A quicksand disaster through a borehole occurred in Longde coal mine. A lot of aeolian sand, the volume of which is between 310,000 m3 and 380,000 m3, has submerged into the underground space in about 70.5 h. The volume flux of quicksand cannot be calculated accurately by the empirical method. Based on the method of fluid mechanics, an all-purpose computing method for quicksand disaster through a borehole was proposed. The result shows that the inrush volume of sand into underground space was between 310,000 m3 and 350,000 m3, which was consistent with the actual result. To apply and popularize this method, the impact laws of water yield properties of an aquifer on the volume flux were discussed. The all-purpose computing method can be suitably used for the volume flux calculation of quicksand disaster through the borehole.
Water inrush is one of the most severe disasters during mining in China [
There are two types of quicksand disaster. Firstly, the quicksand disaster caused by the aeolian sand submerging into underground space through caved zone as shown in Figure
Quicksand disaster schematic diagram. (a) Quicksand trip through overburden strata above a longwall panel [
Flow in the borehole (i.e., in the circular pipe) has been researched by researchers, and a lot of empirical formulas have been put forward.
Manning improved the Manning coefficient based on Chery’s research [
Hazen and Williams [
Based on the research of wood-stave pipe, Scobey [
In addition, there are many other empirical formulas such as Blasius formula [
The volume flux of Longde quicksand disaster was calculated by using the empirical formula with the common value of empirical parameters, and the result is shown as Table
Empirical formula and calculation result [
Formula | Equation | Common value of empirical parameters |
|
|
---|---|---|---|---|
Chezy formula |
|
0.010–0.030 | 5.44–16.32 | 1537–4611 |
Hazen–William formula |
|
100–140 | 15.40–21.56 | 4352–6093 |
Scobey formula |
|
0.3–0.6 | 0.48–0.70 | 137–1977 |
Actual result | — | — | — | 4400–5400 |
Therefore, an all-purpose computing method was proposed for quicksand through the borehole in this paper. The Bernoulli formula [
Longde coal mine is located in southwest of Yulin in Shaanxi province in China, and the shape of this field is similar to a pistol, as shown in Figure
Landscapes of Longde mine field.
A water inrush and quicksand disaster through a borehole happened in Longde coal mine at 14:30, September 17, 2012. A geological team undertook the construction of cable borehole for the central water pump room. The wrong statistics of drilling depth and the cable borehole directly getting into the underground space without the protection measures such as steel casing and seal ring caused immediate disappearance of the drill tower in sand seam and submergence of the water pump room by sand. Then, the central substation could not deliver electricity normally. As a result, the whole coal mine was submerged by sand.
From September 17 to September 20, although emergency measures had been taken by Longde coal mine, a lot of sand flowed into the railway, even main shaft, and auxiliary shaft, as shown in Figure
The profile after water inrush and quicksand disaster.
The total volume of the underground space was 488,000 m3 in Longde coal mine. The statistical data of sand cleaning presented that the actual volume of sand was 380,000 m3. The 77.9% volume of the underground space was submerged by sand. After the disaster, in order to protect the infrastructure such as the air shaft square, protective measures were taken; for instance, the gravity dam was set up with stones and concrete. And based on geological conditions, the sand subsidence area did not present a cone type but an irregular cone type (prismoid), as shown in Figure
Aerial view in subsidence area of aeolian sand.
The coordinate of 7 inflection points is shown in Figure
The calculation result shows that the area of aerial view is 22,019.75 m2 until 70.5 h after the disaster, but it only increases 40 m2 from 70.5 h to 238.5 h. The area percent change only increases 0.18%, which is almost negligible. Therefore, it can be confirmed that the disaster mainly happens within 70.5 h.
It is necessary to calculate the volume of sand subsidence area for the obtainment of quicksand volume. Consequently, the irregular cone type or prismoid type can be assumed for presenting the sand subsidence area based on the method in [
Test of friction coefficient.
To calculate the volume of sand subsidence area, the profile plane equation of each plane is established firstly. The uniform form of plane equation is as follows [
The plane equation parameters of each profile plane are given in Table
Parameters of plane equation.
Parameter | C1-C2 | C2-C3 | C3-C4 | C4-C5 | C5-C6 | C6-C7 | C7-C1 |
---|---|---|---|---|---|---|---|
|
0.8750 | 0.0334 | −0.0057 | −0.0019 | −0.0164 | −0.0071 | −0.3080 |
|
1.0000 | 0.0071 | 0.0099 | 0.0081 | −0.0167 | −0.0017 | 1.0000 |
|
2.1501 | 0.0552 | −0.0185 | 0.0135 | −0.0379 | 0.0118 | −2.7304 |
|
0.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.0000 |
The water level of auxiliary shaft was monitored after the disaster happened 12 h. Figure
Volume flow rate change curve of auxiliary shaft with time in Longde coal mine.
In conclusion, the volume flux of sand was between 4,400 and 5,400 m3/h, while water flow was only 37.05 m3/h. The volume flux of sand was much bigger than that of water. Consequently, it can be confirmed that the disaster of water inrush and quicksand is nearly the flow of solid particle in Longde coal mine. Jaeger et al. [
The photograph of the borehole and chamber after cleaning is shown in Figure There is aeolian sand layer with a thickness of 30 m in the ground. The lithology is silty fine sand with a distinct thickness variation. The sand seam constitutes a unified aquifer together with the Sara Wusu group aquifer below. The Sara Wusu group aquifer is the main aquifer of the coal roof. The main lithology is based on silty fine sand, medium-coarse sandstone, and loam. The units-inflow is between 0.0441 and 0.0569 L·s−1·m−1. The aquifer belongs to low water abundance aquifer, as shown in Table The borehole diameter is 325 mm in quicksand disaster, including a built-in drill pipe with the diameter of 75 mm. And the borehole and drill pipe have not been damaged in the disaster. Therefore, the cross-sectional area
Borehole and chamber photo after quicksand disaster.
Cutaway view of sediment-water flow model.
Division of water abundance level [
Water abundance level | Higher | High | Middle | Low |
---|---|---|---|---|
Units-inflow L·s−1·m−1 | >5 | 1∼5 | 0.5∼1 | <0.5 |
Before finding the methods used for quicksand in Longde coal mine, the fluid condition of sand-water mixture flow has to be judged firstly, as different formulas need to be applied for the calculation of the sand-water mixture flow in different fluid conditions. For instance, the flow is easy to obtain with an accurate analytic solution in laminar flow, while the turbulence flow is complicated, which has to be calculated by semiempirical method. The fluid condition can be judged by Reynolds number:
In general,
When the flow is in effectively smooth flow, the range of Re is
When the flow is in the transition region, the range of Re is
When the flow is in rough flow, the range of Re is
The velocity of sand-water mixture flow is calculated by viscous Bernoulli formula [
Computing model for sediment-water flow.
From the continuity equation of fluid mechanics [
For the borehole drilled with steel casing all the while, the sectional area
The head loss
In laminar flow, the equation is [
In effectively smooth flow, the equation is [
In the transition region, the equation is [
In rough flow, the equation is [
From Equations (
Put Equation (
In conclusion, the computational model diagram is drawn as Figure
Computational model diagram.
The calculating parameters are shown in Table
Parameters of semiempirical calculation.
Parameters | Density (kg/m3) | Dynamic viscosity (Pa·s) | Roughness height (mm) | Water pressure (MPa) |
---|---|---|---|---|
Value | 1652.89 | 9.25 | 0.1–0.4 | 0.187 |
The obtaining way of the roughness height in Table
Roughness height and angle of borehole [
Rock type | Roughness height (mm) | Roughness angle (°) | |
---|---|---|---|
Seol et al. | Gneiss | 1–7 | 1.1–8.0 |
Seidel and Collingwood | Claystone, sandstone | 1.7–16.2 | 1.9–18.9 |
Shale, limestone, etc. | 0.9–6.6 | 1.0–7.6 | |
Lee et al. | Granite, Gneiss | 1–4 | 1.1–4.6 |
Sandstone, andesite | 1–3.5 | 1.1–4.0 | |
Nam | Claystone | 3.6–5.3 | 4.1–6.1 |
Limestone | 3.2–3.7 | 3.7–4.2 |
Max roughness of technical standard in part country.
Country | Max roughness of technical standard (mm) | Technical standard |
---|---|---|
China | 0.4 | GB1031-83 |
USA | 0.1 | BS1134-61/ASAB46.1-62 |
Switzerland | 0.2 | VSM10321-62 |
Italy | 0.1 | UNI13963-60 |
Japan | 0.4 | JISB0601-70 |
Poland | 0. 32 | PN58/M042-51 |
The obtaining of the water pressure is as follows: there are 4 hydrological boreholes near by the position of quicksand disaster. The water level elevation is recorded aperiodically, as shown in Figure
Water level elevation of Sarah Wusu group aquifer in hydrological borehole.
From Equation (
Taking
The velocity is calculated by the simultaneous Equations (
Computing result.
Flow condition | Laminar flow | Effectively smooth flow | Transition region | Rough flow |
---|---|---|---|---|
Velocity (m/s) | 5.87 × 104 | 21.14 | 15.32–17.78 | 15.43–18.19 |
Re | 2.62 × 109 | 9.44 × 105 | 6.84 × 105–7.94 × 105 | 6.89 × 105–8.13 × 105 |
Re range | <2300 | 4000–4.23 × 104/2.01 × 105 | 4.23 × 104/2.01 × 105–2.95 × 106/1.44 × 107 | >2.95 × 106/1.44 × 107 |
Verification result | Wrong | Wrong | Right | Wrong |
As the coal roof aquifer belongs to low water abundance aquifer in Longde coal field, the sand-water mixture flow can be seen as the flow of solid particle of aeolian sand. However, there may be high or higher water abundance aquifers (Table
The density test results of different
Density of sand-water mixture change curve with volume ratio
The dynamic viscosity
Dynamic viscosity ratio change curve with sand concentration of sand-water mixture.
When
The aeolian sand is assumed sufficient in the ground. The roughness height is 0.4 mm. The values of water head height
Velocity of sand-water flow change curves with volume concentration of sand.
An all-purpose computing method was constructed with Bernoulli formula, Darcy–Weisbach formula, semiempirical Nikuradse formula, and Colebrook–White formula to calculate the volume of quicksand. The variation laws of density and dynamic viscosity under different water yield properties were analyzed based on the experimental results. The influence of water yield properties on volume flux was discussed: It can be seen that the total volume of quicksand is between 310,000 m3 and 380,000 m3, and the quicksand disaster duration is about 70.5 h from the statistical results of sand cleaning and the variation laws of sand subsidence area with time. The value of water volume flux is much less than that of sand volume flux. The sand-water mixture can be regarded as dry sand in Longde water inrush and quicksand disaster. The volume of sand between 310,000 m3 and 350,000 m3, i.e., calculated by all-purpose computing method, is contained with the actual result between 310,000 m3 and 380,000 m3. Both the density and dynamic viscosity of sand-water mixture increase with the increase of sand volume concentration. With the fixed value of water head, roughness height, and diameter of borehole, the velocity decreases with the increase of sand volume concentration, which means that the sand volume concentration will be smaller and the velocity will be faster under a higher abundance level aquifer.
The area of sand subsidence
Density
The volume concentration of sand
Volume flux
Diameter of borehole
Hydraulic radius
Head loss
Reynolds number
Frictional head loss
Cross-sectional area
Local head loss
Dynamic viscosity
Hydraulic slope
Velocity
Friction coefficient
Wetted perimeter
Roughness height
Third Cartesian coordinate of cross-sectional area
The length of circular pipe
Flow resistance ratio
Relative pressure.
The data used to support the findings of this study are included within the supplementary information files.
The authors declare that they have no conflicts of interest.
The work was supported by the National Natural Science Foundation of China (Nos. 51708185, 51778215, and 51504081) and the Doctor Foundation of Henan Polytechnic University (Nos. B2017-51 and B2017-53). The authors want to acknowledge these financial assistances.
The surface sand pit (Table 1), water volume flux (Table 2), waterline of Wusu group aquifer (Table 3), density of sand-water mixture flow (Table 4), and dynamic viscosity of sand-water mixture flow (Table 5). Previously reported data, the diameter of borehole, the diameter of drill pipe, and roughness height of borehole, were used to support this study and are available at doi: 10.1007/s10064-014-0714-5 and doi: 10.1016/j.ijrmms. 2007. 09.008. These prior studies are cited at relevant places within the text as references [