The overburden in the study mine consists of alternating sandstone and shale beds with sandstone layers between 9 and 18 m thick. The thinly bedded shale above the Lower Kittanning coalbed ranges from dark gray to carbonaceous clay shale. The Johnstown limestone is located above this sandy zone. Table 1 lists the strength and mechanical properties of the rocks within the immediate roof. As shown by Esterhuizen et al. [6], the Coal Mine Roof Rating (CMRR) [13] is used to estimate the large-scale field strength of the strata.

The support performance was measured by load cells installed underneath the face plates of the cable bolts at the time of installation. The cable bolt load cells and roof extensometer were installed between 20 and 30 m outby the advancing heading. The roof sag was monitored by three 2.4-m-long extensometers (No. 1, No. 2, and No. 3 in Fig. 5a) and one roof extensometer of 6 m length (No. 5 in Fig. 5a).

The primary roof support in the study mine was rows of four fully grouted #6 bars with a 1.8 m height, spaced on 1.2-m centers. Fully grouted bolts were also installed at a 45° angle at the corner of the rib and roof, spaced on 2.4-m centers. The secondary support of the roof was a pair of cable bolts (3 m by 15 mm) installed through a strap every 2.4 m with 1.2 m of resin grout. Secondary support was installed about 18.2 to 30.4 m outby the advancing face. The standing support system was also used in the form of two rows of nine-point wooden cribs, but they are not considered in the models here because from crib load measuring devices, the standing supports did not take noticeable loads until after the second panel mined by.

Tulu et al. [20] constructed a panel-scale model of the study site and validated the stress variation during mining against field measurements by Hollow Inclusion (HI) stress cells. The stress around the gateroad entries in the model was used here to define the boundary condition of the entry-scale models. Stress distribution results from the panel-scale models at the end of the monitoring period with the actual longwall panel layout are shown in Fig. 3.

Figure 4 shows the gateroad loading paths from the model recorded as the vertical and horizontal stresses at different mining stages, recorded 3 m above the roof line. In Fig. 4, each marker on the curves shows a 9-m advance of the longwall face. The initial stress state in the model is with the horizontal stress of 7.1 MPa and vertical stress of 4.2 MPa. Compared to the other two entries, the stress path of the No. 1 (tailgate) entry shows a higher increase in horizontal stress. After the second panel mines by the monitoring site, stress at this location in the model reaches 12.8 and 12.7 MPa in horizontal and vertical directions, respectively. The change in stresses recorded by HI stress cells showed that 8 m above the tailgate roof, the vertical and horizontal stress values were 10.3 MPa and 11.5 MPa, respectively. With this validation, the stress path obtained from the model (Fig. 4) at the tailgate entry (entry No. 1) is applied as the boundary conditions of BBM entry-scale models described in the following section.

Figure 5a shows the entry-scale model constructed for the study site, which is a two dimensional or a vertical slice through entry No. 1. In total, 92 bedding planes in the roof and floor are modeled. Up to 11.5 m above the roof line, 65 slabs each 10 to 20 cm thick are modeled. BBM trigon blocks were generated up to 5 m above the roof line, and the rest of the thinly bedded strata were modeled with no trigons.

The edge of trigons varies from 0.02 to 0.06 m according to the thickness of each slab so that at least four trigons are located across each slab. The mine did not install rib bolts except at the pillar corners, indicating that rib spalling was not a concern during the longwall retreat. Thus, 3 m of ribs are constructed with relatively large trigons of 0.2 m edge to reduce computation time.

The modeling results from previous work are shown in Fig. 5b, as the roof vertical displacement after the second panel is mined by the instrumentation site. Figure 6a shows the roof vertical displacements at the left-hand and right-hand sides of the entry roof, confirming that the values predicted by the model are in agreement with the extensometer readings at the site. Figure 6b confirms the agreement between model and field measurements of the vertical displacements at the center of the roof. The validated model is considered Case A and is used to study support system alternatives under similar conditions.

The cable bolt response under mining-induced stresses is calibrated against the field measurements. Figure 7a shows the response of 8 cable bolts measured by the load cells versus the average roof sag measured by the extensometers. Most of the cable bolts were loaded between 50 to 100 kN when monitoring started, which was a few days after the bolt installation. This initial load can be associated with the thrust of the bolt machine during installation, and the displacement occurred after the installation. The peak load of individual bolts ranged from 190 to 320 kN with an average of 245 kN, which is close to the expected pick strength. The peak load for the cable bolts occurred between 60 to 90 mm of the roof sag. The average stiffness of the cable bolts from the slope of the curve between 16 and 70 mm of roof sag was 2.3 kN/mm, lower than the typical stiffness value measured during a controlled testing setup [19].

In an effort to calibrate the cable bolts under in situ modeling conditions, the model in Fig. 7b is used to conduct a pullout test on one of the cable bolts in the roof. The bolt head is extended to include a block hanging from the roof with a thickness of 0.5 m. The block is pulled downwards, and the load in the bolt is recorded versus the block displacement downwards. Through a trial-and-error approach, the cable and grout parameters are calibrated to match the average response of the cable bolts in Fig. 7a. Figure 7c shows the force–displacement curve of the cable bolt response after calibration. Table 2 lists the calibrated mechanical properties used for modeling the bolts.

One aspect of using a 2D software program to model a 3D environment is the scaling of support properties to account for the support spacing in the third dimension. Donovan et al. [3] showed that linear scaling of material properties is effective in applying effects of regularly spaced patterns in a 3D system on the behavior of materials in 2D environments. For considering the spacing of fully grouted bolts (1.2 m) and cable bolts (2.4 m) along the entry, we scale their mechanical properties. Thus, the elastic modulus and tensile strength of the cables and bolts and the stiffness and cohesion strength of the grout are divided by their spacing along the entry.

Besides the support systems installed in the mine with model results presented above, the effects of different support components on the roof are evaluated through studying four additional cases. Case #2 looks at the support performance without the strap through which cable bolts were installed. Case #3 removes the 45-degree bolts from the support system. In addition to the 45-degree bolts, Case #4 removes the cable bolts and shows the major effects of cable bolts. Finally, Case #5 evaluates the roof response when the support is reduced by 0.3 m (1 ft) to 1.5-m-long bolts across the entry.

As the first step, the effects of strap support on the roof stability are studied by removing the strap through which cable bolts are installed in the mine. The model is run according to the procedure in the modeling methodology section and is loaded through the full abutment loading sequence. Results of the model are shown in Fig. 8a–d. Figure 8a shows the vertical displacement profile of the roof, showing that without the strap support, the roof layers became fragmented between bolts and the three first shale slabs (failure depth of 25 cm) spalled off between fully grouted bolts No. 4 and 5. However, the roof remains stable as shown by the velocity plot in Fig. 8b where the roof velocity remained close to zero after the second panel mine-by. The horizontal stress profile shown in Fig. 8c indicates the transfer of loads to the relatively stronger shale layer, 40–50 cm above the roof line. Figure 8d shows the maximum load in each of the bolts numbered from 1 to 8. Except for the B1 and B8 bolts that took minimal loads, the rest of the bolts have surpassed their yield strengths. The straps are demonstrated to provide local support to the immediate roof between the bolts, preventing the potential for injury by smaller rock fragments.

From Case #2 observation, straps were shown to be useful for controlling local roof falls between bolts at the center of the entry. Also, it was shown that the 45-degree bolts (B1 and B8) seem to have little role in the roof control. To further evaluate B1 and B8 bolt performance, in Case #3, the model run is repeated without installing these two bolts. The results are shown in Fig. 9a–d. From Fig. 9a, the local roof spalling is limited to 10 cm above the roof line, but the overall displacement profile remains the same as that in Fig. 8a. The roof remains stable as shown in Fig. 9b. The horizontal stress is transferred to a stronger rock unit 60 to 80 cm above the roof line, 20 to 30 cm higher than that in the case with B1 and B8 bolts installed. From Fig. 9d, the loads in the bolts stay similar to Case #2, showing that installing B1 and B8 bolts appears to have no significant effects on the roof stability. In fact, the lack of bolts B1 and B8 leads to the transfer of load higher in the roof with less skin damage. The B1 and B8 bolts are no longer installed at the case study mine after conducting an in-mine experiment prior to this study being conducted.

In Case #4, the performance of cable bolts is evaluated by removing them from the support system and repeating the model runs. The results are shown in Fig. 10a–d. In Fig. 10a, the roof is shown to be unstable. The velocity plots in Fig. 10b show that 60 cm of the roof will collapse. Loads are transferred to the layers above 90 cm in the roof but are mainly concentrated in 1.6 m above the roof in the strong shaley sandstone unit (Fig. 10c). Segments of the bolts that are not broken yet take considerable load mainly because their last segment is 25 cm in the strong shaley sandstone, transferring the loads to the upper layers. Thus, in the next case, the length of the bolts is reduced so they are not within the strong shaley sand.

In the last step of the support performance evaluation, a minimal support layout is modeled by installing four fully grouted bolts with 1.5 m length (5 ft) evenly spaced across the entry. The difference with Case #4 is the reduction in the length of the primary bolts by 0.3 m (1 ft). The results are shown in Fig. 11a–d.

Figure 11a shows significant roof movement up to 1.6 m above the roofline where the strong shaley sandstone unit is located. Figure 11b confirms the total collapse of the roof up to this depth. Figure 11c shows that the horizontal stress is close to zero and loads are transferred to the layer 1.6 m above the roof.

The results in Figs. 10 and 11 illustrate under-designed support systems that may lead to roof fall with a height of 0.6 and 1.6 m, respectively. The results demonstrate that the models agree with the judgement of the mine staff that four bolts are needed to provide adequate roof control for the longwall abutment loads and geologic conditions at the mine.