technological lead ore mining pillars); in Poland; (b) Residual (e) Joining pillar; beams (c) General with steel view clamps. of crib; (d) Support of the widened room in zinc and lead ore mining in Poland; (e) Joining beams with steel clamps. In this article laboratory compressive tests on wooden cribs models are presented. Additionally, the maximalIn this article loads laboratory and vertical compressive and specific tests deformations on wooden for cribs empty models cribs are and presented. those filled Additionally, with waste rocksthe maximal were determined. loads and vertical Furthermore, and specific on the deformations basis of load-displacement for empty cribs and characteristics, those filled with the ranges waste ofrocks variability were determined. of the stiffness Furthermore, of empty andon the filled basis cribs of load-displacement with waste rocks were characteristics, calculated asthe a ranges function of ofvariability their compressibility. of the stiffness Furthermore, of empty and in filled this study,cribs with the room waste and rocks pillar were method calculated was designedas a function in the of Phase2their compressibility. numerical program. Furthermore, The aim ofin thethis study study, was the to room determine and pillar the stresses method in thewas inter-room designed pillars.in the BasedPhase2 on numerical the results program. of laboratory The aim and of numerical the study tests, was a factorto determine of safety the was stresses determined. in the inter-room pillars. Based on the results of laboratory and numerical tests, a factor of safety was determined.

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2. Sources of the Mining Losses in the Room and Pillar Method for Lead and Zinc Ore Deposit Due to the complete recognition of the deposit, geological resources are divided into balance Energiesand sub-balance. 2020, 13, x FOR Exploitation PEER REVIEW losses that can be recovered can be divided into hidden and available4 of 21 ones, which in turn can be divided into those prepared and unprepared for exploitation (Figure3). ones, which in turn can be divided into those prepared and unprepared for exploitation (Figure 3). Geological resources are those that meet the limits for the values of the parameters deﬁning the deposit, Geological resources are those that meet the limits for the values of the parameters defining the according to Polish regulations [20,21]. For example, the minimum content of zinc and lead for Polish deposit, according to Polish regulations [20,21]. For example, the minimum content of zinc and lead deposits of zinc and lead appearing in sulﬁde form in a sample contouring the deposit, regardless of for Polish deposits of zinc and lead appearing in sulfide form in a sample contouring the deposit, the degree of oxidation of the ore, should be at least 2%. regardless of the degree of oxidation of the ore, should be at least 2%.

FigureFigure 3. 3. DivisionDivision of of geological geological resources resources..

TheThe production production capacity capacity of of the the mining mining plant plant and and its its lifetime lifetime are are determined during during the the design design ofof mining mining branches branches by by r reducingeducing industrial industrial resources resources by by the the losses losses expected expected in in the the adopted adopted deposit deposit exploitationexploitation system system and and in in the the adopted adopted mineral mineral proc processingessing processes. processes. Mining Mining losses losses or, strictly, or, strictly, the resourcesthe resources lost lostduring during exploitation exploitation are arepart part of the of the balance balance of ofresources resources not not extracted extracted from from the the deposit. deposit. TheThe following following factors affect affect the amount of losses: • geologicalgeological factors factors (arising (arising as as a a re resultsult of of deposit deposit disruption disruption by by discharges, discharges, elevations, elevations, or or fissures, fissures, • asas well as losses resulting fromfrom thethe complicatedcomplicated formform ofof the the deposit: deposit: exclusion, exclusion, irregularities irregularities in in a adeposit deposit occurring); occurring); • hydrogeological factors (losses related to leaving protective pillars, preventing the ingress of hydrogeological factors (losses related to leaving protective pillars, preventing the ingress of water • water or the inability to select a deposit due to water accumulation); or the inability to select a deposit due to water accumulation); • leaving the deposit in pillars to protect capital excavations, surface structures, canals, rivers, leaving the deposit in pillars to protect capital excavations, surface structures, canals, rivers, roads, • roads, and other objects that are within the impact of mining works (pillars left between and other objects that are within the impact of mining works (pillars left between exploitation exploitation fields or individual excavations, to avoid mutual interaction; losses in protective fields or individual excavations, to avoid mutual interaction; losses in protective pillars, and also pillars, and also in pillars left to support the roof in a room methods); in pillars left to support the roof in a room methods); • leaving part of the deposit as a result of changing deposit parameters; leaving part of the deposit as a result of changing deposit parameters; •• the method of transporting the excavated material underground (losses occur as a result of the method of transporting the excavated material underground (losses occur as a result of spilling • spilling the excavated material while loading it onto carts or conveyors); the excavated material while loading it onto carts or conveyors); • losses in non-industrial resources as a result of mining being removed by mining works; • losses in non-industrial resources as a result of mining being removed by mining works; • loosening of the mineral in the filling, during layer exploitation, as well as ore discharge. loosening of the mineral in the filling, during layer exploitation, as well as ore discharge. • In the Olkusz-Pomorzany mine in Poland, the exploration drift grid is 100 m × 100 m, so exploitation fields of 1 hectare are separated. The exploitation field is divided into smaller fields with a width of 12 to 25 m by means of haulage rooms (Figure 4a). Smaller fields are mined by means of rooms with a width of 5 to 6 m. Rooms are mined parallel to the front line, leaving a continuous inter- room pillar with a width of 3 to 4 m. In order to minimize mining losses, the inter-room pillar is selected partly with the help of rooms driven towards goafs. This creates square pillars with a side

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In the Olkusz-Pomorzany mine in Poland, the exploration drift grid is 100 m 100 m, × so exploitation fields of 1 hectare are separated. The exploitation field is divided into smaller fields with a width of 12 to 25 m by means of haulage rooms (Figure4a). Smaller fields are mined by means of rooms with a width of 5 to 6 m. Rooms are mined parallel to the front line, leaving a continuous inter-room pillar with a width of 3 to 4 m. In order to minimize mining losses, the inter-room pillar is Energies 2020, 13, x FOR PEER REVIEW 5 of 21 selected partly with the help of rooms driven towards goafs. This creates square pillars with a side length of of 3 to 4 m (Figure 44b).b). AfterAfter thethe cuttingcutting ofof continuouscontinuous pillars,pillars, the post-mining void is filled.filled. Hydraulic sand sand backfilling backfilling includes includes a a number number of of pillars pillars and and exploitation exploitation rooms rooms from from the the goaf goaf side. side. On the line of the penultimate row of pillars, woodenwooden dams are built in the cutting room. Instead of fillingfilling the dams, it is possible to make a heap fr fromom waste rocks obtained from the workings. A filling filling pipeline is fed through one of the fillingfilling dams (Figure4 4c),c), which which is is shortened shortened as as goafs goafs are are filled. filled.

(b)

(a)

(c)

Figure 4. Room and pillar method with hydraulic backfilling: (a) Division of the exploitation field; Figure(b) Technological 4. Room andpillar pillar with method sphalerite with andhydraulic galena backfilling: minerals in ( thea) Division Olkusz-Pomorzany of the exploitation mine in field; Poland; (b) Technological(c) Construction pillar of a with wooden sphalerite filling damand galena with a fillingminerals pipeline. in the Olkusz-Pomorzany mine in Poland; (c) Construction of a wooden filling dam with a filling pipeline. 3. Laboratory Tests on the Mining Crib Models 3. LaboratoryThe subject Tests of theon the laboratory Mining tests Crib were Models models of mining cribs made of beech wooden beams withThe a circular subject cross-section, of the laboratory currently tests used were in models many underground of mining cribs mines made (Figure of beech5a). Thewooden wood beams used withhad ana circular absolute cross-section, humidity of currently 8%. Models used of in the many cribs underground were made on mines a 1:28 (Figure geometric 5a). scale.The wood The mainused hadreason an forabsolute using humidity such a scale of was8%. Models to best matchof the thecribs crushed were made waste on rocks a 1:28 to geometric the interior scale. of the The wooden main reasoncribs. Thefor using fit consisted such a scale of atight was to adherence best match of the crushed waste rock, withrocks as to little the interior free space of the as possiblewooden cribs.between The the fit rocks.consisted If a of larger a tight scale adherence was used, of the the free crushed spaces rock, between with theas little rocks free would space be as larger possible due betweento the diameter the rocks. of theIf a lumps,larger scale which was in used, the conditions the free spaces of the between Olkusz-Pomorzany the rocks would mine be ranges larger from due to0.1 the m diameter to 0.5 m. of Beams the lumps, measuring which 0.021 in the m condit0.2ions m were of the used Olku tosz-Pomorzany build models mine of cribs. ranges Four-point, from 0.1 × msix-point, to 0.5 m. and Beams eight-point measuring models 0.021 of cribsm × 0.2 without m were filling used were to build constructed models from of cribs. 22, 28, Four-point, and 34 beams, six- point,respectively and eight-point (Figure6a–i). models For theof cribs first without time, the filling beams were were constructed connected from by concave 22, 28, roundand 34 notches beams, respectively(Figure5c). The(Figure mining 6a–i). wooden For the crib first was time, made the beams of longitudinal were connected round beamsby concave arranged round on notches top of (Figureeach other 5c).in The horizontal mining wooden layers, with crib was the beams made of longitudinal adjacent layers round crossing beams and arranged leaning on on top each of othereach other in horizontal layers, with the beams of adjacent layers crossing and leaning on each other in concave notches, creating a structure in the shape of a straight prism or a set of straight prisms, with each layer containing at least two beams, characterized in that the notches are found only in the upper parts of the beams of each layer, except for the roof beams, which do not have notches [22]. This is a very advantageous solution, because only wood is used to connect wooden beams, without the use of steel clamps. In order for the beams to be connected and not move in each beam, concave oval notches were made with a depth of 0.003 m. In addition, the four-point cribs were filled with waste rocks (Figure 6j–l). In the Olkusz-Pomorzany zinc and lead mine, the deposits occur in the form of

Energies 2020, 13, 3564 6 of 20 in concave notches, creating a structure in the shape of a straight prism or a set of straight prisms, with each layer containing at least two beams, characterized in that the notches are found only in the upper parts of the beams of each layer, except for the roof beams, which do not have notches [22]. This is a very advantageous solution, because only wood is used to connect wooden beams, without the use of steel clamps. In order for the beams to be connected and not move in each beam, concave oval notches were made with a depth of 0.003 m. In addition, the four-point cribs were ﬁlled with waste rocks (Figure6j–l). In the Olkusz-Pomorzany zinc and lead mine, the deposits occur in the form of irregular nests and lenses. Exploratory excavations are carried out at a distance of 100 m. Rock lumps (dolomitic limestone) were taken from exploratory drifts where the useful mineral content was below 2%. Regardless of the percentage of useful minerals, all rocks were transported to the discharge grate and then transported to the processing plant. In laboratory conditions, the rock lumps (dolomitic limestone) were ground in a jaw crusher to a particle size of 0.005 to 0.018 m (Figure5b). The compressive strength of dolomitic limestone was 30 MPa [23]. The inner mesh of the crib was polypropylene canvas commonly used for the construction of ﬁlling dams in underground mining. The height of each model was 0.2 m. Energies 2020, 13, x FOR PEER REVIEW 7 of 21

(b) (a)

(c)

Figure 5. General view of mining cribs models: (a) Empty eight-point, six-point, four-point, and Figure 5. General view of mining cribs models: (a) Empty eight-point, six-point, four-point, and four- four-point ﬁlled by waste rocks; (b) Waste rocks; (c) Connection of wooden beams by means of concave point filled by waste rocks; (b) Waste rocks; (c) Connection of wooden beams by means of concave round notches. round notches.

(a) (c) (b)

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(b) (a)

(c)

Figure 5. General view of mining cribs models: (a) Empty eight-point, six-point, four-point, and four- Energiespoint2020 ,filled13, 3564 by waste rocks; (b) Waste rocks; (c) Connection of wooden beams by means of concave7 of 20 round notches.

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(d) (f) (e)

(g) (h) (i)

(j) (k) (l)

FigureFigure 6. 6. Multi-pointMulti-point cribs: cribs: (a) (Four-point,a) Four-point, general general view; view; (b) Four-point, (b) Four-point, top view; top view; (c) Four-point, (c) Four-point, side view;side view;(d) Six-point, (d) Six-point, general general view; view; (e) Six-point, (e) Six-point, top topview; view; (f) (Six-point,f) Six-point, side side view; view; (g ()g )Eight-point, Eight-point, generalgeneral view; view; ( h) Eight-point,Eight-point, toptop view; view; ( i()i Eight-point,) Eight-point, side side view; view; (j) Four-point(j) Four-point filled filled with with waste waste rocks, rocks,general general view; view; (k) Four-point (k) Four-point filled filled with wastewith waste rocks, rocks, top view; top view; (l) Four-point (l) Four-point filled filled with wastewith waste rocks, rocks,side view. side view.

LaboratoryLaboratory compression compression tests tests on on the the wooden wooden crib cribss were were performed performed at at the the Department Department of of Mining Mining EngineeringEngineering and WorkWork SafetySafety at at the the Faculty Faculty of Miningof Mining and and Geoengineering, Geoengineeri AGHng, AGH University University of Science of Scienceand Technology and Technology in Krakow in Krakow (Poland). (Poland). The The load load was was measured measured using using three three strain strain gauges, gauges, while while a aline line encoderencoder waswas usedused toto measuremeasure displacementdisplacement (Figure7 7).). TheThe loadload raterate was 0.5 kNkN/s./s. The The sensors sensors werewere connected connected to to a a universal universal measuring measuring amplifier, ampliﬁer, QUANTUM QUANTUM MX840A, MX840A, which which was was connected connected to to a a computer. The test results were monitored on an ongoing basis using Catman-Easy software. Each crib model was tested five times. The results of the compression tests on the models of cribs are presented in Table 1 and in Figure 8a–d. Detailed load-displacement characteristics of crib models are presented in Figure 9a–d.

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Energies 2020, 13, 3564 8 of 20 computer. The test results were monitored on an ongoing basis using Catman-Easy software. Each crib model was tested ﬁve times. The results of the compression tests on the models of cribs are presented in Table1 and in Figure8a–d. Detailed load-displacement characteristics of crib models are presented Energiesin FigureFigure 20209a–d., 7.13 ,A x FORscheme PEER of REVIEW the laboratory stand: 1—computer, 2—measuring amplifier, 3—force sensors,9 of 21 4—displacement sensor, 5—model of crib, 6—lower base, 7—upper base, 8—hydraulic cylinder, 9— machine base, 10—driven cross head, 11—screw, 12—hydraulic pump, 13—control panel.

Table 1. Load-displacement parameters of tested wooden cribs.

Maximal Load Vertical Displacement Δl/mm Average F/kN (at Maximal Load) Specific Crib Model Deformation From To Average From To Average ε/% Four-point 56.5 65.2 60.9 63.9 73 70.3 35.15 Six-point 172 194 183 74.5 81.7 78.8 39.40 Eight-point 222 235 227 80.7 86.8 83.3 41.65 Four-point

filled with 271 295 283 72 79.1 76.1 38.05 wasteFigure rocks 7. A scheme of the laboratory stand: 1—comput 1—computer,er, 2—measuring 2—measuring amplifier, ampliﬁer, 3—force 3—force sensors, sensors, 4—displacement sensor, sensor, 5—model 5—model of of crib, crib, 6—lower 6—lower base, base, 7—upper 7—upper base, base, 8—hydraulic 8—hydraulic cylinder, cylinder, 9— Averagemachine9—machine base, compressive base, 10—driven 10—driven strength cross cross head, of head, the 11—screw 11—screw,wooden, 12—hydraulic crib 12—hydraulic filled by pump, waste pump, 13—control rocks: 13—control Cs =panel. 8.44 panel. MPa.

Table 1. Load-displacement parameters of tested wooden cribs.

EnergiesAverage 2020, 13, compressivex FOR PEER REVIEW(a strength) of the wooden crib filled by waste rocks:(b) Cs = 8.44 MPa. 10 of 21

(c) (d) (a ) (b ) Figure 8. Models of the wooden cribs after compression tests: (a) Four-point; (b) Six-point; Figure(c) Eight-point; 8. Models (d of) Four-point the wooden ﬁlled cribs with after waste compression rocks. tests: (a) Four-point; (b) Six-point; (c) Eight- point; (d) Four-point filled with waste rocks.

(a)

(b)

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Table 1. Load-displacement parameters of tested wooden cribs.

Maximal Load Vertical Displacement ∆l/mm Average Speciﬁc Crib Model F/kN (at Maximal Load) Deformation From To Average From To Average ε/% Four-point 56.5 65.2 60.9 63.9 73 70.3 35.15 Six-point 172 194 183 74.5 81.7 78.8 39.40 Eight-point 222(c) 235 227 80.7 86.8( 83.3d) 41.65 Four-point ﬁlled with 271 295 283 72 79.1 76.1 38.05 Figure 8. Models of the wooden cribs after compression tests: (a) Four-point; (b) Six-point; (c) Eight- waste rocks point; (d) Four-point filled with waste rocks.

(a)

(b)

Figure 9. Cont.

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(c)

(d)

Figure 9. Load-displacement of the wooden crib models: ( a)) Four-point; Four-point; ( b) Six-point; Six-point; ( c) Eight-point; ((dd)) Four-pointFour-point ﬁlledfilled withwith wastewaste rocks.rocks.

AverageAmong the compressive four-point, strength six-point of and the woodeneight-point crib empty filled bywooden waste cribs, rocks: the Cs eight-point= 8.44 MPa. cribs had the bestAmong load-bearing the four-point, capacity. six-point The average and eight-point value of the empty maximal wooden load cribs, for eight-point the eight-point wooden cribs cribs had thewas best equal load-bearing to 227 kN and capacity. was greater The average by 44 valueand 166.1 of the kN maximal compared load to for the eight-point four-point woodenand six-point cribs wascribs, equal respectively. to 227 kN On and the wasother greater hand, filling by 44 andthe wooden 166.1 kN cribs compared with waste to the rocks four-point (dolomitic and limestone) six-point cribs,increased respectively. their load-bearing On the other capacity hand, by filling 56, 100, the woodenand 222.1 cribs kN withcompared waste to rocks the eight-point, (dolomitic limestone) six-point increasedand four-point their load-bearingcribs, respectively. capacity The by 56,aver 100,age and value 222.1 of kNvertical compared deformation to the eight-point, for the eight-point six-point andwooden four-point empty cribs, cribs respectively. was equal to The 83.3 average mm and value was of greater vertical by deformation 10.3, 4.5, and for 7.2 the mm eight-point compared wooden to the empty cribsfour-point was equal and six-point to 83.3 mm cribs and and was the greater four-poi bynt 10.3, cribs 4.5, filled and 7.2with mm waste compared rocks, torespectively. the empty four-pointBased on andTable six-point 1 it can cribs be andstated the that four-point the four cribs-point filled wooden with waste crib rocks, filled respectively. with waste Basedrocks onis Tablecharacterized1 it can be by stated the highest that the load-bearing four-point wooden capacity. crib One filled of the with basic waste research rocks isgoals characterized was to use by waste the highestrocks in load-bearing the wooden capacity.cribs. Therefore, One of thein order basic researchto better goalsunderstand was to usethe wastemechanism rocks inof thecooperation wooden cribs.between Therefore, waste rocks in order and to wooden better understand cribs, the stress-s the mechanismtrain characteristics of cooperation are presented between waste in Figure rocks 10. and wooden cribs, the stress-strain characteristics are presented in Figure 10.

Energies 2020, 13, 3564 11 of 20 Energies 2020, 13, x FOR PEER REVIEW 12 of 21

FigureFigure 10. 10.Stress-strain Stress-strain characteristics characteristics of of the the wooden wooden crib crib models models ﬁlled filled with with waste waste rocks. rocks.

TheThe surface surface area area of of the the crib crib was was determined determined as theas the sum sum of theof the surface surface of the of woodenthe wooden beams beams and theand surfacethe surface occupied occupied by the by waste the waste rocks rocks inside inside the crib, the incrib, accordance in accordance with Figurewith Figure6k. However, 6k. However,the load the value was determined in accordance with Figure9d. The average compressive strength (C s) of the load value was determined in accordance with Figure 9d. The average compressive strength (Cs) of woodenthe wooden crib filled crib withfilled waste with rockswaste was rocks equal was to equal 8.44 MPa. to 8.44 In FigureMPa. In 10 ,Figure three characteristic10, three characteristic phases of cooperationphases of cooperation between wooden between cribs wooden and waste cribs and rocks wa canste be rocks distinguished. can be distinguished. The first phase The first is related phase tois therelated initial to adjustmentthe initial adjustment of the space of the between space thebetween waste the rocks waste and rocks the beamsand the of beams the crib. of the An crib. initial An elasticinitial compressionelastic compression of the crib of occurred,the crib occurred, as well as as the well matching as the of matching the wooden of the beams’ wooden connection. beams’ Theconnection. stress and The strain stress of theand crib strain for of this the phase crib for were this equal phase to were 1 MPa equal and 10%,to 1 MPa respectively. and 10%, In respectively. the second phase,In the thesecond waste phase, rocks the took waste on the rocks load, took and on the th reductione load, and in distance the reduction between in thedistance beams between of the crib the wasbeams limited of the by crib waste was rocks. limited The by stress waste and rocks. strain The of thestress crib and for strain this phase of the were crib equalfor this to 3phase MPa were and 30%,equal respectively. to 3 MPa and The 30%, third respectively. phase continued The third until thephase maximal continued load until capacity the ofmaximal the cribs load was capacity obtained. of Inthe this cribs phase, was theobtained. beams In of this the phase, crib were the damaged,beams of the the crib continuity were damaged, of the mesh the continuity was broken, of the and mesh the wastewas broken, rocks spilled and the out. waste The rocks stress spilled and strainout. The of stress the crib and for strain this of phase the crib were for equal this phase to 8.8 were MPa equal and 46%,to 8.8 respectively. MPa and 46%, respectively. 4. Numerical Modeling of Principal Stresses in the Inter-Room Pillars 4. Numerical Modeling of Principal Stresses in the Inter-Room Pillars The room and pillar method was modeled in the Phase2 numerical software. In the numerical The room and pillar method was modeled in the Phase2 numerical software. In the numerical modeling, graded mesh and three-noded triangle elements were used. The total number of elements modeling, graded mesh and three-noded triangle elements were used. The total number of elements and nodes was 1034 and 581, respectively. Plain strain analysis was adjusted with the Gaussian and nodes was 1034 and 581, respectively. Plain strain analysis was adjusted with the Gaussian elimination solver type. In the analysis, the maximal number of iterations and the tolerance were 500 elimination solver type. In the analysis, the maximal number of iterations and the tolerance were 500 and 0.001, respectively. Poor quality elements were defined as a side length ratio with a maximum to and 0.001, respectively. Poor quality elements were defined as a side length ratio with a maximum to minimum ratio of more than 30; a minimal and maximal interior angle of less than 2 degrees and more minimum ratio of more than 30; a minimal and maximal interior angle of less than 2 degrees and than 175 degrees, respectively. The rock mass model was a flat 125 m 125 m shield, which was fixed more than 175 degrees, respectively. The rock mass model was a flat ×125 m × 125 m shield, which was on three boundaries. Only from the surface side was the shield not restrained. The rooms and pillars fixed on three boundaries. Only from the surface side was the shield not restrained. The rooms and were subjected to static loads resulting from the weight of overburden rocks. The main purpose of pillars were subjected to static loads resulting from the weight of overburden rocks. The main modeling was to determine the stresses in the inter-room pillars. Modeling was performed on four purpose of modeling was to determine the stresses in the inter-room pillars. Modeling was performed cases of the exploitation system: R1—rock pillars and empty rooms; R2—rock pillars and rooms filled on four cases of the exploitation system: R1—rock pillars and empty rooms; R2—rock pillars and with sand filling; R3—rock pillars replaced by wooden cribs filled with waste rocks; R4—rock pillars rooms filled with sand filling; R3—rock pillars replaced by wooden cribs filled with waste rocks; replaced by wooden cribs filled with waste rocks and rooms filled by sand filling. The model assumed R4—rock pillars replaced by wooden cribs filled with waste rocks and rooms filled by sand filling. that the length of the mining field side was 95.2 m (Figure 11a). The room excavations and pillars The model assumed that the length of the mining field side was 95.2 m (Figure 11a). The room had a width and height of 5.6 m (Figure 11c) and were located at a depth of 110 m below the surface excavations and pillars had a width and height of 5.6 m (Figure 11c) and were located at a depth of (Figure 11b). The strength, deformation and structural parameters of the rocks making up the rock 110 m below the surface (Figure 11b). The strength, deformation and structural parameters of the pillars were determined experimentally on cylindrical samples 50 mm in diameter and 100 mm high, rocks making up the rock pillars were determined experimentally on cylindrical samples 50 mm in diameter and 100 mm high, cut from rock lumps taken from the mining room in the Olkusz-

Energies 2020, 13, 3564 12 of 20

Energiescut from 2020 rock, 13, x lumps FOR PEER taken REVIEW from the mining room in the Olkusz-Pomorzany mine. The waste13 rocks of 21 (dolomitic limesteone) used in this study were characterized by the following parameters: compressive Pomorzany mine. The waste rocks (dolomitic limesteone) used in this study were characterized by strength 30.5 MPa; tensile strength 2.3 MPa; friction angle 42.3◦; cohesion 0.46 MPa; Young’s modulus the following parameters: compressive strength 30.5 MPa; tensile strength 2.3 MPa; friction angle 25,000 MPa; Poisson’s ratio 0.24; unit weight 0.027 MN/m3. The results of the calculations are presented 42.3°; cohesion 0.46 MPa; Young’s modulus 25,000 MPa; Poisson’s ratio 0.24; unit weight 0.027 in Figure 12a–d and in Table2. Additionally, in Figure 13a–d, the mean and standard deviation for the MN/m3. The results of the calculations are presented in Figure 12a–d and in Table 2. Additionally, in principal stresses are presented. Figure 13a–d, the mean and standard deviation for the principal stresses are presented.

(a) (b)

(c)

Figure 11. Mining and geological conditions in the Olkusz-Pomorzany area in Poland: (a) Design of Figurethe room 11. and Mining pillar and method; geological (b) Lithological conditions proﬁle in the forOlkusz-Pomorzany the designed region; area (c in) Perspective Poland: (a) view Design of theof theroom room and and pillar pillar method. method; (b) Lithological profile for the designed region; (c) Perspective view of the room and pillar method.

Energies 2020, 13, 3564 13 of 20

Energies 2020, 13, x FOR PEER REVIEW 14 of 21

(a)

(b)

(c)

(d)

Figure 12. Principal stress for the designed room and pillar method for four cases of exploitation: (a) Figure 12. Principal stress for the designed room and pillar method for four cases of exploitation: (a) Rock pillars and empty rooms (R1); (b) Rock pillars and rooms filled with hydraulic sand filling (R2); Rock pillars and empty rooms (R1); (b) Rock pillars and rooms filled with hydraulic sand filling (R2); (c) (c) Rock pillars replaced by wooden cribs filled with waste rocks and empty rooms (R3); (d) Rock Rock pillars replaced by wooden cribs filled with waste rocks and empty rooms (R3); (d) Rock pillars replaced by wooden cribs filled with waste rocks and rooms filled with hydraulic sand filling (R4). Energies 2020, 13, x FOR PEER REVIEW 15 of 21

pillars replaced by wooden cribs filled with waste rocks and rooms filled with hydraulic sand filling (R4). Energies 2020, 13, 3564 14 of 20

Table 2. Summary of numerical modeling results for four cases. Table 2. Summary of numerical modeling results for four cases. Principal Stresses Occurring in Case Principal Stressesthe Inter-Room Occurring in Pillar the Case Inter-Room Pillar/MPa No Descriptions Minimal/MPa Maximal R1 No Rock pillars Descriptions and empty rooms Minimal 3.25 Maximal 3.50 RockR1 pillars and Rock rooms pillars filled and empty with hydraulic rooms sand 3.25 3.50 R2 3.10 3.13 Rock pillarsfilling and rooms filled with R2 3.10 3.13 Rock pillars replacedhydraulic by wooden sand filling cribs filled with R3 3.60 3.90 Rockwaste pillars rocks replaced and empty by wooden rooms cribs filled R3 3.60 3.90 Rock pillarswith replaced waste rocksby wooden and empty cribs rooms filled with R4 waste rocksRock and pillars rooms replaced filled by woodenwith hydraulic cribs filled sand 3.19 3.21 R4 with waste rocksfilling and rooms filled with 3.19 3.21 hydraulic sand filling

(a) (b)

Figure 13. Mean and standard deviation (SD) for principal stresses in relation to the designed room and pillarFigure method: 13. Mean (a )and Rock standard pillars and deviation empty (SD) rooms for (R1); principal (b) Rock stresses pillars in and relation rooms to filled the designed with hydraulic room andsand pillar filling method: (R2); (c) ( Rocka) Rock pillars pillars replaced and empty by wooden rooms cribs (R1); filled (b) Rock with wastepillars rocks and rooms and empty filled rooms with (R3);hydraulic (d) Rock sand pillars filling replaced (R2); (c by) Rock wooden pillars cribs replaced filled with by wastewooden rocks cribs and filled rooms with filled waste with rocks hydraulic and emptysand filling rooms (R4). (R3); (d) Rock pillars replaced by wooden cribs filled with waste rocks and rooms filled with hydraulic sand filling (R4). In the calculations, the Mohr—Coulomb shear strength criterion [24] was used, which is a linear failureIn criterionthe calculations, requiring the two Mohr—Coulomb parameters, cohesion shear strength and friction criterion angle, [24] which was were used, selected which is using a linear the failureRocklab criterion program requiring [24]. The two Mohr—Coulomb parameters, cohesion criterion and describes friction the angle, linear which relationship were selected between using normal the Rocklab program [24]. The Mohr—Coulomb criterion describes the linear relationship between

Energies 2020, 13, 3564 15 of 20 and shear stresses (or maximal and minimal principal stresses) in the damaged zone. The quantities needed to determine the dependency sought are:

σ + σ σ σ σ = 1 3 1 − 3 sin ϕ (1) 2 − 2 σ σ τ = 1 − 3 cos ϕ (2) 2 Using the expression for stress σ and τ in the limit state equation on a slip surface:

τ = σtgϕ + c (3) | | we get the following relationship:

2 σ1 σ3 σ1 + σ3 σ1 σ3 sin ϕ − cos ϕ = tgϕ − + c (4) 2 2 − 2 cos ϕ where:

σ—total normal stress on the slip surface; τ—shear stress on the slip surface;

σ1—major principal stress; σ3—minor principal stress; (σ1 + σ2)/2—horizontal coordinate of the Mohr circle center; (σ σ )/2—Mohr circle radius; 1− 3 ϕ—eﬀective angle of internal friction; c—eﬀective cohesion.

The principal stress value was determined using the Von Mises stress criterion. Von Mises stress is given by [24]: σ = √3 J (5) VM · where J is given by: q 1 2 2 2 J = (σ1 σ2) + (σ2 σ3) (σ3 σ1) (6) √6· − − − where:

σ1—major principal stress; σ2—intermediate principal stress; σ3—minor principal stress.

In the research, the scale eﬀect was taken into account according to Weibull’s theory [25], which shows that the strength of an element depends on its volume, which is expressed by the relationship:

! 1 R V m 1 = 0 (7) R0 V1 where:

R0—compressive strength of the crib model filled with waste rocks; R1—compressive strength of the crib filled with waste rocks on a geometric scale 1:1; V0—volume of the crib model filled with waste rocks; V1—volume of the crib filled with waste rocks on a geometric scale 1:1; m—Weibull modulus; this can be estimated from the formula [26]: Energies 2020, 13, 3564 16 of 20

1.2 m = (8) CV

Energieswhere: 2020, 13, x FOR PEER REVIEW 17 of 21 Cv—coefficient of variation of the strength of the material, defined as the ratio of the standard deviationunder laboratory to the average conditions value. was It 8.44 was MPa assumed (Table in 1); the the study volume that theof crib volume filled of with the waste crib model rocks filled on a withgeometric waste scale rocks of was 1:1 was 0.00813 175.61 m3 m(Figure3; the material6k,l); the strength compressive coefficient strength of variation determined (forexperimentally models of cribs underfilled with laboratory waste rocks) conditions Cv = 0.02484; was 8.44 the MPa Weibull (Table modulus1); the volume m = 48.309. of crib Taking filled withinto account waste rocks the above on a geometricdata, the predicted scale of 1:1 compressive was 175.61 strength m3; the material of the wood strengthen cribs coe ffifilledcient with of variation waste rocks (for modelson a geometric of cribs filledscale 1:1 with was waste 6.86 rocks) MPa. Cv = 0.02484; the Weibull modulus m = 48.309. Taking into account the above data,For the the predicted room and compressive pillar method strength with of rock the woodenpillars, the cribs mean filled value with of waste the principal rocks on stresses a geometric was scaleequal 1:1 to was3.31 6.86MPa. MPa. The replacement of rock pillars by the construction of wooden cribs filled with wasteFor rocks the (dolomitic room and limestone) pillar method caused with the rock mean pillars, value the of principal mean value stresses of the to principal increase by stresses 0.36 MPa. was equalThe filling to 3.31 of MPa.rooms Thewith replacement the sand backfilling of rock pillars process by reduced the construction the value of woodenprincipal cribs stresses filled by with 0.19 wasteand 0.47 rocks MPa (dolomitic for rock limestone) pillars and caused pillars the meanreplaced value with of principalwooden stressescribs filled to increase with waste by 0.36 rocks, MPa. Therespectively. filling of rooms with the sand backfilling process reduced the value of principal stresses by 0.19 and 0.47 MPa for rock pillars and pillars replaced with wooden cribs filled with waste rocks, respectively. 5. Results 5. Results The varied courses of the load-displacement characteristics are a reflection of the non-uniform mannerThe of varied destruction courses of of individual the load-displacement crib models. Based characteristics on Figure are9a–d, a reflection the range ofof thevariability non-uniform of the mannerstiffness ofof destruction wooden cribs ofindividual was calculated crib models. as a func Basedtion of on their Figure compressibility9a–d, the range (Figure of variability 14 and ofTable the sti3).ff ness of wooden cribs was calculated as a function of their compressibility (Figure 14 and Table3).

Figure 14. TheThe stiffness stiﬀness of the w woodenooden cribs for increasing compressibility.

Table 3. Comparison of the stiffness of the wooden cribs for increasing compressibility.

Four-Point Crib Compressibility Four-Point Crib Six-Point Crib Eight-Point Crib with Waste Rocks C/% Stiffness S/kN/mm 10 1.25 2 2.45 1.65 20 0.87 1.46 1.85 1.67 30 0.75 1.40 1.80 2.30 40 0.77 2.05 2.60 3.72

Energies 2020, 13, 3564 17 of 20

Table 3. Comparison of the stiﬀness of the wooden cribs for increasing compressibility.

Four-Point Crib Four-Point Crib Six-Point Crib Eight-Point Crib Compressibility with Waste Rocks C/% Stiﬀness S/kN/mm 10 1.25 2 2.45 1.65 20 0.87 1.46 1.85 1.67 30 0.75 1.40 1.80 2.30 40 0.77 2.05 2.60 3.72

Three characteristic stiffness phases can be distinguished for the empty crib models. The first phase is related to the initial elastic compression of the crib as well as the matching of the wooden beams’ connection. The range of variability of stiffness for this phase for four-point, six-point, and eight-point cribs is 1.5, 1.85, and 1.98 kN/mm, respectively. The second phase is associated with kneading the beams and reducing the distance between the beams of the crib. The distance between one beam and the other before loading was 15 mm. The range of stiffness variability for the second phase for four-point, six-point, and eight-point cribs is 0.55, 1.58, and 2.05 kN/mm, respectively. The third phase is associated with the increase in load until the maximal load is reached. In this phase, the crib loses its functionality; the beams of the crib become delaminated. The range of stiffness variability for the third phase for four-point, six-point, and eight-point cribs is 1.13, 4.21, and 4.63 kN/mm, respectively. The crib models, which were filled with waste rocks, were equipped with a polypropylene plastic mesh. The basic task of the mesh was to prevent the crushed rock from spilling out. It can be assumed that the mesh used contributed to a close fit of waste rocks inside the cribs. Three characteristic phases can also be distinguished for four-point cribs filled with waste rocks. The first phase is related to the initial adjustment of the space between the waste rocks and the beams of the crib. The stiffness of the crib for this phase is 1.77 kN/mm. In the second phase, the waste rocks take on the load, compared to empty cribs, and the reduction in distance between the beams of the crib is limited by waste rocks. The stiffness of the crib for this phase is 2.13 kN/mm. The third phase, as with the empty cribs, continues until the maximal load capacity of the cribs is obtained. In this phase, the beams of the crib are damaged, the continuity of the mesh is broken, and the waste rocks spill out. The stiffness of the crib for this phase is 5.87 kN/mm. The function of inter-room pillars is to maintain the stability of excavations. The stability of a pillar can be evaluated by calculating a factor of safety (FoS), which is the ratio of the pillar strength to the average stress in the pillar [27–31].

Pstrength FoS = (9) Pstress where: FoS—factor of safety;

Ps—pillar strength/MPa; S—applied pillar stress/MPa. A value of safety factor below 1 may contribute to the loss of functionality of the excavation stability [32,33]. The compressive strength of dolomite samples with a diameter of 50 mm and a height of 100 mm tested in laboratory conditions was 30 MPa. Hedley and Grant [34] proposed to determine the strength of the pillar taking into account the conversion factor of 0.7 for a sample diameter of 50 mm: w0.5 Pstrength = K (10) ·h0.75 where: K—strength of 0.3 m cubic sample = 0.7 uniaxial compressive strength (UCS, 30MPa) (50 mm × diameter sample)/MPa; Energies 2020, 13, 3564 18 of 20

K = 0.7 30 = 21 MPa; × w—pillar width/m; h—pillar height/m.

Taking into account the width and height of the pillar of 5.6 m, according to Equation (10), the strength of the pillar was 13.65 MPa. The value of the rock pillar’s strength therefore is 6.79 MPa higher than for wooden cribs filled with waste rocks. To estimate the value of the factor of safety for cribs filled with waste rocks, the pillar strength was calculated to be 6.86 MPa, while the applied pillar stress value calculated on the basis of numerical methods in accordance with Table2 was in the range of 3.13 to 3.90 MPa. Substituting the calculated values of the pillar strength and applied pillar stress into Equation (9) it can be concluded that the factor of safety for rock pillars replaced by cribs filled with waste rocks is 1.75. Filling the rooms with a hydraulic sand filling increases the factor of safety to the value of 2.19. In a field of exploitation with a surface area 9063.04 m2 (Figure 11a), inter-room pillars occupy 28.02% of the area. The metals that are contained in the inter-room pillars constitute mining losses. The possibility of exploiting the pillars and replacing them with the construction of wooden cribs filled with waste rocks can contribute to a reduction in mining losses, while increasing the level of extraction. Assuming that the volume of a cubic pillar with a side length of 5.6 m is 175.61 m3, that the volume density is 2700 kg/m3, and that the average content of zinc and lead in the pillar is 2%, this means that the resources in one pillar are approximately 9.48 Mg. Considering the average prices of zinc and lead on the London Metal Exchange [35], which as of 2 July 2020 are 2035.50 and 1768.50 USD/Mg respectively, and the calculated resources for one pillar, this means that the value of metals contained in one pillar is around USD 36,028. The total costs of mining the pillar and replacing it with wooden cribs filled with waste rocks, include the cost of excavating the pillar with explosives; the cost of energy related to the ventilation of the rooms; the cost of securing the excavation with a rock bolt support; the cost of transporting the ore; the costs of the processing plant; the cost of purchasing and transporting wooden beams; the cost of transporting waste rocks from excavations to use in the room and pillar method. The estimated total costs of mining the rock pillar and replacing it with a wooden crib filled with waste rocks constitute 80% to 85% of the value of the metals contained in the pillar. For mining excavations where there are no useful minerals, there is no need to take them to the surface; these rocks can be used to fill the wooden cribs. This solution significantly reduces operating costs, while contributing to the management of waste rocks in underground mining excavations, which is environmentally friendly.

6. Conclusions Based on the results of the laboratory tests on mining crib models, it can be stated that:

the four-point empty crib, built of 22 beams, showed an average capacity of 60.9 kN and an • average specific deformation of 35.5%; increasing the number of connections in the crib increased its load; • the six-point empty crib was characterized by a load capacity of more than three times greater and • an average specific deformation greater by 4.25% compared to the four-point crib; the eight-point empty crib was characterized by a load capacity of more than three and a half • times greater and an average specific deformation greater by 6.5% compared to the four-point crib; filling the four-point crib with waste rocks (crushed dolomite with a diameter of 10–25 mm) • meant that its capacity was more than four and a half times greater and that the average specific deformation increased by 2.9% compared to the four-point empty crib; the rigidity of empty four-point, six-point, and eight-point cribs decreases with increasing • compressibility (up to 30%); above 30% compressibility, the stiffness of the cribs increases; the stiffness of four-point cribs filled with waste rocks increases with increasing compressibility. • Energies 2020, 13, 3564 19 of 20

Based on the numerical calculations for the room and pillar method in the mining ﬁeld in cases with a side length equal to 95 m, in which the width, length, and height of the pillar and room are 5.6 m, for the conditions of the Olkusz-Pomorzany zinc and lead mine, it can be concluded that:

the maximal value of principal stresses in the inter-room rock pillars is 3.50 MPa; • the replacement of rock pillars by means of wooden cribs ﬁlled with waste rocks causes an increase • in principal stresses in the inter-room pillars by 0.4 MPa in comparison with rock pillars; the value of the factor of safety for the inter-room rock pillars ranges from 3.9 to 4.25 and ranges • from 1.75 to 2.19 when rock pillars are replaced by wooden cribs ﬁlled with waste rocks.

The new construction of a wooden crib can signiﬁcantly increase the level of extraction, while reducing mining losses. In addition, from an environmental point of view, ﬁlling wooden cribs with waste rocks contributes to development in situ without the need to store materials on the surface.

Funding: This paper was prepared as part of AGH’s scientific subsidy, under number 16.16.100.215. Conflicts of Interest: The author wishes to confirm that there are no known conflicts of interest associated with this publication and that there has been no significant financial support for this work that could have influenced its outcome.

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