Flexibility and Load-Bearing Capacity of Roof Bolting as Functions of Mounting Depth and Hole Diameter

: This paper presents the results of laboratory tensile testing of segmentally-installed glue-in roof bolting. We studied roof bolting of the type Olkusz-16A (Boltech Sp. z o.o., ZGH Bolesław S.A., Bukowno, Poland), additionally equipped with a steel rod coil, which was mounted in steel cylinders ﬁlled with a concrete mixture using multi-part resin cartridges with a diameter of 0.024 m and length of 0.045 m. The mounting depths were 0.1 m and 0.2 m, respectively. Our main purpose was to determine the e ﬀ ect of the bolt hole diameter, which assumed the values 0.028 m, 0.032 m, 0.035 m, and 0.037 m, respectively, on the load-bearing capacity of the roof bolting in relation to the mounting depth. We found that the mounting depth of 0.2 m was su ﬃ cient for the roof bolting to exhibit its full load and displacement properties for all four diameters of the bolt hole. To determine whether the roof bolting was capable of transferring the load in situ, we presented the results of the predicted load on the roof bolting applied in a room and pillar mining method in an underground mine of zinc and lead ore deposits. Our objective was to determine the inﬂuence of the room and pillar mining method geometry on the range of the fault zone of rocks around pits. We designed the deposit excavation model using the Examine3D numerical modeling software, which is based on the boundary element method. We created three-dimensional models for three variants of working space opening widths: featuring two, three, and four rows of rooms. The geometry of rooms and pillars corresponded to the mine conditions; the width, height, and length parameters were all 5 m. We determined the strength, strain, and structural parameters of the rock mass on the basis of laboratory studies of the drill core and rock forms collected from the room longwall. We used the strength factor to specify the maximum range of the fault zone of rocks around pits. In the last stage of research, we compared the load value obtained based on numerical testing with the maximum load obtained in the tensile strength tests of the roof bolting and determined the safety factor of the segmentally-installed roof bolting.


Introduction
Roof bolting, both adhesive and sleeve-anchor installed, is very common in room and pillar mining methods for protecting pits against roof rock cave-ins. Roof bolting is used in both ore and coal mining, installed segmentally or over the whole length using quick-setting and slow-setting resin cartridges. Glue-in roof bolting is installed in long-term preparatory excavations, short-term mining excavations, and in the fractured rock mass, where the expansive head cannot expand against the walls of the bolt hole [1]. In underground mines it often happens that locally, along the boreholes drilled for the bolt, fractured zones (or even bigger gaps) are met, so the diameter is oversized, the contact may be insufficient, and finally, the expansion head will not be effective. The advantage of segmentally installed glue-in roof bolting (Figure 1a) is that it is possible to increase its load-bearing capacity by using a longer installing segment. The diameter and length of the cartridge should be selected in such a way as to reach the full load and displacement properties of the roof bolting. This type of optimization is a significant factor in reducing production costs. Moreover, under shifting geological conditions, a change in the bolting technology is not problematic for roof bolter operators with experience in handling adhesive cartridges. At same locations, the same kinds of rocks may be softer or harder, more or less fractured, fractures may be filled with stronger or weaker material, separated or compacted, wet or dry. All these features may affect the final quality of the roof bolting. The change only involves the addition of several additional cartridges. Some doubts arise from the fact that in a fractured rock mass, the resin cartridge may not be correctly mixed, as the resin will have a tendency to move towards the cracks. Campbell et al. [2] found that an important issue to be considered is the packaging of the resin cartridge, which might serve as a plug that prevents the full utilization of the cartridge mass. Glue-in roof bolting installed along its whole length ( Figure 1b) is usually used in a layered rock mass, where the joint activity of the bolting and the rock mass is based on layer fastening [3]. It should be noted that installation along the whole length of the roof bolting using resin cartridges can cause the bolting to become very stiff. Roof bolting stiffness is determined by the load transfer mechanism at the contact point between the rock mass, resin, and the bolting [4]. Due to very slight deformations, this type of bolting is not recommended for the roof layers of the rock mass which are inclined to bending. Rock bolts may be installed in the hole using quick-setting and slow-setting cartridges ( Figure 1c). For example, in Polish underground copper mines, quick-setting resin cartridge and three or four slow-setting cartridges with a diameter of 0.024 m and length 0.45 m are used [5]. This makes it possible to preload. Due to different gelation times, roof bolting should be installed by experienced operators to prevent the premature shearing of the resin at the point of contact between the rock mass and resin or resin-rod during the rotational movement of the rock bolt [6]. Selecting the technology for installing roof bolting on quick-setting or slow-setting cartridges should be based on striking a balance between the install of potential excavations designated for bolting and the time needed to secure them.  The diversity of conditions under which roof bolting is used requires achieving a joint effect at the roof bolt-resin cartridge (binding agent)-rock mass contact point. Under laboratory conditions, the roof bolting is installed to the drill core [7,8], or the rock mass is simulated using a concrete mix glued to the steel cylinders [9,10]. Marcon et al. [11] divided the failure mechanisms of the glue-in roof bolting under tensile loading into four mechanisms: concrete cone failure, combined failure, splitting failure; and steel failure. Kilic et al. [12] examined the influence of the binding agent on the load-bearing capacity of glue-in ribbed bolts along the whole length in a basalt block. Kilic et al. [13] presented the influence of rock bolt geometry on transferring the load for adhesive installing along the whole length. Li et al. [14] defined the influence of the critical installation depth of the rock bolt with a diameter of 0.020 m on the load-bearing capacity, depending on the binding agent's uniaxial compressive strength. Martin et al. [15] found that the phenomenon occurring at the bolt-binding agent contact point can be described using four parameters: shear stress, shear-and-slide, radial pressure, and radial displacement. Ma et al. [16] developed an analytical model of roof bolting behavior along the whole length under tensile stress, based on the assumption of a correlation between the properties of the binding agent and sliding. Hagan [17] found that for a bolt with a diameter of 0.025 m, the maximum bolt hole diameter should not exceed 0.035 m.

Room and Pillar Methods in Hard Rock Mining
Room and pillar mining methods are used in ore mines and also in coal and chemical resources mines [18,19]. Pillars of various shapes and cross-sections (continuous, square, round, rectangular) are placed between rooms. They are meant to ensure the stability of the post-excavation area (the field or its part). For new fields of exploitations, in which the room and pillar method will be used, monitoring systems of the rock bolt support are designed to optimize the bolting technological parameters [20]. Room and pillar mining methods are dedicated to horizontally or slightly inclined orebodies. For example, in some underground copper mines, at the first stage of this technology, several usually parallel rooms are driven to extract the minerals with drilling and blasting method using explosives. In the same way, as the second phase of the technology, similar perpendicular excavations are constructed. Finally, between the intersecting excavations, some parts of the orebodies are left in their original location, forming pillars [21]. Their role is to support overlying rocks and secure their stability and work safety for miners. Usually, the pillars are insufficient from a stability point of view, and therefore, additional reinforcement is applied using rock bolting as the most effective way. The room and pillar mining method is a very effective and one that enables a high level of mechanization of the technology. The uncovered roof area increases with the progress of orebody excavation, and the pillars sustain an increasing value of loads from the rock mass. For the adopted system geometry, the opening width of the working area and the correct selection of pillar and room dimensions are vital to ensure safe operating conditions with minimum losses of the mineral being mined [22]. Under complex geological and mining conditions, the distribution of stresses in individual pillars, as well as in the mining field, is difficult to accurately predict. This makes it necessary to adopt certain simplifying assumptions. Methods in which pillars between rooms work with the rock mass as the main independent construction elements to bear the loads from their designated rock columns are common in engineering calculations [23]. There are also methods in which the load-bearing structure comprises pillars between rooms and a compact layer of roof rocks, which absorb the load from the remaining layer of the overlying rocks. In addition to this, the pillars between rooms can absorb the load of the unloaded part of the roof, while cooperating with the overlying layer of compact rock (main roof) in transferring the loads of the overlying overburden layers [24].

Geological Conditions of the Modelled Ore Mine
Zinc and lead ore deposits are classified as Mississippi Valley sedimentary deposits. These are stratoid and lentiform-nestlike deposits. Mineralization is present in a given lithostratigraphic horizon and is connected with a specific lithology, the so-called metalliferous dolomites from the Middle Triassic (middle and lower Muschelkalk), rarely Lower Triassic (Röt). The pits are excavated in layers I, III, III in metalliferous dolomites ( Figure 2). Metalliferous dolomites are developed as grey dolomites, finely crystalline, cracked and cavernous in parts, mostly highly compact. In oxidized areas, dolomites can be highly weathered, with a brown and rusty color. The deposits are irregular, brecciated, and feature variable quality parameters. There are minor metasomatic deposits in the form of pseudo-beds. The most common minerals in the primary deposit include sphalerite, wurtzite, colomorphous zinc blende, galena, marcasite, and pyrite. Calcite, aragonite, baryte, and monheimite are found along with sulfides in the peripheral zones of ore bodies. In the weathering zone, sulfide ores are replaced by calamines (smithsonite, goethite, cerusite, hemimorphite, anglesite, and hydrozincite).
areas, dolomites can be highly weathered, with a brown and rusty color. The deposits are irregular, 135 brecciated, and feature variable quality parameters. There are minor metasomatic deposits in the   load-bearing layer (core roof) and if the ratio of mining field width to the excavation depth is larger 151 than 1. For a small span of the mining field, when the ratio of field width to excavation depth is lower 152 than 1 and the pillars between rooms are highly flexible, it is assumed that a relieved zone (elliptical) 153 is formed over the mining field and the pillars between rooms are loaded only with a column of rocks 154 contained in the relieved zone. This assumption is correct when the immediate roof is located over Monkey drifts are located in a 100 m × 100 m arrangement, which involves isolating mining fields with an area of 1 ha. The field is divided by drifts (known as extraction drifts) into mining pillars with widths up to 25 m. The isolated pillars are excavated in 5 m-wide rooms tunnels in parallel to the mining face line. The maximum opening of the mining face ceiling depends on the strength of rocks and usually covers two rows of rooms and two lines of pillars. If no strong layers are present in the overburden and with a sufficiently large span of the mining field, the pillars are loaded with the whole column of overlying rocks. This assumption is used in mines if there is a strong load-bearing layer (core roof) and if the ratio of mining field width to the excavation depth is larger than 1. For a small span of the mining field, when the ratio of field width to excavation depth is lower than 1 and the pillars between rooms are highly flexible, it is assumed that a relieved zone (elliptical) is formed over the mining field and the pillars between rooms are loaded only with a column of rocks contained in the relieved zone. This assumption is correct when the immediate roof is located over the pillars. The loads from the remaining column of rocks are transferred individually by the wide field pillars or by the undisturbed face. If we assume the elliptical shape of the relieved zone (Figure 3), the permissible uncovering of the main roof can be calculated according to formula [25]: where:

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dimensional tasks, which was connected to the discretization of not the whole area, but only its limits.

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We also took into account the possibility to calculate, in linear tasks, the values being investigated 194 not only at nodes but also at any point of the area, without the need to approximate, which was 195 particularly important for zones with considerable function gradients.

Numerical Modeling of Fault Zones around Pits
We prepared a model deposit excavation using a room and pillar mining method in three variants: with two, three, and four rows of pillars (Figure 6a-c) and rooms using the Examine3D software based on the boundary element method. Boundary value problems involve seeking solutions to partial or ordinary differential equations describing a phenomenon occurring in a continuous medium. Functions fulfilling the equations assuming the imposed boundary conditions constitute their solutions. The boundary element method involves the use of a fundamental solution to a given differential equation and requires the approximation of the function constituting the solution only at the boundary of the area, using the so-called boundary elements. These elements are lines in two-dimensional problems and polygons in three-dimensional problems. Selecting this method resulted from the possibility of simplifying mathematical operations, particularly in three-dimensional tasks, which was connected to the discretization of not the whole area, but only its limits. We also took into account the possibility to calculate, in linear tasks, the values being investigated not only at nodes but also at any point of the area, without the need to approximate, which was particularly important for zones with considerable function gradients. dimensional tasks, which was connected to the discretization of not the whole area, but only its limits.

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We also took into account the possibility to calculate, in linear tasks, the values being investigated 194 not only at nodes but also at any point of the area, without the need to approximate, which was 195 particularly important for zones with considerable function gradients.

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We adopted the Hoek-Brown failure criterion [26], taking into account uniaxial compressive 199 strength and empirical material constants m and s selected using RocLab software [26]. The strength, We adopted the Hoek-Brown failure criterion [26], taking into account uniaxial compressive strength and empirical material constants m and s selected using RocLab software [26]. The strength, strain, and structural parameters were selected according to the laboratory tests of boulders. Analysis and determination of fault zones in the rock mass around pits in the numerical model used the strength factor (SF) expressing the relationship between rock strength and the equivalent stress at a given point. If the SF value is lower than 1, the equivalent stress exceeds the strength of the rock mass at the point, and material failure may occur (plastic analysis). Assuming that the system is elastic, no material failure occurs. The results for the fault zone range of rocks around room pits are presented in Figure 7a  The maximum ranges of the stress zone of the rocks in the roof of room pits for two, three, and four rows were 0.91 m, 0.93 m, and 0.95 m, respectively. Assuming the roof bolting-rock mass cooperation model, according to the theory of suspension of weak layers to overlying stronger layers ( Figure 8) and taking into account the bolt span in the mine (1 m × 1 m), the load on the roof bolting can be calculated using the following formula: where: can be calculated using the following formula: where: The roof bolting length was determined as 1.6 using formula 2, We adopted this length for further The roof bolting length was determined as 1.6 using formula 2, We adopted this length for further laboratory research, in which we determined the influence of the installation depth and bolt diameter on load-bearing capacity.

Assessing the Influence of Adhesion Length on the Load-Bearing Capacity of Roof Bolting
The laboratory tests of the glue-in roof bolting were conducted at the Department of Underground Mining of the Faculty of Mining and Geoengineering, AGH in Kraków. The tested roof bolting was Olkusz-16A [5]. The roof bolting was composed of a 1.6 m-long ribbed pole made of EPSTAL steel (grade B500SP). This steel provides enhanced ductility. Steel is characterized by yield strength R from 500 MPa to 625 MPa, and the minimum percentage of elongation A 5 is equal to 16% [27]. In addition, the bolt was equipped with a steel rod with a diameter of 0.006 m (St0 steel grade) coiled along a 0.6 m section, the purpose of which was to mix the resin cartridge (Figure 9a

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At the laboratory test stand, we simulated the rock mass using a concrete block made of a 252 mixture of sand with a particle size of 0.002 m, 42.5R-class Portland cement, diabase aggregate with   At the laboratory test stand, we simulated the rock mass using a concrete block made of a mixture of sand with a particle size of 0.002 m, 42.5R-class Portland cement, diabase aggregate with a particle size from 0.002 m to 0.005 m. The water-to-cement ratio was 0.45. The concrete mixture was also enriched with the Sika ViscoCrete-20HE superplasticizer and the SikaFume-HR/-TU silica fume. Uniaxial compressive strength tests and tensile strength tests (Brasilian test) of cubic concrete samples with 0.15 m-long sides (Figure 10a) were performed using a Controls Automax5 universal testing machine (Figure 10a,b) equipped with Microdata Autodriver software (ver. 1, Controls S.p.A., Milan, Italy). The load speed was 0.6 MPa/s for compressive force and 0.1 MPa/s for tensile force.

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At the laboratory test stand, we simulated the rock mass using a concrete block made of a 252 mixture of sand with a particle size of 0.002 m, 42.5R-class Portland cement, diabase aggregate with  After determining a satisfactory compressive strength within the range from 45 MPa to 50 MPa and tensile strength between 4.1 MPa and 4.7 MPa, we started to fill the steel cylinders (0.1 m diameter, 0.1 m length, and 0.005 m sheet thickness) with concrete mixture. Twenty-eight days after filling the steel cylinders, we drilled holes with diameters 0.028 m, 0.032 m, 0.035 m, and 0.037 m in them. We used SDS Max hammer drills for drilling in concrete with cemented carbide heads and a core drill ( Figure 11).

The Load and Displacement Properties of Segmentally Installed Glue-in Roof Bolting
Segmentally installed glue-in roof bolting was subjected to tensile tests using a universal testing machine in the bolt laboratory of the Department of Underground Mining. Five bolts were tested for each hole diameter. The laboratory test stand (Figure 13a,b) is equipped with a QUANTUM MX840A measurement amplifier (HBM, Spectris plc, Darmstadt, Germany), to which force and displacement sensors are connected [29]. The load increment speed was 0.5 kN/s. The amplifier is connected to a computer with Catman-Easy software installed, which allows live tracking of the load and displacement properties. Tensile strength test results for glue-in Olkusz-16A roof bolting installed along 0.1 m and 0.2 m sections for hole diameters 0.028 m, 0.032 m, 0.035 m, and 0.037 m are presented in Figure 14a-h, Figure 15a-h and Table 1.

Discussion
We used numerical modeling to find the maximum range of the fault zone of the rocks around the pits in a room and pillar mining method. For the first model of deposit shearing covering two rows of pillars and rooms, both for the A-A and the B-B cross-sections, the range of the fault zone in roof rocks was 0.91 m. For the second model, involving three rows of pillars and rooms, the range increased by 0.02 m. For the third model, which involved four rows of pillars and rooms, the range of the fault zone calculated using the strength factor was the largest, ainstalling to 0.95 m. Assuming that the load per bolt corresponds to a cuboid with its base being a 1 m × 1m span of bolts and height corresponding to the range of the fault zone of rocks, taking into account the unit weight of rocks contained within the delimited solid body, it can be stated that the difference in maximum load for all three models does not exceed 4 kN. On the basis of laboratory tensile testing of glue-in roof bolting segmentally installed using resin cartridges, it can be concluded that for the installing depth of 0.1 m, the full load and displacement properties were reached only for the hole diameter of 0.032 m, as in this case, the material discontinuity occurred over the lowest diameter of bolt core.  Figure 14a,c,e,g and Figure 15a,c,e,g show the changes in the values of loads as functions of displacements S measured at the test station. These values resulted from the elongation of the bolt ∆L depending on the value of the active force (stress) and strain characteristics of the material of which it was made (in the analyzed case the properties of steel) and were also affected by the extension of the bolt from the hole ∆W. The figures presented above show two phases of function behavior: A and B. Phase A was characterized by increases in load accompanying increases in displacements until the maximum value of the force equal to the bolt's maximum load-bearing capacity was achieved, while phase B involved a much faster increase in displacements S with relatively low changes in the value of the tensile force recorded. Figures 16a-d and 17a-d present the results of an analysis of phase A, corresponding to the range of the required load-bearing capacity of a bolt in an ore mine, with the following assumptions: Steel bolt elongation occurs within the elastic range and equals: where: ∆L-bolt elongation /mm, F-tensile force on the bolt /kN, L-bolt length minus the glue-in part /mm, d-bolt diameter /mm, E-steel elasticity modulus, E = 210 GPa.
Using Equation (6) Tables 2 and 3, we obtained the following relationships:  Slope Wp in Equation (7) is a bolt's flexibility factor expressed by the ratio of the value of displacement increase to the value of axial tension increase (Figures 16a-d and 17a-d). Table 4 shows that the bolt's extension from the hole constitutes about 63% of the total recorded bolt displacement (extension and elongation) at the measurement station. In addition, Table 4 shows the flexibility factors Wp for all tested hole diameters and installing depths. We show the relationships between the flexibility factor Wp1, involving both the bolt extension and strain (∆W + ∆L) and only extension Wp2 (∆W) ( Table 4) and the bolt hole diameter (Figure 18). For the installing depth of z = 0.1 m, it was found that this factor grows along with the growth of the hole diameter, within the range 0.028 to 0.037 m. No similar relationship was found for bolts with an installation depth of 0.2 m, which might require extending the scope of testing in the future.

Conclusions
Room and pillar mining methods are commonly used in the underground mining of mineral deposits. The working area is secured by technological and remaining pillars and the roof bolting, independent or reinforced with a mesh and lines. The performance and effectiveness of the room and pillar mining method depend on the width of the opening of the working area, among other things. With the optimum dimensions of pillars and rooms, the stability of pits should be ensured with as high a rate of deposit recovery as possible, taking into account the number of support pillars. Based on numerical modeling, which accounted for the use of the room and pillar mining method for deposit excavation with two, three, and four rows of rooms, it can be concluded that the maximum ranges of the fault zone of rocks around pits differed only slightly, and the number of rows did not significantly affect its growth.
The load and displacement specifications, which were investigated under laboratory conditions for the Olkusz-16A roof bolting demonstrate that: • The installation depth of 0.1 m made it possible to obtain the full specifications for the diameter of 0.032 m and maximum load-bearing capacity, 106.87 kN, was recorded.  The bolt's extension from the hole during loading constitutes about 63% of the total recorded bolt displacement (extension and elongation) at the measurement station.

•
For the installation depth of z = 0.1 m, it was found that this factor grows along with the growth of the hole diameter, within the range 0.028 to 0.037 m. No similar relationship was found for bolts with an installation depth of 0.2 m, which might require extending the scope of testing in the future.