ORIGINAL ARTICLE

Assessment of groundwater changing trends throughthe generalized large well method with confined–unconfined flowmodel in open-pit mine area

Tianxin Li • Hongqing Song • Gang Huang •

Ying Bi • Xiyao Li

Received: 10 February 2013 / Accepted: 15 May 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract In this paper, a simple but accurate method

(generalized large well method) is presented to assess

groundwater level trends during mine exploitation. This

method includes a mathematical model of confined–

unconfined well flow and a corresponding analytical solu-

tion. Based on the method, a case study was analyzed with

data from the Yimin open-pit mine. As a result, the radius

of groundwater level rose, along with the increase of the

exploitation intensity. Moreover, a suitable value of

pumping flow could be beneficial to understanding poten-

tial groundwater contamination concerns. Additionally, it

has also been predicted that the groundwater level of the

Yimin open-pit mine will change within the next 3 years.

The Yimin open-pit mine case study demonstrates the

validity of the analytical method explained herein. The

presented methodology provides a theoretical foundation

for assessment of groundwater changing trends in other

open-pit mines with similar hydrogeological conditions.

Keywords Generalized large well method � Confined–

unconfined flow model � China � Groundwater protection �Open-pit mine

Introduction

In recent years, open-pit mines have been rapidly expanded

and developed to meet the demands of social and economic

development in China (Han et al. 2009). Mine exploitation,

including underground mining and surface mining, has a

detrimental influence on the natural environment. Mining

has been known to cause serious damage to the ground-

water system through the reduction of water resources, the

pollution of groundwater, and the decline of aquifer levels

(Dhakate et al. 2008). Therefore, understanding how to

assess the changes in groundwater trends during mine

exploitation is critical to addressing environmental pro-

tection concerns. The movement of groundwater in the

stratum is a complicated process, and it is often difficult to

retrieve accurate data of the geology and hydrogeology in

mining areas, especially underground (Cidu et al. 2009; Li

et al. 2011). These factors make it difficult to address the

problems between groundwater utilization and protection,

and open-pit mine development (Qiao et al. 2011). One of

the greatest concerns is that, once the aquifer water level

declines or water becomes polluted, it is more difficult to

reverse its condition (Wang et al. 2011a, b). In order to

achieve sustainable development and reach a secure status

regarding both quantity and quality of groundwater bodies,

some management methods for environmental protection

should be introduced, particularly in predicting ground-

water change and controlling contamination prior to mine

exploitation (Jimenez-Madrid et al. 2012).

Most previous studies have focused on the assessment of

contamination of groundwater via heavy or toxic metals,

nitrate, chromium, and the reactive transport of contamina-

tion from the mines to groundwater, etc. (Bicalho and Batiot-

GuilheC 2011; Li et al. 2012; Hajhamad and Almasri 2009).

Some studies have emphasized that the decrease of recharge

T. Li � H. Song (&) � G. Huang � Y. Bi

School of Civil and Environmental Engineering, University of

Science and Technology Beijing, Beijing 100083, China

e-mail: songhongqing@ustb.edu.cn

X. Li

Huaneng Yimin Coal and Electricity Corporation,

Hulunbeier 021000, Inner Mongolia Autonomous Region, China

123

Environ Earth Sci

DOI 10.1007/s12665-014-3357-8

has a direct impact on groundwater resources (Wu et al.

2009; Moustadraf et al. 2008; Puraji and Soni 2008). Others

have focused on the land subsidence caused by groundwater

table changes (Hu et al. 2009; Tia et al. 2011). Thus, in past

research, a set of models has been established to analyze the

results, which were useful for predicting the change of

groundwater after mines were exploited (Rolland et al. 2001;

Samato et al. 2004; Rapantova et al. 2007). Previously

established models were successfully developed for pro-

tecting the environment and saving water resources (Gao

2011). However, because the strata are complicated and

anisotropic, it is difficult to construct an accurate model to

describe strata properties. The previous models also dem-

onstrate limited abilities to predict the trends of groundwater

change. In order to improve understanding of the actual

groundwater conditions, it is necessary to build a more

accurate model.

As for open-pit mining, hydraulic head drawdown drops

in the process of pit dewatering, which often causes the

water table of the pumping well to drop under the roof of

the confined aquifer, thus forming groundwater confined–

unconfined well flow (Wu et al. 2004). Therefore, this

paper attempts to present a groundwater model to delin-

eate, analyze, and assess the groundwater changes during

the exploitation of an open-pit mine. As an analytical

method, this model has been validated in the present study

and can be applied to study and predict the trend of

groundwater before exploitation in an open-pit mine.

Model and methods

Description of the generalized large well methods

and assumption of model

Generalized large well method is a method that takes into

account all of the drainage wells in the open-pit mine as

one large well with equivalence in area. Therefore, the

water flowing into the large well is as much as that flowing

into all of the drainage wells (Moldovan et al. 2008).

According to the principle of groundwater dynamics, the

hydrogeologic boundary of the open-pit mine may be

represented by an unlimited supply boundary model (Wang

et al. 2011a, b). Based on this the water yield of the large

well can be approximately calculated based on Dupuit’s

basic equation for steady flow.

In the theory, with the process of dewatering, drainage,

and pumping in a confined aquifer, especially during the

dewatering of groundwater in an open-pit mine, the water

table of mine or pumping well often goes under the con-

fined aquifer for two main reasons: (1) high drawdown of

hydraulic head and (2) in some regions, pumping ground-

water in the fixed water table for a long time with low,

natural hydraulic head will transform groundwater flow

into unconfined water flow in the practical open-pit mine

(Chen and Lin 2011). The whole process is a transforma-

tion from pressure flow to non-pressure flow, with which

the confined–unconfined flow is formed. At the same time,

a phreatic aquifer, which is considered a free surface

change with the time, has the characteristics of unsteady

flow (Xi et al. 2010), as shown in Fig. 1. So the confined–

unconfined, unsteady groundwater flow is formed during

the process of the exploitation of open-pit mine.

According to the geological conditions of different

mines, aquifers in this model are divided into two layers:

the upper layer is phreatic aquifer and the lower layer is

confined aquifer, whose thickness is M, as shown in Fig. 1.

In order to establish the equation of confined–unconfined

well flow, the following conditions are assumed: (1) the

aquifer is taken as an elastomer, being isotropic, horizon-

tally distributed, and of the same thickness; (2) percolation

ought to satisfy Darcy’s law; (3) for a fully penetrating

well, water is assumed to flow into the well evenly; (4)

recharge and evaporation ought to be neglected; (5) the

dropping of the hydraulic head results in the discharge of

groundwater from the storage being instantaneously com-

pleted; (6) hydraulic head surface is horizontal before

pumping; (7) the boundary condition of the hydraulic head

is H0 and the equivalent radius of the well is r0; and (8) the

aquifer is extended unlimitedly as well as laterally (Guo

et al. 2008; Hussien 2013).

Governing equation of confined–unconfined flow model

Based on the analysis above, the ‘‘generalized large well

method’’ is applied to calculate the total pump discharge of

the mine. According to confined–unconfined unsteady flow

(Xi et al. 2010) in existence, a mathematical model

describing the whole process of confined–unconfined

unsteady groundwater flow in an open-pit mine is presented

as follows (Chen et al. 2006):

Homogeneous confined aquifer zone equation:

u ¼ KM H �M=2ð Þ ð1aÞ

Homogeneous unconfined aquifer zone equation:

u ¼ Kh2=2 ð1bÞ

Flow rate in confined–unconfined aquifer equation

(Chen et al. 2006):

Q ¼ 2prKMdH

dr¼ 2pr

dudr

Confined aquiferð Þ ð2aÞ

Q ¼ 2prKhdh

dr¼ 2pr

dudr

Unconfined aquiferð Þ ð2bÞ

In Eq. (2a), (2b), the rate of the cross session is Qr,

which can be presented as

Environ Earth Sci

123

Qr ¼ �2prdudr

ð3Þ

Through the deviation of Eq. (3), the following equation

is obtained:

dQr ¼ �2p ro2uor2þ ou

or

� �dr ð4Þ

As shown in Fig. 1, taking infinitesimal as the research

object, the following equation is produced:

�dQr � dt ¼ 2pr � dr � dH � l; ð5Þ

where l is specific yield, l = le in confined area, and

l = ld in unconfined area (Chen and Lin 2011). Substi-

tuting Eq. (4) into Eq. (5), an equation can be obtained as

follows:

1

lo2uor2þ 1

r

ouor

� �¼ oH

otð6Þ

Based on Eq. (1a) and Eq. (1b), further equations in

which T is the transmissibility coefficient of an aquifer are

obtained as follows:

ouot¼ du

dH

oH

ot¼ oH

ot

d

dHKMH � KM2

2

� �

¼ ToH

otConfined aquiferð Þ ð7Þ

ouot¼ du

dH

oH

ot¼ oH

ot

d

dH

1

2KH2

� �

¼ ToH

otðUnconfined aquifer) ð8Þ

Substituting Eqs. (7) and (8) into Eq. (6), the governing

equations of confined–unconfined areas can be combined

into one:

T

lo2uor2þ 1

r

ouor

� �¼ ou

otð9Þ

Here, the hydraulic conductivity (T) and specific yield

(l) are variables associated with the pumping flow of

confined–unconfined water. Average Tm and lm, which

correspond to different periods, are assumed to be constant.

Thus, Eq. (9) can be linearized, and the defined problem

can be described as (Guo et al. 2008):

Tm

lm

o2uor2þ 1

r

ouor

� �¼ ou

otr0� r\1; t [ 0ð Þ

u r; 0ð Þ ¼ u0 r0� r\1ð Þu 1; tð Þ ¼ u0 t [ 0ð Þ

limr!r0

2prouor¼ Q consð Þ

8>>>>>>><>>>>>>>:

; ð10Þ

in which u0 ¼ KMH0 � 12

KM2,r0 ¼ffiffiffiFp

q¼ 0:564

ffiffiffiffiFp

;

where

F area of mine (m2)

H confined aquifer hydraulic head (m)

H0 initial hydraulic head (m)

K permeability coefficient (m/s)

M confined aquifer thickness (m)

Q flow rate of the whole pumping wells (m3/s)

r radius of groundwater (m)

r0 reference radius (m)

Tm different period corresponding to average hydraulic

conductivity (m2/s)

t time (s)

lm different period corresponding to average specific

yield

u Jilin Gaussian potential function

Fig. 1 Sketch map of the

confined–unconfined

groundwater flow

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123

Analytical solution

Based on the characteristics of groundwater flow in open-

pit mines, an analytical model of special pumping flow

transformation from confined water to unconfined water is

derived as follows:

Boltzmann function transformation (Zhang et al. 2010)

equation u ¼ r2

4at, where a ¼ Tm

lm

Through substitution, the differential equation can be

changed into an ordinary differential equation as shown in

Eq. (11):

ud2udu2þ 1þ uð Þ du

du¼ 0

u uð Þju!1¼ u0

limu!u0

uouou¼ Q

4pconsð Þ

ð11Þ

8>>>><>>>>:

Solving Eq. (11), an equation can be obtained as

follows:

u uð Þ ¼ c1 �Z1

u

e�x

xdxþ c2 ð12Þ

Based on boundary conditions, coefficients c1 and c2 can

be expressed as

c1 ¼ �Q

4pe�u0

c2 ¼ u0 ¼ KMH0 �1

2KM2;

where u0 ¼ r20

4at

The expression of potential function can be presented as

u uð Þ ¼ � Q4pe�u0

�R1

ue�x

xdxþ u0; note W uð Þ ¼

R1u

e�x

xdx,

Du r; tð Þ ¼ u0 � u r; tð Þ ¼ Q

4pe�u0W r2

�4

Tm

lm

t

� �ð13Þ

Substituting Eq. (1a) into Eq. (13), the equation of

unconfined area is

2MH0 �M2 � h2 ¼ Q

2pKe�u0W r2

�4

Tm

lm

t

� �ð14Þ

Substituting Eq. (1b) into Eq. (12), the equation of

confined area is

H ¼ H0 �Q

4pKMe�u0W r2

�4

Tm

lm

t

� �ð15Þ

Thus, the analytical solution models Eqs. (14) and (15)

have been obtained. The physical meaning of the param-

eters is the same as above.

Groundwater transforms from confined well flow into

unconfined–confined well flow. At the stage of confined

well flow, when hydraulic head is greater than or equal to

confined aquifer thickness (hw C M), if r = r0, t = tc, and

u0 ¼ r20

.4 Tm

lmtc, the following equation can be obtained:

H0 �M ¼ Q

4pKMe�r2

0

�4Tm

lmtc

W r20

�4

Tm

lm

t

� �ð16Þ

In Eq. (16), all parameters except tc are given, and thus

the time of transforming from confined well flow into

unconfined–confined well flow (tc) can be calculated.

At the stage of unconfined–confined well flow, when

hw \ M, Tm and lm vary over time. With the advance of

time, changes of hw can be investigated based on the

materials affecting hydrogeological conditions of the mine

(Chen and Lin 2011). Therefore, based on Eq. (14), the

following equation can be obtained:

2MH0 �M2 � h2w ¼

Q

2pKe�r2

0

�4Tm

lmtc

W r20

�4

Tm

lm

t

� �ð17Þ

According to Eq. (17), when the water table in the well

equals hw:Tm

lmt, can be calculated. By substituting this into

Eq. (14) and (15), the depression cone curve corresponding

to the water table in the well (hw) can be obtained.

Results and discussion

Study area

Located in the north of the Inner Mongolia Autonomous

Region, north of China, the studied area covers nearly

65 km2 (Fig. 2). The open-pit mine is a synclinal basin

surrounded by low mountains and hills. The landform of

the south area is the highest point at 906.50 m in altitude

while the altitude of the central area ranges from 644 to

781 m with a gentle slope. The Yimin River, 359 km in

length, flows into the east mine and covers a basin area of

*9,105 km2.

The area is in the mid-temperate zone of China. The

average annual precipitation was 354.73 mm during the

sampling period (2003–2008) and was distributed unevenly

throughout the year with the majority falling from June to

September, and the average annual evaporation was

1,166.0 mm.

Groundwater in the Yimin open-pit mine is developed

from two aquifer types: sand and gravel aquifers (also

called unconsolidated deposits), and bedrock aquifers.

According to borehole data, regional aquifers are divided

into three groups based on vertical direction: quaternary

sand and gravel aquifers, the tertiary sand and gravel

aquifers, and coal seams, respectively. The top aquifer

consists of quaternary sand and gravel aquifer, which flows

continuously. It is distributed widely above the coal seams.

Environ Earth Sci

123

The lithology of an aquifer is made up of sand, gravel,

pebbles, coarse sandstone, and medium sandstone, and

belongs to the category of porous aquifer. The tertiary sand

and gravel aquifer, which consists of well-sorted sand,

gravel, and coarse sandstone, also belongs to the porous

aquifer category. Its hydraulic conductivity and aquosity

are stronger, so it is closely connected with groundwater.

The coal seams aquifer includes coarse sand and gravel,

whose thickness ranges from 40 to 90 m. This aquifer has

the strongest hydraulic conductivity and aquosity. Atmo-

spheric precipitation and recharge from the other aquifers

are the main sources of groundwater.

Confined–unconfined flow model validation

Based on the long observed data of hydrology in the

studied area from the years 2008–2011, some parameter

values were obtained, as listed in Table 1. According to the

Fig. 2 Map of the study area

Table 1 The actual measuring

of parameters in the study areaSymbol H0 (m) K (m/s) M (m) r0 (m) hw (m)

2008 2009 2010 2011

Value 660 3.7209 9 10-4 80 1,009.3 72 69 65 61

Fig. 3 The comparison of

analytical value and real data in

2008–2011

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123

materials concerning hydrogeological conditions of the

mine, pumping discharge obtained is the annual average,

which varies from year to year.

The data of average hydraulic head each year, which

was observed in the studied area, changed with the distance

from the center of the mine to the measured position. The

observed data and calculated values from analytical solu-

tions are shown in Fig. 3. The figure shows that model

predicted values derived here matched well with the

practical data.

The comparison concludes that the trend of groundwater

between calculated value and real value was very close

during the 4 years of study, which was almost the same

around the center of the open-pit mine. The groundwater

depression curve derived by the formula, which is deduced

from the model, is more precise. Therefore, the calculated

value has been validated correctly and may be used to

predict the trend of groundwater in future years. It also can

be applied in other open-pit mines with the same envi-

ronmental and hydrogeological conditions as the Yimin

study site.

Analysis of the trend of groundwater

with the exploitation quantity

We obtained the trend of the groundwater radius with

Eq. (15) in the studied area from 2008 to 2011 in Fig. 4.

The figure clearly shows that the radius of groundwater

gradually increased and the hydraulic head decreased in the

same water table each year. When the hydraulic head was

652 m, the value of groundwater radius was slightly more

than 2,500 m in 2008, but it reached the maximum value of

about 3,700 m in 2011. From 2008 to 2011, the value of

groundwater radius decreased by 1,200 m, which is due to

excessive exploitation.

We acquired exploitation quantity and groundwater

radius from 2008 to 2011, as shown in Table 2, which

showed that the difference of exploitation quantity between

2008 and 2009 reached a maximum of 4.42 9 106 (t), but

the difference between 2010 and 2011 reached the mini-

mum of only 3.3 9 105 (t). As a result, the radius of

depression cone curve increased much from 2008 to 2009.

And from Table 2, it can be seen that the radius of

groundwater increases along with an increase in the

quantity of exploitation.

Analysis the changing trend of groundwater at different

flow rate

We took the year of 2011 as an example to analyze the

radius of groundwater in the condition of different flow rate

values as shown in Fig. 5.

As shown in Fig. 5, the hydraulic head reached the

lowest point of 620 m when Q was at its highest value of

1.09 9 105 m3/day. The radius of groundwater also

reached the maximum value of *5,000 m in the same

water table at 653 m. While the hydraulic head was only

653 m the radius of groundwater was *1,000 m when

Q = 3.89 9 104 m3/day. The lower the flow rate, the

better the groundwater could be recovered. This illustrates

that the pump discharge is relevant to the trend of

groundwater change, which agrees with the results of

Table 2. By changing the values of flow rate it was dis-

covered that the trend of groundwater decreased while the

value of flow rate increased. However, in the real envi-

ronment of open-pit mine exploitation the groundwater

condition was often badly damaged and difficult to recover,

which caused negative effects such as groundwater deple-

tion, ground subsidence, and pollution of groundwater.

According to the analysis above, in the real situation, a

suitable value of pumping flow for rational exploitation and

better protection of groundwater can be achieved.

Groundwater trend prediction

The analytical model was used to predict the trend of

groundwater change over the next 3 years, as shown in

Fig. 6. Pumping discharge (Q) is calculated based on the

pumping discharge over several years.

It can be seen clearly that the changing trend of

groundwater from 2012 to 2014 followed the same trend

seen in 2011. With increased time the hydraulic head value

of the groundwater increased gradually, and the radius of

groundwater declined in the same water table. This shows

that the groundwater table is seriously damaged and that

proper control of several factors, including pumping, is

needed. As shown in Fig. 6 the analytical model managed

Fig. 4 The trend of groundwater in the study area in 2008–2011

Environ Earth Sci

123

to predict the changing trend of groundwater for the

3 years that followed the original study.

The groundwater system and its movement are com-

plicated; therefore, the best way to protect groundwater

during the exploitation of open-pit mines is to know how it

is changing. The analytical model presented herein can be

used to predict the trend of groundwater prior to exploi-

tation. Thus, the model provides a beneficial, basic method

to improve protection of groundwater resources and guid-

ance on how to conduct exploitation operations.

Conclusions

In the present study, based on the special water flow model

(the confined–unconfined, unsteady groundwater pumping

flow model), an analytical model has been derived to cal-

culate the radius of groundwater changes. The Yimin open-

pit mine study area provides long-term observational and

quantitative data. Through the analysis, it can be seen that

calculated values and real values were very close, and the

accuracy of the model was validated. In addition, the trend

of groundwater from 2008 to 2011 has been analyzed,

through which a conclusion that the radius of groundwater

increased along with the increase of the quantity of

exploitation can be drawn. An increase in flow rate values

was found to correspond to a decrease in the groundwater

table. In fact, in the real situation, a suitable value of

pumping flow can be obtained for rational exploitation and

groundwater protection, and it will not be beyond the

condition of recovering. This analytical model also offered

an effective method for predicting future groundwater

changes. Therefore, the use of this model is a suitable

method for studying and predicting the trend of ground-

water change before exploitation, and hopefully to instruct

people on useful methods of protecting groundwater

resources.

Acknowledgments The authors gratefully acknowledge the Public

Welfare Industry Special Research of China under Grant 200909063,

the Fundamental Research Funds for the Central Universities under

Grant FRFTP12003A and the Nature Science Foundation under Grant

41303059 for financial support. The authors also express gratitude to

researchers of Yimin open-pit mine for their cooperation.

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