Engineering geological conditions in the research area

Formation lithology conditions

The research area is situated in the north-west corner of Xishan coalfield. The exposure strata are lower Permian Shanxi formation, lower Permian lower Shihezi formation, higher Permian higher Shihezi formation in Permian system; Neogene upper Pliocene Baode formation, quaternary middle Pleistocene Lishi formation, upper epipleistocene Malan formation, and Holocene stratum. The former three strata mainly exist on both sides of the branches of the Lion river, while the rest mainly spread at the mountain ridges and riverbed regions (^{Mese & Tutuncu, 1997}).

Geological structure condition

Located at the north-west edge of Taiyuan Xishan coalfield, the area is a part of graben formed by Lion River-Malan syncline fold belt of Taiyuan Xishan syncline subsidiary fold, subsidiary fold in Haojiagou north syncline, Jiulongta fault (F17) and Hongyazi fault (F49).

The anticline is located in western research area, whose west wing is the strata of Shanxi formation and lower Shihezi formation in the lower Permian system. The stratigraphic dip generally ranges from 5°-9°, and some can reach 14°. The surface of the east wing of the anticline is largely covered by Neogene and Quaternary strata, underlying is the strata of Shanxi formation and lower Shihezi formation in the lower Permian system. Both wings are substantially symmetric. The axial direction of north-north-east extends close to a line, and the extended length is more than 1500m pitching toward the south.

According to the surface investigation and analysis of the relevant geological data, three normal faults (F17, F19, and F20) are found in the research area whose strike is almost parallel with the Lion River. These faults lean south-east with a larger dip. The fault displacements range from 5m to 40m combined into steps.

F17 normal fault: the fault strikes to north-east of 30°, and leans to the south-east with an angle of inclination of 65°. The fault displacement is about 40m.

F19 normal fault: the fault is about 130 m from the west side of F17 normal fault. It strikes to the north-east of 25° and leans to the south-east with an angle of inclination of 65°. Its fault displacement is about 6m, and the extended length is about 900m.

F20 normal fault: the fault is about 20 m from the west of F17. It strikes to the north-west of 31° and leans to the south-east with 60°. Its fault throw is about 20m, and the extended length is about 350m.

Coal mining activities

The main coal-bearing stratum in the research area distributes at the Taiyuan Formation in the upper carboniferous system and Shanxi formation of the lower Permian system. The research area mines the No.2+3 coal seam, and the working face is arranged in a longwall face along strike when mining. The strike length is 630m, and the inclined length is 120m. the caving method and high-grade conventional mining are used, and the former is applied for managing the roof. The mined-out area is right below the slope top and its area is 24,000 m².

Calculation principle and the establishment of model

Principle

When the finite element technique used by Midas GTS NX is applied for stability analysis, the initial stress field of the mechanical model is calculated, and then the strength reduction method is used to reduce the strength of rock-soil mass continuously in order to reach the non-convergence state. At last, the corresponding fracture point and fracture plane will be found according to the stress field distribution of the research object. The model should comply with the Mohr-Coulomb Criterion. The formula is (^{Irwin, 1977}):

δ₁: the maximum principal stress;

δ₃: the minimum principal stress;

C: cohesive force of the rock-soil mass;

φ: internal friction angle.

Establishing a finite element model

Establishing the model with a width of 400m (in X direction), a length of 470m (in Y direction), a base elevation of 850m at the lower boundary, and the maximum elevation of about 1170m from upper boundary to the surface by using MIDAS/GTS numerical simulation software based on the actual slope topography. And two kinds of geologic models (the faulted and unfaulted) are established to analyze the effect of the fault on the slope body, as shown in Figure 1.

The division of mesh and the establishment of a three-dimensional finite element mesh calculation model for the unstable slope of Fengmaoding are based on the 3 principles. First, it should be able to reflect the geological features of unstable slopes and the underlying mined-out area of Fengmaoding. The unit block in the fault area, the mined-out area, and the surface, etc. should be subdivided to ensure the calculation model's ability in showing the true geometrical features of the rock mass. Then ensure the consistency of the calculation results for stress, displacement, during the numerical calculation.

Third, considering the limits for processing capability and the memory size of computers, the unit size should fit for the calculation program to process. This model has more than 70 thousand units. Whereby, the mesh division of key areas including loess on the earth surface, the F19, F20, and F17 faults, No.2-4 coal seam, mined-out area and No.8, No.9 coal seam, is shown in Figure 2.

Figure 2 Mesh plot of unstable slope in Fengmaoding 

Analysis of numerical simulation results

Comparative analysis of the whole displacement vector field

Faulted condition: The X directions of the foot in front of the slope and the F20 fault footwall (railway and road included) are mainly negative, manifested as the surface is extruding by displacing towards free face and the slope is deforming outward (see Figure 3); The X directions of F20 fault hanging wall and F17 fault footwall are mainly positive, showing that rock-soil mass is displacing towards mined-out areas and the slope is deforming inward as a result of the mining of coal seam (see Figure 3-a). The complex Y displacement vector field is controlled by the subsidence of mountain mass towards mined-out areas, showing that the rock-soil mass on both sides of the mined-out areas is displacing towards mined-out areas (see figure 3-b). The displacement vector field in the Z direction is relatively simple, mainly showing a feature of subsidence, and the largest subsidence displacement value of the mountaintop is in the Z direction as a result of the mining of coal seam. Note that there are red arrows on some parts of the mountainside over the railway, which indicate that the displacement field is uplifting. And it is consistent with the actual deformation features of displacement (see figure 3-c).

Figure 3 Faulted surface displacement (unit: m) 

Unfaulted condition: The surface of the mountain slope is displacing horizontally in the positive X direction which is affected by mining subsidence, and the magnitude of displacement value in the direction deviating from the railway at top of the slope is about 0.03m, which is a large value. While the magnitude of displacement value at the mountainside and at the foot of the mountain is about 0.01m. And the magnitude of displacement value at the foot of the mountain is about 0.006m, which is smaller than the magnitude of displacement value at the mountainside. The soil mass of the steep local part of the slope shoulder is displacing in a negative direction in response to its own gravity, i.e. the soil mass is displacing toward the free face of the slope mass, and the magnitude of displacement value is about -0.01m. From the simulation calculation result, we can see that the existence of fault has a significant impact on the displacement direction in the X direction of surface and the magnitude of displacement value (see Figure 4-a).

Figure 4 Displacement of unfaulted surface (unit: m) 

The whole magnitude of displacement value in the X direction of the surface is relatively small. The magnitude of displacement value at road and railway is about 0.001^~0.005m, the magnitude of displacement value at the mountaintop is about 0.01^~0.03m. The positive displacement in the Y direction is predominant; however, the displacement in some local areas is negative under the control of the topographic condition. The existence of fault has little impact on the displacement direction in the Y direction of the surface and the magnitude of displacement value based on the simulation calculation result (see figure 4-b).

The displacement in the Z direction of the surface is mainly subsided. The magnitude of subsidence displacement value at the top of the slope is about -0.2m, which is large. The vertical subsidence displacement value at mountainside and foot is relatively small, whose magnitude of subsidence displacement value is about -0.1m. And the magnitude of subsidence displacement value at road and railway is about -0.001m^~-0.002m, which is small. The existence of fault under the control of the fault plane has a significant effect on the magnitude of subsidence displacement value in the Z direction of the surface judging from the calculation result (see figure 4-c).

Analysis of deformation of different sections in the Y direction

Existence of fault: Cutting the section in different positions in Y direction (Y=10m, 50m, 100m, 150m, 200m, 250m, 300m, 350m, 400m, 450m, 500m, 550m), as shown in figure 5. The X displacements of different sections are shown in figure 6 and the Z displacements are shown in Figure 7.

Figure 5 Different section positions in the Y direction 

Figure 6 X displacement of different sections in Y direction 

As shown in Figure 7, the displacement varies in different positions because of the mined-out area resulting from the excavation of coal seam. As shown in section Y = 10m, the relatively uniform X displacement map indicates the displacement changes little.

Figure 7 Z direction displacement of different sections along Y-direction (unit: m) 

With the excavation of coal seam, as shown in section Y = 100m, Y = 150m, the F20 fault hanging wall in the position near the mined-out area begins to make a large positive displacement in X direction (the yellow); the F17 fault footwall is making a large negative displacement in X direction toward mined-out area (the light green).

In the maximum coal-mining position, as shown in section Y = 350m, Y = 300m, the largest displacements are the positive displacement in the X direction along the F20 fault in the F20 fault hanging wall (the red), and the negative displacement toward the mined-out area in F17 fault footwall (the blue). Meanwhile, the rock mass in the F20 fault footwall is making a relatively large negative displacement, shown as the displacement toward railway and road.

Though coal seam will not exist in the north of the mined-out area, there is still displacement in X direction affected by the mined-out area, such as the section Y=450m.

The displacement maps of different sections in X-direction indicate that big displacements in X direction basically occur on both sides of the F20 fault, with the hanging wall of F20 having displacement in positive direction (red) and the footwall having displacement in negative direction (green), showing that F20 is an important controlling factor to prevent the mountain from extruding to the free face.

As shown in Figure 7, mined-out areas are formed due to the coal mining, and the displacements are different due to different locations of the mined-out areas. The displacement maps of the sections Y=10m and Y=450m on Z direction are uniform, which means the changes of their displacements are small.

For the parts near the mined-out area, such as section Y=100m and section Y=150m, the roof of the mined void has negative-direction displacement in the Z direction (green), with a manifestation of sinking, the base of the mined-out area has positive-direction displacement in the Z direction (red), with the manifestation of swelling.

For the biggest coal mining area, such as the sections Y=350m and Y=300m, the roof and the base of the mined void have the biggest displacement in the Z direction, with the roof sinking up to 1.44m and the base swelling up to 0.44m.

It indicates that all the big displacement changes occur in the hanging wall of F20, and the displacement of the rock mass is small in the footwall of the F20 fault (yellow), so F20 is an important controlling factor to prevent the mountain body from having subsidence displacement.

Unfaulted condition: Cutting the section in different positions in Y direction(Y=10m, 50m, 100m, 150m, 200m, 250m, 300m, 350m, 400m, 450m, 500m, 550m), as shown in Figure 8. Displacements of different sections are generated in X direction (see Figure 9) and Z direction (see Figure 10) respectively.

Figure 8 Different sections positions in the Y direction. 

Figure 9 X displacement of different sections in Y direction (unit: m) 

As shown in Figure 9, Y=10m in the X direction is uniform, which means the displacement change is small.

The part near the mined-out area forms the mined-out area, Y=100m, and Y=150m, the positive direction displacement happens. Comparing to the faulted condition, the displacement happens only affected by the mined-out area.

At the center of the mined-out area, such as the sections Y=350m and Y=300m, the positive direction displacement in the X direction is the biggest. As section Y=450m, the farther the distance to the center of the mined-out area, the smaller the displacement in the X-direction.

It's showing that the fault is an important controlling factor to prevent the mountain from extruding to the free face.

As shown in Figure 10, in the Z direction, the roof of the mined void has negative-direction displacement, with the manifestation of sinking, the base of the mined void has positive-direction displacement, with the manifestation of swelling. Y=350m and Y=300m, Comparing to the faulted condition, the fault controls the displacement border of the east side and the west side.

Figure 10 Displacement of different sections in Z direction along Y-direction (unit: m)