Home Mining reasonable distance of horizontal concave slope based on variable scale chaotic algorithms
Article Open Access

Mining reasonable distance of horizontal concave slope based on variable scale chaotic algorithms

  • Shuzhao Chen , Tao Shang EMAIL logo and Liu Han
Published/Copyright: December 3, 2020
Download Article (PDF)
Open Physics
From the journal Open Physics Volume 18 Issue 1

Abstract

Horizontal concave slope structure is a common mining structure. It is the basis of mining safety to grasp the reasonable mining distance of horizontal concave slope. Therefore, based on variable scale chaotic algorithm, the reasonable mining distance of horizontal concave slope is studied. The safety factor is used to describe the reliability of the slope. When the slope is in a reliable state, it is a reasonable mining distance. Based on the Warehouse–Mohr strength theory, the four key parameters of rock cohesion and internal friction angle of horizontal concave slope and major and minor stress of element nodes are considered. The similarity of mining safety factor of horizontal concave slope is measured and the objective function is constructed. The target is searched based on variable-scale chaotic algorithm. The output result is the optimal solution of reasonable mining distance for horizontal concave slope. The experimental study shows that the reasonable mining distance of horizontal concave slope can be obtained effectively based on variable scale chaotic algorithm, and the slope height and slope angle are inversely proportional to the mining reliability of horizontal concave slope.

Keywords: variable scale; chaotic algorithm; level; concave slope; mining; reasonable distance

1 Introduction

For open-pit mines, in order to expose ore bodies, the overlying strata of ore bodies need to be separated by layers, so that the open-pit-stope presents a large pit with a diameter of several kilometers. From the surface of the pit to the ore body in the pit, the terrain decreases gradually in the form of steps, forming a slope [1,2]. If the intersection line between the slope surface and the horizontal plane is approximately linear it is called a straight slope. If the intersection line is curved and the center of curvature is inside the stope, then the slope is called concave slope, and the concave slope in the open-pit-stope is widespread. Slow slope leads to a significant increase in production costs of open-pit mining, and over-limit slope is liable to cause slope collapse [3]. The reliability of slope in open pit mining is an important factor related to economic benefit and safe production. Flat slope structure is the basic slope form of open-pit mine with zonal mining. Good engineering effect has been achieved in field application, and it shows remarkable performance in open-pit mine with zonal mining [4,5]. For metal open-pit mines, mineral resources and stripped materials have no obvious stratified interface, the occurrence state is mostly concentrated block distribution, and the burial depth is large. Therefore, the stopes formed by mining are mostly deep concave circular and elliptical structure, and the slope projection is concave in the water level. At the same time, the engineering experience shows that the reliability of the straight structure slope and the horizontal concave slope are quite different.

The stability of horizontal concave mining slope has been studied for a long time [6]. In the early stage, only soil was taken as the object of study. The research method of semi-empirical and semi-theoretical properties based on material mechanics and simple homogeneous elasticity and elastoplastic theory was mainly considered. Because the assumption of shear and tensile damage is unreasonable, this method was applied to the stability study of rock slope, and the calculation results were obtained. The results are quite different from the actual situation [7,8]. With the rapid improvement of computer level and the progress of research on mechanical properties of rock mass, various complex numerical methods are widely used in the study of horizontal concave slope [9,10,11]. The commonly used numerical methods include perfect limit equilibrium method, block theory, finite element method, boundary element method, discrete element method and various coupling calculation methods. Since the 1980s, more theories and methods related to modern science, such as systematic methods, fuzzy mathematics, grey theory, information theory, and numerical modeling, have been used to study the stability of horizontal concave slopes. The combination of numerical calculation and reliability method, grid theory, dynamic programming principle and stochastic fuzzy finite element method can make the results of slope stability calculation more reasonable and close to reality. In this paper, finite element numerical simulation and variable-scale mixing algorithm are combined to study the reasonable mining distance of horizontal concave slope. Chaotic variables generated by logistic are selected to optimize the search, which has the advantage of high search accuracy. The reliability of horizontal concave slope is affected by slope height, slope angle, strength of soil-like material, bending degree of slope, etc. [12,13]. However, there is no unified quantitative conclusion on the reliability of horizontal concave slope due to the redundancy of slope. In the experimental study, the influence of slope height and slope angle on mining reliability of horizontal concave slope is studied in detail, and then the influence of slope height and slope angle on reasonable mining distance of slope is obtained.

2 Application theories of algorithms

2.1 Mining reasonable distance model of horizontal concave slope

2.1.1 Construction of finite element model

Since the development of finite element method in the 1950s, it has become a powerful tool for solving complex geotechnical engineering problems, and is increasingly adopted by the engineering community [14,15]. When researching the reasonable mining distance of horizontal concave slope, a homogeneous isotropic hexahedron model of 2,400 m × 2,400 m × 1,000 m was established by using ALGOR software to simulate circular excavation stope. The central part of the model is a simulated open pit 240 m deep from the surface. At the bottom of the pit is a circular stope with an excavation radius of 50 m, and the slope angle of the whole horizontal concave open pit is 50°. The mechanical parameters of the model take the mechanical parameters of marble, and the simulation figure is shown in Figure 1.

Figure 1 Stereoscopic view of finite element simulation.
Figure 1

Stereoscopic view of finite element simulation.

The mining model of horizontal concave slope has 29,894 nodes and 29,894 elements. There are six free surfaces in the model. The Z direction represents the vertical direction and the X and Y directions represent the horizontal direction, respectively. The boundary conditions of the model consider that X, Y, and Z directions, respectively, restrict three rotational degrees of freedom and one translational degree of freedom of the corresponding direction. The in situ stress of the model is considered with both force and restraint. The magnitude of the in situ stress is derived from the measured in situ stress value of a smelting iron ore. According to the measured law of horizontal in situ stress increasing with depth, the value of in situ stress in simulation calculation is as follows:

(1) σ h maj = 1.5 + 0.57 H

(2) σ h min = 0 + 0.032 H

(3) σ v = γ ⋅ H

In the formula (3), γ denotes the bulk density of rock mass (MN/m3), H denotes the depth of rock mass (m), and σ v representative stress reliability coefficient.

According to the simulation results, the stress magnitude of the joints on the horizontal concave slope can be obtained, and then the reliability analysis of the stress of these joints can be carried out to evaluate the stability of the whole slope mining.

2.1.2 Rational distance and reliability analysis of slope mining

When the mining of horizontal concave slope is in a reliable state, it is in a reasonable mining distance. Structural reliability refers to the probability that the structure completes the predetermined function in the prescribed time and condition [16,17,18]. It is a probability measure of structural reliability. At present, in horizontal concave slope engineering, reliability has the following three scales: stability probability (also known as reliability or reliability probability), failure probability (or called unreliability, unreliable probability), and reliability index. The most commonly used are reliability index and failure probability. A certain relationship exists between these three scales. Reliability analysis has been applied to slope engineering since 1970s and has been highly valued and developed rapidly. In the design, construction and use of horizontal concave slope engineering, in-depth analysis and evaluation of the reliability of the slope has become a key step in the practice of horizontal concave slope engineering.

2.1.3 Reliability research model and limit state equation

In reliability research, the stress–strength interference model is used frequently. In general, stress and strength are independent random variables. On the basis of finite element calculation, reliability analysis of safety factor of element joints on slope is carried out [19,20]. The major and minor principal stresses of each element node can be obtained from the stress distribution map calculated by finite element method, and then the safety factor of the element node on the slope can be obtained by applying Coulomb–Mohr criterion. Because the major and minor principal stresses calculated by finite element method are random variables, the safety factor calculated by Coulomb–Mohr criterion is also random variables, which can be used to carry out reliability analysis, and then to analyze the reasonable mining distance of horizontal concave slope [21,22,23,24]. There are many geotechnical slopes, and it is generally assumed that there is no obvious degradation under normal design, construction, and use conditions. Therefore, when choosing a model, we usually choose a random variable model indirectly considering the influence of time instead of directly choosing a time-related stochastic process model. It can be concluded that the reliability of horizontal concave slope is mainly determined by the stable state presented under certain conditions.

The stability state of horizontal concave slope is controlled by many factors or variables, such as the geotechnical structure, strength and deformation characteristics, groundwater pressure, earthquake, and so on. These variables are uncertain both in time and space, that is, random variables. In this study, the slope state can be described by constructing a stochastic variable function model.

(4) Z = g ( X ) = g ( X 1 , X 2 , … , X n )

The function Z = g ( X ) reflects the state or performance of the slope, which is called the state function or the function, X i is the basic state variable.

Safety is the most basic and important function of horizontal concave slope engineering. Therefore, the limit state equation of a horizontal concave slope can be obtained by using the safety limit state as the criterion to judge whether it is broken or not.

(5) Z 1 = Z = 0

Therefore, the safety factor of the upper unit node of the horizontal concave slope is considered as the basic state variable to analyze the reliability of the horizontal concave slope. If the horizontal concave slope is reliable, the mining of the horizontal concave slope is at a reasonable distance.

2.1.4 Warehouse–Mohr strength theory

Warehouse–Mohr strength theory is based on statistical analysis of test data. The theory holds that rock failure occurs not in simple stress state, but on the basis of different combinations of normal stress and shear stress, the bearing capacity of rock is lost [25,26,27]. Moore proposed the Mohr strength theory in 1900. It is believed that the material damage is caused by the shear stress on a certain surface of the material reaching a certain limit, and the shear stress is related to the frictional resistance caused by the material itself and the normal stress on the failure surface. That is, the destruction of the material is related to the normal stress at that point, in addition to the shear stress at that point. This is currently the most widely used theory in rock mechanics. Therefore, the data of triaxial tests are usually expressed in the form of the limit stress circle composed of the strength envelope shown in Figure 2 and the major and minor principal stresses. When a point on the limit stress circle is tangent to the strength envelope, it means that the rock is destroyed under the stress state.

Figure 2 Warehouse–Mohr strength conditions.
Figure 2

Warehouse–Mohr strength conditions.

The safety factor of horizontal concave slope is generally expressed by the ratio of anti-sliding force to sliding force on the slope. When the safety factor of the slope is considered by the Warehouse–Mohr strength theory, it can be expressed by the ratio of R and r in Figure 2, namely:

The safety factor formula is as follows:

(6) F = R r = ( σ 1 + σ 3 ) ⋅ sin φ + 2 c ⋅ cos φ σ 1 − σ 3

In Figure 2 and formula (6), c and φ are the cohesion and internal friction angles of rock, respectively, σ 1 and σ 3 are the major and minor stresses of element joints, respectively.

2.2 Optimizing reasonable distance based on variable scale chaotic optimization

2.2.1 Variable-scale chaotic optimization method

Variable-scale chaotic optimization method uses the self-rule of chaotic variables to search. In the process of optimization, the search space of optimization variables is continuously reduced, and the search accuracy of optimization variables is continuously deepened [28,29]. The search efficiency is very high.

Chaotic variables generated by Logistic are selected to optimize the search.

(7) x k + 1 = μ x k ( 1 − x k )

In the formula, μ is the control parameter, which is proved as follows: when μ = 4 , formula (7) is in the state of complete chaos. If n parameters need to be optimized, n different initial values of (0, 1) interval are set arbitrarily, and n chaotic variables with different trajectories are obtained.

Let a global minor optimization problem be:

(8) min f ( x 1 , x 2 , … , x n ) , x i ∈ [ a i , b i ]

The basic steps of the optimization method are (at this time, f ( x 1 , x 2 , … , x n ) is defined as f ( x i ) ):

  1. Initialization k = 0, r = 0, f ∗ = ∞ , x i k = x i ( 0 ) , a i r = a i , b i r = b i , i = 1 , 2 , ⋯ , n . k is the iteration mark of chaotic variables, r is the fine search mark, and f ∗ is the minor of the current objective function.

  2. Mapping x i k to the value interval of the optimization variable becomes m x i k , then:

    (9) m x i k = a i r + x i k ( b i r − a i r )

  3. By using chaotic variables to optimize, it searches the objective function value f , if f = f ( m x i r ) < f ⁎ , then make f ⁎ = f , x i ⁎ = x i k , m x i ⁎ = m x i k , otherwise continue. m x i ⁎ and x i ⁎ are the current optimal chaotic variables and chaotic search variables, respectively.

  4. Formula (7) takes μ = 4 and iterates with chaotic variables.

  5. Repeat steps (2) to (4) until f ∗ remains almost unchanged within a certain number of steps.

  6. Reduce the search scope of each variable:

    (10) a i r + 1 = m x i ∗ − λ ( b i r − a i r )

    (11) b i r + 1 = m x i ∗ − λ ( b i r − a i r )

    where, λ = ( 0 , 0.5 ) , in order to guarantee the boundary conditions of the new range, is treated as follows: if a i r + 1 < a i r , then a i r + 1 = a i r ; if b i r + 1 < b i r , then b i r + 1 = b i r , in addition, x i ⁎ needs to be treated as follows:

    (12) x i ⁎ = m x i ∗ − a i r + 1 b i r + 1 − a i r + 1

  7. The linear combination of x i ⁎ and x i k is searched as a new chaotic variable:

    (13) v i k = ( 1 − α ) x i ∗ + α x i k

    In the formula, α takes a smaller value.

  8. By using v i k as a new chaotic variable, the operation of steps (2)–step (4) is carried out.

  9. Repeat steps (7) and (8) until f ⁎ remains almost unchanged within a certain number of steps.

  10. Formulas (10) and (11) are used to continue to narrow the search scope of each variable, reduce the value of α , and repeat the operation of steps (6)–(9).

  11. The optimization calculation is completed after repeated operations on formula (7), where m x i ∗ is the optimal solution obtained by the algorithm and f ⁎ is the minor of the objective function.

The variable scale chaotic optimization algorithm is applied to search the reasonable mining distance of horizontal concave slope, and formula (20) is taken as the objective function. In essence, finding the reasonable mining distance of horizontal concave slope is the clustering center when the range of safety factor is given and the objective function is minimized [30,31]. The research flow of reasonable mining distance of horizontal concave slope based on variable scale chaotic optimization algorithm is shown in Figure 3.

Figure 3 Flow chart for determining reasonable mining distance of horizontal concave slope based on variable scale chaotic optimization algorithm.
Figure 3

Flow chart for determining reasonable mining distance of horizontal concave slope based on variable scale chaotic optimization algorithm.

2.2.2 Similarity measure

According to the analysis of Warehouse–Mohr strength condition, the mining data of horizontal concave slope is aggregated into X = [ c , φ , σ 1 , σ 3 ] . The study of reasonable mining distance of horizontal concave slope is to classify the mining distance whose safety factor is in a reasonable range into a group. Clustering method is used to classify the mining distance. First, the similarity measure between mining data samples of horizontal concave slope, distance, should be determined [32]. The smaller the distance is, the more reasonable the mining distance of horizontal concave slope is. On the contrary, the lower the mining distance of horizontal concave slope is. Because the range and dimension of each data of horizontal concave slope are different, it is necessary to eliminate the influence of different measurement units on the grouping results, so the data of mining properties of horizontal concave slope should be normalized. The methods are as follows:

(14) c i 1 = c i − c min c maj − c min

(15) φ i 1 = φ i − φ min φ maj − φ min

(16) σ i 1 1 = σ 1 i − σ 1 min σ 1 maj − σ 1 min

(17) σ 3 i 1 = σ 3 i − σ 3 min σ 3 maj − σ 3 min

In the formula, c i 1 , φ i 1 , σ 1 i 1 , and σ 3 i 1 represent the normalized values of rock cohesion, internal friction angle, major stress, and minor stress of element node under mining distance of horizontal concave slope of type i, respectively. c min , c maj , φ min , φ min , σ 1 min , σ 1 maj , σ 3 min , and σ 3 maj are the minor and major values of the above four variables, respectively. The Euclidean distance is used to represent the mining distance data of the above four horizontal concave slopes. The similarity measure of mining data of two groups of horizontal concave slopes is as follows:

(18) D 2 ( X i , X j ) = ( c i 1 , c j 1 ) 2 + ( φ i 1 , φ j 1 ) 2 + ( σ 1 i 1 , σ 1 j 1 ) 2 + ( σ 3 i 1 , σ 3 j 1 ) 2

2.2.3 Objective function

The range of safety factor X j ( j = 1 , 2 , … , n ) of N kinds of mining is set to P, and the cluster center of each group is V j ( i = 1 , 2 , … , p ) . The definition of u i j indicates that the j-th safety factor belongs to the membership degree of the i-th clustering center. The details are as follows:

(19) u i j = 1 D 2 ( X j , X i ) ∑ k = 1 p 1 D 2 ( X j , X i ) − 1

Then the objective function is:

(20) C = ∑ j = 1 n ∑ i = 1 p u i j D 2 ( X j , X i )

Formula (20) is the objective function for the reasonable mining distance of horizontal concave slope in this paper. The ratio of R and r is obtained by calculating the mining safety factor of horizontal concave slope. When the safety factor range P is given, the cluster center combination which minimizes the fuzzy objective function C is the reasonable mining distance required for horizontal concave slope.

3 Results

3.1 Experimental model setting

3.1.1 Mining calculation model of horizontal concave slope

In the mining model of horizontal concave slope, the width and height of the calculation model are 800 and 300 m, from horizontal elevation +1,150 to surface +1,450 m. The model consists of 50,000 plane elements with an average mesh size of 2 × 2.5 m. Figure 4 shows the final excavation form of the open pit slope. In order to evaluate the reliability of the slope, monitoring points are set up at the transportation platform of the slope and the steps with poor mechanical properties.

Figure 4 Spatial structural chart of horizontal concave slope.
Figure 4

Spatial structural chart of horizontal concave slope.

In order to weaken the influence of compound mining on slope stability, the whole position of open-cut hole is moved left away from the slope, and the translation distance of the slope is 11, 18 and 25 m, respectively. After translation, the vertical corresponding step elevation of the open-cut hole is +1,405 m platform.

The spatial structure of the horizontal concave slope used in the experiment is shown in Figure 4.

3.1.2 Setting of mechanical parameters

In the calculation, the ideal elastic-plastic constitutive model, Mohr–Coulomb yield criterion, and the strain softening model are used to simulate the coal body. The theory of soil shear strength expressed by the Coulomb formula is called the Mohr–Coulomb strength theory, also known as the Mohr–Coulomb theory. That is, when the shear stress at a point on any plane in the soil is equal to the shear strength of the soil, the point is in a critical state of failure, and the critical state is called “limit equilibrium state.” The relationship between various stresses in this state is called “limit equilibrium condition.” According to the rock mechanics test results provided by field geological survey and related research, the mechanical parameters of coal and rock mass used in the simulation calculation are given in Table 1.

Table 1

Mechanical parameters of rock mass

Lithology Layered thickness/m Bulk density/kg m−3 Elastic modulus/Mpa Poisson ratio Cohesion/Mpa Internal friction angle/° Tensile strength/Mpa
Loess 32 1,970 15 0.53 0.14 19 0.0136
Weathered sandstone 15 2,400 2,100 0.47 2.4 39 0.26
Sandstone 31 2,480 4,300 0.43 3.1 40 0.3
Mudstone 25 2,500 2,900 0.45 2.1 39 0.2
Siltstone 13 2,430 4,700 0.43 3.6 37 0.36
Sandstone 13 2,490 5,600 0.41 4.1 41 0.4
4# coal 9 1,550 1,100 0.49 1.7 37 0.3
Shale 16 1,560 2,500 0.44 3.1 43 0.3
Siltstone 16 2,700 4,900 0.43 5.1 39 0.5
Shale 11 2,690 3,100 0.46 5.1 39 0.5
9# coal 14 1,440 1,300 0.47 1.7 40 0.295
Sandstone 11 2,490 7,000 0.39 5.1 42 0.5
11# coal 6 1,500 1,400 0.46 1.7 37 0.295
Sandstone 13 2,700 13,000 0.36 5.1 45 0.5

3.1.3 Simulation and loading of excavation process

Simulating excavation process: forming initial stress field according to original geomorphology; mining 4 coal seams first, advancing 240 m, then nine coal seams, advancing 240 m; were forming slope, in which +1,405 and +1,345 m platforms are 35 m wide transportation platforms.

Loading: loading on elevation +1,405 and +1,345 m transport platforms. The load is calculated by the total weight of a full-load vehicle and an empty-load vehicle at the same time, and the dynamic load coefficient is 1.2.

3.2 Analysis of reasonable mining distance

Eight groups of horizontal concave slope data are given in Table 2. This method is used to determine whether the mining of horizontal concave slope is in a reasonable range under different data grouping conditions. The judgment results are shown in Table 3. At the same time, the real judgment results are given to analyze the effectiveness and accuracy of this method.

Table 2

Horizontal concave slope data

Data grouping Rock cohesion/Mpa Internal friction angle of rock/° Major stress of element node/Mpa Minor stress of element node/MNpa
1 10 38 21 56
2 11 39 25 54
3 12 40 39 51
4 13 41 19 48
5 14 42 28 48
6 15 43 26 53
7 16 44 37 52
8 17 45 34 57
Table 3

Research results of reasonable mining distance for horizontal concave slope

Data grouping of horizontal concave slope 1 2 3 4 5 6 7 8
Is it at a reasonable mining distance? Yes No Yes No Yes Yes Yes No
Real result Yes No Yes No Yes Yes Yes No

According to the data in Tables 2 and 3, this method is very accurate for the study of reasonable mining distance of horizontal concave slope. It can accurately judge whether the horizontal concave slope can safely carry out mining activities under different structural data settings. It shows that this method is reliable and effective.

3.3 The influence of mining opening position on the reliability of horizontal concave slope

The upper platform of horizontal concave slope is mainly affected by mining disturbance, and the settlement deformation is the main factor, while the middle and lower platform is mainly horizontal deformation. Therefore, the displacement comparison of horizontal concave slope platform is carried out to study the influence of the location of the openings on the stability of horizontal concave slope. The vertical displacement of the platform with elevation +1,405 m is compared with that of the platform with elevation of 1,345 m. The horizontal displacement trend of the monitoring points outside the platform is compared with that of the platform with elevation +1,405 m. With the increase of the translation distance of mining openings, the vertical displacement of the upper platform decreases gradually, as shown in Figure 5, and the horizontal displacement of the middle and lower platform decreases gradually, as shown in Figure 6.

Figure 5 Vertical displacement of elevation +1,405 m transportation platform.
Figure 5

Vertical displacement of elevation +1,405 m transportation platform.

Figure 6 Horizontal displacement of outside monitoring points of elevation +1,345 m transportation platform.
Figure 6

Horizontal displacement of outside monitoring points of elevation +1,345 m transportation platform.

The analysis of Figures 5 and 6 shows that when the mining openings move 11 and 18 m, the change trend of monitoring points on the outer side of +1,345 m platform shows that after the slope excavation, the horizontal displacement of the platform still keeps increasing, and the slope has potential slip hazards. The horizontal displacement of +1,345 m platform decreases obviously when the displacement is 25 m. After the slope excavation, the horizontal displacement of monitoring point keeps constant and no longer increases, and the stability of platform is good. It can be seen that the translation of the mining opening position plays a positive role in reducing the settlement of the upper platform and eliminating the potential slip surface of the slope.

3.4 Effect of slope angle on reliability of horizontal concave slope

The angle of horizontal concave slope is changed continuously from 30–54° and the reliability of four kinds of horizontal concave slope models with different heights, 110, 130, 150 and 170 m, are analyzed. The safety factor of horizontal concave slope mining is obtained by this method, and the change of safety factor is recorded. At the same time, the reliability of horizontal concave slope with the same height and slope angle is compared, and the correlation curve is obtained as shown in Figure 7.

Figure 7 Curve of relationship between stability factor and slope angle at different heights. (a) Height of horizontal concave slope = 110 m. (b) Height of horizontal concave slope = 130 m. (c) Height of horizontal concave slope = 150 m. (d) Height of horizontal concave slope = 170 m.
Figure 7

Curve of relationship between stability factor and slope angle at different heights. (a) Height of horizontal concave slope = 110 m. (b) Height of horizontal concave slope = 130 m. (c) Height of horizontal concave slope = 150 m. (d) Height of horizontal concave slope = 170 m.

From Figure 7, it can be seen that the safety factor of horizontal concave slope decreases linearly with the increase of slope angle; when the slope height is changed, the safety factor of horizontal concave slope is inversely proportional to the slope height at the same slope angle, the higher the slope height, and the smaller the slope safety factor. Therefore, when the slope height is high, the safety factor of the slope is low and the reliability is poor, so the safe mining cannot be carried out.

4 Discussions

The experiment mainly studies the influence of mining opening location, slope height, and slope angle on the reasonable mining distance of horizontal concave slope. The results are as follows:

  1. the influence of different mining opening location on the reasonable mining distance of horizontal concave slope is obtained by changing the translation of mining opening. Previous studies have shown that mining has an impact on the reliability of horizontal concave slope. For the upper part of the slope, the impact is manifested as settlement and deformation, that is, vertical displacement; for the middle and lower parts of the slope, the impact is manifested as horizontal displacement. The study shows that after the end of mining, the horizontal displacement of the platform in the middle and lower parts of the slope increases gradually. When the translation of the mining openings is small, the horizontal displacement of the platform increases significantly, and the slope is in a high-risk state. When the displacement of mining openings is large, the horizontal displacement of the platform is basically stable, the slope restores to a reliable state, and the horizontal concave slope is gradually in a reasonable mining distance. The displacement of the cutting hole position plays an active role in reducing the settlement of the upper platform and eliminating the potential slip surface of the slope.

  2. The slope angle of the horizontal concave slope model is 30–54° and it is in a continuous state of change. Four different heights of 110, 130, 150, and 170 m are defined. The reliability analysis of the horizontal concave slope model is constructed to analyze the reasonable mining distance of the horizontal concave slope. The results show that the slope angle and height are inversely proportional to the reliability of the slope. With the increase of the slope height and angle, the reliability of the slope decreases gradually. In summary, in the mining process of horizontal concave slope, the influence of mining opening position, slope height and slope angle should be considered, the slope angle and height should be reduced appropriately, the displacement of mining opening should be increased, the stability and reliability of slope mining should be improved effectively, and the optimum reasonable mining distance should be found.

5 Conclusion

This paper studies the reasonable mining distance of horizontal concave slope based on variable scale chaotic algorithm. Compared with chaotic algorithm, it has the advantage of optimizing the search space. In the optimization process, the variable-scale chaotic algorithm reduces the search space of optimization variables, deepens the search accuracy of optimization variables, and has high search efficiency. Based on variable scale chaotic algorithm, the reasonable mining distance of horizontal concave slope can be obtained accurately, which provides scientific basis for ensuring mining safety, improving mining efficiency, and reducing mining cost.

Acknowledgements

This work was financially supported by the National Key Research and Development Plan(2016YFC0501103), National Natural Science Foundation of China (No. 51804298), National Natural Science Foundation of China (No. 51774271, No. 51674245), and the Fundamental Research Funds for the Central Universities (No. 2014XT01).

References

[1] Dunnington DW, Spooner IS. Modeling the effect of convex upward sediment deformation and horizontal core sectioning on paleolimnological data. J Paleolimnology. 2017;57(4):361–8.10.1007/s10933-017-9947-1Search in Google Scholar

[2] Pandey VC, Jadoun VK, Gupta N. Improved fireworks algorithm with chaotic sequence operator for large-scale non-convex economic load dispatch problem. Arab J Sci Eng. 2017;43(11):2919–29.10.1007/s13369-017-2956-6Search in Google Scholar

[3] Fu X, Zhang F, Feng ZL. Research of chaos genetic algorithm based on parallel computing for anti-missile warning radar disposition. J China Acad Electron Inf Technol. 2016;11(3):276–82.Search in Google Scholar

[4] Fattahi H. Risk assessment and prediction of safety factor for circular failure slope using rock engineering systems. Environ Earth Sci. 2017;76(5):224.10.1007/s12665-017-6549-1Search in Google Scholar

[5] Zhang YD, Zhang CP, Zhang RL. Research on temperature control of explosion-proof diesel exhaust system. Computer Simul. 2017;34(6):121–4.Search in Google Scholar

[6] Yang W. Research on joint probability data association based on CHNN and chaos algorithm. Autom Instrum. 2016;199(5):183–4.Search in Google Scholar

[7] Liu Y, Chen Y, Guo SX. Synchronization of different structures for generalized translational chaotic systems. J Jilin Univ (Sci Ed). 2017;55(4):973–8.Search in Google Scholar

[8] Liu L, Hao S, Lin J. Image block encryption algorithm based on chaotic maps. IET Signal Process. 2018;12(1):22–30.10.1049/iet-spr.2016.0584Search in Google Scholar

[9] Gao W, Wang W. A tight neighborhood union condition on fractional (g, f, n′, m)-critical deleted graphs. Colloq Mathematicum. 2017;149(2):291–8.10.4064/cm6959-8-2016Search in Google Scholar

[10] Li Y, Ge G, Xia D. Chaotic hash function based on the dynamic S-Box with variable parameters. Nonlinear Dyn. 2016;84(4):2387–402.10.1007/s11071-016-2652-1Search in Google Scholar

[11] Yang A, Li Y, Kong F, Wang G, Chen E. Security control redundancy allocation technology and security keys based on Internet of things. IEEE Access. 2018;6:50187–96.10.1109/ACCESS.2018.2868951Search in Google Scholar

[12] D’Alimonte D, Kajiyama T. Effects of light polarization and waves slope statistics on the reflectance factor of the sea surface. Opt Express. 2016;24(8):7922.10.1364/OE.24.007922Search in Google Scholar PubMed

[13] Zhang Y, Tang J, Li G. Influence of depth-thickness ratio of mining on the stability of a bedding slope with its sliding surface in concave deformation. Int J Min Sci Technol. 2016;26(6):1117–23.10.1016/j.ijmst.2016.09.022Search in Google Scholar

[14] Li Z, Chen YF, Zhang B. Study on failure mechanism of switched-inductor boost converter and chaos control scheme based on parameter-perturbation. J Power Supply. 2017;15(3):148–55.Search in Google Scholar

[15] Ramane HS, Jummannaver RB. Note on forgotten topological index of chemical structure in drugs. Appl Math Nonlinear Sci. 2016;1(2):369–74.10.21042/AMNS.2016.2.00032Search in Google Scholar

[16] Gao W, Wang WF. The fifth geometric–arithmetic index of bridge graph and carbon nanocones. J Diff Equ Appl. 2017;23(1-2SI):100–9.10.1080/10236198.2016.1197214Search in Google Scholar

[17] Liu F, Liu Y, Jin D, Jia X, Wang T. Research on workshop-based positioning technology based on internet of things in big data background. Complexity. 2018(6):7875460.10.1155/2018/7875460Search in Google Scholar

[18] Wiemer G, Kopf A. Influence of diatom microfossils on sediment shear strength and slope stability. Geochem Geophys Geosyst. 2017;18(1):333–45.10.1002/2016GC006568Search in Google Scholar

[19] Harraga H, Yebdri M. Attractors for a nonautonomous reaction–diffusion equation with delay. Appl Math Nonlinear Sci. 2018;3(1):127–50.10.21042/AMNS.2018.1.00010Search in Google Scholar

[20] Wei G, Xu W, Shuang D. Study on stability of high embankment slope based on black hole algorithm. Environ Earth Sci. 2016;20:1381.Search in Google Scholar

[21] Gao W, Farahani MR, Aslam A, Hosamani S. Distance learning techniques for ontology similarity measuring and ontology mapping. Clust Comput J Netw Softw Tools Appl. 2017;20(2SI):959–68.10.1007/s10586-017-0887-3Search in Google Scholar

[22] Leiva LA, Alabau V. Polyglot machine translation. J Intell Fuzzy Syst. 2017;32(1):613–27.10.3233/JIFS-152533Search in Google Scholar

[23] Mi C, Shen Y, Mi WJ, Huang YF. Ship identification algorithm based on 3D point cloud for automated ship loaders. J Coast Res. 2015;73(1):28–34.10.2112/SI73-006.1Search in Google Scholar

[24] Peng P, Cheng HX, Chen XC. Estimation of state of charge of Li-ion battery based on adaptive Kalman filtering. Chin J Power Sources. 2017;41(11):35–38.Search in Google Scholar

[25] Luek A, Rasmussen JB. Chemical, physical, and biological factors shape littoral invertebrate community structure in coal-mining end-pit lakes. Environ Manag. 2017;59(4):652–64.10.1007/s00267-017-0819-2Search in Google Scholar PubMed

[26] Mei D, Hui H, Jie S. Combined methodology for three-dimensional slope stability analysis coupled with time effect: A case study in Germany. Environ Earth Sci. 2018;77(8):311.10.1007/s12665-018-7497-0Search in Google Scholar

[27] Qiang Z, Zhang JX, Han XL. Theoretical research on mass ratio in solid backfill coal mining. Environ Earth Sci. 2016;75(7):586.10.1007/s12665-015-5234-5Search in Google Scholar

[28] Aledo JA, Diaz LG, Martinez S, Valverde JC. Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs. Appl Math Nonlinear Sci. 2018;3(2):593–602.10.2478/AMNS.2018.2.00046Search in Google Scholar

[29] Chen H, Jiang J, Cao D, Fan X. Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory. Appl Math Nonlinear Sci. 2018;3(1):175–86.10.21042/AMNS.2018.1.00014Search in Google Scholar

[30] Lara M. Complex variables approach to the short-axis-mode rotation of a rigid body. Appl Mathe Nonlinear Sci. 2018;3(2):537–52.10.2478/AMNS.2018.2.00042Search in Google Scholar

[31] Huang H, Deng G, Došenović T, Hussain N. Note on recent common coupled fixed point results in multiplicative metric spaces. Appl Math Nonlinear Sci. 2018;3(2):659–68.10.2478/AMNS.2018.2.00050Search in Google Scholar

[32] Yan W, Fu JL. Noether’s theorems of variable mass systems on time scales. Appl Math Nonlinear Sci. 2018;3(1):229–40.10.21042/AMNS.2018.1.00017Search in Google Scholar
Received: 2020-06-02
Accepted: 2020-10-15
Published Online: 2020-12-03

© 2020 Shuzhao Chen et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Regular Articles
  2. Model of electric charge distribution in the trap of a close-contact TENG system
  3. Dynamics of Online Collective Attention as Hawkes Self-exciting Process
  4. Enhanced Entanglement in Hybrid Cavity Mediated by a Two-way Coupled Quantum Dot
  5. The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions
  6. Diagnostic model of low visibility events based on C4.5 algorithm
  7. Electronic temperature characteristics of laser-induced Fe plasma in fruits
  8. Comparative study of heat transfer enhancement on liquid-vapor separation plate condenser
  9. Characterization of the effects of a plasma injector driven by AC dielectric barrier discharge on ethylene-air diffusion flame structure
  10. Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid
  11. Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model
  12. Novel numerical analysis for nonlinear advection–reaction–diffusion systems
  13. Heuristic decision of planned shop visit products based on similar reasoning method: From the perspective of organizational quality-specific immune
  14. Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel
  15. Dynamic triaxial constitutive model for rock subjected to initial stress
  16. Automatic target recognition method for multitemporal remote sensing image
  17. Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method
  18. Adaptive magnetic suspension anti-rolling device based on frequency modulation
  19. Dynamic response characteristics of 93W alloy with a spherical structure
  20. The heuristic model of energy propagation in free space, based on the detection of a current induced in a conductor inside a continuously covered conducting enclosure by an external radio frequency source
  21. Microchannel filter for air purification
  22. An explicit representation for the axisymmetric solutions of the free Maxwell equations
  23. Floquet analysis of linear dynamic RLC circuits
  24. Subpixel matching method for remote sensing image of ground features based on geographic information
  25. K-band luminosity–density relation at fixed parameters or for different galaxy families
  26. Effect of forward expansion angle on film cooling characteristics of shaped holes
  27. Analysis of the overvoltage cooperative control strategy for the small hydropower distribution network
  28. Stable walking of biped robot based on center of mass trajectory control
  29. Modeling and simulation of dynamic recrystallization behavior for Q890 steel plate based on plane strain compression tests
  30. Edge effect of multi-degree-of-freedom oscillatory actuator driven by vector control
  31. The effect of guide vane type on performance of multistage energy recovery hydraulic turbine (MERHT)
  32. Development of a generic framework for lumped parameter modeling
  33. Optimal control for generating excited state expansion in ring potential
  34. The phase inversion mechanism of the pH-sensitive reversible invert emulsion from w/o to o/w
  35. 3D bending simulation and mechanical properties of the OLED bending area
  36. Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics
  37. The measure of irregularities of nanosheets
  38. The predicted load balancing algorithm based on the dynamic exponential smoothing
  39. Influence of different seismic motion input modes on the performance of isolated structures with different seismic measures
  40. A comparative study of cohesive zone models for predicting delamination fracture behaviors of arterial wall
  41. Analysis on dynamic feature of cross arm light weighting for photovoltaic panel cleaning device in power station based on power correlation
  42. Some probability effects in the classical context
  43. Thermosoluted Marangoni convective flow towards a permeable Riga surface
  44. Simultaneous measurement of ionizing radiation and heart rate using a smartphone camera
  45. On the relations between some well-known methods and the projective Riccati equations
  46. Application of energy dissipation and damping structure in the reinforcement of shear wall in concrete engineering
  47. On-line detection algorithm of ore grade change in grinding grading system
  48. Testing algorithm for heat transfer performance of nanofluid-filled heat pipe based on neural network
  49. New optical solitons of conformable resonant nonlinear Schrödinger’s equation
  50. Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model
  51. Circularly symmetric algorithm for UWB RF signal receiving channel based on noise cancellation
  52. CH4 dissociation on the Pd/Cu(111) surface alloy: A DFT study
  53. On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science
  54. An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation
  55. Mining reasonable distance of horizontal concave slope based on variable scale chaotic algorithms
  56. Mathematical models for information classification and recognition of multi-target optical remote sensing images
  57. Hopkinson rod test results and constitutive description of TRIP780 steel resistance spot welding material
  58. Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient
  59. Analytical solution of one-dimensional Pennes’ bioheat equation
  60. MHD squeezed Darcy–Forchheimer nanofluid flow between two h–distance apart horizontal plates
  61. Analysis of irregularity measures of zigzag, rhombic, and honeycomb benzenoid systems
  62. A clustering algorithm based on nonuniform partition for WSNs
  63. An extension of Gronwall inequality in the theory of bodies with voids
  64. Rheological properties of oil–water Pickering emulsion stabilized by Fe3O4 solid nanoparticles
  65. Review Article
  66. Sine Topp-Leone-G family of distributions: Theory and applications
  67. Review of research, development and application of photovoltaic/thermal water systems
  68. Special Issue on Fundamental Physics of Thermal Transports and Energy Conversions
  69. Numerical analysis of sulfur dioxide absorption in water droplets
  70. Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part I
  71. Random pore structure and REV scale flow analysis of engine particulate filter based on LBM
  72. Prediction of capillary suction in porous media based on micro-CT technology and B–C model
  73. Energy equilibrium analysis in the effervescent atomization
  74. Experimental investigation on steam/nitrogen condensation characteristics inside horizontal enhanced condensation channels
  75. Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data
  76. Investigation on thermal-hydraulic performance prediction of a new parallel-flow shell and tube heat exchanger with different surrogate models
  77. Comparative study of the thermal performance of four different parallel flow shell and tube heat exchangers with different performance indicators
  78. Optimization of SCR inflow uniformity based on CFD simulation
  79. Kinetics and thermodynamics of SO2 adsorption on metal-loaded multiwalled carbon nanotubes
  80. Effect of the inner-surface baffles on the tangential acoustic mode in the cylindrical combustor
  81. Special Issue on Future challenges of advanced computational modeling on nonlinear physical phenomena - Part I
  82. Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications
  83. Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems
  84. Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics
  85. Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water
  86. Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena
  87. Some misinterpretations and lack of understanding in differential operators with no singular kernels
  88. Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics
  89. Calculation of focal values for first-order non-autonomous equation with algebraic and trigonometric coefficients
  90. Influence of interfacial electrokinetic on MHD radiative nanofluid flow in a permeable microchannel with Brownian motion and thermophoresis effects
  91. Standard routine techniques of modeling of tick-borne encephalitis
  92. Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena
  93. Exact solutions of space–time fractional KdV–MKdV equation and Konopelchenko–Dubrovsky equation
  94. Approximate analytical fractional view of convection–diffusion equations
  95. Heat and mass transport investigation in radiative and chemically reacting fluid over a differentially heated surface and internal heating
  96. On solitary wave solutions of a peptide group system with higher order saturable nonlinearity
  97. Extension of optimal homotopy asymptotic method with use of Daftardar–Jeffery polynomials to Hirota–Satsuma coupled system of Korteweg–de Vries equations
  98. Unsteady nano-bioconvective channel flow with effect of nth order chemical reaction
  99. On the flow of MHD generalized maxwell fluid via porous rectangular duct
  100. Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation
  101. Numerical solution of two-term time-fractional PDE models arising in mathematical physics using local meshless method
  102. A powerful numerical technique for treating twelfth-order boundary value problems
  103. Fundamental solutions for the long–short-wave interaction system
  104. Role of fractal-fractional operators in modeling of rubella epidemic with optimized orders
  105. Exact solutions of the Laplace fractional boundary value problems via natural decomposition method
  106. Special Issue on 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  107. Joint use of eddy current imaging and fuzzy similarities to assess the integrity of steel plates
  108. Uncertainty quantification in the design of wireless power transfer systems
  109. Influence of unequal stator tooth width on the performance of outer-rotor permanent magnet machines
  110. New elements within finite element modeling of magnetostriction phenomenon in BLDC motor
  111. Evaluation of localized heat transfer coefficient for induction heating apparatus by thermal fluid analysis based on the HSMAC method
  112. Experimental set up for magnetomechanical measurements with a closed flux path sample
  113. Influence of the earth connections of the PWM drive on the voltage constraints endured by the motor insulation
  114. High temperature machine: Characterization of materials for the electrical insulation
  115. Architecture choices for high-temperature synchronous machines
  116. Analytical study of air-gap surface force – application to electrical machines
  117. High-power density induction machines with increased windings temperature
  118. Influence of modern magnetic and insulation materials on dimensions and losses of large induction machines
  119. New emotional model environment for navigation in a virtual reality
  120. Performance comparison of axial-flux switched reluctance machines with non-oriented and grain-oriented electrical steel rotors
  121. Erratum
  122. Erratum to “Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications”
https://doi.org/10.1515/phys-2020-0198
Keywords for this article
variable scale; chaotic algorithm; level; concave slope; mining; reasonable distance
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Model of electric charge distribution in the trap of a close-contact TENG system
  3. Dynamics of Online Collective Attention as Hawkes Self-exciting Process
  4. Enhanced Entanglement in Hybrid Cavity Mediated by a Two-way Coupled Quantum Dot
  5. The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions
  6. Diagnostic model of low visibility events based on C4.5 algorithm
  7. Electronic temperature characteristics of laser-induced Fe plasma in fruits
  8. Comparative study of heat transfer enhancement on liquid-vapor separation plate condenser
  9. Characterization of the effects of a plasma injector driven by AC dielectric barrier discharge on ethylene-air diffusion flame structure
  10. Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid
  11. Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model
  12. Novel numerical analysis for nonlinear advection–reaction–diffusion systems
  13. Heuristic decision of planned shop visit products based on similar reasoning method: From the perspective of organizational quality-specific immune
  14. Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel
  15. Dynamic triaxial constitutive model for rock subjected to initial stress
  16. Automatic target recognition method for multitemporal remote sensing image
  17. Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method
  18. Adaptive magnetic suspension anti-rolling device based on frequency modulation
  19. Dynamic response characteristics of 93W alloy with a spherical structure
  20. The heuristic model of energy propagation in free space, based on the detection of a current induced in a conductor inside a continuously covered conducting enclosure by an external radio frequency source
  21. Microchannel filter for air purification
  22. An explicit representation for the axisymmetric solutions of the free Maxwell equations
  23. Floquet analysis of linear dynamic RLC circuits
  24. Subpixel matching method for remote sensing image of ground features based on geographic information
  25. K-band luminosity–density relation at fixed parameters or for different galaxy families
  26. Effect of forward expansion angle on film cooling characteristics of shaped holes
  27. Analysis of the overvoltage cooperative control strategy for the small hydropower distribution network
  28. Stable walking of biped robot based on center of mass trajectory control
  29. Modeling and simulation of dynamic recrystallization behavior for Q890 steel plate based on plane strain compression tests
  30. Edge effect of multi-degree-of-freedom oscillatory actuator driven by vector control
  31. The effect of guide vane type on performance of multistage energy recovery hydraulic turbine (MERHT)
  32. Development of a generic framework for lumped parameter modeling
  33. Optimal control for generating excited state expansion in ring potential
  34. The phase inversion mechanism of the pH-sensitive reversible invert emulsion from w/o to o/w
  35. 3D bending simulation and mechanical properties of the OLED bending area
  36. Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics
  37. The measure of irregularities of nanosheets
  38. The predicted load balancing algorithm based on the dynamic exponential smoothing
  39. Influence of different seismic motion input modes on the performance of isolated structures with different seismic measures
  40. A comparative study of cohesive zone models for predicting delamination fracture behaviors of arterial wall
  41. Analysis on dynamic feature of cross arm light weighting for photovoltaic panel cleaning device in power station based on power correlation
  42. Some probability effects in the classical context
  43. Thermosoluted Marangoni convective flow towards a permeable Riga surface
  44. Simultaneous measurement of ionizing radiation and heart rate using a smartphone camera
  45. On the relations between some well-known methods and the projective Riccati equations
  46. Application of energy dissipation and damping structure in the reinforcement of shear wall in concrete engineering
  47. On-line detection algorithm of ore grade change in grinding grading system
  48. Testing algorithm for heat transfer performance of nanofluid-filled heat pipe based on neural network
  49. New optical solitons of conformable resonant nonlinear Schrödinger’s equation
  50. Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model
  51. Circularly symmetric algorithm for UWB RF signal receiving channel based on noise cancellation
  52. CH4 dissociation on the Pd/Cu(111) surface alloy: A DFT study
  53. On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science
  54. An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation
  55. Mining reasonable distance of horizontal concave slope based on variable scale chaotic algorithms
  56. Mathematical models for information classification and recognition of multi-target optical remote sensing images
  57. Hopkinson rod test results and constitutive description of TRIP780 steel resistance spot welding material
  58. Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient
  59. Analytical solution of one-dimensional Pennes’ bioheat equation
  60. MHD squeezed Darcy–Forchheimer nanofluid flow between two h–distance apart horizontal plates
  61. Analysis of irregularity measures of zigzag, rhombic, and honeycomb benzenoid systems
  62. A clustering algorithm based on nonuniform partition for WSNs
  63. An extension of Gronwall inequality in the theory of bodies with voids
  64. Rheological properties of oil–water Pickering emulsion stabilized by Fe3O4 solid nanoparticles
  65. Review Article
  66. Sine Topp-Leone-G family of distributions: Theory and applications
  67. Review of research, development and application of photovoltaic/thermal water systems
  68. Special Issue on Fundamental Physics of Thermal Transports and Energy Conversions
  69. Numerical analysis of sulfur dioxide absorption in water droplets
  70. Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part I
  71. Random pore structure and REV scale flow analysis of engine particulate filter based on LBM
  72. Prediction of capillary suction in porous media based on micro-CT technology and B–C model
  73. Energy equilibrium analysis in the effervescent atomization
  74. Experimental investigation on steam/nitrogen condensation characteristics inside horizontal enhanced condensation channels
  75. Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data
  76. Investigation on thermal-hydraulic performance prediction of a new parallel-flow shell and tube heat exchanger with different surrogate models
  77. Comparative study of the thermal performance of four different parallel flow shell and tube heat exchangers with different performance indicators
  78. Optimization of SCR inflow uniformity based on CFD simulation
  79. Kinetics and thermodynamics of SO2 adsorption on metal-loaded multiwalled carbon nanotubes
  80. Effect of the inner-surface baffles on the tangential acoustic mode in the cylindrical combustor
  81. Special Issue on Future challenges of advanced computational modeling on nonlinear physical phenomena - Part I
  82. Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications
  83. Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems
  84. Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics
  85. Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water
  86. Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena
  87. Some misinterpretations and lack of understanding in differential operators with no singular kernels
  88. Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics
  89. Calculation of focal values for first-order non-autonomous equation with algebraic and trigonometric coefficients
  90. Influence of interfacial electrokinetic on MHD radiative nanofluid flow in a permeable microchannel with Brownian motion and thermophoresis effects
  91. Standard routine techniques of modeling of tick-borne encephalitis
  92. Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena
  93. Exact solutions of space–time fractional KdV–MKdV equation and Konopelchenko–Dubrovsky equation
  94. Approximate analytical fractional view of convection–diffusion equations
  95. Heat and mass transport investigation in radiative and chemically reacting fluid over a differentially heated surface and internal heating
  96. On solitary wave solutions of a peptide group system with higher order saturable nonlinearity
  97. Extension of optimal homotopy asymptotic method with use of Daftardar–Jeffery polynomials to Hirota–Satsuma coupled system of Korteweg–de Vries equations
  98. Unsteady nano-bioconvective channel flow with effect of nth order chemical reaction
  99. On the flow of MHD generalized maxwell fluid via porous rectangular duct
  100. Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation
  101. Numerical solution of two-term time-fractional PDE models arising in mathematical physics using local meshless method
  102. A powerful numerical technique for treating twelfth-order boundary value problems
  103. Fundamental solutions for the long–short-wave interaction system
  104. Role of fractal-fractional operators in modeling of rubella epidemic with optimized orders
  105. Exact solutions of the Laplace fractional boundary value problems via natural decomposition method
  106. Special Issue on 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  107. Joint use of eddy current imaging and fuzzy similarities to assess the integrity of steel plates
  108. Uncertainty quantification in the design of wireless power transfer systems
  109. Influence of unequal stator tooth width on the performance of outer-rotor permanent magnet machines
  110. New elements within finite element modeling of magnetostriction phenomenon in BLDC motor
  111. Evaluation of localized heat transfer coefficient for induction heating apparatus by thermal fluid analysis based on the HSMAC method
  112. Experimental set up for magnetomechanical measurements with a closed flux path sample
  113. Influence of the earth connections of the PWM drive on the voltage constraints endured by the motor insulation
  114. High temperature machine: Characterization of materials for the electrical insulation
  115. Architecture choices for high-temperature synchronous machines
  116. Analytical study of air-gap surface force – application to electrical machines
  117. High-power density induction machines with increased windings temperature
  118. Influence of modern magnetic and insulation materials on dimensions and losses of large induction machines
  119. New emotional model environment for navigation in a virtual reality
  120. Performance comparison of axial-flux switched reluctance machines with non-oriented and grain-oriented electrical steel rotors
  121. Erratum
  122. Erratum to “Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications”
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 13.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/phys-2020-0198/html
Scroll to top button