Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 13, No. 1, 2024 

 

40 

Solving	the	Ultimate	Water	Accumulation	Depth	of	
Artificial	Dam	in	Coal	Mine	Underground	Reservoir	
Based	on	The	Galerkin	Method	
Zhuangzhuang Hou 

School of Civil Engineering, Henan Polytechnic University, Jiaozuo 454000, China 

 

Abstract: In order to improve the problem of low utilization rate of groundwater in the process of coal mine production, some 
mining areas in northwest China use the goaf of the working face as a water storage space, and establish underground reservoirs 
to realize water retention mining. In order to solve the problem of the stability of the underground reservoir structure, this paper 
studies the ultimate water level height that the artificial dam can bear. The concrete wall of the artificial dam under the action of 
water pressure is simplified as the mechanical model of the four-sided solid support plate, and the expression of the strain 
deflection and the expression of the internal stress function of the dam are derived by using the Galerkin method. The ultimate 
head height that the dam can withstand is calculated to be 22m. 

Keywords: Underground reservoirs; artificial dams; elastoplastic mechanics. 
 

1. Introduction 
China is a country with coal as the main energy source, and 

coal accounted for 57.7~63.8% of China's total energy 
consumption in 2015~2019. In the process of coal mining, the 
cracks of the roof gradually develop under the influence of 
mining, which conducts the aquifer and produces a large 
amount of mine water, resulting in a serious waste of 
groundwater resources. According to statistics, the amount of 
groundwater resources wasted in the coal mine production 
process in China reaches about 8 billion tons every year, and 
the effective utilization rate is only about 25%. [1]. With the 
gradual depletion of coal resources in the central and eastern 
parts of China, the focus of the development of China's coal 
resources has gradually shifted to the west. However, the 
climate in the western part of China is dry, the precipitation is 
small, and the evaporation is much greater than the 
precipitation, and the discharge of mine water to the surface 
will cause a large evaporation loss. This makes the 
contradiction between the development of coal resources and 
the shortage of water resources in the western region 
particularly prominent [2]. In this regard, Academician Gu 
Dazhao proposed a coal mine underground reservoir with 
"guiding and storing use" as the core, using the goaf to store 
groundwater resources [2,3]. After reviewing the relevant 
literature, it is found that there are few studies on the stability 
of artificial dams in underground reservoirs, and the stability 
of concrete structures is mostly focused on the stability 
analysis of surface reservoir dams [4–5]。Chen yang [6] The 
seepage field around the dam was simulated by a combination 
of numerical simulation and similar experiments, and the 
seepage flow around the dam was calculated. Fang Jie [7] 
Through the combination of theoretical derivation, similar 
model experiments and numerical simulation, the stress-strain 
law and failure mode of the artificial dam under the action of 
water pressure are studied, and the seepage law of the 

artificial dam and the trench site are summarized, and the 
comprehensive evaluation criteria for the stability of the 
artificial dam are summarized and analyzed according to the 
research results. Bai Dongyao et al [8] Through numerical 
model and theoretical analysis, the vulnerable position and 
maximum bearing capacity of the artificial dam of the 
underground reservoir of Lijiahao Coal Mine under the action 
of water pressure were studied. Fan Fan et al [9] The influence 
of confining pressure on the stability of artificial dam was 
studied by using FLAC3D numerical simulation software, 
and the results showed that low confining pressure could 
effectively improve the stability of the dam, but high 
confining pressure would promote the failure of the artificial 
dam. Zhi Guojun[10] Based on the shallow burial and large 
mining height working face in Shendong mining area, 
FLAC3D numerical simulation software was used to study 
the development and displacement of the plastic zone of the 
artificial dam excavation part, and the trenching parameters 
of the artificial dam in Shendong mining area were reasonably 
designed. 

2. Establishment and Solution of 
Mechanical Model of Artificial Dam 
Mass 

In order to prevent the reservoir water from entering the 
adjacent working face through the coal pillar roadway, the 
concrete wall is poured in the roadway, because the 
surrounding rock stress has been in a stable state at this time, 
the concrete wall structure of the artificial dam is less stressed 
by the surrounding rock after construction, and mainly bears 
the action of horizontal water pressure. In order to simplify 
the calculation, the water pressure is regarded as a uniform 
load, and the concrete wall can be regarded as a plate-like 
structure with four sides fixed support and one side applied 
uniform load, and its simplified model diagram and 
coordinates are shown in Figure 1. 

 



 

41 

O x

y

a

b

a

b

 
Figure 1. Simplified mechanical model of artificial dam 

 
The Galerkin method in elastic mechanics is used to 

analyze the mechanical model, and the coordinates are set as 
shown in Figure 1, then the boundary conditions are as 
follows: 

 

𝜔 0 
𝜕𝜔
𝜕𝑥

0 𝜔 , 0 
𝜕𝜔
𝜕𝑦

0 

 
The expression for the deflection is: 

 

 𝜔 𝐶 𝜔 𝑥 𝑎 𝑦 𝑏 𝐶 𝐶 𝑥 𝐶 𝑦 ⋯  (1) 

 
It can be seen that no matter how the value of the 𝐶  is 

taken, the above equation can meet the boundary conditions 
of the model. Take only one item for calculation, i.e.: 

 
𝜔 𝐶 𝜔 𝐶 𝑥 𝑎 𝑦 𝑏       (2) 

 
The result is: 
 
 

𝜔 𝜔 𝑥 𝑎 𝑦 𝑏         (3) 
 
 

𝛻 𝜔 2            (4) 

 
8 3 𝑦 𝑏 3 𝑥 𝑎 4 3𝑥 𝑎 3𝑦 𝑏 𝐶  

 
The uniform load on the surface of the thin plate is q, 

considering the symmetry of the model, which can be 
obtained by the Galerkin method: 

 

4𝐷 8 3 𝑦 𝑏 3 𝑥 𝑎 4 3𝑥
𝑎 3𝑦 𝑏 𝐶 𝑥 𝑎 𝑦

𝑏 d𝑥d𝑦 4𝑞 𝑥 𝑎 𝑦 𝑏 d𝑥d𝑦    (5) 
 
After the points, the 𝐶  is obtained 
 

𝐶               (6) 

 
where 𝐷  is the bending stiffness of the sheet, and the 

expression is:𝐷  

Substitution 2: 
 

𝜔              (7)  

 
Therefore, the stress component in the plate can be 

expressed as 𝜔 as follows:  

 

 

𝜎
7𝑞𝐸𝑧 3𝑥 𝑎 𝑦 𝑏 𝜇 𝑥 𝑎 3𝑦 𝑏

32𝐷 𝑎 𝑏
4
7 𝑎 𝑏 1 𝜇

 

𝜎
7𝑞𝐸𝑧 𝜇 3𝑥 𝑎 𝑦 𝑏 𝑥 𝑎 3𝑦 𝑏

32𝐷 𝑎 𝑏
4
7𝑎 𝑏 1 𝜇

 

𝜏
7𝑞𝐸𝑧 𝑥 𝑥 𝑎 𝑦 𝑏 𝑦 𝑥 𝑎 𝑦 𝑏

32𝐷 𝑎 𝑏
4
7𝑎 𝑏 1 𝜇

 

(8) 

 

The formula for calculating the principal stress is:  



 

42 

𝜎
𝜎 𝜏        (9) 

Equation 8 and Equation 9 can obtain the expression of 
principal stress at a certain point in the dam as follows: 

 

𝜎
𝜎

21𝑞𝑧 1 𝜇 𝜇 3𝑥 𝑎 𝑦 𝑏 𝑥 𝑎 3𝑦 𝑏

16 𝑎 𝑏
4
7𝑎 𝑏

⎷
⃓⃓
⃓⃓
⃓⃓
⃓⃓
⃓⃓
⃓⃓
⃓⃓ 21𝑞𝑧 1 𝜇 𝜇 3𝑥 𝑎 𝑦 𝑏 𝑥 𝑎 3𝑦 𝑏

16 𝑎 𝑏
4
7𝑎 𝑏

7𝑞𝐸𝑧 𝑥 𝑥 𝑎 𝑦 𝑏 𝑦 𝑥 𝑎 𝑦 𝑏

32𝐷 𝑎 𝑏
4
7𝑎 𝑏 1 𝜇

 

(10) 

 
The artificial dam is made of C25 concrete, and according 

to the Code for Concrete Structure Juice Design GB50010-
2010, the design value of tensile strength of C25 concrete is 
1.270MPa, and the design value of compressive strength is 
11.900MPa. The size of the roadway is 5m wide, 3m high, 
and 1m thick. From equation 4-7, it can be seen that the 
maximum deflection of the dam occurs at the midpoint of the 
dam, and the maximum principal stress should also occur at 
the midpoint of the dam's backwater surface, which is 
calculated by substituting the dam parameters and the 
coordinates of the center point of the dam's backwater surface. 
When the head height is 21m, the water pressure q=0.21MPa, 
and the maximum tensile stress of the dam is 1.26MPa, which 
is less than the ultimate strength of the material. When the 
head height is 22m, the water pressure q=0.22MPa, and the 
maximum tensile stress of the dam is 1.32MPa, which is 
greater than the ultimate strength of the material. 

Therefore, through theoretical calculation, 21m is taken as 
the limit head of the artificial dam. 

3. Conclusion 
A theoretical analysis model was established by using the 

elastic mechanics thin plate problem, combined with the 
elastic mechanics Galerkin method and the plane stress 
problem solving method, to establish the expression of the 
strain deflection of the concrete wall of the artificial dam 
under the action of water pressure in the goaf and the 
expression of the internal stress function. Through the 
calculation, the ultimate head height that the dam can 
withstand is 21m. 

References 
[1] Xie heping, Qian Gaoming, PPeng Suping, et al. Sustainable 

Capacity of Coalmining and Its Strategic Plan[J]. Strategic 
Study of CAE, 2011, 13(6): 44-50. 

[2] Gu Dazhao, Zhang Yong,Cao Zhiguo. Technical Progress of 
Water Resource Protection and Utilization by Coal Mining in 
China[J]. Coal Science and Technology, 2016, 44(1): 1-7. 

[3] Gu Dazhao.Water Resource Protection and Utilization 
Engineering Technology of Coal Mining in“Energy Golden 
Triangle”Ｒegion[J]. Coal Engineering, 2014, 46(10): 34-37. 

[4] Xu Daoyuan, Fu Xiaoling, Zhu Weixuan, et al. Damage-
fracture Model for Concrete of Dam[J]. Journal of Dalian 
University of Technology, 1997(S1): 3-8. 

[5] Xu Daoyuan, Wang Xiangdong, Zhu Weixuan, et al. Damage 
to Concrete Dams and Its Simulation Calculation[J]. Journal of 
Hohai University (Natural Science Edition), 2002(4): 14-17. 

[6] Chen Yang. Research on theSeepage Prevention and Seepage 
Control Effect of Coal Mine Underground Reservoir Water 
Retaining Dam[D]. Tsinghua University, 2016. 

[7] Fang Jie. Study on Deformation Failure Mechanism and 
Stability Evaluation of Artificial Dam of Underground 
Reservoir in Coal Mine[D]. China University of Mining and 
Technology (Beijing), 2021. 

[8] Bai Dongyao, Ju Jinfeng, Xu Jialin, et al. Stability Analysis of 
Mine Underground Reservoir Artificial Dam in Lijiahao 
Mine[J]. Journal of China Coal Society, 2017, 42(7): 1839-
1845. 

[9] Fan Fan, Liu Chenyi, Xu Jiansheng. Stability Analysis of 
Artificial Dam Body in Coal Mine Groundwater Reservoir[J]. 
Coal engineering, 2020, 52(11): 120-125. 

[10] Zhi Guojun, Liu Run, Yang Ruigang, et al. Research on 
Optimization of Cutting Parameters for Structuring Artificial 
Dam around Underground Reservoir in Coal Mine, 2022, 
41(02): 18-22.