INVESTIGATION OF THE GEOMECHANICAL STATE OF SOFT ADJOINING ROCKS UNDER PROTECTIVE CONSTRUCTIONS

The conditions of coal seam mining in the mines of Ukraine have been considered. The problem of conducting coal mining by longwalls in the conditions of soft adjoining rocks, which concerns the protection of mine roadways located near the face, has been revealed. In such conditions, the existing protective constructions are ineffective due to the fact that they yield and get pressed into the soft rocks of the footwall. This indicated the need for research into the geomechanical state of soft rocks of the footwall. According to the results of known studies on the mechanism of rock mass failure around roadways and the data of physical and mechanical properties of the coal mass, which is represented by soft rocks, the correlation dependence has been obtained, the use of which allowed for the determination of the parameters of the rock deformation diagram and the establishment of the stability criterion of footwall rocks under the protection means and stability conditions of the geotechnical system “protective construction – adjoining rocks.” They are the basis of a new approach to ensure the stability of the roadways, which are supported behind the faces, by controlling the stress state in the system “protective construction – adjoining rocks.” This may be the basis for the development of new methods of protecting roadways in conditions of soft adjoining rocks.


Introduction
Coal is still an important energy source for many countries of the world. Ukraine is no exception, where proven coal reserves are almost 34 billion tons, which is almost 4% of the world (URL1).
Coal mining in Ukraine is carried out underground. Thin and medium-thickness layers with a drop from horizontal to steep are mainly developed. Working out of layers is produced by long columns through stretching, falling or rising. This technology is widespread throughout the world, when the extraction is carried out by longwalls, which are serviced by roadways, and are mostly protected in the rock mass and by coal pillars (see Figure 1) (Galvin, 2016). Longwall mining systems are generally characterized by high productivity, low operation costs, and continuity of operations (Heydari et al., 2020;Norouzi et al., 2021). However, this technology has some disadvantages: a high level of injuries Aghababaei et al., 2020) and limited use on the soft adjoining rocks due to significant deformations in the adjacent faces and roadways (Nehrii, Sakhno et al., 2018;Bondarenko et al., 2021).
For most mines in Ukraine, leaving coal pillars to protect the roadways is unacceptable due to significant mineral loss, or because coal may be prone to spontaneous combustion (Gamiy et al., 2020). Therefore, as a rule, they use technologies where artificial constructions made of wood, concrete, ordinary rock, etc. (see Figure  2) are used instead of pillars. However, in any case, there is a general problem of ensuring the operational condition of the mine roadways adjacent to the breakage faces and are in the zone of their influence. This question is most relevant in conditions when there are soft adjoining rocks around, the strength of which is less than 40 MPa for uniaxial compression.
Pillars or artificial protective constructions that are supposed to ensure the maintenance of roof rocks and the operational condition of the adjacent working space (in the face, chamber, roadway) in the conditions of soft adjoining rocks are ineffective due to the fact that, in addition to their contraction, they are also pressed into the footwall rocks. All these processes inevitably lead to landslides and loss of cross-section of the working space. This is well illustrated in the paper (Galvin, 2016), which shows the mechanism of pressing protection constructions and its consequences. The work (Dolinar, 2010) shows how cylindrical supports are pressed into the footwall, after which rock protrusion shafts are formed around them. The same pattern is observed around pillars (Zhao, 2017), wooden сribs (Chase, 2002) and other protective constructions.
In the conditions of soft adjoining rocks of coal mines in Ukraine, contraction and pressing of protective constructions, which are set next to the roadway behind the face, are also observed. This mechanism is illustrated in Figure 3. The pressing of the protective construction adjacent to the roadway is identical to the pressing of the construction shown in Figure 4. This has been proven by the results of numerical simulations in the study of the mechanism of pressing the constructions which are located near the roadway (Nehrii, Kultaev et al., 2020) and further away (Nehrii, Bachurin et al., 2019).
The main factors that determine the displacement of rocks on the contour of the roadways are (Farmer, 1985): stresses around the workings and arising as a result of mining, coal seam rigidity, the strength of adjoining rocks and their water content, geological features around the workings, the method of working out, parameters of roadway walling, the mutual spacing of breakage faces and the yield of the applied protective construction.
Consequences of deformations of rocks and fastenings of roadways supported behind a breakage face are hanging and éboulement of rocks outside the next-to-longwall space (Dychkovskyi et al., 2020). The nature of these deformations largely depends on the type of protective construction. Rigid protective construction prevents the lowering and stratification of roof rocks, but pliable protective construction leads to a significant lowering of rock layers, their failure and éboulement. At the same time, the rigid means of protection cause a significant heaving of the foot rocks, whereas the pliable ones slow down this process. In general, increasing the rigidity of constructions leads to improvement in the condition of the roadways, except for conditions with soft rocks. In this case, the increase in the rigidity of the constructions is reduced by their pressing into the foot. So, on soft footwall rocks, it is necessary to ensure a balance in the geotechnical system «means of protection -adjoining rocks.» To do this, in addition to reducing the pliability of the protective construction, it is necessary to ensure the stability of the rocks on which it is located. This issue is relevant for coal mines in Ukraine, which are worked within the promising areas of Donbas, where the adjoining rocks are represented by soft shales. However, it is no less relevant for coal and ore mines with similar mining and geological conditions. In order to develop any engineering solutions to ensure the system, it is necessary to study the geomechanical state of the adjoining rocks around the protective constructions, which this article is devoted to. Therefore, its purpose is to study the geomechanical state of soft adjoining rocks under protective constructions.

Methods
Consider this question on the example of coal mines, where the coal-bearing stratum is represented by soft adjoining rocks, the strength of which does not exceed 40 MPa.
Methods that have been used to achieve the goal: analysis and generalization of modern scientific and technical achievements in the field of protection of development workings, methods of geomechanics, correlation analysis, analysis and interpretation of the obtained results.
The stability of the rocks underlying the means of protection depends on their physical and mechanical characteristics, water content and the degree of failure. A manifestation of the loss of stability of the underlying rocks is the subsidence of protection means relative to their surface. This subsidence provokes the displacement of the roof rocks both over the protective construction and over the roadway. It is also accompanied by extrusion of the footwall rocks into the cavities around the means of protection, including in the roadway which is protected. In such conditions, it is important to study the mechanism of indentation of protection means in the footwall rocks and to establish the main factors on which the magnitude of their subsidence depends. Their results can be the basis for the development of measures to ensure balance in the geotechnical system "protective construction -adjoining rocks." The processes of deformation and failure of the rock mass containing the roadway, are studied in (Petrenko, 2008;Zong et al., 2020). An analytical-experimental method for calculating the size of the zone of inelastic deformations, consisting of the zone of destroyed rocks and the zone of plastic deformations, has been suggested. In particular, Equation 1 has been proposed to predict the size of the area of destroyed rocks, which is: (1) Where: r z -is the radius of the zone of destroyed rocks (m), r w -initial radius of roadway (m),  it follows that the place of construction of protective equipment falls on the area of destroyed rocks (see Figure 5), which is already fully or partially formed by the time of maintenance of the roadway in the area of influence of the mining works. Then the resistance of the accontour rocks is determined by the residual strength of the rocks R res (MPa), which characterizes the ability of rocks to maintain load-bearing capacity as a whole construction. The geomechanical balance of the discrete rock environment around the protection means is ensured by the residual strength of the destroyed rocks, which is maintained on a significant range of further deformations.
Deformation of the accontour rock mass is characterized by two stages (see Figure 6): pre-limiting and overlimiting. The boundary between these stages is the ultimate resistance of rocks to compression, exceeding which their destruction and drop in strength to residual, which depends on the type of rocks and the value of adjoining resistance and, according to many studies, is from 3 to 95% of ultimate strength ( According to the "correspondence hypothesis" (Hapieiev, 2014), the mechanical phenomena that occur during the "hard" failure of the rock specimen in the mode of given deformations (see Figure 6) correspond to the processes occurring when deforming an arbitrary unit volume of rock mass around the mine. In this case, the role of the "rigid" loading device is played by the area of the rock environment, which is elastically deformed and located behind the area of inelastic deformations. The upper branch of the complete deformation diagram (see Figure 6) is responsible for the formation of the external dimensions of the zone of inelastic deformations, and the lower -for movement on the contour of the roadways, which allows for an accurate prediction and ensures the stability of roadways (Hapieiev, 2014). However, the strength of the rocks in the sample differs significantly from the strength of the rocks in the mass, but the difference between the strength in the rock mass and the strength of the sample is estimated by the coefficient of structural weakening.
In the pre-limiting stage between stresses and deformations, there is a connection close to linear to the ultimate strength, and the modulus of elasticity Е (conditionally -instantaneous modulus of deformation) in this zone remains constant. At the over-limiting stage, the strength of the samples decreases nonlinearly (Maslo, 2014), but at any load level, the remaining structural bonds provide their strength and ability to elastic deformation, as evidenced by hysteresis loops obtained under cyclic loading and unloading (Shashenko et al., 2008). In many works (Babyiuk, 2005; Solodiankyn, 2009; Shashenko et al., 2008) the simplistically accepted parallelism of hysteresis loops and the modulus of deformation of rocks in the over-limiting area E n is equal to the modulus of elasticity E. Such equality was introduced to solve certain problems, but to establish the reasons for indentation of protective constructions in the underlying rocks, this simplification is not appropriate, because the modulus of deformation characterizes the stiffness of the rocks and its over-estimation leads to a misrepresentation of the result. Indeed, this modulus is several times smaller than the modulus of elasticity. For example, according to (Lezyna, 1992) it was found that for coal samples with a strength of 23 MPa (without adjoining pressure), the modulus E n (400 MPa) is 6 times smaller than the modulus E (2400 MPa). In (Ruppeneit, 1975), the values of these modules were determined in the calculations, taking into account the fractured rocks, according to which the E/E n ratio for some rocks is from 3.05 to 11.0. For rock specimens, this ratio is 5.9 (Matveev, 2012), and for the rock mass -3.2 (Baklashov and Kartozyia, 1975). So, on average for samples of soft rocks, in the calculations we can take E/E n = 6.0, but the most accurate will be its experimental evaluation.
To simplify the calculations, take a linear approximation of some sections of the deformation graph, which is used in many studies (Alejano et al., 2009;Lin et al., 2018;Santarelli, 1987;Babyiuk, 2005;Solodiankyn, 2009;Shashenko et al., 2008). In this case, the hysteresis loops are absent, and unloading and reloading occur in a straight line. This determines the achieved residual deformation. This approach was used in the study (Solodiankyn, 2009). The modulus of deformation of rocks in the area of residual strength E n was equal to the modulus in the elastic section E, although they differ. The linearity of the sections of the diagram is justified when the values of loads do not exceed the ultimate and residual strength in the respective sections of rock deformation and in the area of the descending part of the diagram. When the residual strength is exceeded, the structural bonds in the destroyed rock volume are broken, with its subsequent compaction. This compaction may be accompanied by displacements and rotation of the rock pieces with each other. The sections of the diagram where these deformations take place are nonlinear, and their linearization requires scientific substantiation. Further, we proceed to determine the parameters of the deformation diagram of the rock mass.
To study the behavior of destroyed underlying rocks, it is advisable to operate not only strength but also deformation properties, as the latter characterize the elastic and plastic deformation of rocks under loads. There is a correlation between rock strength and modulus of elasticity based on porosity (Rzhevskyi and Novyk, 1984), which can be shown as degree (Santarelli, 1987  The residual strength of a certain mining rock is simply defined as a fraction of the ultimate strength. In order to obtain more accurate data, it is established experimentally or experimentally-analytically. In the first case, laboratory tests of rock samples are carried out with the establishment of the necessary characteristics, and in the second -the existing methods are used, the initial data to which the experimental data is compared. In the work (Tutluoglu et al., 2015), based on the results of tests of rock samples, a correlation dependence is proposed to determine the relative strength of the rock mass, which is shown by Equation 4: The initial characteristic in Equation 4 is only the ultimate strength of the mining rock in the sample, which makes the expression easy to use and allows for operational calculations. However, the expression is generalized and is based on the results of tests of igneous, metamorphic and sedimentary rocks in a wide range of strength (1.2… 89.6 MPa). For sedimentary rocks, the dependence also takes the form of σ res/ σ c =-a lnσ cs +b, but the values of the coefficients a and b may differ from those given in Equation 4. To determine these coefficients, it is sufficient to use the known strength characteristics of the respective rocks.
Since the nature of deformation of the rock mass in the area of inelastic deformations around the roadway is similar to their deformation in the sample, which is deformed in the mode of given deformations (Hapieiev, 2014), it is assumed that a loss of the bearing capacity of rocks between their characteristics in nature and samples, proportionality remains, in particular Equation 5: Where: R res -resistance of rocks to compression at the limit of residual strength (MPa), R c -resistance of rocks to compression at the limit of ultimate strength (MPa). The resistance of rocks to compression at the ultimate strength, taking into account the disturbance of rocks, their water content and rheological properties, is determined by Equation 6 (Bondarenko et al., 2008): Where: k w -coefficient that takes into account the softening of watered rocks as a result of filtration on the water mass (un.), (k w = 0.4…0.8), k t -coefficient that takes into account the reduction of rock resistance to uniaxial compression under prolonged loading (un.). It is determined by Equation 7: Where: x/β -rheological indicator (un.) (Bondarenko et al., 2008). So, the resistance of rocks to compression at the ultimate strength is determined by Equations 8: According to the above method, it is possible to determine the parameters of the deformation diagram of the rock mass, which can be the initial data for assessing the condition of adjoining rocks around the mine roadways.

Results and Discussion
Consider the conditions of stability of mine roadways and protective constructions on the basis of the proposed method. To do this, use the known mechanical characteristics of mine rocks of the South-Donbas and Pokrovsk coal-bearing areas and the Western Donbas which are given in works (Bondarenko et al., 2008;Melnikov, 1975).
On the basis of limit values of mechanical characteristics of mine rocks of these regions, we specify the correlation dependence of the strength of the host rocks on the conditional instantaneous modulus of their deformation (see Figure 7), which has the form of Equation 9:  (Bondarenko et al., 2008) and (Melnikov, 1975) Rudarsko-geološko-naftni zbornik i autori (The Mining-Geology-Petroleum Engineering Bulletin and the authors) ©, 2021, pp. 61-71, DOI: 10.17794/rgn.2021.4.6 (9) In Equation 9, the multiplier 0.0028 is the critical longitudinal deformation e lim for soft adjoining rocks in the conditions of the South Donbas, Pokrovsk and the Western Donbas coal-bearing areas.
The parameters of the descending section of the rock deformation diagram (see Figure 6) must be determined. According to (Fadeev, 1987) the ratio e f /e lim is equal to 3.0, but in the work (Babyiuk, 2005) the range from 2.8 to 3.4 is specified. So, at the moment of reaching the limit of the descending section and the residual strength section, the overall longitudinal deformations of the rock (e lim +e f ) are 0.012 (12‰), above which the rocks pass into the area of destroyed rocks (see Figure 5). In this area, the rocks have a constant residual strength and are cyclically deformed when it is exceeded by stresses from the rock mass. On each deformation cycle, there is a load of the destroyed rock volume which leads to the closing of cracks in it and the formation of structural bonds, after which their quasi-elastic deformation with the modulus Е п (see Figure 6) is observed until the current stresses exceed the residual strength again. After that, the cycles can be repeated, and each cycle is accompanied by shifts in the surrounding rocks. This mechanism explains the deformation processes in the area of the destroyed rocks, including the subsidence of the means of protection relative to the surface of the underlying rocks. This subsidence occurs when the stresses on the part of the structure exceed the compressive strength of the rocks at the limit of residual strength. More often it occurs in the area of bearing pressure, where there is an increase in stress over the means of protection.
To determine the relative residual strength of soft sedimentary mine rocks, a correlation dependence of the relative residual strength on their ultimate strength in the sample for uniaxial compression has been established for the characteristics of rocks of the coal-bearing mass of the Western Donbas. Dependence is graphically shown in Figure 8 and has the form of Equation 10: The resulting regression dependence has a coefficient of determination of 0.94 for significant t and F -criteria, demonstrating an extremely close relationship between relative residual strength and ultimate strength (R 2 =0.94; t>t lim (102.19>3.18); F>F lim (25.14>9.55)). The residual strength values determined from Equation 10 for sedimentary rocks, under equal conditions, are two times less than those determined by Equation 4. Therefore, to determine the residual strength of sedimentary rocks, Equation 10 is more acceptable.
So, the resistance of rocks to compression at the ultimate strength for these conditions is determined by Equation 11 from Equations 8 and 10: From the means of protection, the load with stresses k / γH affects the underlying rocks. To ensure the stability of rocks under the means of protection, the condition which must be met is R res ³ k / γH or R res /k / γH ³ 1. This ratio can be considered a criterion for the stability of rocks k st , underlying the means of protection, which is determined by Equations 12 and 13: Where: k st -the criterion for the stability of rocks (un.), k' -is the coefficient of stress concentration at the contact of the protection means and the footwall rocks (un.), (k' = 1.0...1.3) (Nehrii and Nehrii, 2020). If k st ³1, the underlying rocks remain stable, but at k st <1 -they are pressed under the protective construction, so the condition of their stability takes the form of Condition 14: If Condition 14 is not met, there is a subsidence of the protective construction relative to the surface of the footwall. In this case, the relative total subsidence of the means of protection should be determined by Equation Where: e * -total subsidence of the means of protection (un.), μ п -coefficient of relative transverse deformation of the footwall rocks (un.), Е п -modulus of deformation of rocks at the limit of residual strength (MPa). The natural resistance of the underlying rocks R res is determined experimentally or with Equation 11. If the natural resistance is not enough to ensure the stability of the underlying rocks, then through the use of technological measures (anchoring the footwall, compaction, injection strengthening of destroyed rocks by binders, etc.) it is necessary to increase it up to R res . Due to such measures, it is possible not only to change the deformation properties of the rock mass, but also to qualitatively modify its over-limiting behavior.
In general, the stability of the geotechnical system «protective construction -adjoining rocks" should be provided both by increasing the stability of the footwall rocks, and by increasing the bearing capacity of the protective construction. The condition for the stability of the geotechnical system "protective construction -adjoining rocks" is to ensure a balance between the operating stresses of the roof rocks k'γH (MPa), the bearing capacity of the protective means Р constr. and the resistance of the underlying rocks R res . To do this, Condition 16 must be met: Where: Р constr. -the bearing capacity of the protective means (MPa), R res -resistance of rocks to compression at the limit of residual strength (MPa). At the moment, there are technologies for the protection of development roadways, which are based on the management of the stress-strain state of the rocks around the roadway and the strengthening of soft footwall rocks under the means of protection. However, these technologies are designed for certain conditions, and in most cases, they are expensive and time consuming. Additional research in this direction is still needed.

Conclusions
As a result of identifying new approaches to solving the problem of ensuring the stability of the development roadways, which are supported behind the faces, by managing the stress around the means of protection or increasing the bearing capacity of the destroyed rocks around them, the following conclusions have been made: 1. The underlying rocks of the footwall at the time of construction of the means of protection are in the stage of over-limiting deformation and their resistance is determined by the residual strength; 2. The correlation between the relative residual strength of sedimentary rocks with their ultimate compressive strength to determine the resistance of destroyed rocks to compression at the limit of residual strength, taking into account their water content, fracture and rheological properties; 3. The subsidence of the protective means relative to the surface of soft underlying rocks is cyclic and occurs in the area of residual friction of destroyed rocks, when the total longitudinal deformation of the rock layer exceeds 12%, and the stress from the protective means exceeds the resistance of rocks to compression at the limit of residual strength, accompanied by a disturbance of structural bonds in the destroyed rock volume with its subsequent compaction, due to displacements and rotations of rock segments; 4. The stability of roof rocks over the means of protection must be ensured by technical means, both in the protective construction and in the underlying rocks, which increase the bearing capacity of the protective means and resistance of these rocks or reduce the load on them through the means of protection.