Research Journal of Applied Sciences, Engineering and Technology 4(22): 4835-4839, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: May 08, 2012
Accepted: June 08, 2012
Published: November 15, 2012
Study of Block Stability of Surrounding Rock Mass of Main Transformer
Chamber Based on VATS Program
Zhongchang Wang and Huijun Wu
School of Civil and Safety Engineering, Dalian Jiaotong University, Dalian 116028, China
Abstract: The fracture of rock mass for main transformer chamber in HuangGou hydropower station is
very developed. The blocks slide along the discontinuous face or free face with the excavation of cavern. It
leads to the failure of normal construction. In the study, according to geology of disclosed discontinuous
face in detecting cavern and local three-dimensional coordinate of underground caverns, the vector analysis
program for tunnel stability VATS is compiled by using the method of vector analysis of the block theory
which is applicable to analyze the discontinuous rock mass and numerical software MATLAB. The
occurrence of joints, the coordinate of measuring point, the radius and vertical wall height of underground
caverns and other relevant engineering datum is required to input the program. The combination of
discontinuous face, boundary condition, geometric parameter, the mode of failure and stability factor of
existent unstable blocks is obtained. The geometry distributing characteristic of block and key
discontinuous faces in different position is figured by the AUTOCAD software. The guidance for
construction of underground caverns is provided.
Keywords: Block, key discontinuous face, main transformer chamber, the distributing characteristic,
vector analysis for tunnel stability
blocks is obtained. The guidance for construction of
underground caverns is provided.
INTRODUCTION
Block theory (Shi, 1997) and discontinuous
deformation analysis (Li et al., 2010) is a method which
develops currently for stability analysis of rock-mass
engineering. Its core conception is to find out the key
block of the free face under known combinations of
discontinuous faces (Shi, 1997), and judges briefly and
effectively movability and finite of the block rock by
Vector Analysis Method (Liu and Li, 2004; Pei and Shi,
1990), full space stereographic Method (Shi, 1977) and
half space stereographic net (Zhang and Aiqing, 2007).
Block theory is also widely applied with deepening the
theory (Hu et al., 2009; Liu et al., 2010). In the study,
there are lots of separated blocks which are formed by
the combinations of free face and the exposure
discontinuous faces in vault and side wall location.
These blocks are randomly distributed and the stability
is different. The instability of some key block is
possible to affect the whole stability of surrounding
rock mass. According to the attitude of disclosed
discontinuous face in detecting cavern and measuring
point coordinate, the vector analysis program for tunnel
stability is compiled by using the method of vector
analysis of block theory which is applicable to analyze
the discontinuous rock mass and numerical software
MATLAB. The combination of discontinuous faces, the
certain location and the parameter of stability of key
THE DESIGN OF VATS PROGRAM
The schematic diagram of VATS program flow is
shown in Fig. 1.
The solution of point of intersection between
discontinuous face and block: The coordinate system
of left hand is used for local three-dimensional
coordinate system of underground caverns. The x axis
is parallel to the axis of main transformer chamber. The
geometric parameters of geological structure face of
detecting cavern is Ai (xi, yi, zi, ai, ai). (xi, yi, zi) is the
coordinate of measuring point. ai, ai is respectively the
tendency and angle of inclination. The subscript i
denote the i geological structure surface. The space
equation of geological structure face is composed of the
coordinate of measuring point and normal vector:
pi 4  p i1 x  pi 2 y  p i 3 z
(1)
where,  pi1 , pi 2 , pi 3  is the normal vector. Table 1
shows the transformation relation of measuring point
coordinates for main transformer chamber. Table 2 gives
the parameter of main transformer chamber.
Corresponding Author: Zhongchang Wang, School of Civil and Safety Engineering, Dalian Jiaotong University, Dalian
116028, China
4835
Res. J. Appl. Sci. Eng. Technol., 4(22): 4835-4839, 2012
Introduction of engineering
Terrain
Rock property
Structure
Structural character of surrounding
rock of powerhouse
Attitude of structural face
Mechanical parameters
of structural faces
Measuring coordinate
Key block theory
Design of program
Input parameters
of structural
face and free face
Geometric analysis, find
limit and moveable block
Mechanical analysis, certain
the key block and calculate
the factor of stability
Deletion long and
narrow block
Kinematic analysis,
find out the
possible instability
The output and
disposal of data
End
Fig. 1: Schematic diagram of VATS program flow
Table 1: Transformation relation of measuring point coordinates for main transformer chamber
Main transformer chamber
X/m
Y/m
x'-28.93
y'+51.84
Z/m
z'+14.63
Table 2: The parameter of main transformer chamber
Parameter
------------------------------------------------------------------------------------------------------------------------------------------------- 0 /°
Chambers name
R/m
Height of arc/m
Span/m
Height of side wall /m
Density of rock-mass/t/m3
Main transformer
chamber
49
12.31
5.13
20
The function for circular arch wall may be expressed
as:
y 2  z  z c   R 2
2
18.10
other forms of blocks can be the collection of
tetrahedral. The volume formulation of tetrahedron is
expressed as:
(2)
where, z c is z coordinate of the center of circle in local
coordinate. R is the radius of circular arch.
The function of side wall is:
y
1
B
2
2.63
(3)
by the combination of the functions of structure face,
function for circular arch wall and side wall.
y0
1 xi
V 
6 xj
yi
xk
y
z0
zi
1
1
j
zj
1
yk
zk
1
(4)
The weight of block is:
W  V
The vertex coordinates of block A0 x 0 , y 0 , z 0  ,
Ai x i , y i , z i  , A j x j , y j , z j  , Ak x k , y k , z k  is obtained
x0
(5)
where,  is the density of rock mass.
The judgment of mode of movement: The mode of
movement of block is devided into three cases of
stability, collapse and slide. The stable block is limited
by the different structure faces and keep static. It is:
The calculation of the volume and weight of block:
Taking the tetrahedron as the most basic shape of block,
4836 Res. J. Appl. Sci. Eng. Technol., 4(22): 4835-4839, 2012
where
Wi

ri , rj is respecticvely the projection of structure

faces i and j of r .
Si
Hi
The calculation of the factor of stability: The
mechanical state of block on slide face is shown as
Fig. 2. When the block slide along single face, the
safety factor is:
Ni
βi
αi
Fig. 2: Block mechanics status of sliding face
fs 

r  Nl  0
(6)

where, r is the vector of resultant of forces. N l is the
normal vector of the structure face l pointing to the
inner of block.
The block collapses into the cavern without the
constaint of any structure face. The direction of
movement of block agree with the resultant of forces. It
is:

r  Nl  0
(7)
The block slides along single face when the
movement of block is affected by structure face i. The
expression is written as:
 
 
r  N l  0， s  N l  0
l  i 

where, s is the direction of movement of block.
 
 
 
ri  N j  0，r j  N i  0，s  N l  0
l  i  j 
(9)
Table 3: The parameters of structural planes for main transformer chamber
Name of structural faces
Trend/°
Tendency/°
J1
85
175
J4
275
5
J7
280
10
J8
275
5
J10
55
325
J11
85
355
J12
85
355
J13
80
350
J14
67
157
J15
55
325
J16
275
5
J19
280
190
J20
285
15
J21
285
195
J23
295
205
J24
280
190
J26
60
330
J30
70
340
J31
70
340
J32
345
75
J33
330
60
(10)
When the block slides along the intersection of two
discontinuous faces:
fs 
Wi cos  i tani  W j cos  j tan j  ci Ai  c j Aj
(Wi  W j ) sin
(11)
where, W is weight of the block, c is the cohesion, 
is inner friction angle, A is the area if sliding face.  is
the angle of shear stress and horizontal direction.  is
the angle of the intersection of joint face and horizontal
line.
THE CERTAIN SEARCH OF BLOCKS OF
SURROUNDING ROCK MASS
(8)
When the block slides along the intersection of two
discontinuous faces when the movement of block is
affected by structure faces i and j . The expression is
written as:
Wi cos  i tan   c i A i
Wi sin  i
Engineering geology of main transformer chamber:
The length of main transformer chamber of the Huanggou pumped-storage power station is 115.55 m.
The width is 20 m. The height is 18.1 m. The axial
direction is N49oW. The powerhouse is arranged in the
middle of rock mass of water diversion tunnel. The
embedded depth is 290 m. The surrounding rock of
powerhouse is fresh granite. The rock is hard and
Angle of inclination/°
55
175
80
85
20
35
35
50
55
85
75
50
75
70
70
85
60
45
25
70
80
4837 Coefficient of friction
0.575
Cohension/kPa
100
Res. J. Appl. Sci. Eng. Technol., 4(22): 4835-4839, 2012
Table 4: The data of exist block of main transformer chamber
Discontinuous faces
Weight of block/t
Sliding faces
J1, J10, J32
3333.38
J1, J32
J1, J31, J32
2.63
J1, J32
J4, J10, J12
192.02
J10, J12
J4, J10, J23
7.67
J4, J23
J4, J11, J23
176.62
J4, J23
J4, J12, J23
50.93
J4, J23
J7, J10, J12
28.91
J10, J12
J8, J10, J12
1069.49
J10, J12
J10, J12, J16
3078.25
J10, J12
J10, J12, J20
1954.20
J10, J12
J10, J12, J21
4864.29
J10, J12
J10, J12, J23
447.20
J10, J12
J10, J13, J16
3554.56
J13, J16
J10, J13, J19
167.22
J10, J 13
J10, J13, J21
236.19
J13, J21
J10, J19, J32
1473.10
J19, J32
J13, J16, J21
6472.21
J13, J16
J14, J15, J30
535.36
J15, J30
J14, J26, J30
42.19
J14, J26
J15, J19, J31
797.34
J15, J19
J19, J24, J31
3346.85
J24, J31
J26, J30, J33
93.14
J26, J33
The factor of stability
9.580
63.251
29.349
27.790
10.550
14.960
59.481
16.570
12.793
29.532
11.482
39.922
8.018
148.824
20.831
13.870
7.852
14.710
100.673
4.360
13.715
5.871
The location of block
Two points on the right side wall
Three points on the right side wall
Three points on the left side wall
Three points on the left side wall
Three points on the left side wall
Three points on the left side wall
Three points on the left side wall
Two points on the left side wall
Two points on the left side wall
Three points on the left side wall
One point on the left side wall
Three points on the left side wall
Two points on the left side wall
Three points on the vault
One point on the left side wall
Three points on the vault
Two points on the left side wall
Three points on the right side wall
Three points on the left side wall
Three points on the left side wall
Two points on the left side wall
Two points on the right side wall
integrity. The extension contains the whole the
underground caverns. The following principle should
be considered for analysis:

Vault
The discontinuous face is distributed in the whole
underground powerhouse if the discontinuous face
is disclosed on every wall.
The discontinuous face is not considered if it is not
disclosed on every wall. According to the above
principle, the statistical result of main
discontinuous faces is shown in Table 3.
The position of block in main transformer chamber
is searched by the VATS program.
The position of block in main transformer chamber
is searched by the VATS program, there are 26 blocks.
And the number of exist instable blocks is 22. The
combination of discontinuous face, boundary condition,
geometric parameter, the mode of failure and stability
factor of existent unstable blocks is shown in Table 4.
To intuitively display the geometry and the
position of block in main transformer chamber, the
drawing software AUTOCAD is used to display the
spatial distribution and geometric character of block, as
is show in Fig. 3. It can be seen that the instable block
of main transformer chamber mainly lies in the range of
the 10-60 m distance of point of origin in the location
of the left wall and left-vault. This is identity to the
development of joint and fault. The distribution of
block is concentrated on the left and right wall.
Therefore, the key range of main transformer chamber
is the range of 10-60 m. The safety monitoring and
support of the range should be strengthened to insure
the stability of surrounding rock of the powerhouse.
The more the number of block is, the more serious the
rock mass in the direction is incised by a key fault. The
Vault
right wall
0m
50m
100m
150m
Fig. 3: The distribution of plane location of instable blocks in
main transformer
14
12
10
8
6
4
2
0
J1
J4
J7
J8
J10
J 11
J12
J 13
J 14
J1 5
J 16
J19
J2 0
J21
J 23
J24
J2 6
J3 0
J 31
J 32
J33

left wall
Fig. 4: The column of key block number made of fracture for
main transformer chamber
number column of instable blocks made of fractured
faces for underground powerhouse is shown in Fig. 4. It
can be seen that the times of J10, J12, that formed the
key blocks is large, the times of J10 are thirteen.
Therefore the discontinuous face J10 should be paid
more attention.
4838 Res. J. Appl. Sci. Eng. Technol., 4(22): 4835-4839, 2012
CONCLUSION
The program MATLAB is used to compile the
calculating program VATS (Vector Analysis for Tunnel
Stability). The position of block in main transformer
chamber is searched by the VATS program. The
geometry distributing characteristic of block and key
discontinuous faces in different position is figured by
the AUTOCAD software. The number of blocks cut by
discontinuous faces in main transformer chamber is 26.
The number of the instable block is 22. And the blocks
are mainly located in the left and right wall which is in
the range of 10-60 m distance from point of origin. This
agrees with the development of discontinuous faces.
Therefore, the key range of powerhouse is the range of
10-60 m. The safety monitoring and support of the
range should be strengthened to insure the stability.
ACKNOWLEDGMENT
The author would like to thank the financial
support by the National Natural Science Foundation of
China (Grant No. 51009015) and Education Foundation
of Liaoning (No. L2010038).
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