Rock mass—mine workings interaction model for Polish copper mine conditions

International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

Rock mass—mine workings interaction model for Polish copper mine conditions W. Pytel* CBPM ‘‘Cuprum’’ Ltd., Pl. 1 Maja 1-2, Wroclaw, Poland Accepted 15 February 2002

Abstract Geological and mining conditions characteristic for the Polish Legnicko–Glogowski Okreg Miedziowy (LGOM) copper mines as well as various exploitation systems utilized in that area are presented. The historical background of mining systems development as well as their classification are also reviewed. Presently, due to difficult mining conditions, a new more universal analytical tool for mine workings geometry selection is required. Therefore, a very useful in design process multi-plate analogy based physical model of rock mass—mine workings interaction has been developed and presented in the paper. The model utilizes the analytical approximation of pillar compression including the effect of pillar critical and residual strength on roof strata deflection resulting in the definite bump hazard level. The research performed in the past which dealt with the effect of size and slenderness on pillar strength is reviewed. A new approach for pillar strength calculation and its utilizing in a general problem of overburden–mine workings interaction is proposed. The problem has been illustrated by numerical examples concerning a rock mass static and dynamic behavior in the area of one of the underground Polish copper mines. By solving the numerical model based on the finite element method formulated in three dimensions, the effect of extraction path on mine workings safety in a static load domain has been proved. The dynamic load transfer from mine workings to a shaft lining has also been determined. r 2003 Elsevier Science Ltd. All rights reserved.

1. Introduction In the Foresudetic Monocline region, the working face length and technological pillars bearing capacity are the basic, related to geometry, parameters of utilized copper mining systems. For practical purposes, these parameters, established on model and pilot exploitation basis, are included in the so-called stiffness factor. It concerns technological pillars within the working zone, and depends on actual rock strength parameters, seam thickness and pillar size. In a case of thick deposit extraction, the specific geologic conditions of the copper ore location in the basin, as well as a diversity in the geotechnical parameters of roof and entry rocks, result in multi-cut room-and-pillar technology with the initial cut taken from the top of the ore, with succeeding benches as needed. In strong dolomite conditions, the roof is bolted *Tel.: +48-71-781-2403; fax: +48-71-344-3536. E-mail address: [email protected] (W. Pytel).

in the initial cut, while after the last cut, the entire workings are hydraulically backfilled. Mining systems supplemented with backfilling are practiced in those Lubin and Rudna mines locations where ore deposit is thicker than 7 m. These systems reveal a high diversity due to differences in local mining and geological conditions. Thin ore deposits are usually mined using room-andpillar technique with the face wide opened and roof deflected. New solutions tend towards low clearance, self-propelled equipment use. The extraction method suitable for deposits up to 2 m in thickness has been developed and is presently employed in Polkowice– Sieroszowice mine, while avenues for 1.5 m extraction height are currently analyzed. Till today, the copper ore has been extracted from about 38 km2 of the deposit area, using various systems and roof control methods. Due to this activity there were created a large number of barrier pillars of different size resulting in local stress concentrations and higher bump hazard in the adjacent areas. The first

1365-1609/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1365-1609(03)00028-5

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W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

bump events took place in Polkowice mine in 1972, while in Lubin mine, in 1975, 6 years after mining was commenced. Since then, bump hazard has gradually increased and due to exploitation progress and increased dimension of mined-out areas, bumps have become the major hazard facing the Polish Legnicko–Glogowski Okreg Miedziowy (LGOM) Basin deep copper mines. The analysis data concerning the monitored bump events permitted the formulation of the following conclusions: *

*

*

*

*

Bumps may be categorized by their mechanisms as follows: pressure bumps when the locations of rock bursts and the tremor are the same, and shock bumps, when these locations are different; actually, the load conditions decide in which category the bump may develop, bumps are mostly located in the area of stress concentrations, i.e. closely to the old mined-out areas and in the area ahead of the working face, pillars of size ranging from 20 to 25 m are the most sensitive and usually fail; smaller and significantly larger pillars are less prone to violent failure, during the bump process, rib material is violently propelled into a mine opening; the roof usually remains intact, or sometimes 2 m caving may occur, bumps are frequently associated with a limited floor heave.

The main bump causes in the LGOM copper mines are related to dynamic processes within overburden strata which occur due to some natural causes and technological reasons as well. Among the natural causes, the following ones seem to be the most important: *

*

* *

High strength parameters of roof carbonate rocks which are able to accumulate a significant amount of strain energy and release it in a violent manner, significant thickness of carbonate and anhydrite rocks within overburden strata resulted in strong, massive roof lying close to or on the ore deposit, great depth of exploitation, and proximity of faults, folds and similar geologic disturbances.

The following are the main technological parameters influencing bump hazard: *

* * *

Complex shape and significant size of mined-out areas which are associated with barriers and protective pillars, the utilized exploitation systems, significant concentration of mine workings, and length and depth of mining face.

In few cases, bumps developed within barriers containing main road entries, located between large mined-out areas. Two of them took place spontaneously, while the remaining occurred in 130–150 m

wide barriers being attempted to mine. After bump effects were serious and covered openings of hundred meters in length. When selecting mining methods for the LGOM mines, Polish and worldwide, particularly American, Swedish, Canadian, Soviet and French metal mining industry experiences were examined and evaluated. A symptomatic example of Lorraine iron mines, where up to 1950 longwall systems with steel support were utilized, was carefully analyzed. After 1950 all these mines have redesigned their mining systems, introducing room-and-pillar mining technology with roof bolting and self-propelled equipment. In May 1967, for the first time in the LGOM Basin ore extraction commenced using a pilot longwall panel, while the pilot room-and-pillar panel was ready in November, the following year. The wall length ranged from 80 to 100 m, while extraction height reached 2.15 m and a steel frictional support was used. In the first research work phase, openings were backfilled pneumatically using dry fill, however, since October 1968 they have been filled by roof caving induced by blasting. In the course of copper extraction, research on strata behavior in the entire section vicinity was initiated. Special research openings were driven, among them a roof drift about 65 m above the pilot panel was developed. On the first wall, research on overburden strata behavior, based on deformation measurements was conducted using surveying, geophysical and tensometric methods. The research and measurement program permitted estimating the changes within the surrounding strata, and this in turn allowed developing a practical experience providing mine operators with safe and highly productive mine systems. Using the longwall mining system, the ore was exploited from the 36 000 m2 deposit area, of which 15 000 m2 was backfilled pneumatically. The rest of the pilot panel was decided to be mined using room-andpillar technology. In November 1968 mining commenced in the room-and-pillar panel located in the level directly below the longwall panel. In the primary phase of mining, the ore was cut into rectangular pillars of 25
35 and 25
25 m. Finally, during secondary mining, the large pillars were split into small remnant pillars of 5
5 m in size. When ore extraction covered about 2 ha area, the first immediate roof caving occurred. After situation analyses, blasting in 3-m-long drillholes was utilized as an additional tool forcing roof falls. At the same time, large-scale attempts concerned with roof bolting implementation were carried out. Experiments conducted on longwall and room-andpillar extraction systems have proved the advantage of the latter, which since that time has been applied on a routine basis in all LGOM copper mines. This mining technology permits full mechanization of mining operations as well as provides a high productivity associated

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499

Longwall system (1967)

Room-and-pillar system (1968)

Sedimentary (1971)

Without roof caving (1968)

With roof caving (1969)

One-phase

With limited roof caving (1987)

Two-phase

With hydraulic backfilling (1974)

With roof deflection (1988)

With roof deflectionfor thin ore seam (1990)

wide opening

Fig. 1. Exploitation systems evolution in KGHM PM copper mines [1].

with high extraction ratio. Any further modifications of mining systems were based on analytical solutions as well as on small-scale experiments (see Fig. 1). Generally, in the LGOM copper mines, one- and twophase room-and-pillar mining systems are utilized. In the first step of the two-phase extraction (see Fig. 2), openings are driven to divide the copper deposit into rectangular or square large-size pillars (30
50 m), which in the second step are split crosswise to obtain, most often, two rows of technological pillars. Finally, openings are filled with loose rocks due to roof caving or with a hydraulically placed backfill. The primary cutting reveals a number of advantages. Among others, it permits detailed deposit exploration and equipment access to additional roadways enabling communication between the face area and development entries. The basic disadvantage of the two-phase extraction system is its ability to disturb the initial strata equilibrium during step one operations. In the second phase of mining, high stress concentrations, which may increase the bump hazard, can develop within pillars located in the face area. This was the reason why the two-phase system is less commonly used in the LGOM mines. The one-phase room-and-pillar mining creates a face consisting of few stopes connected with parallel entries. Between them, small technological pillars are left to provide an efficient roof support in the working area (see Fig. 3). This approach overcomes disadvantages of

Fig. 2. Schematic of two-phase room-and-pillar mining system with hydraulic backfilling.

primary splitting which is characteristic for two-phase systems, and develops better load distribution in the face area. One-phase systems with roof caving are widely utilized for mining in medium and thin deposits. With greater exploitation depth and with higher variability in ore deposit and roof conditions, some difficulties in system behavior were experienced due to increased overburden pressure. Problems in suitable panel layout selection in the actual mining conditions were encountered. A technological pillar size selection is the most important problem, since an appropriate solution has to provide roof stability in the working area with a

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Fig. 3. Schematic of one-phase room-and-pillar mining system.

relatively low level of elastic energy accumulated. Therefore, the one-phase extraction approach reveals high diversity due to frequent modifications. Filling up the openings excavated during underground mining operations permits better ground strata control, which in turn creates safer conditions for a personnel and equipment operations. There are two basic methods applied for excavation filling: backfilling and complete or partial roof caving. In the LGOM copper mines, hydraulic backfilling, blast induced caving, or deflection of immediate roof resting on yield remnant pillars are used. A thick deposit extraction is always supplemented with hydraulic backfilling, which for surface protection purposes is applied if required. Up to the early 1990s, one-phase systems with technologically forced roof caving were most often utilized. A blast induced caving met several technical barriers, particularly where the appropriate caving height could not be reached and suitably broken gob material could not fill the excavated volume completely. This resulted in insufficient roof support and therefore bumps and uncontrolled roof falls occurred in the working zones. Furthermore, roof blasting was associated with high amount energy released, resulted in possible mine working instability. Under such conditions, systems allowing roof deflection on remnant pillars and roof caving without blasting, were widely implemented. This approach provides immediate roof strata protection within the working zone, as well as advantageous stress distribution due to instant support of main roof strata on technological yield pillars. The wide implementation of such partial extraction mining systems at a considerable depth of 1000–1200 m, where gradually crushed technological pillars work as yield pillars and serve as a flexible face support accumulating high amount of strain energy, is the great achievement of the Polish copper mining industry. Recent developments permit maintaining the ore losses

at a relatively low level. An appropriately selected geometry of mine operations bears resemblance to the secondary mining system. The main idea behind the room-and-pillar mining with a roof-deflected system consists in cutting the ore body with a room system separated with the so-called technological pillars whose size permits yielding simultaneously with lowering and deflected roof strata. Crushed yield pillars of wedge-column shape behave similarly to a deformable artificial support, e.g. timber piles or dry backfilling strips used in conventional mining systems, which do not accumulate elastic strain energy. They should be made as narrow and rooms as wide as roof conditions are preserved, i.e. pillar residual bearing capacity should not permit roof exfoliation and its excessive lowering. The required pillar bearing capacity has to be determined by taking into account the mining conditions, mining depth and strata strength property. This concerns pillars located between the face line and the gobbed area boundary. The distance between these two lines reaches values of few tens to several hundred meters. A partial roof fall may develop in a significant distance from the working face, while in the face area, the bolted roof should deflect without any damages. The copper ore body, located in the Foresudetic Monocline region covering a surface of about 550 km2, consists of deep (600–1200 m) copper profitably graded tabular deposits made of sandstone, shale and limestone which thicknesses vary from less than 1.0 m up to more than 10 m. Diversity and variability of ore lithological characteristics, tectonic disturbances, as well as considerable depth of exploitation are the most important factors affecting technical and technological assumptions concerned with the excavation process. Among them, the bump hazard is the main technical obstacle associated with exploitation. Due to a different deposit thickness and its mineralization, there was a necessity to develop such exploitation systems, which would permit safe excavation and rational deposit management, particularly within protecting pillars, where a significant portion of the ore deposit is located. Geological characteristics of the copper ore deposit located between ! as well as its in situ conditions, were Lubin and G3ogow, the main factors influencing progress in the exploitation system development. The methods of excavation were always based on recent knowledge of identification, prediction and fighting mine hazards, as well as on the latest technologies utilized in roof support and equipment use. The knowledge of roof/overburden rock strata mechanical parameters is the basis for any prediction methods, mine workings design and fighting mining hazards. Therefore, the ore surrounding rock exploration becomes particularly important. In the LGOM copper mines in situ strength tests have not been

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

ROOF STRATA

DOLOMITE

STREAKY DOLOMITE

OPENING

SANDSTONE

FLOOR STRATA RED FLOOR SANDSTONE

Distance from roof surface (m)

ANHYDRITE

501

16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8

0 100 200 300 Unconfined Compressive Strength (MPa)

Fig. 4. Lithological cross-section typical for the LGOM mines area.

performed, however, wide laboratory work has been done on normalized rock samples and models have been prepared as well. During the past years, geological survey recognized that the roof/floor/overburden strata in the area consist dominantly of the so-called white and red floor sandstone, copper bearing shale and Zechstein limestone. Depending on the copper content, mining face changes its location within vertical profile. Therefore, floor strata is always composed of various kinds of limestone, while immediate roof strata consist of various kinds of limestone. Sandstone deposits having uniform composition of basic minerals, quartz grain mainly, reveal significant variability in amount and kind of binders. Sandstones of the carbonate and locally anhydrite cement are rocks of coherent structure and high values of strength-deformation parameters. The average volumetric share of these binders reaches about 30 pct. Unlike the above mentioned kind of rocks, sandstones consisting clay binder (5–15 pct. volumetric share) or ferruginous (5–15 pct. volumetric share)

cement are the brittle and breakable rocks of low strength parameters. The copper bearing shale occurs in the organic-argilliferous (the so-called pitchy) or the dolomitic-argilliferous varieties. The first, very brittle, breakable and tectonically compressed, favors strata deformations in the mine workings vicinity due to possible slippage, while the latter, revealing high integrity, is significantly stronger, competent rock. The carbonate rocks within the entries are represented by marlaceous and streaky dolomite with detrital additivities and, therefore they are significantly weaker than other carbonate rocks which are generally massive, coherent, very strong, and prone to bumps and dynamic disintegration at the critical load. A typical lithological cross-section in the LGOM mines area is presented in Fig. 4. Such a geological structure reminds a unique mechanical system consisting of flat copper ore seam sandwiched between very stiff and strong overburden plate and very soft and weak sandstone floor strata. This system behavior will affect strongly the utilized mining technologies.

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2. Methods for mine workings design The room-and-pillar extraction system is a dominant mining technology utilized in underground metal and chemical raw material mines in Poland. Mine workings rational design requires the ability for pillar bearing capacity prediction as well as its load-deformation characteristics since these factors permit control of pillar loads and roof deflection. On the other hand, the load acting onto a given pillar depends on some effects created by the surrounding geological and mining environment. A mutual interaction between adjacent exploited panels as well as mining within barriers and protective pillars, are the main reasons that safety problems presently are the highest priority issue recognized by Kombinat Gorniczo-Hutniczy Miedzi ‘‘Polska Miedz’’ S.A. (KGHM PM S.A.), the owner of those copper mines. Unfortunately, techniques presently utilized in mines for bump hazard prediction are based mainly on ground behavior monitoring and therefore they are not able to develop certain predictions in virgin areas and in different geological and mining conditions. So far, the available numerical methods, based on stress–strain– energy relationships, due to their limited scale and simplifying assumptions involved, are not routinely used in practice yet. In order to understand roof strata movement, much research work has been done over the years resulting in different approaches. Techniques and procedures utilized for mined-out rock mass behavior prediction engage a number of physical three-dimensional static models [2–5], among which the plate or multi-plate analogy seems to be quite adequate for the LGOM copper mines geological conditions. This model is similar to the Peng’s [6] approach, developed basically to illustrate longwall mining, distinguishing three different zones within undermined overburden strata: (a) cavity zone within the immediate roof, (b) fractured zone where lateral and vertical fractures may happen after bed separation, and (c) continuous deformation zone deforming without any serious damages. This physical model has been adapted for solving the general static-dynamic floor–pillar–roof interaction problem suitable for the LGOM copper mines area. In the presence of dolomite and anhydrite massive plates located over the flat-plane copper deposit, the multiplate overburden model is able to explain the causes of the occurrence of most seismic events, and also permits, in a clear and simple way, the formulating of strength– strain criterions governing a likelihood of instability occurrence within the main overburden strata. Therefore, Pytel has developed a new computational technique validated in the field, based on the finite element

method, but with some special features modeling surfaces of weakness within the overburden strata. The main ideas behind the developed technique are as follows: 1. Using a 3D finite element code, several historic mine working geometries developed in a given area are modeled. The models should explicitly include all pillars and openings in the area of interest as well as the actual geological conditions such as strata location, thickness, deformation parameters, extended faults, etc. 2. The general model is applied to a special case of bedded formations covering flat ore deposits. The overburden is divided into several plate-like strata made of solid finite elements, with contacts provided by the so-called gap elements. These elements the carry load with essentially no relative deflection when a gap opening is closed, and they do not restrict motion when a gap is opened. Furthermore, when closed, the gap element may exhibit friction effects on the contact surface. 3. The consecutive model solutions are submitted to inspection from safety margin point of view, and those solid elements within roof strata which reveal negative safety margin (formulated as a difference between the acting load and the material strength which usually is expressed by the limits of inequalities defining stress or strain allowable range) are transformed into elements made of an artificial soft material with the modulus of deformation significantly reduced. The choice of a suitable strength hypothesis is based on the compatibility between the observed seismic events location and the determined negative strength margin zones. Pillar modeling elements are analyzed using a technique shown below. The static solution obtained for a mine numerical model provides the initial conditions for its transient behavior analysis. The rock mass dynamic response on local instabilities is definitely more complex than a case of static relationships. This is due to mass inertia effects and damping processes engaged in the differential equation of motion and therefore the following simplifying assumptions have been utilized [7]: 1. The mechanical structure of static and dynamic numerical models are identical. 2. The initial deformation state immediately before instability occurrence may be computed using the static model. 3. The total time period of system excitation due to the seismic event is very short compared to time horizon defined by the rate of face advance. 4. Seismic events are modeled as a sudden material softening within the rock mass volume confined

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Fig. 5. Physical model of roof bending in the LGOM copper mines.

within the finite elements revealing the lowest negative values of strength margin. 5. Since the velocity and acceleration values characteristic for an excited rock mass are much lower than those which may be found in typical soil and rock dynamic problems (e.g. machine foundation), the applicability of classic dynamic coefficients of subgrade reaction [8]) in strata dynamic problems is basically doubtful. Therefore, the static deformation parameters, which may be refined in a course of data collecting, may be utilized.

3. General model of rock mass—mine workings interaction In this paper, a special model of vertically loaded pillar behavior is introduced to the general floor–pillar– roof system interaction model. This permits analyzing the behavior of a system including the effect of pillar yielding with the stress–strain characteristics based on Wilson and Ashwin [9] and Hardy et al. [10] research work done for coal pillars. Yield pillars offer a number of advantages that may result in (a) (b) (c) (d)

improved stability in gate and tail entries, increased production, reduced seismic risk, and reduced subsidence curvature and slope values.

This was proven in the deep coal mines in Alabama [11] as well as in Polish copper mines [12] where the socalled ‘‘roof deflection’’ technology based on yield pillar mechanics has been successfully implemented. However, since the trial-and-error technique has been used for yield pillar size selection, the parameters and design criteria suitable for those regions have found a limited application in different conditions of other fields.

Fig. 6. Overburden model as a pile of thick plates of different stiffness (Hi ; EIi —ith plate thickness and flexural stiffness, respectively).

The relevant literature review concerned with (a) strata physical models, (b) mechanisms of high energy tremors, and (c) case studies and numerical modeling, has shown that a multi-plate overburden model might be accepted as a basic physical model for the LGOM mines conditions with the following simplifying assumptions (see Figs. 5 and 6): (a) overburden strata consists of a pile of several homogeneous rock plates reflecting the real lithology in the area, (b) contact mechanism on surfaces between particular plates permits relative movement and developing bed separation,

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(c) strata movement on the contact surfaces is dependent on the degree of strata bonding (various values of cohesion and angle of friction create different strength characteristics on contacts), and (d) technological and remnant pillars work effectively within post-critical phase, but the value of carried loads depends on pillar size and actual extraction ratio.

4. Strength and strain characteristics of yielding hard rock pillars A pillar design procedure may be based on more or less approximate models and their estimates as well as on practical experience, however, there is no general design methods suitable for all geological and mining conditions. So far the most popular over the world method used in mining industry for pillar design in room-and-pillar and longwall extraction techniques, is the so-called ‘‘conventional method’’ based on safety factor approach. The value of 1.5–2.1 is commonly recommended for safety factor depending on the importance and location of given mine workings. The safety factor may be determined by following three basic steps as follows: *

*

*

Determine the average external load acting onto the pillar using simplified (e.g. the tributary area theory) or more complex (e.g. three-dimensional FEM) methods. Determine the pillar strength in the following two steps: (a) material strength in situ is estimated based on a laboratory specimen strength C0 and the so-called scale factor, and (b) pillar strength is calculated as a function of rock strength in situ and pillar shape B/H. Determine safety factor as a ratio of pillar strength and the actual pillar load.

The pressure on a pillar depends upon the direction and distribution of the forces they transfer from the roof to the floor. Much effort has been devoted to the development of pillar pressure prediction methods. The techniques currently in use may be divided into one of two categories: (a) those which ignore the mining caused changes in pillar stress conditions (e.g. the tributary area theory) or (b) those which utilize one of the modern numerical techniques, e.g. beam or plate theory, FEM, BEM [2,4,13], etc., taking into account the changes within surrounding areas induced by mining. If correctly formulated, the models based on the methods of group (b) may provide reasonable estimates of pillar load quite often, however, due to ignored bed separation and sliding between beds in the main roof, the obtained results may not be entirely satisfactory [14]. In such a case very useful are the methods which take advantage

of the special geometry of tabular excavations, e.g. the seam element method [15], displacement discontinuity method [16] or the laminated models [17–19], which are represented by piece-wise homogeneous isotropic strata where the interfaces between beds are parallel and generally free of friction. The theory of thin plates is applied in these models. Generally, the methods applied for pillar strength estimation fall into the following five groups depending on the mathematical tools engaged in the analysis: *

*

*

*

*

Empirical methods: Based on experience and monitoring, dominant in practice up to the 60-ties, presently applied sometimes in barrier pillar design. Semi-empirical methods: Very popular in early 60-ties, however, till today they are willingly applied in pillar design for shallow and moderate depth extraction in room-and-pillar as well as longwall technology (e.g. [20–25]). An empirical dependency between material strength and pillar size without considering the actual stress and strength distribution within pillar crosssection is typical for these methods. Semi-analytic methods: Specially developed for mine workings design for room-and-pillar and longwall mining with an extremely high extraction ratio [26– 28] involving non-uniform load distribution within pillar horizontal cross-sections. Analytic methods: Based on principles of theoretical geomechanics for closed solutions development [29]. These methods may be utilized in relatively homogeneous conditions. Numerical methods: Theoretically and potentially the most ‘‘exact’’ methods most often based on the FEM; however, there occur some difficulties in material behavior formulation, boundary conditions description as well as in significant volume of input and output data (e.g. [30]).

One of the most important problems in determining pillar strength is the effect of specimen size on mechanical properties of rocks. These problems have been investigated for many years. The research was performed as large-scale pillar compression tests or laboratory work using small-scale specimens. Presently, there is no controversy in the opinion on the role of specimen size on rock strength characteristics. A decrease in strength with increasing laboratory specimen size has been reported by a number of researchers, among them by Bieniawski [31]—coal and norite, Koifman et al. [32]—limestone, Il’nitskaya et al. [33]—marble, gabbro, basalt, granite, Pratt et al. [34]— diorite, and many others. The laboratory test results are in agreement with the data obtained from in situ largescale tests on rock pillars. In the USA, the first large compressive tests on square in plan coal specimens (B=0.8–1.6 m; B/H=0.5–1.0) were conducted by Greenwald et al. [35,36]. In 1966

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

Jahns [37] reported on four large-scale in situ tests in compression of iron ore specimens of cubical shape and widths up to 1 m (30 cm, 2
50 cm, 1 m), while in the next year Bieniawski [31,38,39] had started his investigations on compression of large-scale square coal specimens (b ¼ 0:522:0 m) of different heights (B/H up to 3,1). Pratt et al. [34] applied a unique technique for the determination of strength properties of a quartz diorite rock mass. Loading the specimens of an equilateral triangular prism of up to 2.75 m in side length, they showed that the strength of diorite decreased with increasing specimen size. The complete load-deformation curves of large coal specimens were obtained by Cook et al. [40] for the first time in situ. The Cook’s approach was also followed by Wagner [41]. Based on field experiments Wagner [42] proved that due to lateral constraint provided to the central portion of the pillar by the roof and floor contacts, extensive fracturing may be expected at the pillar circumference. The extent of the sidewall fracturing into the pillars is equal approximately to pillar height [43]. Hard rock behavior was also investigated by Hedley and Grant [44]—quartzites, Kimmelmann et al. [45]—metasediments, Krauland and Soder [46]—limestone, Potvin et al. [47]—Shield, . Sjoberg [48]—marble and skarn, and others. Generally, the strength of pillars, determined empirically, depends on three parameters: (a) the specimen (pillar) size, (b) the specimen shape and (c) the unconfined compressive strength of specimen material. The generalized forms of expression for coal prism strength-shape relationships were proposed by Bieniawski [49] as follows:
 B Ba sp ¼ a þ b ð1Þ or K b ; H H where a; b; a; b are the constants, K the uniaxial compressive strength of a cube of specified dimension. Based on Hustrulid’s [50] work one may conclude that the size and shape effects from all data may be expressed by two separate equations, one for size effect and the second for the shape effect. Size effect (D in meters) is as follows:

where sp is the pillar strength. Eq. (2) for the in situ rock strength (specimen of the D size) may be transformed into the form which involves any laboratory data as follows: sd sd sc ¼ pffiffiffiffiffiffiffiffiffi or pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for DX0:914; ð4Þ D=d 0:914=d where sd is the strength of specimen of d size. Based on laboratory tests performed by Lis [52,53] on sandstone and dolomite cylindrical specimens of 44 mm in size from the LGOM mines, and assuming that the relationship for specimen strength has a product-like form: rffiffiffiffiffiffiffiffiffiffiffi

 B d B sp ¼ sc f ¼K f ; ð5Þ H 0:044 H where sp is the strength of specimen of B width and H height, sc the strength of material in situ, K the strength of the cube specimen of 44 mm size, the shape effect function f ðB=HÞ has been identified as (see Figs. 7 and 8): 8
0:484 B > > > ðdolomiteÞ; 0:92 > > H > >
 >
0:546 < B B ð6Þ f ¼ 0:93 ðsandstoneÞ; > H H > > >
0:514 > > > B > : 0:93 ðdolomite þ sandstoneÞ: H Eq. (6) have proved that a shape effect for typical rocks in the LGOM mines may be approximated by a square root function of the reciprocal of pillar slenderness. Most of the empirical formulae treat the entire pillar as a single structural element whose strength is calculated as an average value without consideration

dolomite 2.5

2 y = 0.9183x0.4842 1.5

ð2Þ

where sc is the strength in situ of the specimen of the D size, k is a constant for coal, numerically equal to the strength of a 0.0254 m cube (Wilson [28] proposed the reduction factor 15 instead of 16), and the shape effect is as follows:
 sp B Ba ¼ aþb or c b ð3Þ H sc H

f(B/H)

8 k 0:159 > > < pffiffiffiffi ðwhen Do0:914 EÞ Gaddy ½51; D s¼ > k > : ðwhen DX0:914 mÞ; 6

505

1

0.5

0 0

1

2

3

4

5

B/H Fig. 7. Approximated shape function for dolomite specimens from the LGOM mines area (B; H—specimen width and height, respectively).

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the stress distribution at ultimate load within the pillar horizontal cross-section. However, tests conducted a quarter of a century ago have proved that the distribution is highly non-uniform, and large sections of a loaded pillar yield long before the entire pillar fails [41]. Therefore, the concept was proposed [9] that a loaded (coal) pillar consists of an outer yield zone providing constraint to a confined core working still in

sandstone 3 2.5

f(B/H)

2 1.5 1 y = 0.93x0.5463 0.5 0 0

1

2

3

4

5

B/H Fig. 8. Approximated shape function for sandstone specimens from the LGOM mines area (B; H—specimen width and height, respectively).

an elastic manner. Knowing an expression for the vertical stress gradient within the yield zone and assuming that there is no change in stress value within yield zone once the material yielded, the pillar strength value may be determined by integrating an equation for the stress gradient over the entire pillar cross-section area. Based on these assumptions Mark and Iannaccione [54] found the stress gradient in the yield zone predicted by several well-known formulae for pillar strength. All of them (except that based on the Holland [21] formula) are linear functions of a distance from the nearest pillar rib. The assumption that the stress gradient within the yield zone does not change with load (material perfectly plastic) has to be limited only to that load path which leads to a total exhaustion of pillar resistance ability - pillar failure. The author assumed that with the load increase, pillar behavior characteristics transform from the critical into the post-critical type with bearing capacity reduction down to sr (residual strength) due to entire pillar yielding (elastic– plastic model with strain softening). It is also assumed that residual pillar strength sr ; being a portion of pillar bearing capacity (pillar critical strength), may be determined as above, i.e. integrating rock strength (peak or residual, see Fig. 9) over the horizontal cross-section of the pillar. In 1977 Hardy et al. [10] presented the model of peak and residual strength based on that presented by Wilson and Ashwin [9]. They assumed that the peak strength qp varies bi-linearly with the breaking point located at a

Fig. 9. Stress–strain relationship for yield pillar (sp ; sr —pillar critical and residual strength; qp , qr —local peak and residual strength of material; a, b—transition zone limits).

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

depth of one seam height and with peak strength envelope declining to zero at the pillar face. The residual strength envelope is initially very low and rises with depth until the peak and residual strengths coincide at the depth of three seam heights (q% p ): qr ¼ q% p




x 3Hp

D ;

ð7Þ

where D is the power factor. These assumptions suggest that beyond three seam heights into the seam, the material has infinite strength and therefore theoretically a pillar of B=H > 6 always having a central elastic core of material is indestructible. Because this is unrealistic, the author has introduced [55,56] the following expression for the peak strength envelope: rffiffiffiffiffiffiffiffiffi x qp¼ q% p ð8Þ 3Hp and later [57] for residual strength: 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 > > x 3 > > for 0pxpa; q% p > > > 3Hp > > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffi " >
 ffi# > > < q% p b a 3 ðx  aÞ þ ðb  xÞ qr ¼ 3Hp 3Hp ba > > > > > for aoxob; > > > rffiffiffiffiffiffiffiffiffi > > x > > > : q% p 3H for xXb; p

ð9Þ

where x is the horizontal depth into the pillar from a free face, a; b are the range of transition zone (Fig. 9) within which the rock peak strength contribution increases significantly in the total value of pillar residual strength. Integrating that stress functions over the pillar crosssection the author obtained [55,56] the pillar strength formula in the following form:
sffiffiffiffiffiffiffi B B sp ¼ 0:272q% p 1  ; ð10Þ 5L Hp where q% p ¼ 1:025C0 is the peak strength at 3Hp depth into pillar (C0 is the unconfined compressive strength of rock specimen tested in laboratory having cube size or diameter d ¼ 4:55 cm), B and L are pillar width and length, respectively, Hp the pillar height. In practice, Eq. (10) brings to light the scale reduction factor (Fr ¼ 0:272) whose value depends on the shape of peak stress gradient within pillar volume. It was also assumed that Eq. (10) deals with all kinds of rocks, therefore it may be utilized not only in coal but also in metal mines. The residual pillar strength formulae were determined using a similar approach, however, based on Eq. (9).

507

Finally, they were developed in the following form: if Bp2a s
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  
q% p B 3 3B ð11aÞ 1 sr ¼ pffiffiffi Hp 7L 15 6 if 2apBp2b
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi 4q% p a B 20 a a 3 1þ  sr ¼ L 7 L 3Hp 5 B 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s
3ffi 2a 2a a þ 1 q% p 4 1  L L 3Hp
 1 1a 1 B ðB  2aÞ   þ 4 3L 12 L ðb  aÞ 2sffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi33
 b a 3 55
4  3Hp 3Hp if 2bpB sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 
ffi
4q% p a a 3 B 20 a sr ¼ 1þ  3Hp L 7 L 5 B 2sffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3
3 b a 5 þ q% p 4  3Hp 3Hp

 b a B 4 a 2b  þ
1þ  B B L 3 L L sffiffiffiffiffiffiffiffiffi " 32q% p 1 B B b pffiffiffi þ þ 15 4 2 L 3Hp 2B
sffiffiffiffiffiffiffiffiffi# 3b 5B b 4
 þ L 2L 3Hp 3 sffiffiffiffiffiffiffiffiffi
" B 1 B pffiffiffi
1 L 2 2 3Hp sffiffiffiffiffiffiffiffiffi#
 b b b a þ 2q% p   B 3Hp B B 
 B a b þ
1þ 2 L L L ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi s
 a 3
: 3Hp

ð11bÞ

ð11cÞ

In the case when elastic solution results indicate pillars overloading (sz > sp ; where sz -vertical average pillar load) those pillars are removed from the model and automatically replaced by a constant vertical pressure whose value is equal to sr acting normally to immediate roof and floor strata (see Fig. 5). In Figs. 10 and 11 the selected results of calculation concerning pillar strength according to the developed approach are presented. From Table 1, where the author has summarized most of the available formulae utilized for determining the

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

508

coal and hard rock pillars strength, one can conclude that the research on pillar strength in the past focused mostly on coal pillars behavior, while hard rocks were rather outside the main stream of interest. This probably happened because hard rock pillars, due to its significantly higher ultimate capacity, have been less troublesome in practice so far. Presently however, these problems have become issues of highest importance in the LGOM Copper Basin because of their relevance to roof control and possible bump occurrences in the area. Due to very complex mining conditions, currently the problem of hard rock pillar strength needs to be included in the mine workings design process. Assuming that all research work concerning coal pillar strength may be, by an analogy, utilized in the problems which are characteristic for hard rocks behavior, all available pillar strength formulae have been reviewed (see Table 1 and Fig. 12) and it was found that the Pytel [56] approach is sufficiently representative for limestone and sandstone measure rocks typical for the LGOM mines conditions. 1


r /
p

0.8 0.6 0.4 a = Hp L/B=1 0.2 0 0

2

4

8

6

10

B/H wg [57] dla b/a=1.25

wg [57] dla b/a=3.0

wg [57] dla b/a=2.0

Fig. 10. Ratio of pillar residual strength and pillar critical strength for different stress distribution within yield pillars (B—pillar width, H— pillar height; a, b—transition zone limits; sr —pillar residual strength, sp —pillar critical strength).

All of the above mentioned methods allow the determining of the highest vertical load value which a given pillar is able to carry out without any serious damages. This load is named the ‘‘ultimate bearing capacity’’, ‘‘critical load’’, ‘‘yielding load’’, depending on the authors. A continued increasing of the load leads the pillar into the so-called ‘‘post-critical’’ phase of strain which is associated with a sudden reduction of load carrying ability down to the so-called ‘‘post-critical’’ or ‘‘residual load. This load is only a portion of the maximum load and depends on mine workings geometry. Despite the fact that this problem has been recognized for many years, postcritical pillar load has not played a significant role in mine workings design yet. This may change quickly because of the introduction into practice of new numerical techniques based mainly on the finite element method for roof control, estimation of shafts response on static and dynamic load due to exploitation within the adjacent areas, bump events predictions, etc. The theory of the compressed hard rock pillar which includes such terms as ‘‘pillar peak strength’’ and ‘‘pillar residual strength’’ is one of the important elements of the new design philosophy in the LGOM copper mines. Generally, all planning and design work in the LGOM mines is based on special regulations [69] addressed exclusively to underground copper mining in geological conditions specific for the area. They are also based, however indirectly, on a pillar strength parameter using the so-called pillar stiffness factor M which is a product of pillar slenderness and the average strength of rocks within pillars located in the working area. This parameter, however, does not involve the scale reduction factor (approximately ranging from 13 to 14) and, therefore, it may be used as a relative measure of pillar stability based on large-scale pillars monitoring [70]. From this point of view, the approach represented by the regulations [69], may be treated as a semi-empirical technique.

L/B=4 a/Hp=0.5 b/a=1.5

L/B=1 a/Hp=1 b/a=1 1.2

1

1 σp /Co

σp /Co

0.8 0.6 0.4 0.2

0.8 0.6 0.4 0.2 0

0 0

5

critical strength

10 B/H

15

20

residual strength

0

5

critical strength

10 B/H

15

20

residual strength

Fig. 11. Normalized value of critical and residual strengths for selected types of pillars (B—pillar width, H—pillar height; a, b—transition zone limits; C0 —unconfined compressive strength, sp —pillar critical strength).

Material

Coal

Coal

Coal

Coal

Coal

Coal

Coal

Coal

Coal

Coal

Coal

Coal

Author(s)

Coal Greenwald et al. [35]

Greenwald et al. [36]

Bieniawski [31]

Bieniawski [49]

Cook and Wagner [41]

Van Heerden [58]

Wang et al. [59]

Hazen and Artler [60]

Zern [61]

Morrison et al. [62]

Holland and Gaddy [63]

Sheorey et al. [64]

B0:16 H 0:55

rffiffiffiffiffi B H

B H

sp ¼ s1 þ 0:28Ho

pffiffiffiffi B H

rffiffiffiffiffi B H

rffiffiffiffiffi B H

rffiffiffiffiffi B H

sp ¼ k

sp ¼ sc

sp ¼ sc

sp ¼ sc




sp B ¼ 0:78 þ 0:22 H sc

sp ¼ 10 þ 4:2

sp ¼ sc

sp B ¼ 0:64 þ 0:3 H sc

sp ¼ 7:6

rffiffiffiffiffi B H

sp ¼ 34:32

rffiffiffiffiffi B H

sp ¼ 4:826

Formula sp (MPa)

B 1 H

Agapito and Hardy [67] also in [24,68]

Hardy and Agapito [24]

H0 –cover depth

Pytel [55,56]

. Sjoberg [48]

Potvin et al. [47]

Krauland and Soder [46]

Kimmelmann et al. [45]

Hedley and Grant [44]

Hard rocks

Salamon and Munro [23]

Holland [21]

Obert and Duvall [22]

Bunting [65]

Author(s)

k–constant for the coal (numerically but not dimensionally is equal to the strength of a 1 in cube)

Cited by Farmer [66]

Cited by Farmer [66]

Cited by Farmer [66]

B=H ¼ 4:48213:6 cited by Farmer [66]

B=H ¼ 1:1423:39

sc —in situ coal strength

Valid for B=H > 1 and B > 1:5 m

Valid for B=Ho1 and Bo1:5 m

B=H ¼ 0:4121:68 (approximation assuming H ¼ 0:75 m)

B/H=0.5–1.03

Remarks

Table 1 Summary of pillar strength formulae (B—pillar width, L—pillar length, H—pillar height)

Oil shale

Oil shale

Limestone sandstone

Marble/skarn

Canadian shield

Limestone

Metasediments

Quartzites

Coal

Coal

Coal

Coal

Material

rffiffiffiffiffi B H

sp ¼ s0

sp ¼ s0

V1 Vi

a

B0:597 H 0:951





rffiffiffiffiffi sp B B ¼ 0:393 1  5L H C0


 sp B ¼ 0:308 0:778 þ 0:222 C0 H


 sp B ¼ 0:42 H C0


 sp B ¼ 0:354 0:778 þ 0:222 H C0


0:46 sp B ¼ 0:501 C0 H

rffiffiffiffiffi sp B ¼ 0:3867 C0 H

sp B0:46 ¼ sc H 0:66

sp ¼ sc

sp B ¼ 0:778 þ 0:222 H sc

sp B ¼ 0:7 þ 0:3 sc H

Formula sp (MPa)

s0—laboratory compressive strength V1—volume of laboratory specimen Vi—in situ volume of pillar a—volume reduction coefficient

s0—in situ unconfined compressive strength

C0 —unconfined compressive strength of rock specimen tested in laboratory having size or diameter d ¼ 4:55 cm,and height of 9.1 cm

Cited by Martin and Maybee [30]

Cited by Martin and Maybee [30]

Cited by Martin and Maybee [30]

Cited by Martin and Maybee [30]

Statistical data

Laboratory data

Laboratory data

Remarks

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526 509

510

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

0.9

normalized pillar strength σp /Co

0.8 0.7 0.6 0.5 0.4 0.3 0.2 1

1.2

1.6

1.4

1.8

2

B/H [43] [47]

[44] [55] for B/L=1

[45] [55] for B/L=0

[46]

Fig. 12. Relationship between the normalized hard rock pillar strength and their shape according to various authors (B—pillar width, L—pillar length, pillars, sp —pillar strength, C0 —unconfined compressive strength).

The basic requirement in any yield pillar design procedures is the knowledge of pillar strain characteristics (s  e) and pillar peak and residual strength. Only this creates the full possibility of successful ground control with subsidence and load prediction during mining, including the effect of pillar orientation within the whole panel, its time-dependent geometry and strength and the deformation parameters of surrounding rocks.

5. Discussion Some valuable conclusions may be drawn by applying principles of the similitude theory to predict full-scale pillar strength from the compression tests performed in laboratory conditions. Generally, the behavior of one system (e.g. full-scale pillar) may be predicted from the other system behavior if the so-called scale factors are known [71,72]. They are the simple conversion factors relating characteristics (e.g. strength) of both systems, and may be determined using dimensional analysis which is the most important dimensional technique. The basic condition providing a successful analysis is the knowledge of physical quantities governing the process of pillar (specimen) failure. The scheme of the system and variables upon which it depends are shown in Fig. 13 and Table 2. All 13 variables may be expressed in two dimensions: force and length (time effect is not included) and therefore there are 13  2 ¼ 11 the so-called p terms. All p terms may be formed by grouping appropriately B

and E with the remaining variables: s c p1 ¼ ; p2 ¼ n; p3 ¼ ; E E Er p4 ¼ f; p5 ¼ ; p6 ¼ nr ; E H L dB p7 ¼ ; p8 ¼ ; p9 ¼ ; B B B dL dH p10 ¼ ; p11 ¼ B B

ð12Þ

and pillar behavior may be summarized as the following function:
 s c Er H L dB dL dH G ; n; ; f; ; nr ; ; ; ; ; ¼0 ð13Þ E E B B B B B E or alternatively:
 s c Er H L dB dL dH 0 ¼ G n; ; f; ; nr ; ; ; ; ; : E E B B B B B E

ð14Þ

From the Buckingham’s theorem [73] it is known that the mathematical formulation of any physical phenomenon can be reduced to an equation involving a complete set of dimensionless products: p1 ¼ Fðp2 ; p3 ; y; pn Þ

ð15Þ

and if the above equation is written once for the prototype (pillar) and once for the model (compression test specimen), the following quotient may be formed: p1p Fp ðp2p ; p3p ; y; pnp Þ ¼ p1m Fðp2m ; p3m ; y; pnm Þ

ð16Þ

and if the complete similarity between the pillar and the laboratory specimen compression is to be

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

511

Fig. 13. Scheme of rectangular pillar. Table 2 Variables upon which the system depends and their dimensions dimension

s 1

E 2

n 3

c 4

f 5

Er 6

nr 7

H 8

B 9

L 10

dB 11

dL 12

dH 13

F (force) L (length)

1 2

1 2

0 0

1 2

0 0

1 2

0 0

0 1

0 1

0 1

0 1

0 1

0 1




maintained, then p2m ¼ p2p ; p3m ¼ p3p ; y; pnm ¼ pnp ; 4 ‘ p1p ¼ p1m :

ð17Þ

Scale factors may be arbitrarily chosen for only two quantities, i.e. for pillar width (sB ) and for pillar modulus of deformation (sE), while the remaining scale factors are as follows: ss ¼ sE ; sn ¼ 1; sc ¼ sE ; sf ¼ 1; sEr ¼ sE ; snr ¼ 1; sH ¼ sB ; sL ¼ sB ; sdB ¼ sB ; sdL ¼ sB ; sdH ¼ sB

ð18Þ

sp ¼ sc

sp ¼ ss sm ; np ¼ nm ; cp ¼ sE cm ; fp ¼ fm ; Erp ¼ sE Erm ; nrp ¼ nrm ;

ð20Þ

Assuming that both the model and the prototype are made of the same kind of material ðsE ¼ ss ¼ 1Þ; pillar strength may be determined from the laboratory cube specimen compression test as the following general quotient: f4

and therefore:

Hp ¼ sB Hm ; Lp ¼ sB Lm dBp ¼ sB dBm ; dLp ¼ sB dLm ; dHp ¼ sB dHm :


 cc Erc f3 ðfc Þ f4 sc ¼ Ep f1 ðnc Þ f2 Ec Ec


 Hc Lc dBc
f5 ðnrc Þ f6 f7 f8 Bc Bc Bc

 dLc dHc
f9 f10 : Bc Bc







 dBp dLp dHp Erp Hp Lp f5 ðnrp Þ f6 f7 f8 f9 f10 Ep Bp BE Bp Bp B



p ; Erc dBc dLc dHc f4 f5 ðnrc Þ f6 ð1Þ f7 ð1Þ f8 f9 f10 Ec Bc Bc Bc

ð21Þ ð19Þ

Since one can prove [74] that the effect of all dimensionless variables may be separated, the final equation (Eq. (14)) for pillar and laboratory specimen strength may be presented in a product form:

 cp Erp sp ¼ Ep f1 ðnp Þ f2 f3 ðfp Þ f4 Ep Ep

 Hp Lp
f5 ðnrp Þ f6 f7 Bp Bp


 dBp dLp dHp
f8 f9 f10 Bp Bp Bp

which for horizontally bedded material compressed in the same boundary conditions (the same clamping platen characteristics) transforms into the following relationship:

 f10 ðdHp =Bp Þ Hp Lp f6 sp ¼ sc f7 : ð22Þ f6 ð1Þ f7 ð1Þ f10 ðdHc =Bc Þ Bp Bp pffiffiffiffiffiffiffiffiffiffi Finally, assuming f6 ðH=BÞ ¼ffi B=H ; f7 ðL=BÞ ¼ ð1  pffiffiffiffiffiffiffiffiffiffiffi 0; 2B=LÞ; f10 ðdH =BÞ ¼ dH =B; the following expression for pillar strength may be obtained (see also Eq. (10)): rffiffiffiffi rffiffiffiffiffi
 b B B sp ¼ Asb ; ð23Þ 1 B H 5L

512

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

where A is the constant, b the width of a cube specimen, sb the unconfined compression strength of a cube specimen and B; L; H are the pillar width, length and height, respectively. Almost all pillar strength formulae mentioned in Table 1 conform to the rules of dimensional analysis. Only few of them [23,24,31,64] are dimensionally incorrect or need the introduction of new parameters whose physical meaning should be better defined. The unique formula proposed by Agapito and Hardy [67] which is dimensionally correct, is based on the comparison between volumes of specimens. This may lead, however, to fallacious results, unless cube specimens are considered ðB ¼ L ¼ HÞ: The parameter a (volume reduction coefficient) engaged in that formula seems to be too low to get a similar strength reduction due to specimen size as the other formulae may suggest. This might be due to the following two reasons:

theories. The measure of the fitting of a given strength theory to the actual conditions is a percent of the theory explained instabilities which occurred in the area of interest. In rock mass strength analyses the following strength theories were involved: Maximum normal stress theory, which takes principal stress as the criterion for strength and assumes that yielding starts when the maximum principal stress becomes equal to the yield point stress of the (ductile) material in simple tension (T0 ) or the minimum principal stress becomes equal to the yield point stress in simple compression (C0 ). The safe intervals are characterized as follows:

(a) It is not obvious that the statistical theory of extreme values is the best mean for strength prediction in compressed rocks. The assumption that strength is distributed according to Weibull’s distribution and depends on the material volume is not necessarily certain, particularly in the case where flaws or weakeness planes are not distributed homogeneously over the material volume. (b) When strength reduction due to specimen size is investigated, the same boundary (support and load) conditions should be maintained (Eq. (21)). This means that using the Teflon-lead swivel heads for one specimen size and steel platens for another [25] may form different confinement conditions significantly affecting the specimen strength.

where m is a dimensionless parameter determined in laboratory tests. Since these two strength theories involve the maximum principal stress, this category of stress is assumed to be a good indicator of potentially unstable roof conditions. Therefore, the numerical analysis of actual mine workings behavior will be focused on looking for areas of highest s1 concentrations within roof strata. The maximum principal stress spatial distribution will also serve as a criterion of ‘‘goodness’’ of the actual mine workings design. For shaft lining made of concrete, the maximum distortion strain energy theory with the following failure condition: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 sHM ¼ pffiffiffi ðs1  s2 Þ2 þ ðs2  s3 Þ2 þ ðs1  s3 Þ2 pC0 2 ð26Þ

6. Roof safety margin as failure (bump) likelihood measure

was utilized.

In the presented model, pillar instability is one of the important phenomena that may be expected to occur and for which the operator has to be prepared for. Thus, the entire system safety is determined mainly by strong roof strata behavior and therefore they have to be examined in actual stress–strain conditions utilizing the appropriate strength theories. It is assumed that the so-called safety margin, representing the relation between load intensity and material strength, may serve as the basic indicator of possible roof instability development. The safety margin may be estimated by comparing the actually computed components of stress–strain tensor with ultimate values characteristic for a given material determined in laboratory. This may be done using some functions of load intensity formulated in the form of various strength

7. Development of alternate mine workings geometry using the presented physical model

C0 ps1 pTo; C0 ps2 pTo; C0 ps3 pT0 :

ð24Þ

Hoek–Brown strength theory with failure condition: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð25Þ s1 ¼ s3 þ C0 s3 m þ C02 ;

In order to illustrate the effect of technological pillar size on roof strata stability, the mining sequence in one of the ‘‘Lubin’’ Mine districts (Fig. 14) was modeled using the finite element method formulated in three dimensions [75]. Finite elements represented overburden and floor solid strata as well as partially extracted copper ore deposits as a mixture of solid and void space. Generally, the linear elastic behavior of all materials is assumed, however, only up to the limits described by Eqs. (24)–(26). If even one of those limits is not fulfilled within an element, the element is softened significantly (1/100 of Young’s modulus) for a purpose of local instability modeling.

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

In the area the copper ore deposit, located at the depth of about 780 m, is almost flat and is covered by very thick and stiff main roof strata consisting of a 60 m layer of coherent dolomite overlying by a 155 m thick strong anhydrite plate and a 135 m thick competent sandstone stratum. An averaged lithology over the considered area and estimated rock mass parameters are given in Table 3. In order to verify additionally the developed model, correlation analysis between location (Fig. 14) of seismic events which occurred in the area on 27 January 1998 (energies: E ¼ 7:2E7 and 5E7 J) and the computed values of safety margins within overburden strata was performed.

513

The problem was solved by utilizing solid mechanics principles assuming different materials within different rock mass strata, however, additional horizontal planes of discontinuity (5 cm in width) were designed within the model. They were located at 20 m (within dolomite), 40 m (dolomite) and 60 m (dolomite-anhydrite contact) above the copper deposit. The discontinuity surface mechanics permits bed separation but restricts the mutual element penetration. This behavior was provided by gap type elements used as the connectors. The model boundaries are characterized using the following conditions: (a) Bottom - vertical displacements not allowed and (b) side walls - no movement perpendicular to the wall surface permitted. External load was divided into the following groups: (a) Deadweight of the rock mass—each element located up to z ¼ 258:5 m is subjected to gravitational load, and (b) elemental load q ¼ 14:89 MPa distributed uniformly on the plane z ¼ þ285:5 m, representing Tertiary and Quaternary soft deposits. Assuming the range of a main yield zone within pillars as a ¼ H (see Fig. 9) and using a back calculation procedure based on a compatibility between the convergence data and the calculated roof vertical movement, the inner range of the pillar transition zone was approximated as b ¼ 1:25 H [57]. All the remaining data concerned with pillars in the working area are presented in Table 4. A calculation non-linear procedure included the following phases: *

*

Fig. 14. Mine workings geometry in the area.

The adjustment iterative phase: With modification of overloaded pillars based on elastic solutions—pillars subjected to load sz > sp ; are replaced by an uniformly distributed load equal to pillar residual strength sr : The final phase: Checkout of safety margin within roof strata for the final mine structure obtained in the adjusting phase.

Table 3 Average values of rock deformation parameters Kind of rock

Stratum thickness (m)

Bulk weightgo (MN/m3)

Poisson’s ratio n

Reduction factor

Modulus of elasticity E (MPa)

C0 (MPa)

T0 (MPa)

Sandstone Shale Anhydrite Dolomite Copper ore Red floor sandstone

135 30 155 60 3.5 150

0.027 0.027 0.027 0.027 0.027 0.027

0.3 0.18 0.26 0.24 0.18 0.13

0.25 0.25 0.25 0.125 0.125 1

10000 3375 13875 8550 2039 15000

57.5 88.5 88.5 135.9 67.59 18.4

3.55 6.25 6.25 8.8 3.0 0.8

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

514

All modeling and computational analyses were performed using the UAI/NASTRAN code [75], the complete and entirely integrated system for modeling, solving and output assessment, utilizing the finite element method. The system is able to solve problems concerning, among others, the linear and non-linear statics, buckling, linear and non-linear dynamic response, heat transfer etc., engaging different finite element features, different material properties, and different load types and boundary conditions. The extremely fast, sparse, direct and iterative equation solvers reduce significantly solution time, so the system may be exploited within personal computers environment. Selected calculation results obtained for the following extraction paths: Extraction Sequence No. 1 applied in practice (Fig. 15), Alternate Extraction Sequence No. 2 significantly different than Extraction Sequence No. 1 (Fig. 16),

*

*

are presented in Figs. 17–20. It has been proved that mining according to the extraction sequence No. 2 is Table 4 Pillar load characteristics Pillar location

Pillar size B
L (m)

Pillar strength sp (MPa)

Pillar residual strength sr (MPa)

Development area Large-size pillars (existing)

8
22

25.78a

9.53

16
64

37.365

28.42

a

C0=67.59 MPa.

associated with significantly lower roof deflection curvature (lower probability of roof fall) and, what is most important, with radically lower values of maximum principal stresses within the roof strata. This may result in the reducing of bump occurrence hazard and a more safe environment. It has also been confirmed that a high stress concentration was located in the area where the above mentioned seismic events were observed. In a case where roof strata consist of good quality rocks, the remnant pillar size is a problem of less importance due to their low support ability and therefore insignificant influence on main roof behavior. The main role which they are intended for is separated immediate roof strata support as well as opposing roof fall occurrence. A technological pillar size, however, is a problem of highest importance. This especially deals with a sequence and directions of large size pillars splitting in the development phase of mining. As the numerical modeling showed, in all geological and mining conditions the likelihood of roof bump may always be reduced by implementing a suitable mining sequence. It is necessary, however, to prevent the large size (B > Bcr ; where Bcr is the critical pillar size which, for opening width W ¼ 6 m, may be determined from Fig. 21 depending on the factor ab ¼ ðq0 =C0 Þ2 H; where q0 is the overburden vertical pressure at the mining depth, C0 represents unconfined compressive strength of pillar material, and H is a pillar height) pillars development within stress relieved zones. If such a squat pillar is located in the area of future development, it has to be split and transformed into a yield pillar, well before the mining face approaches.

Fig. 15. Extraction sequence No. 1 within G-7 district in the ‘‘Lubin’’ mine.

Fig. 16. Extraction sequence No. 2 within G-7 district in the ‘‘Lubin’’ mine.

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Fig. 17. Maximum principal stress distribution s1 (MPa) on the level 5 m above the immediate roof surface—final phase of extraction according to extraction sequence No. 1.

Fig. 19. Maximum principal stress distribution s1 (Mpa) on the level 5 m above the immediate roof surface—final phase of extraction according to extraction sequence No. 2.

Fig. 18. Maximum principal stress distribution s1 (MPa) on the level 15 m above the immediate roof surface—final phase of extraction according to extraction sequence No. 1.

Fig. 20. Maximum principal stress distribution s1 (Mpa) on the level and 15 m above the immediate roof surface—final phase of extraction according to extraction sequence No. 2.

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expect the velocity of about 27–95 mm/s on the shaft lining located in the distance of 330 m from the event source (closest distance from the considered shaft and the panel planned to be mined-out in the future). Additionally the following assumptions were accepted: *

*

the highest values of dynamic load are directly proportional to the highest values of accelerations generated at a given location, the function of acceleration transfer within rock mass may be expressed as: aðxÞ ¼ að0Þexpbx ;

Fig. 21. Critical size of technological pillars (B—pillar width, L—pillar length, ab ¼ ðq0 =C0 Þ2 H). *

8. Example of dynamic load transfer onto shaft lining determined using the presented above model

where aðxÞ is the wave acceleration at the distance x from the seismic event source, að0) the acceleration at the source and b the constant, therefore, if the dynamic effect at the distance xo from the source is known, the effect in stress domain at any distance x may be estimated from: DsðxÞ ¼ Dsðx0 Þ expbðxx0 Þ :

Presently, the scale of influence of seismic events on shaft lining stability in the LGOM mines is evaluated by using a direct measurement of shaft vibrations at selected monitoring points. There have been found the following characteristics of shaft lining response on the arriving dynamic signal [76]: *

*

*

*

*

the highest values of acceleration (up to 4 m/s2 by frequency of several tens of Hz) have been measured at the shafts’ bottom (lower, concrete part of shafts); in the upper, concrete part of the shaft, a vibration significant damping has been observed; the highest values of velocity have been measured at the lower part of the cast iron lining located within glacial deposits (the maximum value ever measured was 24.4 mm/s by frequency of several Hz induced by the tremor of energy 3.3E6 J occurred at the distance of 915 m); the highest velocities are associated with seismic events of energy greater than 106 J; so far there is no evidence of a negative effect of dynamic events on the technical conditions of shaft lining.

Taking into account the actual geometry of shaft protecting pillars, the closest distance of prospective seismic events is evaluated on about 300–400 m. Knowing the load in the source and assuming the appropriate function of a wave transfer, the characteristics of shaft lining vibration may be calculated. In practice, results of measurements done in the near wave field zone may be treated as the forced motion signal. Based on the estimated [76] relationship between the wave velocity and the distance for seismic events of energy greater than 105 J monitored in the near wave field, one may

ð27Þ

ð28Þ

An example of dynamic load assessment applied to one of the LGOM mine’s shafts is presented below. The actual geometry in the shaft vicinity as well as the area of prospective extraction are shown in Fig. 22, while the rock mass parameters and remaining data necessary for numerical modeling are presented in Tables 5 and 6. The problem was solved as above, however, different horizontal planes of discontinuity (5 cm in width) were designed within the model. They were located at 20 m (within dolomite), 43 m (dolomite) and 55 m (dolomiteanhydrite contact) above the copper deposit. The results of numerical three-dimensional modeling (the finite element method, multi-plate overburden structure as above) of static effects within one of the LGOM shaft protective pillars have shown that: *

*

*

presently there is no instability hazard within castiron lining at the upper part of the shaft, however the stress level in the lower, concrete part is relatively high, effective stress state within shaft lining depends mainly on the conjunction of effects caused by rock mass dewatering and roof-floor convergence in the adjacent areas as well and the calculated deformations of the shaft head remain in agreement with the Knothe theory [77].

The static problem solution was a base for solving the problem of dynamic load transfer from a remote point of instability within rock mass to the shaft lining. The problem was considered using the finite element method (UAI/NASTRAN code [75]) which permits solving the following equation of motion: Mdd u. d ðtÞ þ Bdd u’ d ðtÞ þ Kdd ud ðtÞ ¼ 0;

ð29Þ

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

Fig. 22. Shaft location with the areas of prospective exploitation.

517

where Mdd is the inertia matrix, Bdd the damping matrix, Kdd the stiffness matrix, ud the movement vector, with the initial conditions identical to the static solution. Eq. (29) has been solved using the transient response analysis (provided by UAI/Nastran code), i.e. the most general method for computing forced dynamics response. The main purpose of this analysis is to compute the behavior of a rock mass structure subjected to time varying excitation due to external load expressed by enforced motion or forces. In the paper, enforced displacements generated by the point force Px or Pz; acting at the selected node within rock mass, were used as the initial conditions of the excitation process. The results, obtained from the transient analysis, have included displacements, velocities, and accelerations of the model nodes, and stresses in the finite elements composing the numerical model as well. In the paper, the direct method has been used for a transient response analysis. This method is based on direct numerical integration of a set of coupled equations of (29) type. The fundamental structural response (displacements) was solved at discrete times involving 200 steps of the time Dt ¼ 0:005 s.

Table 5 Average rock mass parameters in the considered shaft vicinity Kind of rock

Strata thickness (m)

Strata distance from copper ore bottom (m)

Unconfined compression strength C0 (MPa)

Tensional strength T0 (MPa)

Modulus of elasticity E (GPa)

Poisson’s ratio n

(1) Tertiary and Quaternary deposits Sandstone Clayey shale Anhydrite Dolomitic limestone Gray dolomite Copper ore Gray sandstone Red sandstone of deep floor

(2) 373

(3) 293–666

(4) —

(5) —

(6) 0.07

(7) 0.3

107 26 105 22

186–293 160–186 55–160 43–55

— — — —

— — — —

20 6.75 27.75 24.40

0.3 0.18 0.25 0.26

39.5 3.5 7 143

3.5–43 0–3.5 (7)–0 (7)–(150)

124.6 105.3 — —

7.1 — — —

31.10 13.94 15.95 9.0

0.25 0.21 0.16 0.15

Table 6 Characteristics of representative pillars located within the shaft protective pillar Name of parameter

Pillar width B (m)

Pillar length L (m)

Pillar design strength sp (MPa)

Pillar residual strength sr (MPa)

(1) Pillars in the area of development Existing large size pillars Existing small size pillars

(2) 8

(3) 10

(4) 32.76

(5) 3.29

24 18

44 20

60.18 47.97

49.56 35.54

Pillar: Hp=3.5 m, C0(r)=94.8 MPa, Immediate roof: C0(r)=112.14 MPa.

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acceleration (m/s2)

In a general case the damping matrix Bdd ; used to represent energy dissipation characteristics of a rock mass, is comprised of several matrices involving complex coefficients. Since transient response analysis does not permit using complex coefficients, structural damping G had to be expressed by equivalent viscous damping. Due to the lack of reliable rock measure data, the value of rock mass damping G ¼ 0:01 has been established as the lowest value characteristic for compacted cohesionless soil [78]. This assumption has created the underdamped conditions for a rock mass motion. Additionally, the value of o ¼ 10 Hz representing the system’s first natural frequency was used to convert structural damping G to equivalent viscous damping accepted by the UAI/ Nastran code. A dynamic load transfer within rock mass was recognized by applying a special kind of load at the node N7069 localized 43 m above the copper seam at a distance of 330 m from the considered shaft (see Fig. 22). The static solution analysis has indicated that in that location the maximum principal stress concentration may occur and therefore rock mass may work in instability favoring conditions. The applied load consisted alternatively of concentrated horizontal force Px ¼ 100 GN (scheme No. I) or vertical force Pz ¼ 100 GN (scheme No. II). Due to the sudden removal of the mentioned forces there were modeled two separate dynamic events with an energy of 2.38E10 J (scheme No. I) or 3.12E10 J (scheme No. II) emitted. Knowing that seismic energy is a very small portion, estimated at several promiles, of the total energy of the event [79], one may assume that the movement vector parameters for both the schemes represent the effect of tremor emitting the seismic energy of about 10E7–

10E8 J. The location of finite element E7760 (high s1 level) confined in one of the corners with the loaded node N7069, is shown in Fig. 22. Calculated values of stress increment as well as dynamic excitations and their derivatives (velocities and accelerations) for selected points of shaft lining are shown in Figs. 23–36.

9. Results of dynamic analysis From the calculated parameters, an excitation velocity equal to about 0.042 m/s and the acceleration equal to 1.25 m/s2 are in good agreement with the parameters measured in situ. However, the values of that order were attributed to seismic events occurred at a distance of about 500 m and therefore seismic events detected at a distance of about 330 m should give higher values of velocity estimated at no more than 0.09 m/s. On the other hand, the calculated maximum displacement of about 0.007 m is significantly higher than the value measured from the distance of 85 m resulted from the event of energy of about 10E7 J. The differences between the calculated and measured values may be explained by the effect of the frequency band which was chosen to be in the area of interest. The adequate frequency range depends on a number of elements, especially on the characteristics of the dynamic impulse which should model appropriately the actual mechanism of instability within the rock mass. This problem has not been sufficiently recognized yet and needs more investigation. The calculation results were also a base for the estimation of the minimum distance from which the event of energy 1.E7–1.E8 J (considered above) would

Node No. 7506, Px = 100 GN

1.2 1.4 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time (sec) Ax 2

Ay

Az

Fig. 23. Acceleration components (m/s ) at node 7506 located on shaft lining; horizontal force Px ¼ 100 GN.

acceleration (m/s2)

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Node No. 7506, Px = 100 GN

1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 0

0.1

0.2

0.3

0.4

0.5

0.7

0.6

0.8

0.9

1

time (sec) Ax

Ay

Az

2

Fig. 24. Acceleration components (m/s ) at node 7506 located on shaft lining; vertical force Pz ¼ 100 GN.

Node No.7506, Px = 100 GN 0.03 0.02

velocity (m/s)

0.01 0.00 -0.01 -0.02 -0.03 -0.04 -0.05 0

0.1

0.2

0.3

0.4

0.6

0.5

0.7

0.8

0.9

1

time (sec) Vx

Vy

Vz

Fig. 25. Velocity components (m/s) at node 7506 located on shaft lining; horizontal force Px ¼ 100 GN.

not damage the concrete shaft lining in a compressiontype failure mode. The suitable procedure should include the following steps: (1)

(2)

(3) (4)

Select the maximum value of total acceleration within the source of horizontal enforced motion (Fig. 29)-ax ð0Þ ¼ 425:9 m/s2. Select the maximum value of total acceleration at node 7506 located on shaft lining due to horizontal enforced motion (Fig. 30)-ax ð330Þ ¼ 1:269 m/s2. From Eq. (27) calculate the exponent parameter b-bx ¼ ðln 1:269=425:9Þ=330 ¼ 0:0176: From Fig. 33 select the maximum value of reduced stress increment in the shaft lining due to horizontal enforced motion -Dsx ð330Þ ¼ 0:33 MPa.

(5)

(6)

(7)

(8)

Evaluate the actual safety margin for shaft concrete lining -DsðxÞ ¼ ½strength2½load; based on static analysis performed in [80], the safety margin value for the considered shaft (Fig. 22) has been determined as DsðxÞ ¼ 6:3 MPa. From Eq. (28) one may calculate: xh ¼ 330 þ ln DsðxÞ=Dsx ð330Þ=bx ¼ 162:4 m which is the safe distance in case of a horizontal event occurrence. Select the maximum value of total acceleration within the source of vertical enforced motion (Fig. 29) -az ð0Þ ¼ 328:0 m/s2. Select the maximum value of total acceleration at node 7506 located on shaft lining due to vertical enforced motion (Fig. 30) -az ð330Þ ¼ 1:143 m/s2.

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Node No.7506, Pz = 100 GN

0.04 0.03

velocity (m/s)

0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 -0.05 0.1

0

0.2

0.4

0.3

0.5

0.6

0.7

0.8

0.9

1

time (sec) Vx

Vy

Vz

Fig. 26. Velocity components (m/s2) at node 7506 located on shaft lining; vertical force Pz ¼ 100 GN.

Node No.7506, Pz = 100 GN 500.0 400.0

acceleration (m/s2)

300.0 200.0 100.0 0.0 -100.0 -200.0 -300.0 -400.0 -500.0 0

0.1

0.2

0.4

0.3

0.5

0.6

0.7

0.8

0.9

1

time (sec) Ax

Ay

Az

2

Fig. 27. Acceleration components (m/s ) at node 7069 (source); vertical force Px ¼ 100 GN.

(9)

From Eq. (27) calculate the exponent parameter b-bz ¼ ðln 1:143=328:0Þ=330 ¼ 0:0171 (10) From Fig. 34 select the maximum value of reduced stress increment in the shaft lining due to vertical enforced motion -Dsz ð330Þ ¼ 0:72 MPa. (11) Evaluate the actual safety margin for shaft concrete lining -DsðxÞ ¼ ½strength2½load; based on static analysis performed in [80], the safety margin value for the considered shaft (Fig. 22) has been determined as DsðxÞ ¼ 6:3 Mpa. (12) From Eq. (28) one may calculate: xv ¼ 330þ ðln DsðxÞ=Dsz ð330ÞÞ=bz ¼ 203:1 m; the safe distance in case of a vertical event occurrence.

It has been proved that the event of seismic energy of about 1.E7–1.E8 J is not a hazard to concrete shaft lining unless it is located closer than d ¼ 162:42203:1 m (depending on direction of instable rock mass movement). The procedure shown above should be performed for several points located on the shaft lining, and the final value of safe distance may be chosen as the maximum value from the calculated set. The mining face should not be located closer than the safe distance enlarged by about 50 m (safety reason). It must be emphasized, however, that these results were obtained assuming constant static load, characteristic for mine geometry shown in Fig. 22 (no effect of closer mined-out areas).

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Node No.7506, Pz = 100 GN

400.0

acceleration (m/s2)

300.0 200.0 100.0 0.0 -100.0 -200.0 -300.0 -400.0 0

0.1

0.2

0.4

0.3

0.7

0.6 0.5 time (sec)

Ax

Ay

0.8

0.9

1

Az

2

Fig. 28. Acceleration components (m/s ) at node 7069 (source); vertical force Pz ¼ 100 GN.

Node No.7069 450.0

total acceleration (m/s2)

400.0 350.0 300.0 250.0 200.0 150.0 100.0 50.0 0.0 0

0.1

0.2

0.3

0.4

0.6 0.5 time (sec)

0.7

0.8

0.9

1

Px=100GN

Pz=100GN

Fig. 29. Total acceleration of node No. 7069 located at the event center.

10. Conclusions and future work 10.1. Conclusions The experience gained in the course of designing the sequence and geometry of mining in deep Polish copper mines, using the presented interaction model, permitted drawing the following conclusions: *

The unique (featured in a sandwich-like form) geological formation of overburden strata in the area and the applied extraction technology may be analyzed using the presented multi-plate rock mass model whose weakest element is a set of yielding pillars compressed between very strong roof strata

*

and more deformable floor bed. The initial pillar softening achieved by relatively small size selection (Fig. 21) permitted eliminating pillars as a source of bumps of the pressure type and focusing attention on the reduction of bump hazard generated by roof strata subjected to bed separation. The developed model permitted introducing into the analysis new, clearly defined, decisive parameters governing the time-dependent rock mass deformation process. For instance, a rational selection of backfilling material parameters (e.g. compaction ratio, degree of opening fulfillment, etc.) as well as pillar size and its location and orientation towards the mining face, allowed better ground control management and bump hazard virtual reduction.

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Node No.7506 1.4

total acceleration (m/s2)

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.2

0.1

0

0.4

0.3

0.7

0.6 0.5 time (sec)

Pz=100GN

0.9

0.8

1

Px=100GN

Fig. 30. Total acceleration of node No. 7506 located on shaft lining.

N7506 Pz = 100 GN

displacement (m)

displacement (m)

N7506 Px = 100 GN 0.002 0.001 0 -0.001 -0.002 -0.003 -0.004 -0.005 -0.006 -0.007 -0.008 0

0.1 0.2

0.3 0.4 0.5 0.6 0.7 0.8 time (sec) T1

T2

0.9

1

*

*

*

Since the curvature of deflected and separated roof strata depends on reactive effectiveness of softened support pillars, the knowledge of their critical and residual strength is the basic element of any properly conducted geomechanical analysis of rock mass behavior. From this point of view, the developed model of axially compressed pillar is a very unique but still relatively simple analytical tool. The physical meaning of parameters governing the distribution of vertical support reaction (the most important element of the stress tensor defining the pillar–roof interaction) developed within pillar crosssection area has been shown in the paper. The calculated (using the developed interaction model) pillar strength values were generally found to be in agreement with the values predicted by other formulas and observed in field conditions.

0

0.1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 time (sec) T1

T3

Fig. 31. Displacement components (m) of node 7506 located on the shaft lining; horizontal load Px ¼ 100 GN.

0.001 0.0005 -0.0005 0 -0.001 -0.0015 -0.002 -0.0025 -0.003 -0.0035 -0.004 -0.0045

T2

1

T3

Fig. 32. Displacement components (m) of node 7506 located on the shaft lining; vertical load Pz ¼ 100 GN.

*

*

*

Based on the dimensional analysis principles, the developed pillar strength formula was proved to have a dimensionally correct shape and also the origin and role of scale effect in the problem of full-scale pillar strength assessment from small-scale laboratory tests was explained. The computational examples have proved that a continuous solid rock mass analogue should not be incorporated in the stratified roof strata behavior analyses since possible bed separation may affect significantly stress and strain spatial distribution within overburden strata. The developed rock mass—mine workings interaction model has also been found to be very effective in the problem of assessment of the safe distance of mining to preserve the existing shafts stability. A dynamic approach was proposed which confirmed a

W. Pytel / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 497–526

Pz = 100 GN

0.4

0.4

0.3

0.3

stress σ1 (MPa) increment

stress σH-M (MPa) increment

Px = 100 GN

0.2 0.1 0 -0.1 -0.2 -0.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

E10958

0 -0.1 -0.2 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time (sec)

E13720 E8196

E10958

E13720

Fig. 35. Increment of s1 stress, Mpa, in the shaft lining—element 8196 located 48 m above the copper seam, element 10 958 located 172 m above the copper seam and element 13 720 located 346 m above the copper seam; horizontal load Px ¼ 100 GN.

Pz = 100 GN

0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7

Pz = 100 GN

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time (sec) E8196

E10958

stress σ1 (MPa) increment

stress σH-M (MPa) increment

0.1

0

Fig. 33. Increment of sHM stress, Mpa, (Eq. (26)) in the shaft lining—element 8196 located 48 m above the copper seam, element 10 958 located 172 m above the copper seam and element 13 720 located 346 m above the copper seam; horizontal load Px ¼ 100 GN.

0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7

0

0.1

0.2 0.3 0.4

significance of the knowledge of the actual stress tensor within shaft linings strongly related to the structure margin of safety. The developed model also allowed proving that most of dynamic phenomena may be avoided by utilizing the appropriate sequence of extraction and by an early splitting of squat pillars located in front of the mining face.

10.2. Future work The presented above approach based on multi-plate analogue has proved to be an effective tool which may be used in any prognosis of the stress-strain effects of mining operations conducted below a stiff, stratified

0.5 0.6

0.7

0.8 0.9

1

time (sec)

E13720

Fig. 34. Increment of sHM stress, Mpa, (Eq. (26)) in the shaft lining—element 8196 located 48 m above the copper seam, element 10 958 located 172 m above the copper seam and element 13 720 located 346 m above the copper seam; vertical load Pz ¼ 100 GN.

*

0.2

-0.3

time (sec) E8196

523

E8196

E10958

E13720

Fig. 36. Increment of s1 stress, Mpa, in the shaft lining—element 8196 located 48 m above the copper seam, element 10 958 located 172 m above the copper seam and element 13 720 located 346 m above the copper seam; vertical load Pz ¼ 100 GN.

roof strata, especially in the area where important mine objects and structures are located. By implementing any optimization procedure in the proposed approach one may design the exploitation sequence (path) in order to maximize production while maintaining all required safety conditions. The proposed design procedure may permit verifying the presently utilized mining systems as well as creates avenues for new and more effective technologies. It has been proved that such mine system parameters as pillar strength and residual pillar strength may, and should, be incorporated into any procedure concerned with mine workings geometry selection. However, there has been no conclusive opinion yet on the scale and shape effects on hard rock pillar strength, specifically in the LGOM mines geological conditions.

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Therefore, a broad research program will be implemented in that area next year. The program will include investigations on full-scale pillar behavior using multipoint borehole extensometers, instrumented rock bolts and convergence meters. In cooperation with Strata Control Technology Pty. Ltd., Australia, a complementary research work will also be done using the overcoring techniques for the identification of complete stress tensor components in the entire area of the LGOM copper mines. This should permit refining all important parameters governing roof–pillar–floor interaction, and therefore may help to validate the presented above numerical model. The validated in the LGOM Basin model will be an effective analytical tool for bump hazard prediction, particularly in extremely important areas of present mining activity such as mining within shaft and main entries protective pillars, as well as the optimization and development of alternative, more profitable exploitation systems. However, if the proposed model is to transform into a reliable design tool, new areas of knowledge should be investigated earlier, among others: *

*

*

*

criterions of rock mass failure and their correlation with actual encountered bump mechanisms, rules for estimation of mine structure resistance against deformations induced by mining in the adjacent areas, dynamic events hazard and mining process optimization through ground control in static and dynamic domain as well, quantitative analysis of different mining systems, including roof deformation and pillar load control in complex mining conditions, e.g. within shaft protective pillars.

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