5
The mechanical properties of the caprock (limestone) and
the main roof (shale) are summarized in Table 2. To evalu-
ate the effect of the maximum horizontal stress angle on
entry and crosscut stability, the safety factor was calculated
at different roof elevations (6 inches and 2 ft (0.61 m) from
the roofline). The strength of roof elements was estimated
using the Hoek-Brown strength criterion, while induced
stresses were obtained from the FLAC3D models. The fail-
ure percentage was calculated as the ratio of elements with
a safety factor below 1.0 to the total number of elements.
The FLAC3D model dimensions are 498.6 ft × 505.1 ft
× 226.3 ft (152 m × 154 m × 69 m) in the X, Y, and Z
directions, respectively. The model was solved in four steps:
first, the geostatic step to initialize the in-situ stresses sec-
ond, the development of Entry 1 third, the excavation of
the crosscut and lastly, the development of Entry 2. The
zone relax excavate command in FLAC3D was used to sim-
ulate the excavation process and mitigate unrealistic results
caused by the sudden removal of rock material. The model
boundaries were constrained to move only in the vertical
direction, while the bottom was fixed in the X, Y, and Z
directions. The immediate roof at the study mine consists
of limestone, with a thickness ranging from 2 to 8 ft (0.61
to 2.4 m). This limestone layer is overlain by shale, which
forms the main roof. An interface is assumed between the
limestone and shale, with its properties listed in Table 3.
Both the shale and the limestone are considered massive
and free from geological discontinuities.
Figure 6 illustrates the variation in failure percentage
in the caprock of Entry 1 and the crosscut under differ-
ent orientations of maximum horizontal stress, with a cap-
rock thickness of 2 ft (0.61 m). The failure percentage is
minimal when the maximum horizontal stress is aligned or
nearly aligned with the entry direction. In contrast, the fail-
ure percentage is highest when the stress is perpendicular or
nearly perpendicular to the entry. Since the crosscut is per-
pendicular to the entry as shown in Figure 5, the optimal
orientation for minimizing failure in the entry leads to the
worst performance in the crosscut, and vice versa.
Before mining, the maximum stress in the roof was
around 1,595 psi (11 MPa). After mining, if the heading
was aligned perpendicular to the maximum horizontal
stress, it caused significant disturbance in the stress field,
as illustrated in Figure 7a. The maximum stress in the roof
increased to more than double over the excavated area,
while the stress in the unmined roof near the middle of the
excavation at the sides decreased by nearly half, creating a
relief zone. In contrast, aligning the heading parallel to the
maximum horizontal stress resulted in minimal disturbance
in the stress field, leading to more stable conditions for the
roof, see Figure 7b.
Figure 5. Plan view of the FLAC3D model geometry. The
mine geometry is rotated by an angle q relative to the
maximum horizontal stress, which is aligned with the Y-axis
Table 2. Summary of the geotechnical parameters used in the
model
Rock Type Parameter Value
Immediate
roof
(limestone)
Unconfined compressive strength,
(MPa)
110
Poisson’s ratio 0.20
Intact Young’s Modulus, (GPa) 45.5
Hoek-Brown m
i Parameter 9.98
Hoek-Brown s Parameter 1.0
Geological strength index (GSI) 70
Main roof
(shale)
Intact Young’s Modulus, (GPa) 22.5
Poisson’s ratio 0.25
Table 3. Mechanical properties for the interface used in the
model
Parameter Value
Normal stiffness, MPa/m 13,000
Shear stiffness, MPa/m 2,600
Friction angle, degree 20.0
Friction-residual, degree 12
Cohesion, MPa 0.50
Cohesion-residual, MPa 0.1
Tension, MPa 0.1
Tension-residual, MPa 0.05
The mechanical properties of the caprock (limestone) and
the main roof (shale) are summarized in Table 2. To evalu-
ate the effect of the maximum horizontal stress angle on
entry and crosscut stability, the safety factor was calculated
at different roof elevations (6 inches and 2 ft (0.61 m) from
the roofline). The strength of roof elements was estimated
using the Hoek-Brown strength criterion, while induced
stresses were obtained from the FLAC3D models. The fail-
ure percentage was calculated as the ratio of elements with
a safety factor below 1.0 to the total number of elements.
The FLAC3D model dimensions are 498.6 ft × 505.1 ft
× 226.3 ft (152 m × 154 m × 69 m) in the X, Y, and Z
directions, respectively. The model was solved in four steps:
first, the geostatic step to initialize the in-situ stresses sec-
ond, the development of Entry 1 third, the excavation of
the crosscut and lastly, the development of Entry 2. The
zone relax excavate command in FLAC3D was used to sim-
ulate the excavation process and mitigate unrealistic results
caused by the sudden removal of rock material. The model
boundaries were constrained to move only in the vertical
direction, while the bottom was fixed in the X, Y, and Z
directions. The immediate roof at the study mine consists
of limestone, with a thickness ranging from 2 to 8 ft (0.61
to 2.4 m). This limestone layer is overlain by shale, which
forms the main roof. An interface is assumed between the
limestone and shale, with its properties listed in Table 3.
Both the shale and the limestone are considered massive
and free from geological discontinuities.
Figure 6 illustrates the variation in failure percentage
in the caprock of Entry 1 and the crosscut under differ-
ent orientations of maximum horizontal stress, with a cap-
rock thickness of 2 ft (0.61 m). The failure percentage is
minimal when the maximum horizontal stress is aligned or
nearly aligned with the entry direction. In contrast, the fail-
ure percentage is highest when the stress is perpendicular or
nearly perpendicular to the entry. Since the crosscut is per-
pendicular to the entry as shown in Figure 5, the optimal
orientation for minimizing failure in the entry leads to the
worst performance in the crosscut, and vice versa.
Before mining, the maximum stress in the roof was
around 1,595 psi (11 MPa). After mining, if the heading
was aligned perpendicular to the maximum horizontal
stress, it caused significant disturbance in the stress field,
as illustrated in Figure 7a. The maximum stress in the roof
increased to more than double over the excavated area,
while the stress in the unmined roof near the middle of the
excavation at the sides decreased by nearly half, creating a
relief zone. In contrast, aligning the heading parallel to the
maximum horizontal stress resulted in minimal disturbance
in the stress field, leading to more stable conditions for the
roof, see Figure 7b.
Figure 5. Plan view of the FLAC3D model geometry. The
mine geometry is rotated by an angle q relative to the
maximum horizontal stress, which is aligned with the Y-axis
Table 2. Summary of the geotechnical parameters used in the
model
Rock Type Parameter Value
Immediate
roof
(limestone)
Unconfined compressive strength,
(MPa)
110
Poisson’s ratio 0.20
Intact Young’s Modulus, (GPa) 45.5
Hoek-Brown m
i Parameter 9.98
Hoek-Brown s Parameter 1.0
Geological strength index (GSI) 70
Main roof
(shale)
Intact Young’s Modulus, (GPa) 22.5
Poisson’s ratio 0.25
Table 3. Mechanical properties for the interface used in the
model
Parameter Value
Normal stiffness, MPa/m 13,000
Shear stiffness, MPa/m 2,600
Friction angle, degree 20.0
Friction-residual, degree 12
Cohesion, MPa 0.50
Cohesion-residual, MPa 0.1
Tension, MPa 0.1
Tension-residual, MPa 0.05