1 Introduction

Roof fall takes place in the newly developed faces during mine development or depillaring owing to the resettlement of excavation-induced stresses. Roof fall is more vulnerable mainly for fragile rock formation encountered with more geological discontinuities. It leads to detrimental effects such as fatal or serious injuries to workers, stoppages in mining operations, and breakdown of equipment [1]. Most injury-causing roof falls involve falls of small chunks of roof rock from the immediate roof [2]. According to Ashish et al. (2016), 41% of accidents occur due to ground movement. The fall of the roof provides constructive information relating to the behavior of the immediate roof strata under specific geo-mining conditions. An investigation of roof falls reveals the principal causes of the roof fall and it is also of prime importance to establish or develop suitable support design based on the study of site-specific rock mass conditions [3]. Rock reinforcement using roof bolts has proved successful and is the principal support in underground development headings. The perception of the causes of roof failure is key in solving the problem of support-related issues. The complexity of geological disturbances and intricacy of the mining environment with respect to shale degradation, stress condition, and mining condition are some of the broad causative factors of roof failure in coal mines. Rock mass classification system and selection of appropriate type and capacity of support contribute to the decrease of roof fall in underground mines [4].

Rock mass classification systems, which are empirical in approach, are helping in the design of support system for underground mine openings and tunnels for more than a century now and are continuously evolving [5]. Thus, the limitations of such rock mass classification systems need to be understood properly for their application and design of a rational support system [6]. A rock mass classification system is a simple method to deal with complex rock mechanics problems in engineering design. Primarily, the system facilitates the estimation of rock mass properties like modulus of deformation and also provides proper support design guidelines and the stand-up time for underground entries [7]. The empirical approach helps in proper rock load estimation and in turn also increases the stability of the mine openings [8].

Application of the numerical modeling is a persuasive tool for the stability analysis of mines [9]. It is being widely used for the assessment and design of pillar stability as well as stability of underground mine openings with respect to in situ ground condition [10]. Both empirical and numerical approaches are implemented for stability analysis and support design for underground openings [11, 12]. Modelling and simulation with varied design inputs and geometry are viable methods for solving the complex geotechnical problems [13]. Intact and rock mass properties determined in field and laboratory data are required as input parameters used as stress, depth, RMR, cohesion, angle of internal friction, and tensile strength for numerical modelling. With the help of aforesaid input parameters, the failure zone (rock load height) is determined which helps design and selection of appropriate support for rock mass [14, 15]. Numerical modelling techniques were successfully used by several researchers for the simulation of the stability of mine openings in different geo-mining conditions ([11, 16,17,18]. The most important thing in numerical modelling is the selection of an appropriate method for simulation [19, 20]. Given the appropriate input parameters numerical modelling can predict the horizon of the roof failure which is also termed rock load height. In this paper, attempts were made to determine the rock load height using the Mohr-Coulomb model followed by validation from the empirically developed RMRdyn rock load predictor model. The propagation of rock failure can be more accurately predicted using the elastoplastic model (Mohr-Coulomb) compared to elastic models, and hence, this model was selected for the analysis. In this study, RMRdyn was developed, based on key limitations of the existing CMRI-ISM RMR system. Sonic velocity (P-wave velocity) of roof rocks was included as one of the parameters in the newly developed system with a perspective to involve geological variations to it.

2 Rock Mass Classification: a Review

Rock mass classification forms the backbone of the empirical design approach and is widely employed in rock engineering [14]. It has been experienced that when used correctly, a rock mass classification approach serves as a practical basis for the design of complex underground structures. The classification system in the last 50 years of its development has taken cognizance of the new advances in rock support technology starting from steel rib support to the latest supporting techniques like rock bolts and steel fiber reinforced shotcrete. The benefits and limitations of some of the well-known rock mass classifications are given in Table 1. After a detailed literature review, it was found that the presence of geological features like bedding planes, joints, and their orientation was the dominant parameter which affects rock stability during excavation. The research emphasis was placed on the CMRI-ISM RMR system as it was developed for Indian geo-mining conditions. However, the predominance of roof failure cases in spite of following the CMRI-ISM RMR system for support design is the key concern deserving a revisit.

Table 1 Benefits and limitations of well-known rock mass classifications [21]
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Thus, the objective of the present research was based on the re-examination of the failed and stable roof cases for identification of the crucial parameters and in turn development of a modified rock mass classification by incorporating P-wave as rock mass rating dynamic (RMRdyn) for addressing the roof failures.

2.1 Study Area

A total of 79 coal mine sites were investigated covering four major coalfields, i.e., Jharia Coalfield, IB Valley Coalfield (MCL), Godavari Valley Coalfield, and coalfields of South Eastern Coalfields Limited (SECL). Altogether, six coalfields of SECL were covered in the study namely Korba Coalfield, Sohagpur Coalfield, Bishrampur Coalfield, Chirimiri-Kurasia Coalfield, Jhilimili Coalfield, and Johilla Coalfield. Data were collected from the mine sites under varied geo-mining conditions to strengthen the objectives of the research work. Out of 79 investigated coal mine sites, thirty-one mine sites were selected, and twenty-nine mine sites were delineated where the roof condition was fragile and weak as the estimated RMR was categorized in poor roof condition with also a history of roof failure. The other two mine sites were selected from comparatively better roof condition to cover a wider RMR range. Thus, fragile/weak roof needs special attention while designing the support system because they are more vulnerable to roof fall causing injuries to the miners. The roof fall in such weak and fragile roof condition can take place because of the various reasons such as the presence of shear zone, slickenside, clay band, high horizontal stress, weak rock formation, and erroneous/faulty method of mining. Hence, safe mining under such roof condition becomes the key aspect for mine management by designing an appropriate and safe support system after a proper assessment of the roof condition. The study areas are demarcated in Fig. 1.

Fig. 1
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Map of India showing different coalfields covered in the study (After Dutta et al., 2011)

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2.2 Basic Numerical Modeling Methods

The application of numerical modelling methods is commonly seen for solving various complex rock mechanics problems by converting them into simpler ones through discretization techniques. During this process, the total domain is discretized into smaller zones and meshes. Discretization is done, particularly, in the concerned area of stability assessment, for better evaluation of results. After the discretization model is defined with proper boundary conditions, different input rock properties are given according to the range defined. Horizontal and vertical stress values are also defined in the models with appropriate depth of the workings [36]. The main input parameters to be taken into account for analyzing the stability-related geotechnical problems are the geometry of the area, rock/rock mass properties (elastic modulus, strengths, RMR, etc. and in-situ stress field).

Some of the well-known numerical methods used for underground stability analysis are finite element method (FEM), finite difference method (FDM), boundary element method (BEM), distinct element method (DEM), discrete fracture network (DFN) method, and hybrid models. In FEM, the whole area of the model is divided into a number of elements/meshes, and then respective rock properties are given with boundary conditions ([37]; Shivakumar and Maji, 2014). This technique is found suitable for solving the geomechanics problems related to the stability of any opening [38,39,40]. For FDM, the discretization of the study domain is done in the same manner as that of FEM [41,42,43]. This method is used for solving a wide range of problems by partial differential equations. This method can be applied to different boundary shapes with different materials for any region [44]. BEM needs very less computer memory for the storage of data as the boundary of the selected domain area is discretised or converted into smaller mesh. This method is applicable for three-dimensional analysis as it has a facility for the reduction in model size [45] and can be used for stability analysis of underground excavations. DEM is based on the principles of discontinuum mechanics [46, 47]. This method basically treats the zone of interest in the form of deformable rocks and is better suited for the study of a geotechnical problem [48] with geological discontinuities efficiently. DFN method is useful for the application in fractured rock mass where the study of flow is to be analyzed [49] and where an equivalent continuum model is difficult to be established. This method has a capability to model the flow rate of liquid for fractured rock mass through simulation of packer tests [50, 51]. Hybrid models are generally applicable where the assessment of stress and deformation of the rock is a major concern. The main advantage of these models is that they take very less computing time for solving the complex geomechanics problems [52,53,54].

2.3 Numerical Modeling

2.3.1 Mohr-Coulomb Elastoplastic Model for Analysis

The Mohr-Coulomb criterion is based on elastoplastic analysis. In the elastoplastic analysis, the results are accurate and precise compared to the elastic analysis. Hence, to predict the propagation of rock failure accurately, the Mohr-Coulomb criterion was selected for the study. The Mohr-Coulomb model is most commonly used in the field of geotechnical engineering for analysis of rock behavior when subjected to stress. The analysis is based on the linear relationship between the normal and shear stress when applied to the intact rock samples. A linear relationship is generated by plotting the shear strength and applied normal stress, expressed as:

$$\uptau =\upsigma\ \tan\ \left(\Phi \right)+\mathrm{c}$$
(1)

where τ is the shear strength, σ is the normal stress, c is the intercept on the shear strength axis, and Ф is the angle of internal friction. The basic concept of this model postulates that the failure takes place when the normal stress exceeds the shear strength of the rock. Material properties required as input parameters for Mohr-Coulomb elastoplastic model in numerical modeling using FLAC3D are:

  1. (i)

    Density of rock mass (t/m3)

  2. (ii)

    Bulk modulus (GPa) and

  3. (iii)

    Shear modulus (GPa)

Instead of using Young’s modulus of elasticity and Poisson’s ratio directly, FLAC3D uses bulk modulus and shear modulus. Both bulk modulus and shear modulus are evaluated using Young’s modulus and Poisson’s ratio by the following equations.

$$\boldsymbol{K}=\frac{\boldsymbol{E}}{\textbf{3}\left(\textbf{1}-\textbf{2}\boldsymbol{v}\right)}\ \mathrm{GPa}$$
(2)
$$\boldsymbol{G}=\frac{\boldsymbol{E}}{\textbf{2}\left(\textbf{1}+\boldsymbol{v}\right)}\mathrm{GPa}$$
(3)

where E is the Young’s modulus in GPa, K is the Bulk modulus in GPa, G is the Shear modulus in GPa, and v is the Poisson’s ratio.

The modeling was conducted in four stages as shown in Fig. 2.

Fig. 2
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Sequential steps for estimation of rock load by numerical models

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Factors affecting the rock load height (extent of failure zone) are discussed below:

  1. i)

    In Situ Stresses

The in situ stresses affect the stability of the underground mine openings. The idea of horizontal in situ stress condition is important for designing underground mining structures, especially during the development of a coal seam. The knowledge of in situ stress condition during the excavation is very important so that the support design for the excavated area is done accordingly. Sheorey [55] proposed an equation for the average in-seam horizontal stress which was based on a thermo-elastic shell model of the earth. He observed that the mean in situ horizontal stress (mean of the major and minor horizontal stresses) depends on the elastic constants (E, ν), the coefficient of thermal expansion (β), and the geothermal gradient (G). This theory gives the value of mean horizontal stress as:

$${\boldsymbol{\sigma}}_{\boldsymbol{h}}=\frac{\boldsymbol{\upsilon}}{\textbf{1}-\boldsymbol{\upsilon}}{\boldsymbol{\sigma}}_{\boldsymbol{v}}+\frac{\boldsymbol{\beta} \boldsymbol{EG}}{\textbf{1}-\boldsymbol{\upsilon}}\left(\boldsymbol{H}+\textbf{1000}\right)\mathrm{MPa}$$
(4)

where H is the depth cover in meters, σv is the vertical stress, and σh is the horizontal stress. Sheorey et al. [56] developed an equation that is in agreement with the existing stress measurement data from different parts of the world. This does not include actual measured data from Indian coalfields. In situ stresses were simulated with reference to Indian geo-mining condition.

The vertical in situ stress, induced due to gravity, was taken as:

$${\sigma}_v=0.025\ H\mathrm{MPa}$$
(5)

According to Sheorey [56], the values of different parameters of Eq. 4 for Indian coal measures are given as:

$$\nu =0.25,\upbeta =3\ \mathrm{x}10-5/{}^{\circ}C,E=2000\ \mathrm{MPa},\mathrm{G}=0.03{}^{\circ}\mathrm{C}/\mathrm{m}$$

After substituting the above values, the relation obtained for mean horizontal stress is expressed as:

$${\sigma}_h=2.4+0.01\ H\mathrm{MPa}$$
(6)
  1. ii)

    Depth of Cover

Depth of cover affects the loading behavior of the overlying strata on the immediate mine roof. Generally, mining-induced stresses are high for greater depth of cover [57]. Thus, the depth of cover is considered one of the major factors for the estimation of rock load height in the numerical models. The depth of cover taken into consideration for different models varied from 45 to 400 m for rock load prediction. All these depth values were taken up to the roof of the seam.

  1. iii)

    Boundary Conditions

Fine discretization was done for the roof rocks up to the height of 5 m for precise and accurate results for delineating the rock load height. The mesh size was kept uniform (0.25 m) on the roof of the roadway. The modelling of the roadways/galleries was done using a plane-strain model. The boundaries were kept sufficiently away from the excavation (minimum 50 m on all sides). Half of the roadway was modelled by applying a symmetric boundary condition using a vertical plane of symmetry passing through the center of the roadway. Fixed boundary conditions were used at the bottom. The side boundaries were restricted in lateral movement but kept free for vertical movement (“roller” boundaries). The surface was kept free. All modelling was done using the well-known software FLAC3D, which computes in finite difference method [58]. The analysis of the results for roadway stability was done using Mohr-Coulomb elastoplastic analysis.

2.3.2 Experimental Procedure

  1. i)

    Density

Vernier caliper is used to measure specimen dimensions to an accuracy of 0.1 mm. The mass of the sample is kept above 50 g as recommended by the ISRM [59] suggested method. The specimen bulk volume is calculated from an average of several caliper readings for each dimension. The specimen is dried to a constant mass at a temperature of 105°C, allowed to cool for 30 min in a desiccator, and its mass is determined. Density (γ) is calculated as the ratio of mass to volume.

  1. ii)

    Uniaxial Compressive Strength

Uniaxial compressive strength, σc, is intended to measure the strength of a rock sample in uniaxial compression of a specimen of regular geometry. Test specimens are right circular cylinders having a height-to-diameter ratio of 2.5–3.0, and a diameter is kept approximately 54 mm. Load on the specimen is applied continuously at a constant stress rate such that failure will occur within 5 to 10 min of loading. The compressive strength of the specimen was determined using the following formula:

$${\sigma}_{\mathrm{c}}=\frac{\mathrm{F}}{\mathrm{A}}$$
(7)

where:

σc: uniaxial compressive strength (MPa)

F: load applied (N)

A: cross-sectional area of the specimen (mm2)

The placement of the sample during uniaxial compressive strength determination is shown in Fig. 3.

Fig. 3
figure 3

Laboratory testing for σc test

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  1. iii)

    Tensile Strength

The specimen diameter is maintained at approximately 54 mm and the thickness is approximately equal to the specimen radius. Load on the specimen is applied continuously at a constant rate such that failure in the weakest zone of the specimen occurs within 15–30 s (Fig. 4). The tensile strength is arrived at using the following formula:

$${\sigma}_t=0.636\ \mathrm{P}/\mathrm{Dt}$$
(8)

where:

Fig. 4
figure 4

Laboratory testing for σt test

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σ t: Brazilian tensile strength (MPa)

P: load at failure (N)

D: diameter of the specimen (mm)

t: thickness of the specimen (mm)

  1. iv)

    Angle of Internal Friction (Ф) and Cohesion (c)

The strength value (UCS) is calculated by dividing the axial load (failure load) by cross-section of the area of the specimen. The obtained strength value is plotted against the corresponding confining pressure. The strength envelope is obtained by the best-fit straight line curve for the respective strength and confining pressure values as shown in Fig. 5. The point of y-axis intercept the (axial stress) is termed as “b,” and the slope of the line is referred to as “m.” The value of b and m is further used for the determination of cohesion (c) and angle of internal friction (Ф) from the following relationship:

$$\varPhi =\mathrm{arc}\ \sin \frac{\mathrm{m}-1}{\mathrm{m}+1}$$
(9)
$$\mathrm{C}=\mathrm{b}\ \frac{1-\mathrm{sin}\Phi\ }{2\mathrm{cos}\Phi}$$
(10)

where:

Fig. 5
figure 5

Strength envelope for determination of C and Ф

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Ф: angle of internal friction

C: cohesion

m: gradient of the line

b: intercepts of the Y-axis (axial stress)

  1. v)

    Young’s Modulus

Young's modulus, E, is measured at a stress level equal to 50% of the ultimate uniaxial compressive strength. The Young’s modulus is measured using strain gauges mounted on a rock sample as shown in Fig. 6

Fig. 6
figure 6

Laboratory testing for determining Young’s modulus

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The sample is loaded under a stiff testing machine (MTS). The data acquired by a data acquisition system (SPIDER 8) is analyzed using Catman software. The results are formulated in the form of a table. The Young’s modulus is different for different rocks as the mineral composition and quartz content differ from one rock to another.

  1. vii)

    Poisson’s Ratio

Poisson’s ratio, v, is calculated from the slope of the axial stress-strain curve and the slope of the diametric stress-strain curve (Fig. 7) and calculated using the following equation.

Fig. 7
figure 7

Format of axial and diametric stress-strain curves

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$$\nu =-\frac{\mathrm{slope}\ \mathrm{of}\ \mathrm{axial}\ \mathrm{stress}-\mathrm{strain}\ \mathrm{curve}}{\mathrm{slope}\ \mathrm{of}\ \mathrm{diametric}\ \mathrm{stress}-\mathrm{strain}\ \mathrm{curve}}=-\frac{E}{\mathrm{slope}\ \mathrm{of}\ \mathrm{diametric}\ \mathrm{curve}}$$

Here, the slope of the diametric curve is calculated in the same manner as that for Young’s modulus. Poisson’s ratio in this equation has a positive value, since the slope of the diametric curve is negative.

2.3.3 Input Parameters

Proper estimation of strength and failure characteristics of rock mass is always required for any type of numerical simulation, whether it is related to support design or any other rock engineering design. Generally, Poisson’s ratio values are in the range of 0.2 to 0.25 for all coal measure rocks, namely sandstone, shale, and coal. The least tested value of Poisson’s ratio, i.e., 0.25, was taken considering the worst condition of the rock for coal and coal measure rocks, while the real values of remaining rock parameters were taken in modeling as listed in Tables 2 and 3.

Table 2 Elastic constants taken for numerical simulation
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Table 3 Input parameters taken for numerical simulation for intact rock
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2.3.4 Modeling Output

Rock load height (RLH) was determined for thirty-one mine sites by numerical modeling; a few of the models with varied gallery widths are shown in Figs. 8, 9, 10, 11, and 12. The roadway stability is depicted with respect to RHL and gallery width. The height of the shear and tensile zone, representing the gallery stability, determines RLH. Thus, the rock load is obtained by multiplying the RLH with the weighted density of the rock. Numerical modeling for the cases investigated considers the failure mode as both tensile and shear and the likely rock loads in such conditions.

Fig. 8
figure 8

Modelled result showing yield zones for KTK 6 mine (gallery width 3.6 m)

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Fig. 9
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Modelled result for PVK shaft and JK 5 incline (gallery width 3.6 m and 4.2 m)

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Fig. 10
figure 10

Modelled result for JK 5 incline and Bartaria mine

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Fig. 11
figure 11

Modelled result for Rajanagar RO and Haldibari mine

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Fig. 12
figure 12

Modelled result for Pinoura and Nowrozabad mine (4.5 m and 4.2 m gallery width)

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2.4 Rock Load Estimation by Empirical Method

2.4.1 CMRI-ISM RMR

The stability of the roof is a function of several geo-mining factors such as geological anomalies, physicomechanical properties of rock, and stresses (virgin and induced). Based on a literature survey, detailed geotechnical studies, and statistical analysis, five major parameters were identified in CMRI-ISM RMR [60]. Each parameter was allocated a rating. The summation of individual parameter rating yields the rock mass rating (RMR). For simplicity, the minimum and maximum values of RMR were taken as 0 and 100 respectively. The individual parameters and their maximum rating based on their influence on roof stability are provided in Table 4.

Table 4 Maximum rating of parameters in CMRI-ISM RMR System (Venkateswarlu et al., 1987)
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Weighted RMR is developed considering the number of rock layers in the roof up to a height of 2 m.

$$\mathrm{Combined}\ {\mathrm{RMR}}_w=\frac{\sum \left(\mathrm{RMR}\ \mathrm{of}\ \mathrm{each}\ \mathrm{bed}\ \mathrm{X}\ \mathrm{bed}\ \mathrm{thickness}\right)}{\sum \left(\mathrm{Thickness}\ \mathrm{of}\ \mathrm{each}\ \mathrm{bed}\right)}$$
(11)

The adjustments for blasting and depth of working were applied for the RMR based on the geo-mining conditions. The adjusted RMR is then used for estimation of rock load in galleries and junctions from the following equations:

$$\mathrm{Rock}\ \mathrm{load}\ \mathrm{in}\ \mathrm{gallery}\ \left(\mathrm{t}/{\mathrm{m}}^2\right)=\mathrm{B}\times \mathrm{D}\times \left(1.7-0.037\ \mathrm{RMR}+0.0002{\mathrm{RMR}}^2\right)$$
(12)

where RMR, rock mass rating; B, roadway width (m); and D, dry density (t/m3).

Overall, from 79 investigated mine sites, 31 mine sites were selected, covering 29 mine sites with low RMR value and with roof fall cases, and two mine sites for stable cases.

2.4.2 Rock Load Estimation by RMRdyn

A 3-channel handheld seismograph was used for P-wave determination for the minimum gallery width of 3.6 m without any difficulty. P-wave velocity is a proven technique to detect the layers of rock and to delineate the competence of rock mass. RMRdyn was determined for 31 mine sites considering four parameters, i.e., P-wave velocity, structural features, slake durability, and groundwater condition using a new rock mass rating system. UCS and layer thickness were replaced by P-wave velocity. Site-specific layer thickness determination is difficult in the underground mines if the strata are not exposed. Similarly, for UCS, the roof gets damaged due to the blasting of solid and affects the strength of the surrounding rock. If such rock samples are taken from the mine roof and tested for UCS, the actual representing value of compressive strength is not obtained. The P-wave velocity (also known as compressional wave velocity), a new parameter, replaced layer thickness and UCS in the present research. P-wave velocity was used to assess the extent of damage in the roof caused due to blasting-off-solid (BOS) in the underground mines and obtaining in situ rock mass condition. Hence, P-wave velocity was taken in the new model. The other parameters along with their respective rating remained the same as that of CMRI-ISM RMR. Thus, the new rating table for the determination of RMRdyn is given in Table 5.

Table 5 Parameters of RMRdyn [21]
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The maximum RMRdyn of 61.67 (good roof condition) was found in KTK 6 mine, III seam main dip/3LS, and a minimum of 29.5 (poor roof condition) in KTK 6 mine, I seam 13LN/BD.

Rock load was determined using the following relation

$$\mathrm{RL}\ \left(\mathrm{t}/{\mathrm{m}}^2\right)={\mathrm{B}}^{\ast }{\upgamma}^{\ast}\left(31.85{\mathrm{R}\mathrm{MR}}_{\mathrm{dyn}}^{-0.79}-1.14\right)\left({\mathrm{R}}^2=0.95\right)$$
(13)

where RL, rock load (t/m2); B, gallery width (m); and γ, rock density (t/m3).

A comparison of RMR determined by CMRI-ISM RMR and RMRdyn for 31 mine sites is shown in Fig. 13.

Fig. 13
figure 13

RMR determined by CMRI-ISM RMR and RMRdyn at different mine sites

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3 Actual Rock Load Determination

The actual rock load was determined in 31 mine sites under varied geo-mining conditions. Roof fall patterns observed in the field were used as a benchmark for the estimation of rock load, shown in Fig. 14.

Fig. 14
figure 14

Field observation of roof fall [21]. a Roof fall exposing the side roof, b loading arch with clear bending of coal seam, c exposed bolts due to detachment of layered beds

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The different methods used for the estimation of rock load were roof fall height, exposed bolt length, and instrumentation using a load cell. The procedure for determination of rock load from roof fall height is obtained by multiplying the weighted density of roof rocks with the examined roof fall height. Similarly, the rock load estimated from exposed bolt length is the product of the measured exposed length and weighted density of roof rocks.

In general, for coal mine development galleries, 5–10 ton load cells are used, and in this research, the load-bearing capacity of the load cells used for the determination of rock load was 5 tons for improving the resolution of measurement and for precise roof monitoring. Vibrating wire load cells were installed at the center of the roof bolts in the development galleries for measuring the rock load. The load is measured with the help of 3 to 6 vibrating wire sensors. The reading from individual sensors is averaged and used with a calibration factor given to the load cell to calculate the applied load. The rock loads estimated by different methods for actual field conditions are shown in Figure 15.

Fig. 15
figure 15

Different methods of rock load determination in the field

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Rock load estimated from the field with different methods with stable and failed cases along with its roof bolt reaction is illustrated in Table 6.

Table 6 Rock load estimation by different approaches
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4 Validation

The rock load was determined for every site by multiplying the rock load height obtained from the model with the weighted density. The rock load obtained by the numerical method was compared with the rock load estimated by RMRdyn as given in Table 7. A maximum standard deviation of 1.65 was observed. In most of the cases, a marginal deviation was observed.

Table 7 Estimation of rock load height and rock load by numerical and empirical models
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A correlation between rock load estimated by numerical and empirical approaches is presented as shown in Fig. 16. Both are in close agreement with each other with a coefficient of correlation as 0.87 and an index of determination (R2) as 0.77.

Fig. 16
figure 16

Correlation of rock loads obtained by numerical and empirical approaches

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Rock load determined by numerical and empirical methods was validated with actual field data as shown in Figs. 17 and 18. The index of determination (R2) for actual rock load and RMRdyn was observed as 0.94. However, in the case of actual rock load and numerical approach, the index of determination (R2) was estimated as 0.82.

Fig. 17
figure 17

Correlation of actual rock loads and empirical approach (RMRdyn)

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Fig. 18
figure 18

Correlation of actual rock loads and numerical approach

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The deviation in rock load from the actual was compared with all the three approaches, i.e., CMRI-ISM RMR, numerical modeling, and RMRdyn as shown in Fig. 19, and the corresponding average percentage deviation is shown in Fig. 20. A minimum percentage deviation of 7.19 % was obtained in the RMRdyn method.

Fig. 19
figure 19

Deviation in rock load by different approaches with actuals

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Fig. 20
figure 20

Percentage deviation of rock load by different approaches with actuals

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Compared to other approaches, the correlation obtained between the actual rock load and RMRdyn is high (R2 = 0.94) with a minimum percentage deviation of 7.19 %. Hence, RMRdyn can be used for rock load estimation for development galleries in underground coal mines under varied geo-mining conditions.

5 Results and Discussion

A critical review was done by comparing earlier rock mass classification systems. The review reveals that excavation technique, the presence of beddings and joints, and their orientation are the most dominant parameters causing instability of underground openings. Moreover, the adjustments proposed are repetitive in nature for some of the cases apart from being time-consuming. The main thrust was given to the CMRI-ISM RMR system as it was developed for Indian geo-mining conditions and is the suggested practice. The objective of the research comes into the limelight as there still exists a number of roof failure cases in spite of following the CMRI-ISM RMR system for support design. Thus, the present research aims at revisiting the failed and stable cases to identify the key parameters and attempt to develop a modified rock mass classification for addressing the roof failures.

RMR was obtained for 31 mine sites by empirical method applying CMRI-ISM RMR system and RMRdyn. The RMR estimated for CMRI-ISM RMR was found in the range of 29.27 to 60.62. Similarly, RMRdyn recorded in 31 mine sites ranged from 29.5 to 61.67. The minimum and maximum value of RMR for both the approaches was found in the Godavari Valley Coalfields of Singareni Collieries Company Limited (SCCL). Few sites showed high RMR due to high compressive strength, greater P-wave, high slake durability, and less jointed rock mass with dry roof condition. On the other hand, low RMR values were due to less compressive strength and P-wave, highly weathered and jointed rock mass, and a watery roof condition with the occurrence of prominent slip.

After determining RMR, the rock load was obtained by applying empirical, numerical and actual field measurement. The variation in the rock load found for CMRI-ISM RMR system was scaled in the range of 1.5 t/m2 to 5.90t/m2. Similarly, for RMRdyn, the range of rock load was noted between 0.77 and 8.06 t/m2. Rock load was measured in the field by roof fall height, exposed bolt length, and instrumentation. The rock load variation was observed between 1.1 and 6 t/m2. For all the approaches, the maximum rock load values were found for KTK 6 mine I seam 13LN/BD and minimum rock load values for KTK6 mine III seam dip/3LS of Godavari Valley Coalfields (SCCL). The maximum and minimum values of estimated rock load were due to a variation in compressive strength, P-wave velocity, slake durability, presence of joints, and dry and wet roof conditions. Rock load determined by numerical modeling was found on the scale of 1.63 to 5.85 t/m2. For numerical models, the maximum rock load values were found at Jamuna 1/2 Incline mine of South Eastern Coalfields Limited (SECL), and the minimum rock load value was at KTK6 mine III seam dip/3LS of Godavari Valley Coalfields (SCCL).

Furthermore, the rock load obtained by numerical and empirical approach (RMRdyn) was correlated. The coefficient of correlation of 0.87 and index of determination as 0.72 indicated a good relation. The study was further extended by comparing the deviation in rock load from all the three approaches (CMRI-ISM RMR, RMRdyn and numerical modeling) with rock load obtained from actual field measurement. After comparing all the approaches, it was seen that the RMRdyn showed a minimum deviation of 7.19%. Thus, statistical analysis and inter-relationship indicated that the newly developed rock load by RMRdyn was reliable and significant in all means and hence can be used as a rock load predictor equation for the estimation of rock load for development galleries for underground mines.

6 Conclusions

RMRdyn was determined in 31coal mine sites out of 79 investigated sites covering four coal fields, namely coalfields of South Eastern Coalfields Limited (SECL), Jharia Coalfield (BCCL and Tata Steel Limited), IB Valley Coalfield, and Godavari Valley Coalfield (SCCL). A critical review of the rock mass rating system in terms of its significance and function related to the application in Indian coal mines revealed that the presence of joints was the most dominant parameter for roof failure in underground mines.

In spite of the well-established CMRI-ISM RMR system for support design, still, the occurrence of a number of roof failure cases modified rock load predictor equation RMRdyn was developed. RMR was determined for 31 mine sites applying CMRI-ISM RMR system and RMRdyn. The RMR estimated for CMRI-ISM RMR was found in the range of 29.27 to 60.62. Similarly, RMRdyn was on the scale of 29.5 to 61.67. The maximum RMRdyn of 61.67 (good roof condition) was found in KTK 6 mine, III seam main dip/3LS, and a minimum of 29.5 (poor roof condition) in KTK 6 mine, I seam 13LN/BD.

The rock load found for the CMRI-ISM RMR system was scaled in the range of 1.5 to 5.90 t/m2, and for RMRdyn, the range of rock load varied between 0.77 and 8.06 t/m2. The range of rock load found from actual field measurement was observed between 1.1 and 6 t/m2.

The propagation of rock failure can be more accurately predicted using the elastoplastic model (Mohr-Coulomb) compared to elastic models of numerical modeling, and hence, this model was selected in the analysis for the determination of rock load. The maximum and minimum rock load values obtained from numerical models were 5.85 t/m2 and 1.63 t/m2.

The rock load determined by empirical (RMRdyn) and numerical methods was validated with actual rock load with a respective index of determination (R2) of 0.94 and 0.82. The deviation of rock load of all the three approaches compared with actual field measurement showed minimum deviation in RMRdyn with 7.19%. Thus, it may be concluded that the derived new rock load predictor equation using RMRdyn is reliable and can be used for the estimation of rock load for development headings of underground coal mines.