A floor aquifuge usually bends and fails when mining above a confined aquifer, which may lead to water inrush disaster. The floor aquifuge was simplified as a thin disc model in this paper, and a series of coupled bending-seepage tests of sandstone were carried out by a patent test system. The variation characteristics of load-displacement, load-time, and permeability-time were analyzed. The deflection and stress in the thin disc rock samples were deduced; the initiation and propagation of cracks were analyzed. The failure behavior of the thin disc rock samples was described. It shows the following: (1) The bending failure behavior relates to the stress distribution and crack evolution inside the thin disc. (2) The main cause of crack initiation is a tension-shear failure. (3) The 5 mm thickness thin discs form petal-shaped cracks, due to tensile stress, while petal-shaped cracks only appear at the cap block of the 10 mm discs, which are sheared into two pieces along the conical surface with an inclination about 45°. (4) Water inrush occurs after bending failure in the floor aquifuge, and it is an opportune moment to grout along the crack propagation trend lines to prevent the water inrush disasters.
Due to the gradual depletion of shallow mineral resources, mining activities are shifted to the deep. In deep mining activities, geological conditions become complex; confined water pressure increased. Continuous deep mining may result in bending deformation and failure of the floor aquifuge, which may link the groundwater to the working face, and induce water inrush accidents [
Scholars began to study the mechanism of floor breakage and water inrush since the last century. Some important theories have been proposed successively, such as the key stratum theory, three-underlying belts theory, in situ rifting and zero failure theory, relative aquifuge thickness and water inrush coefficient method, and water inrush critical index method [
A large-scale model test is one of the effective means to reproduce the process of water inrush from floor breakage. Zhao et al. [
The similar model test can reproduce the process of floor’s breakage and water inrush, but it still has some disadvantages; for example, the model sizes are usually too large, cost too much, and last for long test periods. Therefore, theoretical research and numerical calculation are essential.
Miao et al. [
The research above studied the stress distribution [
To this end, this paper established a thin disc model, conducted the bending-seepage tests of different thicknesses and lithology under the coupled bending-seepage condition, calculated the deflection and stresses inside the thin disc gray sandstone and red sandstone, revealed the formation and propagation mechanism of the cracks in the thin disc rock with different thicknesses and lithology, and described the bending failure behavior in the floor aquifuge, as well as the bending-failure-induced water inrush behavior. This research is expected to provide references for the description of floor failure and the prevention of water inrush.
With coal extraction continuing, the confined water pressure and the mining-induced stress become the force sources. Subject to their joint action, the floor aquifuge undergoes bending deformation. In the bending floor aquifuge, the cracks are formed, developed, and penetrated, and water flow changes from seepage to turbulence and rushes into the working face, which may cause water inrush disaster.
A simplified model is shown in Figure The floor aquifuge in practical engineering is assumed as a circular thin plate relative to the stratum; the self-weight of the thin disc rock sample is ignored. Owing to the strength and stiffness of the surrounding rock mass that are far greater than those of the floor aquifuge, the constraint of the thin disc rock sample is peripheral clamping. The floor aquifuge is assumed above the confined aquifer. The confined water pressure is regarded as a uniformly distributed pore pressure, Excavation disturbances induce floor heave; the upward bending deformation is applied to the thin disc rock sample, which is realized by applying an upward concentrated force,
Simplified model for floor aquifuge.
As shown in Figure
In order to simulate the heave and breakage of the floor aquifuge and realize the coupled bending deformation and water flow applied on the floor aquifuge, a testing system that can conduct the coupling bending-seepage test is designed and manufactured [
Testing system.
As the core of the testing system, the permeameter subsystem contains a bottom plate, a cylinder, a permeable piston, a conical indenter, a retaining ring, seals, etc., shown in Figure
Schematic of the permeameter.
The test adopted the steady-state permeation method. Stable pore water pressure was provided by driving oil pressure in the pore pressure loading and controlling subsystem. Water flowed through the pressure transducer, flow transducer, and the inlet at the bottom plate, entered the conical indenter, and evenly distributed on the lower surface of the thin disc rock sample to simulate the action of the confined water pressure on the floor aquifuge. An axial load was applied onto the piston of the permeameter, then loaded on the upper surface of the thin disc rock sample through the retaining ring as circumferential load. Under the bidirectional actions of concentrated force from the conical indenter and circumferential load from the retaining ring, the rock sample underwent bending deformation, which was used to simulate the floor heave bending deformation of the floor aquifuge due to excavation disturbances.
The floor aquifuge in Pan mine in Sichuan is taken as the example in this paper, which is mainly gray sandstone and red sandstone. All samples were acquired from a single rock block to ensure their similar physical properties, respectively. The physical and mechanical properties are listed in Table
Physical and mechanical properties of gray sandstone and red sandstone.
Lithology | Gray sandstone | Red sandstone |
---|---|---|
Uniaxial compressive strength ( | 54.7 | 51.2 |
Tensile strength ( | 5.02 | 4.71 |
Elastic modulus ( | 32.0 | 29.2 |
Poisson ratio ( | 0.23 | 0.16 |
Density ( | 2473 | 2574 |
Internal friction angle ( | 47.8 | 43.0 |
Cohesion ( | 21.2 | 22.9 |
Based on the simplified model of the floor aquifuge and the diameter of the permeameter cylinder, the rock sample was processed as a 50 mm diameter disc. According to the definition of the thin plate theory, the thickness-diameter ratio should be less than 1/5. Therefore, two thicknesses, 5 mm and 10 mm, are selected in this research.
Samples were examined before testing to exclude those with obvious macroscopic defects and to ensure the testing values free from the impacts of macrojoints and fissures. The structures of the selected thin disc rock samples were compact, and there was no visible natural microfissure. Then, thin disc rock samples were polished to keep the surface smooth at two ends.
Taking lithology and thickness as the influencing factors, four independent tests were carried out, marked GS05, GS10, RS05, and RS10. Three samples were tested in each independent test.
At the beginning of testing, water was injected into the permeameter to saturation at least half an hour. Then, the pore pressure was loaded, and the sealing performance of the system was timely checked. According to relevant geological data, the pore pressure was set as 2 MPa in this test. When the pore pressure was completely stable at 2 MPa, the rock sample was loaded by the axial loading subsystem in the displacement control mode at a loading rate of 0.5 mm/min till the rock sample failed.
In addition, the pore pressure
Permeability,
Figure
Load-displacement curves of four different sandstone samples.
Four-stage dividing sketch of load-displacement curves.
The section of the
The
The
The peak values for different samples.
Sample number | GS05 | GS10 | RS05 | RS10 |
---|---|---|---|---|
Peak load (kN) | 4.065 | 6.419 | 5.915 | 7.283 |
Displacement on the peak load (mm) | 0.609 | 0.603 | 1.162 | 1.363 |
After the peak value,
Figure
Time-varying characteristics of load and permeability.
GS05
GS10
RS05
RS10
The permeability of the intact thin disc rock sample is about 10-17 m2 at the beginning of the experiments, which is consistent with the testing result of standard intact rock samples [
As shown in Figure
The lagging times for different samples.
Sample number | GS05 | GS10 | RS05 | RS10 |
---|---|---|---|---|
Time on the peak load occurrence (s) | 310 | 118 | 193 | 186 |
Time on the peak permeability occurrence (s) | 356 | 174 | 203 | 190 |
Lagging time (s) | 46 | 56 | 10 | 4 |
The sample GS05 experienced the longest time; this is because the sealing material between the outer boundary of the sample and the cylinder wall was compacted for a long time. The compression of the sealing material only prolongs the test time but does not affect the deformation measurement of the sample. Because of the difference in experimental operation, the peak load and permeability occurrence times of four samples cannot be compared separately. Only the lagging time can be analyzed; it shows that the lagging time of gray sandstone is longer than that of red sandstone. It is because the brittle behaviors of the thin disc in the postfracture stage are different, which relates to the crack propagation. The longer the lagging time is, the longer the time that can be used for water inrush prevention and control is, the more effective the water inrush risk can be reduced.
Figure
Bending failure patterns.
GS05
GS10
RS05
RS10
Obviously, when the thin disc rock samples are under the coupled bending-seepage condition, their failure behaviors belong to the problem of structural failure. It is related not only to material properties but also to the structural properties and external force characteristics. In order to analyze the bending failure behavior in-depth, the stress distribution and crack evolution in the thin disc rock structures should be studied further.
The hard rock floor aquifuge is mainly a local plastic failure, and the stability coefficient is generally high; it can be solved with the elastic solution [
Based on the simplified model in Figure
In polar coordinates, as shown in Figure
A semi-inverse method is used to solve the differential Equation (
Based on the boundary conditions in the mechanical model, the deflection is expressed as
Applying Equation (
The deflection distributions along the radius direction when
Deflection distribution curves.
When
When
Figure
It is worth noting that these deflections are the elastic ultimate load-bearing displacements. The displacements are different from the values in Table
The maximum deflections both occur at the center of the thin disc rock sample when
Sandstone is a typical brittle material at room temperature; its elastic deformation is weak. The bending failure of the thin disc rock sample mainly results from the strength, but not the stiffness. Therefore, in addition to analyzing the deformation in the disc, stress distribution should be emphasized.
As Figure
Internal force distribution of microelement in the thin disc rock sample.
Using Equation (
Internal force distribution curves.
As seen in Figure
It can be seen from Figure
It can be seen from Figure
From Equations (
Using Equation (
Stress distribution at the dangerous cross-section.
Stress distribution at the central dangerous cross-section along the thickness direction
Stress distribution at the edge dangerous cross-section along the thickness direction for the sample of GS05
As seen in Figure
Summing up, the location and stresses of the dangerous points in the thin disc rock samples can be calculated and are shown in Table
The location and stresses of the dangerous points in the thin disc rock samples.
Samples | Location/stresses |
---|---|
GS05 | The upper and lower points of the central cross-section/ |
The upper and lower points of the edge cross-section/ | |
The upper and lower points of the central cross-section/ | |
The neutral point of the central cross-section/ | |
GS10 | The upper and lower points of the central cross-section/ |
The upper and lower points of the central cross-section/ | |
The neutral point of the central cross-section/ | |
RS05 | The upper and lower points of the central cross-section/ |
The upper and lower points of the central cross-section/ | |
The neutral point of the central cross-section/ | |
RS10 | The upper and lower points of the central cross-section/ |
The upper and lower points of the central cross-section/ | |
The neutral point of the central cross-section/ |
As illustrated in Table
It also shows that the sample RS05 has the largest
The stress state of dangerous points in the thin disc rock samples can be described as shown in Figure
Stress state of dangerous points.
The biaxial tensile stress state
The biaxial compressive stress state
The uniaxial tensile stress state
The uniaxial compressive stress state
The pure shear stress state
Figure
The location of the danger points on thin discs.
The details of the stress state at the dangerous points.
Stress state | Location of the dangerous points |
---|---|
The upper points of the central cross-section in samples of GS05, GS10, RS05, and RS10. | |
The lower points of the central cross-section in samples of GS05, GS10, RS05, and RS10. | |
The lower points of the edge cross-section in the sample of GS05. | |
The upper points of the edge cross-section in the sample of GS05. | |
The neutral points of the central cross-section in samples of GS05, GS10, RS05, and RS10. |
Based on the description for the location and stress state of the dangerous points on the thin discs, these dangerous points are in the biaxial tensile/compressive stress state, the uniaxial tensile/compressive stress state, and the pure shear stress state, respectively. The structural failure of the thin disc rock sample is mainly due to the stress reaching or exceeding its strength limit, and therefore, the strength condition should be established to reveal the failure mechanism.
Sandstone is a kind of brittle material so that we use the Maximum Tensile Stress Theory and Mohr-Coulomb Strength Theory to analyze the bending failure behavior.
Combining Figures
Meanwhile, the lower points of the edge cross-section in sample GS05 are also the dangerous points. They are in the uniaxial tensile stress state, and the principal stresses of the dangerous points are
In addition, the neutral points of the central cross-section in the four thin disc rock samples are also dangerous points, which are in the pure shear stress state, and the principal stresses of the dangerous points are
In summary, the crack initiation points for the samples GS10, RS05, and RS10 are
As seen in Table
The mechanism of crack propagation.
GS05
RS05
GS10 and RS10
For sample RS05, the cracks propagate from the center, where
For samples GS10 and RS10,
During mining activities, the floor aquifuge is bending; the deflection and stress are changing timely. It is safe when the deflection and stress are far less than the allowable values. The cracks initiate and propagate with the increase of stress, and the confined water pressure split and expand the cracks continuously. When bending failure occurs, the maximum tensile stress exceeds the allowable values; the cracks propagate to penetrate.
Although the occurrence of bending failure is really very dangerous, the water inrush disaster does not happen immediately, because of the water inrush lagging. There is a short time to take measures to grout the cracks and to prevent the water inrush accident. According to the crack initiation and propagation (Figure
A simplified thin disc model was introduced to study the bending failure of the floor aquifuge. Based on a self-designed experimental system, thin disc gray and red sandstone samples were tested under coupled bending-seepage condition to study the failure behavior. The failure behavior in thin disc sandstone with two different lithologies and thicknesses were analyzed. The main conclusions can be drawn as follows: The failure process of thin disc sandstone can be divided into four stages: adaptive adjustment and elastic deformation stage, plastic deformation and microcrack development stage, bearing capacity strengthening and macrocrack formation stage, and postfracture stage, of which water inrush disaster occurs at the postfracture stage. The permeability changes from 10-17 m2 to 10-11 m2 in the thin disc structure, and the sharp increase leads to more sudden and intense water inrush. The peak permeability always lags the peak load, and the lagging time of water inrush in gray sandstone is longer than that in red sandstone owing to the difference of crack propagation. The crack initiation point occurred at the center because of the tangential tensile stress and shear stress. The crack propagation is related to disc thickness and lithology. Water inrush accident occurs after the bending failure in the floor aquifuge. It is an opportune moment to grout along the crack propagation trend lines to prevent the water inrush disasters.
Radius of the thin disc rock sample (L)
Coefficients (-)
Cohesion (ML-1T-2)
Bending stiffness of thin disc (ML2T-2)
Elastic modulus (ML-1T-2)
Circumferential load (MLT-2)
Shearing internal forces (MLT-2)
Permeability (L2)
Force couple (ML2T-2)
Internal force couples (ML2T-2)
Concentrated force (MLT-2)
Peak load (MLT-2)
Confined water pressure/pore pressure (ML-1T-2)
Water flow (L3T-1)
Radial direction in polar coordinates (-)
Testing time (T)
Displacement (L)
Seepage speed (LT-1)
Deflection (L)
Symmetrical axis (-)
Thickness of the disc (L)
Tangential direction in polar coordinates (-)
Dynamic viscosity of water (ML-1T-1)
Poisson ratio (-)
Density (ML-3)
Uniaxial compressive strength (ML-1T-2)
Radial stress (ML-1T-2)
Maximum radial stress (ML-1T-2)
Tensile strength (ML-1T-2)
Tangential stress (ML-1T-2)
Maximum tangential stress (ML-1T-2)
Shear stresses (ML-1T-2)
Maximum shear stress (ML-1T-2)
Internal friction angle (-).
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflict of interest.
The authors gratefully acknowledge the support provided by the National Natural Science Fund (11502229), the Natural Science Foundation of Jiangsu Province of China (BK20160433), the Program of Yellow Sea Elite in Yancheng Institute of Technology (2019), the Program of Outstanding Young Scholars in Yancheng Institute of Technology (2014), the Program of Yellow Sea Team in Yancheng Institute of Technology (2019), and the Program of innovative training program for College Students in Yancheng Institute of Technology (2020).