INTRODUCTION
The present studies show that about eighty percents of floor water inrush accidents
relate to the faults directly or indirectly. Therefore fault water inrush is
becoming one of the hot issues in mine water inrush research. Scholars discuss
the fault water inrush’s laws with the methods of the theoretical mechanics
(Huang et al., 2010), numerical simulation (Li
et al., 2009; Bu and Mao, 2009; Li
et al., 2011; Guo et al., 2012),
experimental study (Huang et al., 2009) and
others (Liu and Wang, 2012; Shi
and Li, 2012; Zhang and Dong, 2011; Zhang
and Deng, 2012), which obtain large useful results. Such as, the failure
mechanism of waterresisting floor affected by fault is studied with rock shear
failure theory and the water inrush criterion is proposed according to the deduced
formula of critical water pressure (Huang et al.,
2010). Based on the model of hydromechanical coupling, the fault water inrush
process is simulated with RFPA^{2D}FLOW or other numerical simulation
software (Li et al., 2009; Bu
and Mao, 2009; Li et al., 2011). The effect
laws of faults on the height of water flowing fractured zone in floor is obtained
by similar simulation tests (Huang et al., 2009).
Also the fault water inrush is forecasted with microseismic monitoring technique
(Zhang and Dong, 2011; Zhang and
Deng, 2012). In one word, these researches focus on the effect or process
of the fault water inrush mostly, but the inner mechanics of water inrush is
not revealed, especially the research on fault open displacement affected by
water pressure is few in present.
In fact, combined with the water pressure and the ground pressure, just the
opening fault is the water conductive fault, which will lead to the happening
of water inrush. And it will provide certain theory basis and practical foundation
to the water inrush quantity prediction of fault or the floor water inrush that
study the law of the fault’s
open displacement affected by water pressure. Based on the clamped beam theory
of material mechanics, the law of the fault’s
open displacement affected by water pressure discussed in the study.
CALCULATION PRINCIPLE
Force analysis of fault: Under the influence of ground pressure, the
fault will active in mining stope and the fault can be named as the actived
fault. Its producing process can be divided into two parts, one is the compression
shear process along the initial fault plane and the other is tension process
along the top of fault.

Fig. 1: 
Schematic diagram of fault opening under water pressure 
The mechanical character of the fault plane is compressive, generally the normal
positive stress of the fault plane is (Shi and Han, 2004):
where, σ_{n} is the normal positive stress of the fault plane
and its unit is MPa. γ is the bulk density of the overlying strata and
its unit is kN_{●}m^{3}.
H is the mining depth and its unit is meter. α is the dip angle of the
fault and its unit is degree.
Under the condition of mining, the stress of the coal seam floor will release
gradually, which leads to the uncoordinated deformation of the fault’s
two walls. On the other hand, the fault plane will be expanded by the water
pressure from the aquifer. Thus, the wall of the fault near the goaf will move
towards the goaf and the actived fault will open. Then, the fault becomes the
water conductive fault. If the water flowing fractured zone of the coal seam
floor connects with the water conductive fault, the fault water inrush will
happen. The schematic diagram of fault opening under water pressure is shown
in Fig. 1. Where, P is the water pressure of aquifer, h is
the vertical distance from the coal seam floor to the aquifer.
Calculating model of fault open displacement: Based on the clamped beam
theory of material mechanics, the fault open displacement affected by water
pressure can be calculated. Of course, some mechanical hypotheses are necessary
in order to calculate the problem easily. The water pressure in the fault is
assumed as an invariable value. The rock strata between the floor and the aquifer
is considered and the overlying one on the coal seam is ignored when calculates
the normal positive stress of the fault plane. And the rock strata is a single
one, its bulk density can be used as the average one of the practical rock stratum.

Fig. 2: 
Calculating model 
Then, the normal positive stress of the fault plane is:
According to the clamped beam theory of material mechanics, the spandepth
ratio of the clamped beam is over eight times. Obviously, the fault meets this
condition. Therefore, the calculation of the fault open displacement affected
by water pressure can be considered to the rock beam bending problem with both
ends fixed and uniform load. The calculating model is shown in Fig.
2.
Where, F =Pγ hcos α. L is the length of the fault between the coal
seam and the aquifer. L^{’}
is the length of the fault between the aquifer and the mining face promoting
point which is shown in Fig. 1.
Then, the moment equation of rock beam is (Liu, 2004):
When L’≈L, then:
Thus, the flexing equation of the rock beam is:
where, v is the displacement corresponding to the point x, that is the open
displacement of the fault at point x. E is the elastic modulus of the rock beam.
I is the moment inertia of the rock beam. When x∈(0, L), the equation can
be integrated and simplified as:
And:
where, b is the width of the rock beam and h^{’} is the height
of the rock beam respectively. By institution of them, the equation becomes
as:
Here, v is the maximum open displacement of the fault. The equation is the
expression of the fault’s maximum open displacement affected by water pressure,
which can be used to distinguish the fault opening or not under the water pressure.
If P_{c} is the critical water pressure and v = 0 when the fault opens:
Thus, if P≤P_{c}, the fault closes. Inversely, if P>P_{c},
the fault opens. And the fault becomes the water conductive fault, which can
lead to the happening of water inrush easily under high water pressure. In fact,
h can be considered as the thickness of the impermeable layer in Eq.
8. Obviously, the bigger h is, the larger P_{c} will be. Therefore,
the water inrush will not happen easily if the thickness is big, which is consistent
with the engineering practice. And it proves that the discriminant method of
the critical water pressure is correct.
EFFECT FACTOR’S ANALYSIS
OF FAULT OPEN DISPLACEMENT
Effect of water pressure: If the value of water pressure P changes from
1.0 to 5.0 MPa, the values of other parameters are shown in Table
1. Because the range of the joint area near the fault is about 20 m generally
(Kang, 1996), the value of h^{’} is chosen
as 20 m. By institution of them into Eq. 7, the results of
the calculation are shown in Fig. 3. It shows that the fault’s
open displacement increases with the increasing of the water pressure. The closing
fault is opening gradually affected by the water pressure. Then, the fault changes
into the water conductive fault. When the coal face is driven near to the fault,
the water inrush will happen easily. The effect law of the water pressure is
coefficient with the practice water inrush. Such as the hydrogeology condition
is complex in Jiaozuo mining area (Liu, 2007). And
the water pressure value of the Ordovician limestone aquifer is over 6 MPa in
several mining area. So, the coal production is on the risk of the high water
pressure of the aquifer seriously.

Fig. 3: 
Relationship between the fault’s open displacement and
water pressure 
Table 1: 
Calculation parameters of water pressure 

For example, the water inrush accident of Zhongmacun mine in Jiaozuo mining
area caused by the fault in 1958. The value of the water pressure is 2.5 MPa
and the water inrush quantity reached over 6060 cubic h^{1}, which
led to flooded wells. And the accident is one of the typical water inrush accidents
in China.
Effect of rock’s elastic modulus: According to the rock mechanics,
the elastic modulus of rock or rock mass expresses the difficult degree of the
rock or rock mass deformation. The bigger the value of the elastic modulus is,
the larger the stress will need when the rock or rock mass produces certain
elastic deformation. It shows that its stiffness is bigger than others. Conversely,
the smaller the elastic modulus is, the smaller the stiffness of the rock or
rock mass will be. Generally, the lithology of the rock or rock mass near the
fault is weaker than that of other rock and its elastic modulus is also smaller
than others. So it is assumed that the elastic modulus value of the rock beam
varying from 1.0 to 10 GPa and the value of water pressure is 2.0 MPa. The values
of other parameters are shown in Table 1. By institution of
these values into Eq. 7, the results of the calculation are
shown in Fig. 4. It shows that the value of the fault open
displacement increasing with the decreasing of the rock’s elastic modulus
affected by the water pressure. It expresses that the weaker the lithology of
the rock is, the easier the opening of the fault is. Now, the compression fault
evolves into the open fault and the waterinconductive fault changes into the
water conductive fault.

Fig. 4: 
Relationship between the fault’s open displacement and
rock modulus 
Therefore, the weak lithology of the rock will cause the fault water inrush
easily because of the effect of high water pressure. It is consistent with the
study result of Huang et al. (2010).
EXAMPLE AND RESULTS
Discriminant of fault water inrush: Zhangcun mine lies in the central
part of Chaochuan mining area in Ruzhou City Henan Province. In present, the
main mining coal seam is the □_{1} coal seam. The geological structure
condition is medium to complexity. The direct water filling aquifer is Taiyuan
group limestone aquifer and the indirect one is the Cambrian limestone aquifer.
And the distance between the two aquifers is about 20 m. The most effect faults
on the mining of □_{1} coal seam include F_{47}, F_{59}
and F_{60}. The three faults all cut the stratum from □_{1}
coal seam to the Cambrian limestone aquifer. The Cambrian limestone aquifer
will provide sufficient water source for the faults because it can supply the
upper aquifer such as the Taiyuan group limestone aquifer directly. Therefore,
the effect of the Cambrian limestone aquifer on the faults is considered.
In order to distinguish the faults open or not, the method proposed above is
used. All related parameters are shown in Table 2, where P
is the practice water pressure of the Cambrian limestone aquifer and γ
is the average bulk density of rock stratum in coal seam floor. All parameters
are instituted in Eq. 8 and the calculating results are shown
in the last column of Table 2. It is found that P>P_{c}.
According to the discriminant method, the faults are all open affected by high
water pressure, which will lead to the happening of water inrush. Also it has
been proven with the engineering practice.
Table 2: 
Calculation results of critical water pressure 

Table 3: 
Calculation results of critical water pressure 

Table 4: 
Calculation results of critical water pressure 

Prediction of fault water inrush’s
quantity: With the deduced equation of fault open displacement under water
pressure, the open displacements of faults in Zhangcun mine can be calculated.
The values of parameters are shown in Table 2 and 3,
respectively. The calculating results lie in the last column of Table
3. Though every value of fault open displacement is small, its effection
is great on the quantity of fault water inrush.
According to the mechanism of seepage conversion, the initial quantity of fault
water inrush can be predicted under water pressure. The calculating equation
is as follows (Wu et al., 2009):
where, Q is the initial quantity of fault water inrush, its unit is m^{3}
h^{1}. b_{0} is width of fault water inrush tunnel, which can
be instituted with the width of fault zone. And γ_{0} is the bulk
density of water. μ is the dynamic viscosity of water, which is a constant.
n expresses the porosity of rock in fault zone. Other parameters are introduced
in Eq. 8.
In order to consider the effect of fault open displacement on the quantity
of fault water inrush, b_{0} is chosen as the sum of the fault open
displacement and the width of fault zone. The values of parameters and calculating
results are shown in Table 4. It can be found that the values
of Q are all more than 500 m^{3}•h^{1} from the table.
In fact, the mix mum quantity of fault water inrush happening in Zhangcun mine
before is 400 m^{3}•h^{1} and the maximum one is 943
m^{3}•h^{1}. Therefore, the calculating results are reasonable.
And the effect of fault open displacement on Q is obvious from Eq.
9. It shows that the application of fault open displacement is important
to predict the quantity of fault water inrush.
CONCLUSION
Based on the clamped beam theory of material mechanics, the maximum open displacement
equation of mining fault affected by the water pressure is deduced as:
and the discriminant method to distinguish the fault open or not caused by
the effect of water pressure is proposed.
The effect laws of the water pressure and the elastic modulus of rock beam
on the fault open displacement are analyzed. The results show that the fault’s
open displacement increases with the increasing of the water pressure. And the
weak lithology of the rock will cause the fault water inrush easily because
of the effect of high water pressure.
The example analysis shows that affected by water pressure all faults in Zhangcun
mine will open distinguished by the proposed method, which is proven with the
engineering practice. And the application of fault open displacement is important
to predict the quantity of fault water inrush.
ACKNOWLEDGMENTS
This study is funded by the National Natural Science Foundations of China (No.
51274095, 51104058 and 41204035), the Doctoral Fund of Henan Polytechnic University
under Grant B2011019 and the Young Key Teacher Foundation of Henan Polytechnic
University.