Study on the Risk Evaluation Method of Ground Collapse in the

Mined-Out Area Based on D-S Evidence Theory

Zheng Yang

1, *

, Guangyao Yang

, Feng Guo

, Zhongqiang Wang

and Chenkang Wei

Shaanxi Xiaobaodang Mining Company, Dabaodang Town, Shenmu City, Shaanxi Province 719302, China

College of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an City,

Shaanxi Province, 710054, China

Keywords:

D-S Evidence Theory, Reverse Distance Weighting Method, Information Entropy, Data Fusion, Interval

Number, Probability Distribution.

Abstract: In the process of coal mining, it is easy to cause geological disasters such as ground collapse, so as to reduce

the loss caused by ground collapse, so it is necessary to evaluate the stability evaluation of the mining area

and the prediction of ground collapse. Ground subsidence is affected by geological, hydrological and weather,

the evaluation of ground subsidence based on multi-source information fusion, with the help of machine

learning, data fusion, integrates geological exploration drilling data, coal mining data and hydrological data.

Based on the mining area, this paper establishes the risk identification framework of 4 states, establishes the

stability evaluation index system with 9 influencing factors, calculates the basic probability distribution of the

indexes and distributes the information entropy, and finally integrates the probability distribution of the

indexes. It provides a new feasible way for risk assessment of mine mining area.

1 INTRODUCTION

China is rich in mineral resources and has a history of

thousands of years of coal mining. Depending on

relevant data, as of December 2004, the total mining

subsidence area of coal mines in China has exceeded

7,000 square kilometers, with a loss of more than 50

billion yuan. The average mining collapse area of key

coal mines accounts for about 10% of the coal

containing area. At present, the mined-out area has

become one of the main hazardous resource affecting

mine production safety (State Administration for

Work Safety, 2003), and it is also one of the two

hidden dangers in production safety. It impacts on

mineral development, life safety, and the natural

environment so seriously that the establishment of

this system has its necessity and urgency.

At present, multi-source information fusion

technology (MSIF: Multi. Sourse Infomation Fusion)

is mostly used in this direction. In the field of research

assessment of ground subsidence risk in the mining

area, many scholars use a single machine learning

model and empirical formula to evaluate, without

considering the uncertainty and correlation between

factors, so data fusion can solve this problem well.

Some scholars also use the information fusion

technology to conduct the risk assessment of the

mined space area, and make full use of the

complementarity and comprehensiveness of the

multi-source data to greatly improve the quality of the

evaluation index information. For example, they use

the hierarchical analysis method (Liu, 2020) to assess

the risk. This algorithm determines the weight ratio

of individual factors mainly based on the relationship

between their respective influence factors and

historical disaster points. It has the advantage of less

quantitative information required, but also, the results

are not convincing. And when there are too many

indicators, the accuracy is also difficult to guarantee.

Another example is the risk matrix evaluation

method. (Liu, Bhote, 2020) Making a subjective

judgment on the risk importance level standard, risk

possibility, and severity of the consequences may

affect the accuracy of the use. (Jin, 1998)

Therefore, this paper adopts the multi-source

information analysis and fusion based on D-S

evidence theory (Wang, 2005) to calculate the

stability level according to the fusion results, and

provides a new way for the stability evaluation of the

mining area. (Jin, 2006)

Yang, Z., Yang, G., Guo, F., Wang, Z. and Wei, C.

Study on the Risk Evaluation Method of Ground Collapse in the Mined-Out Area Based on D-S Evidence Theory.

DOI: 10.5220/0011735200003607

In Proceedings of the 1st International Conference on Public Management, Digital Economy and Internet Technology (ICPDI 2022), pages 297-301

ISBN: 978-989-758-620-0

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

297

A MULTI-SOURCE

INFORMATION FUSION

MODEL BASED ON DS

EVIDENCE THEORY

Let all the possibilities of the problem or event be

expressed in a set, and the results are mutually

exclusive and can fully cover all the results of the

problem or event, and the answer to the question we

study is a subset of this set. The identification

framework θ is a non-empty and limited set, which

meets the collection algorithm. The identification

framework is the foundation of evidence reasoning.

Definition 1: Make θ the identification

framework ,R a set class in the power set 2

, and A a

subset of θ. If the function m:R → [0,1]

Meet the following conditions:

1)(

0)(

=Σ

(1)

Definition 2: Make θ the identification

framework, R a set class in the power set 2

, A a

subset of θ, and m a mass function on θ, and Bel: R

→ [0,1] meets:

)(m)( BABel

AB⊆

Σ=

(2)

Bel is called the probability assignment function

on the identification framework θ. To any proposition

A. Bel (A) is called the confidence of proposition A,

suggesting the full degree of confidence of

proposition A.

Definition 3: Make θ the identification

framework, R a set class in the power set 2

, and A a

subset of θ, and m a mass function on θ, and Pl: R →

[0,1] meets:

)(m)( BABel

≠∩

Σ=

(3)

Then Pl is referred to as the plausible function on

the recognition framework. And for any proposition

A,PI (A) is called the plausibility of the proposition

A. The function Pl represents the degree not opposed

to the proposition A. [Bel (A), PI (A)] indicates the

uncertainty interval of the evidence, which is also the

uncertainty of the evidence. One of the purposes of

evidentiary inference is to reduce the uncertainty

interval.

Definition 4: assuming that two different pieces of

evidence A and B focal elements are summed

respectively, and the mass function is sum

respectively, the D-S combinatorial formula of the

result of m=m

⊕ m

is as follows:

)()(

)(

21 iiBABA

BmAm

iiii

⋅Σ

−

⊆∩=∩

(4)

)()(

21 iiBA

BmAm

⋅Σ=

∩

(5)

The k conflict coefficient, which reflects the

degree of conflict between the evidence. The greater

the k, the greater the conflict; when k = 1, it is a

complete conflict and is not suitable for this formula.

ANALYSIS OF THE STABILITY

FACTORS IN THE MINED-OUT

AREA

The factors causing geological disasters in the mined-

out area are various and a complex problem.(Gong,

2008) The data in the geological report are processed

and classified, and the influencing factors are divided

into the ore body factors and the collection

parameters of the mined-out area. The evaluation

indicator system of the mined-out area is established

as shown in Figure 1.

Figure 1: Stability evaluation index system of mined space area.

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4 THE RISK EVALUATION

METHOD BASED ON D-S

EVIDENCE THEORY

Based on D-S evidence theory, the risk evaluation

method with evidential reasoning is proposed. With

data from a coal mined in Yulin, this part gives the

main experimental processes of the method.

4.1 Identification of the Risk

Assessment and Identification

Framework of the Mined-Out Area

According to D-S evidence theory, assuming that all

possible results we can recognize after the problem

occurs can be expressed in terms of a set called the

identification framework θ. For the risk assessment of

coal mined-out area (Ding, 2009; Chen, 2013), based

on the fact that we want to know the current safety of

an area of the mined-out area, all possible results of

the problem obtain the identification framework for

the mined-out area hazard assessment of this problem

θ = {safety state, basic safety state, critical state,

failure state}. The identification framework can

basically comprehensively express the judgment of

the slope safety assessment

. Conclusions reached

using evidential reasoning methods, it is a confidence

measure vector on a subset of evaluation objects in

the recognition framework. In the research conducted

in this paper, the result is the confidence vector of a

certain mined-out region on the identification

framework (safe state, basic safety state, critical state,

failure state)

4.2 The D-S Evidence Argument

Synthetic

4.2.1 Division of the Basic Index Interval

Combined with the risk assessment indicator system

of the mined-out area and the basic probability

division based on interval number, the collected 8

indexes are divided according to the four states of the

identification framework. See in Table 1.

4.2.2 Probability Allocation

Similarly, the basic index selected on the

identification framework, giving the basic probability

distribution process of the mining thickness ratio:

(1) Determines the number of intervals.

According to Table 1 the result of thickness ratio on

identification frame is: [25,35], [15,25], [10,15],

[0,10], using the four interval number as the interval

number model.

(2) Determines the identification interval. The

mining thickness ratio of mined out area No. 1 is

22.74.

The identification interval of the thickness ratio

is: [22.74,22.74].

(3) Calculates the interval distance. The distance

of the deep mining thickness ratio under the

identification framework θ is calculated, and the

results are as shown in Table 2:

Table 1: Division of the risk assessment index interval in the mining space area.

Evaluation indicators Highest

Securit

level

Normal Security

level

Hidden

dan

ers

Damage

state

Deep mining and thickness ratio [25, 35] [15, 25] [10,15] [0,10]

Top plate thickness (m) [15, 25] [10, 15] [5, 10] [0, 5]

Coal seam inclination angle(°) [0,15] [15, 30] [30, 45] [45,60]

Slope-dip angle is (°) [0, 15] [15, 25] [25, 45] [45,60]

Compressive Strength (Mpa) [70, 100] [50, 70] [30, 50] [0, 30]

Tensile strength (Mpa) [5,10] [3, 5] [1.5, 3] [0, 1.5]

Shear off strength (Mpa) [6, 10] [4,6] [2, 4] [0, 2]

Note: In some index interval division, the maximum interval value cannot be given. For example, the compressive strength

is considered greater than 70, but a determined interval is needed in the calculation, so a maximum value is set artificially,

which does not affect the calculation result.

Table 2: Interval distance.

Identification framework Highest

Security level

Normal

Security level

Hidden dangers Damage state

Basic probability matching 0.1595 0.3992 0.2565 0.1847

Study on the Risk Evaluation Method of Ground Collapse in the Mined-Out Area Based on D-S Evidence Theory

299

Table 3: Interval similarity.

Identification framework Highest Security

level

Normal Security

level

Hidden dangers Damage

state

Distance 10.1459 9.2748 12.0798 14.9161

Table 4: Basic probability allocation of all indicators in the mined space area No. 1.

Evaluation indicators Highest

Security level

Normal

Security level

Hidden

dangers

Damage state

Deep mining and thickness ratio 0.1595 0.3992 0.2565 0.1847

Top plate thickness 0.1522 0.3838 0.2872 0.1768

Coal seam inclination angle 0.4242 0.2949 0.1633 0.1177

Slope inclination angle 0.3615 0.3554 0.219 0.0642

Compressive strength 0.1889 0.3921 0.2606 0.1585

Tensile strength 0.1356 0.3785 0.3179 0.1679

Shear-off strength 0.1528 0.3793 0.2888 0.1791

Lithology 0.25 0.35 0.2 0.2

Table 5: Credibility of the risk grade of some mined-out areas.

Mined-out Area

Num

Caularea risk level credibility

Level I Level II Level III Level IV

Mined-out Area No.1 0.0502 0.4278 0.5132 0.0087

Mined-out Area No.10 0.1392 0.7222 0.1359 0.0026

Mined-out Area No.11 0.1335 0.7332 0.1308 0.0025

Mined-out Area No.34 0.5687 0.3505 0.0783 0.0024

Mined-out Area No.35 0.5854 0.3354 0.0766 0.0025

(4) Calculates the interval similarity. The

similarity between the mining thickness ratio and the

four intervals is calculated by formula. Results are

shown in Table 3.

(5) The normalization treatment of interval

similarity obtains the probability allocation of each

state under the recognition framework and get the

result.

This probability distribution is shown in Table 4.

Through the judgment matrix obtained from the

basic probability allocation function, the index

weight is:

w = [0.1171, 0.0496, 0.2988, 0.2587, 0.1090, 0.0265, 0.0659, 0.0743].

We weighted evidence fusion for mined-out area

1, and the mass function for the influence indicators

of mined-out area 1 is as follows:

Mining thickness ratio (𝑚



),𝑚



{Level I, Level II,

Level III and Level

IV}=(0.1595,0.3992,0.2565,0.1847);

Top plate thickness is (𝑚



),𝑚



{Level I, Level II,

Level III and Level

IV}=(0.1522,0.3838,0.2872,0.1768);

Coal seam dip angle (𝑚



),𝑚



{Level I, Level II,

Level III and Level

IV}=(0.4242,0.2949,0.1633,0.1177);

Slope angle (𝑚



),𝑚



{Level I, Level II, Level III

and Level IV}=(0.3615,0.3554,0.2190,0642);

Compressive strength (𝑚



),𝑚



{Level I, Level II,

Level III and Level

IV}=(0.1889,0.3921,0.2606,0.1585);

Tensile strength (𝑚



),𝑚



{Level I, Level II, Level

III and Level IV}=(0.1365,0.3785,0.3179,0.1679);

Shear strength (𝑚



),𝑚



{Level I, Level II, Level

III and Level IV}=(0.4242,0.2949,0.1633,0.1177);

Top slab lithology (𝑚



), 𝑚



{Level I, Level II,

Level III and Level IV}=(0.25,0.35,0.20,0.20).

The mass functions on 4 identification

frameworks are fused, so the 𝑚



−𝑚



− fusing

result is M, M{Ⅰ} = 0.08, M{Ⅱ} = 0.54, M{Ⅲ} =

0.26, M{Ⅳ} = 0.12, then the new mass function is M

{I, II, III, IV} = (0.08,054,0.26,012). According to the

fusion results of the first two mass functions and the

third mass function, the results of the second fusion

and the fourth mass function, thus the security level

credibility of the final No.1 on the identification

framework 𝜣 after n-1 fusion, and the No.10,11,34

and 35 are randomly selected for the above fusion

calculation. The results are shown in Table 5.

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4.3 DS Evidence Theory Fusion Result

Analysis

Combining the above calculation results, the multi-

source information fusion based on D-S evidence

theory is used to determine the selected 5 mined-out

areas, and to get the basic credibility on the

identification framework 𝜣. As it appears from Table

5, the credibility of No.1 is 0.0502. From the

perspective of probability, the probability that mined-

out area No.1 is safe is 5.02%. The probability of

relative safety is 42.78%. The probability of being in

a dangerous state is 51.32%, The probability of being

in very dangerous is 0.87%, Therefore, the final risk

assessment result of No.1 mined-out area is relatively

dangerous, which means Col collapse may occur.

Similarly, the evaluation result of No.10 is level

II ,which is relatively safe; the evaluation result of

No.11 is level II and is relatively safe. The evaluation

result of No.34 and 35 is level I and they are in a very

safe state.

5 CONCLUSIONS

According to the method proposed in this paper, the

risk identification framework of four states was

established using data from a mine in YuLin, nine

influencing factors were selected to establish the

stability evaluation index system, and the D-S

evidence theory is used to weight the probability

distribution of the index. At last, the experimental

result is consistent with the actual situation of the

mine,

The effectiveness of the multi-source information

fusion method is verified, and a new feasible way is

provided for the mine mining area Hazard

assessment.

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