J. Cent. South Univ. (2020) 27: 1320-1333

DOI: https://doi.org/10.1007/s11771-020-4369-z

Fractal evolution mechanism of rock fracture in undersea metal mining

LIU Zhi-xiang(刘志祥)¹, HAN Ke-wen(韩科文)¹, YANG Shan(杨珊)¹, LIU Yu-xi(刘雨曦)^{1, 2}

1. School of Resources and Safety Engineering, Central South University, Changsha 410083, China;

2. Engineering Faculty, Monash University, Melbourne 3800, Australia

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: Through rock mechanics test, similar simulation experiment, borehole photographic observation of rock fissure, numerical simulation calculation of plastic zone distribution and deformation monitoring of rock mass during undersea mining, the fractal evolution mechanisms of rock fracture in undersea metallic deposits of Sanshandao Gold Mine were studied by fractal theory. The experimental researches on granite mechanics test in undersea deposit indicate that with the increase of load, the granite deformation energy and the fractal dimension of acoustic emission (FDAE) increase gradually. However, after reaching the peak stress of specimen, the fractal dimensions of acoustic emission (FDAEs) decrease and the granite specimen fails. Therefore, the fractal dimension evolution of rock failure can be divided into four stages, which are fissure inoculation stage, fissure growth stage, fissure expansion stage and fracture instability stage, respectively. By calculating and analyzing the damage photographs of rock specimens in Sanshandao Gold Mine, the fractal dimension of rock fissure is 1.4514, which is close to the average value of FDAE during granite destruction, i.e., 1.4693. Similar simulation experiments of undersea mining show that with the excavation proceeding, the FDAE in rock stratum increases gradually, and when the thickness of the isolation roof is less than 40 m, the FDAE begins to decrease, and meanwhile the sign of water inrush emerges. The numerical simulation researches on the plastic zone distribution of undersea mining in Sanshandao Gold Mine indicate that the fractal dimension of plastic zone (FDPZ) where the failure characteristics occur is 1.4598, close to the result of similar simulation experiment of 1.4364, which shows the sign of water inrush. Meanwhile, the thickness of the isolation roof for undersea mining should be more than 40 m, which is consistent with the results of similar simulation experiment. In Sanshandao Gold Mine, the rock fissures in undersea mining were observed by borehole photography and the rock mass deformation was monitored by multi-point displacement meters, and at the same time the fractal dimensions of strata borehole fissure distribution and energy release ratio (ERR) of rock mass were calculated by fractal principle, which are 1.2328 and 1.2685, respectively. The results demonstrate that rock deformation and fissure propagation are both in the second stage of fissure growth, and have not reached the fourth stage of fracture instability. Therefore, the conclusion can be obtained that the undersea mining in Sanshandao Gold Mine is safe at present.

Key words: undersea mining of metal deposit; evolution of rock fracture; fractal theory; energy of rock failure

Cite this article as: LIU Zhi-xiang, HAN Ke-wen, YANG Shan, LIU Yu-xi. Fractal evolution mechanism of rock fracture in undersea metal mining [J]. Journal of Central South University, 2020, 27(4): 1320-1333. DOI: https://doi.org/10.1007/s11771-020-4369-z.

1 Introduction

After more than 60 years of high-intensity mining, as the surface and shallow metal mineral resources have been exhausted, the mining cost of deep metal mineral resources is increasing gradually. The coastal and undersea resources will be regarded as a new direction of China’s metallic resources exploitation. The undersea metal deposits have their unique characteristics, such as thick ore body, complex genesis and deep burial depth, especially the below-sea-level mining sites, so the mining method is quite different from that of land resources. Moreover, because the undersea metallic deposits are mostly thick ore body with steep dip, undersea mining also has the following difficulties. Firstly, the mining location must be in the same area for many years, and the stress field will change constantly during the process of undersea mining; Secondly, the overburden strata will constantly deform and subside, and the joints and fissures in the strata will expand. Thirdly, the elastic and fractured zones in undersea stratum will constantly change, so the undersea stratum may be destroyed. If the strata movement in undersea mining can’t be effectively controlled, the fractured zone will penetrate the seawater, and a large number of water inrushes will occur. Furthermore, serious safety accidents of pit destruction and human death may take place.

At present, scholars at home and abroad have done a lot of researches on the water-inrush disaster in mineral deposit mining [1-7]. DING et al [8] studied the water-inrush effect of the fault zone under the excavation in undersea ore body. CHEN et al [9] established the geo-mechanics model in Sanshandao Gold Mine according to the similarity theory, and studied the mechanism of water inrush induced by fissure seepage of stope roof in undersea mining. MA et al [10] analyzed the possible failure forms of anti-outburst structure of F1 fault in Xinli mining area of Sanshandao Gold Mine. HU et al [11] established a 5-level assessment system for vulnerability of mine water-inrush channel which could carry on the early warning analysis for the mine inrush disaster. Besides the above achievements, in order to study the mechanism of water inrush more intuitively, many scholars have carried out numerical simulation on the process of mine water inrush. YAO et al [12] established a multi-field coupling mechanical model of deformation-seepage-erosion to reveal the water inrush mechanism of coal mine collapse column, and theoretical basis for prevention of water-inrush was provided. GOLIAN et al [13] used MODFLOW code of GMS software to predict inflow rate as the tunnel boring machine gradually advances. LI et al [14] established the dynamic simulation model of fracture evolution in the process of mine water inrush. HUANG et al [15] studied the variation characteristics of stress field and seepage field in Dongtan Coal Mine with the numerical calculation software FLAC^3D and revealed the mechanism of water inrush by simulating the whole process of water inrush around the collapse column. WILDEMEERSCH et al [16] simulated the formation of water-inrush channels caused by the coupling effect of water pressure in the mining process. Taking Sima Coal Mine as the engineering background, WANG et al [17] analyzed the water inrush of hidden depressed column in the confined coal seam under the fluid-solid coupled interaction. All of the above studies indicated that the expansion of original fractures led by the perturbation of mining operations is the main cause of water inrush in the ore body.

In order to study the complex mechanical process of fracture evolution in rock mass, the fractal and chaotic theories are adopted by scholars from home and aboard. XIE et al [18] applied fractal geometry theory to study the self-similarity distribution laws of mining-induced rock mass fracture, which shows that the fractal dimension of fracture can be used to characterize the fracture development law and fracture network evolution law of mining rock mass. ZHOU et al [19] established the relationship between rock damage variable and fractal dimension based on the fractal geometry theory, which indicates that rock quality can be judged by fractal dimension. ZHANG et al [20] studied the fractal laws of rock mass fracture evolution in goaf caving zone, fracture zone and sinkhole zone. YU et al [21] considered the relationships between the evolution of stress state, mechanical properties and chemical properties in the deformation of rock mass with the fractal dimension values, and revealed the fractal property as well as the chaotic characteristics in the dynamic evolution of rock mass. SUN et al [22] carried out the uniaxial compression and acoustic (AE) tests on two common rock samples with strong rock burst tendency, and got different fractal dimension evolution modes, which provides theoretical guidance for the safety of underground engineering. SONG et al [23] quantitatively analyzed the evolution laws of overlying strata fissures in mining and post-mining process with fractal theory. XU [24] studied the dynamic evolution of fractal dimension between mining-induced rock fissures with the different mining width using non-linear fractal geometry. ZHU et al [25] studied the fragmentation evolution and fractal characteristics of deep coalbed rocks that were subjected to underground pressure. FENG et al [26] set up a formula about fractal dimension of mining-induced fractures and mining depth in high-dip coal seam. They also established the relationship between percolation probability and mining depth, and realized the quantitative description of the fractures’ evolution. LI et al [27] proposed a new strategy and mining mode which can be “convert harm into benefit” for the deep rare, valuable and strategic resources exploitation. GIRI et al [28] researched the fractal evolution of pore and fracture propagation in rock mass during the process of rock subsidence. In summary, the above results indicate that the fractal theory can be applied to studying the evolution laws of complex fissures in rock mass.

Based on the mining experiences at home and abroad, during the process of mining in the steeply inclined thick ore body, the overlying strata are constantly disturbed, and thus the fissure evolution and water-inrush mechanism in undersea metal mining are very complex. However, the fractal and chaos theories provide a new idea to study the mechanism of fissures seepage evolution and water inrush. According to the mining characteristics of metal deposit, by using similar simulation experiment, fractal and chaos theory, fluid-solid coupling numerical analysis method and mechanical model establishment, the deformation and fissure evolution of overburden stratum were analyzed, and the laws of energy dissipation in the undersea mining were also researched. Moreover, the water- inrush mechanisms in undersea mining were revealed, and the theoretical basis for safely mining in metallic deposits was also provided.

2 Calculation principle of fractal dimension

2.1 Fractal dimension calculation principle of rock fracture evolution

In 1967, MANDELBROT proposed the fractal theory [29]. Self-similarity and fractal dimension are the basic characteristics of the fractal theory. To be more specific, fractal dimension quantitatively describes the degree of self-similarity and irregularity of fractal structure. In the traditional Euclidean geometric space, the dimensions of point, line, square and cube are 0, 1, 2 and 3, respectively, while the object’s fractal dimension is not necessarily an integer, but a fraction. For example, calculated by Hack, the fractal dimension between the length of main river courses and their area of river basins in the Northeast United States is 1.22, and the fractal dimension between the number of American rivers and their average length is 1.83, and the fractal dimension of the British coastline is 1.4, calculated by Mandelbrot. It can be inferred that the self-similarity and fractal dimension could also be applied to researching the failure mechanism of rock. In the process of rock deformation and failure, as the evolution of main fractures is accompanied by the development of micro and secondary fissures and these fissures are just like the main stream and tributary of a river, the evolutionary distributions of rock fissures can be identified to be fractal. Therefore, the fractal dimension of fissure propagations in plane or space can be calculated by the box dimension theory.

The calculation principle of box dimension is shown as follows.

Let (A, ε) be a metric space, and set ε to be a non-negative real number. Assume A(x, ε) to be a closed sphere with a center x and radius ε, and create a non-empty compact set A in X. For each positive ε, let N(A, ε) denote the minimum number of closed spheres covering A [30], that is:

N(A, ε)≈Cε^-D                                  (1)

where ε and C are constant. Then the box dimension of A is:

D≈                       (2)

Let ε_n=Crⁿ, where r is the side length of box, then:

D=                        (3)

Let N_n(A) be the number of boxes intersecting A, and the side length of box is 1/2ⁿ, then:

D=　　　　　　　　　　　　　(4)

In engineering practice, calculate the value of ln(2ⁿ) and lnN_n(A) by counting the box number with different sizes, where n ranges from 1, 2, 3, …, N sequentially, and draw the graph with ln(2ⁿ) as abscissa and lnN_n(A) as ordinate respectively. Do linear regression based on the graph, with the box dimension D shown as the slope of the straight line.

2.2 Fractal dimension of acoustic emission and rock deformation

In the failure process, rock failure is accompanied by acoustic emission, and its characteristic parameters include rock audio frequency, large event frequency and energy efficiency, while in the deformation process, rock deformation is accompanied by energy release, and its characteristic parameter is the energy release ratio (ERR). All the parameters of AE or ERR are time-series parameters. Let the time series of these parameters be x₁, x₂, x₃, …, x_n, and reconstruct the phase space Y_j with the time interval p=△t:

Y_j=(x_j, x_j+p, x_j+2p, …, x_j+(m-1)), j=1, …, m       (5)

where m is the embedding dimension of reconstructed phase space.

After reconstructing the phase space of AE or ERR parameters, the new trajectories are generated, and thus the correlation dimension of the time series can be obtained according to the associated characteristics of the phase points. Assuming that the number of the m dimensional vectors Y_j is N, set an arbitrary decimal ε, and calculate the proximal point distance |Y_i-Y_j| in the phase space. The ratio of the number of neighboring point distances less than ε to N² is denoted as C(ε):

                (6)

where θ is the Heaviside function.

According to Eq. (6), the curve about lnC(ε) and lnε can be drawn, and the curve slope of linear part is the correlation dimension D of time series. As can be seen from the curve, when the embedding dimension of m is small, the correlation dimension increases as m increases. But fractal dimension tends to be stable with little or no change while m approaches to the saturated embedding dimension, and D in this condition is the fractal dimension.

3 Fractal evolution and energy dissipation characteristics of granite fracture

Sanshandao Gold Mine is the first gold mine implementing undersea mining in China, and its rock type of ore body is granite. In order to study the mechanical properties in the undersea deposits, using granite samples taken from the ore body in Sanshandao Gold Mine, a large number of experiments have been completed. Testing press apparatus was the INSTRON electro-hydraulic machine (shown in Figure 1), and the performance parameters of the maximum load, loading speed, loading grid and displacement grid were 2000 kN,4 mm/800 s, 5 kN/grid and 0.02 mm/grid, respectively. SE310 AE instrument and DH-5932 datum acquisition recorder were applied to testing AE and dynamic strain (shown in Figure 2). The sizes of the sample were 5 cm×5 cm×5 cm (shown in Figure 3(a)). Additionally, the mechanical parameters of granite are obtained that the density,the compressive strength, the elastic modulus and the Poisson ratio are 2.71 g/cm³, 119.52 MPa,8.26 GPa and 0.19, respectively.

Figure 1 INSTRON test machine

Figure 2 Data acquisition system

Figure 3 Rock sample (a) and fissure distribution (b)

Meanwhile, the stress-strain and AE event rate of sample are obtained by using strain gauge and AE probe (shown in Figure 4). According to the testing results, under the condition that the strain rates are 0.001, 0.002, 0.003, …, 0.007, respectively, and the deformation energy values of per unit volume rock, also called specific energy, are 0.0085, 0.0365, 0.0855, 0.158, 0.255, 0.354 and 0.431 MJ/m³, respectively. Based on the calculation principle of the fractal dimensions of acoustic emission (FDAEs), the FDAEs in the above strain rate stages are 1.165, 1.191, 1.286, 1.365, 1.493, 1.543 and 1.372, respectively. Thus, the specific energy and the fractal dimension in each stage are shown in Figure 5.

These results indicate that with the increases of load, the deformation of granite specimen, the specific energy, the AE event rate and the FDAE all increase gradually. When the load exceeds 119.6 MPa, the bearing capacity of rock specimen, the specific energy and the FDAE decrease gradually, which demonstrates that the fissures begin to expand and the sample fails.

Figure 4 Stress-strain and AE curve

Figure 5 Specific energy and fractal dimension evolution

Analyzing the evolution of the fractal dimension of AE from rock tests (Figure 5), the failure processes of rock can be divided into the following four stages.

Stage I is the fissure inoculation stage. Under the compression condition, the original pores in specimen are compacted, and micro-cracks are incubated and generated, meanwhile the curve slope of FDAE in this stage is gentle.

Stage II is the fissure growth stage. With the increased pressure adding continuously on the rock sample, the energy storages in rock specimen gradually increase, and the internal grains in the rock begin to slip; at the same time, cracks in the specimen begin to grow from micro to macro. Additionally, the curve slope of FDAE begins to increase.

Stage III is the fissure expansion stage. With the further increase of load, the macro cracks in the rock specimen begin to expand. At this stage, rock cracks in the sample are not yet interconnected, and the plastic phenomena in the specimen occur. Meanwhile the curve slope of FDAE becomes steeper significantly.

Stage IV is the fracture instability stage. When the pressure reaches peak load, the fissures in the rock specimen continuously extend and widen. At this stage, with the fissures being interconnected, the FDAEs reach the peak; when destruction characteristics appears in the rock specimen, the FDAEs start to show a downward trend.

According to the fracture photographs of the damaged rock specimen, the fissures distribution is depicted as shown in Figure 3(b). Using the calculation principle of box dimension, the specimen sizes are 5 cm×5 cm, covering a 5 cm range photo with 2.5 mm grid, and the fissures occupy 79 grids. In the same way, covering the photo with grid of 1.25, 0.625 and 0.3125 mm, the number of grids occupied by fissures are 219, 578 and 1635, respectively. Do linear regression analysis for the data, and the regression equation is y=1.4514x+ 0.0223, while the regression coefficient is R²=0.9974 (shown in Figure 6). The fractal dimension of fissure distribution in the granite specimen is 1.4514, which is close to the average value of FDAE of rock destruction, 1.4693.

Figure 6 Fractal dimension regression analysis

4 FDAE evolution in undersea mining by similar simulation test

4.1 Similar simulation experiment in undersea mining

A similar simulation test platform was developed to simulate the undersea deposit mining in Sanshandao Gold Mine. The similar simulation test system consists of a test-bed, hydraulic pump station, vertical and horizontal pressure loading devices, top water pressure loading equipment and measuring apparatus, etc. The completed test system is shown in Figure 7. The main technical indexes are the maximum vertical load of 300 kN, the maximum horizontal load of 300 kN, the maximum hydraulic load of 1.0 MPa, horizontal displacement of 0-100 mm, and model sizes of 1600 mm×800 mm×200 mm (length×height× width).

Figure 7 Similar simulation test system

In the simulation experiment, using paraffin as the cementing agent, adopting barite powder and riversand as aggregate, and the design similarity ratio is 1:100. Through the trial mixture and strength testing, when the mass ratio of the cementing agent (paraffin) to aggregate (barite powder and river sand) is 1:4.3:5.6 and the solid-liquid ratio reaches 1:0.75, the mechanical properties of the model accord with the designing similar ratio of 1:100. In this case, the material strength and the elastic modulus are 1.19 and 75 MPa. Moreover, the sizes of the simulation test model are 1595 mm×795 mm×195 mm (length× height×width), slightly less than the size of the model. In order to obtain the mechanical data of model in the excavation process during undersea mining, DH3816 type static strain testing system and PCI-2 type AE monitoring system are applied, and the arrangement of AE sensors and strain gauges is shown in Figure 8.

The undersea metal deposit in Sanshandao Gold Mine is mined under 10 m sea level and 35 m sea mud. Considering this condition, in order to suit the similarity ratio of design, set the water pressure to 1150 Pa and the vertical load to 8185 Pa at the top of the model. The whole mining processes are completed in ten steps, and the excavation is carried out from the middle to both sides with the width of 0.04 m. When the excavation span is over 0.4 m, the interconnection cracks in the roof lead to water inrush, as shown in Figure 9.

Figure 8 Arrangement of AE probe and strain gauge

4.2 FDAE and fissures evolution in undersea metal deposits mining

Through similar simulation test in undersea mining, the AE energy evolution of the model was obtained, as shown in Figure 10. According to the calculation principle of FDAE, the FDAEs in the seven stages (from step 3 to 10) are 1.185, 1.213, 1.252, 1.317, 1.476, 1.518 and 1.345, respectively. The results indicate that with the mining going, the AE signals in the central of the roof and their FDAEs increase continuously, and the expanded fissures are caused by excavation. When the width of excavation reaches to 0.4 m, the AE events tend to increase sharply, and the crack propagates rapidly, meanwhile the FDAEs begin to decrease, showing signs of water inrush.

Analyzing Figure 10, in the early stage, the FDAEs are gradually rising during the similar simulation experiment in undersea mining. But in later stage, the FDAEs will reduce if the fissures interconnect, and the characteristics of water inrush occur. These phenomena are the same as the evolution characteristics of FDAE in granite test, and there are also four stages: fissure inoculation stage, fissure growth stage, fissure expansion stage and fracture instability stage, as shown in Figure 10.

According to the photo and sketch of fissures (Figures 11(a) and (b)) in the similar simulation test, the original sizes of photo are 10 cm×10 cm. By the same principle of box dimension, covering the photo with different precision grids again, using grids with precision of 1.0, 0.5, 0.25 and 0.125 cm in turn, the numbers of grids occupied by fissures are 28, 75, 208 and 556, correspondingly. Regressive analyzing the data, the regression equation is y=1.4364x+0.0254, and the regression coefficient is R²=0.9965 (Figure 12). Therefore, the fractal dimension of fissure is 1.4364, which is close to the fractal dimension of the granite failure, 1.4514, and the status is in the fourth stage (fracture instability stage).

Figure 9 Fissure water flowing meso-process map

Figure 10 AE and fractal dimension of similarity simulation test

Figure 11 Fissures observation diagram (a) and description (b) of similar simulation test rock fissures

Figure 12 Fractal dimension regression in similar simulated tests

Based on the results of similar simulation test that in the roof strata water inrush occurs when the excavation width reaches 0.4 m, the safe height of roof can be calculated by the formula of thickness-span ratio:

H≥0.5RnW                              (7)

where H, R, n and W are the safe height of roof, the similarity ratio of simulation test, safety factor and the stope span, respectively.

Set n as 2.0 and R as 100, and calculate H by Eq. (7), and then we obtain H=40 m.

In conclusion, the calculating results show that when the safe thickness of roof is less than 40 m, water inrush in the roof strata will take place in Sanshandao Gold Mine of undersea mining.

5 Borehole observation and fractal analysis of rock fissures in undersea mining

At the -165 m horizontal tunnel in Xinli mining area of Sanshandao Gold Mine, using borehole camera to observe the fissures of undersea strata, the drilling observation images in the range of 0 to 18 m are shown in Figure 13, and the fissure distributions are depicted in Figure 14.

In the same way, by the calculation principle of box dimension, supposing that the original borehole image sizes are 2.0 m×2.0 m in Figure 14, covering Figure 14 at the grids with the precision of 0.2, 0.1, 0.05 and 0.025 m in turn, the numbers of grids occupied by fissure are 91, 225, 524 and 1277 correspondingly. Regression analyzing by Eq.(4),the regression equation is y=1.2685x+ 1.5903, and the regression coefficient is R²=0.9888 (shown in Figure 15). Thus, the regression results reflect that the fractal dimension of fissures is 1.2685, and the failure feature of undersea strata is in the second stage of fissure growth, which indicates that the current mining in Sanshandao Gold Mine is safe.

Figure 13 Borehole observation of rock fissures in undersea mining (m)

Figure 14 Distribution of rock fissures in undersea mining

6 FDPZ in undersea mining

According to the conditions of undersea mining in Sanshandao Gold Mine, the point-column mechanized horizontal slicing and filling mining method is adopted to mining ore body above -165 m. The point column sizes in cross section are 4 m×4 m, and the spacing of point pillars is 12 m along the ore body inclination, also 12 m along the ore body strike. The length of panel mining is 100 m, and the continuous pillars of 5 m width are set with the interval of 100 m. Furthermore, the numerical calculation model established by FLAC^3D program is shown in Figure 16, and the mechanical parameters applied in the numerical simulation are listed in Table 1.

Figure 15 Fractal dimension regression analysis of rock fractures

Additionally, in the model of numerical simulation calculation, undersea mining in Sanshandao Gold Mine starts from the level of -115 m, and layered upward mining height is 10 m, meanwhile the filling is carried out immediately after mining. In this case, there are five steps in total; the ranges of each step are from -115 to -105 m, -105 to -95 m, -95 to -85 m, -85 to -75 m and -75 to -65 m, respectively.

Analyzing the results of numerical simulation of undersea deposits mining in Sanshandao Gold Mine, in the mining area, there are some sporadic plastic zones caused by tensile or shear during mining at the level of -115 to -105 m, which occurred in the first mining step. In the second mining step at the level of -105 to -95 m, the plastic zones in the mining numerical model are enlarged and distributed sporadically. After the third mining step at the level of -95 to -85　m, the plastic zones are further expanded, and still do not interconnect. But in the fourth mining step at the level of -85 to -75 m, the ranges of the zone continue to increase and some of them are interconnected. Furthermore, after the fifth mining step at the level of -75 to -65 m, the significantly increased plastic zones are interconnected, which indicates that the micro and macro fissures extend and finally interpenetrate with each other, and the channels of sea water inrush in the undersea rock strata are formed. The distributions of plastic zone in step 2 to 5 are shown in Figure 17.

Figure 16 Numerical simulation model in undersea mining

According to the distributions of plastic zone in Figure 17, and by the same calculation principle of box dimension, the fractal dimensions of the plastic zone (FDPZs) in the above second to fifth mining step are shown in Figure 18.

By comparing the FDAEs of granite test (shown in Figure 5) with the FDAEs of similar simulation test (shown in Figure 10) and the FDPZs in numerical simulation calculation (shown in Figure 18), the following conclusion can be obtained. In the second mining step at the level of -105 to -95 m, the FDPZ is 1.2237, and the status of undersea rock stratum is in the second stage of fissure growth. Furthermore, in the third mining step at the level of -95 to -85 m, the FDPZ is 1.2712, and the status of undersea rock stratum is in the third stage of fissure expansion. Meanwhile, the undersea stratum is stable. However, in the fourth and fifth mining steps at the level of -85 to -65 m, the FDPZs reach 1.4598 and 1.5053, respectively, and the status of undersea strata is in the fourth stage which is fracture instable. At the same time, the undersea strata fails and water inrush characteristics appear.

Table 1 Mechanical parameters of rock mass and backfill body

Figure 17 Distribution of plastic zone of undersea mining in mining steps:

Figure 18 Fractal dimension evolution of plastic zone in undersea mining

The results of numerical simulation reflect that it is reasonable to mine the highest level of -85 m in Xinli mining area of Sanshandao Gold Mine, and the safety thickness of isolation roof should be more than 40 m, which accords with the results of similar simulation test.

7 Deformation monitoring of undersea rock stratum and fractal characteristics of ERR

To study the laws of rock strata deformation in undersea mining of Sanshandao Gold Mine, multi-point displacement meters were installed on the exploration lines of 55, 63 and 71 at -165 m level of Xinli mining area, as shown in Figure 19. The convergence signals of rock mass displacement were collected by a reading instrument, and signal data were transmitted to the computer. It should be noticed that the deformation data of monitoring point 2 are the most representative, as shown in Figure 20.

The maximum deformation of monitoring point 2 within 221 d is 31.28 mm. Thus, the deformation specific energy of rock mass in undersea mining can be calculated as follows:

                              (8)

where U is the specific energy of rock mass deformation, also called ERR, MJ/m³; E_R is rock elastic modulus, MPa; ε is the deformation of unit length in stratum.

Figure 19 Installation location plan of multi-point displacement meters in Xinli mining area

Figure 20 Deformation curve of monitoring point 2 during undersea mining

According to mechanical parameters of rock mass in Sanshandao Gold Mine listed in Table 1, the elastic modulus of ore body is 5510 MPa. Using the monitoring data in Figure 20, and calculating by Eq. (8), the ERRs of rock mass deformation in different stages are shown in Figure 21. Comparing Figure 20 with Figure 21, it can be seen that the ERR curve and deformation curve of rock strata have similar change processes.

Based on the calculating principle of fractal dimension of rock deformation, the analyzing processes of correlative dimension of stratum ERR are shown in Figure 22, where C_m(r) is the value of correlation integral when r>0.

Figure 21 ERR curve of rock formation at monitoring point 2

Figure 22 Calculated correlation dimension of ERR (curve 1: m=2, D=0.5613; curve 2: m=3, D=0.9217; curve 3: m=4, D=1.2328; curve 4: m=5, D=1.2681; curve 5: m=6, D=1.2909)

Analyzing Figure 22, the correlation dimension of ERR has little change when m is greater than 4, thus the saturated embedding dimension of ERR is 4 and the correlation dimension of ERR is 1.2328. Comparing the FDAE of granite test (shown in Figure 5), it can be deduced that the status of undersea strata is in the second stage of fissure growth, and the undersea mining in Sanshandao Gold Mine is safe at present.

8 Conclusions

1) The results of the granite mechanics experiment indicate that with the increase of load, both the FDAE and specific energy of specimens increase. When the specimen is loaded to 119.6 MPa, the fissures extend and interconnect, and the FDAE and the slope of specific energy gradually reduce. Meanwhile the specimen shows failure characteristics. Furthermore, the evolution processes of rock failure can be divided into four stages, which are fissure inoculation stage, fissure growth stage, fissure expansion stage and fracture instability stage, respectively.

2) A similar simulation experiment platform was established for undersea mining, and the similar simulation test with the similarity ratio of 1:100 was conducted. The results of the similar simulation experiment show that with the excavation proceeding, the AE signals in rock strata enhance and the FDAEs increase. But when the excavation width reaches 0.4 m, series abnormal signs of water inrush are emerged; at the same time, AE events increase sharply, cracks grow rapidly, and FDAEs begin to decrease. As the same as the granite mechanics experiment, there are also four stages in fractal dimension evolution. Therefore, the maximum width of excavation span should be less than 0.4 m in the similar simulation experiment. Additionally, it can be concluded that the safe thickness of roof should be more than 40 m in undersea mining of Sanshandao Gold Mine.

3) The results of numerical simulation established by FLAC^3D program reflect that when the mining height exceeds the level of -85 m, the FDPZ reaches 1.4598, and the status of undersea rock stratum is in the fourth stage, fracture instability, with the water inrush characteristics appearing. Thus, it is reasonable to mine to -85 m level in Xinli mining area of Sanshandao Gold Mine, and the thickness of safety isolation layer must be more than 40 m, which is consistent with the experiment results of similar simulation in undersea mining.

4) In Sanshandao Gold Mine, the fractal dimensions of the borehole camera observation and the ERR of deformation monitoring are 1.2685 and 1.2328, respectively. The results indicate that the statuses of undersea mining strata are both in the second stage of fissure growth, and have not yet reached the fourth stage (fracture instability stage). Therefore, the current mining operation in Sanshandao Gold Mine can be identified to be safe at present.

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(Edited by ZHENG Yu-tong)

中文导读

金属矿海底开采岩层裂隙的分形演化机理

摘要：本文通过三山岛金矿海底金属矿床开采岩石力学测试、相似模拟试验、岩层裂隙钻孔摄像观测、塑性区分布数值模拟计算和岩层变形监测，研究了金属矿海底开采岩层裂隙的分形演化机理。海底矿床花岗岩力学试验结果显示，随着载荷的增大，岩石变形能逐渐增大，声发射事件分形维数逐渐升高，达到峰值应力后，岩石声发射事件分形维数开始降低，破坏特征显现；岩石破坏分形维数演化分为四个阶段：裂隙孕育阶段、裂隙发育阶段、裂隙扩展阶段和破裂失稳阶段；计算得出花岗岩破坏裂隙分形维数为1.4514，与岩石声发射在破坏附近的平均分形维数1.4693相近。海底开采相似模拟试验结果表明，随着开挖的进行，岩层声发射分形维数逐渐增大，当顶板岩层安全厚度小于40 m后，声发射分形维数开始降低，呈现突水征兆。通过三山岛金矿海底开采塑性区分布数值的模拟得出，出现破坏特征的塑性区分布分维数为1.4598，与相似模拟试验呈现突水特征的裂隙分形维数1.4364相近，三山岛金矿海底开采安全隔离层厚度需40 m以上，验证了海底开采相似模拟试验结果。三山岛金矿海底开采岩层裂隙钻孔摄像和岩层变形多点位移计监测结果显示，岩层钻孔摄像裂隙分布和岩层变形能量释放的分形维数分别为1.2685和1.2328，表明岩层变形与裂隙扩展均处于裂隙发育的第二阶段，岩层裂隙扩展与变形未达到破坏失稳的第四阶段，三山岛金矿目前开采是安全的。

关键词：海底金属矿开采；岩层裂隙演化；分形理论；岩石破坏能量

Foundation item: Project(2019sdzy05) supported by the Major Scientific and Technological Innovation Project of Shandong Province, China; Projects(51674288, 51974359) supported by the National Natural Science Foundation of China

Received date: 2019-12-21; Accepted date: 2020-03-23

Corresponding author: YANG Shan, PhD, Associate Professor; Tel: +86-13975890427; E-mail: yangshan@csu.edu.cn; ORCID: 0000- 0002-8249-0183