10th Asian Regional Conference of IAEG (2015)

A New Method for Characterization of Discontinuity Based on Digital Borehole Camera
Technology
Zengqiang HAN(1), Chuanying WANG(1), Hanhui WANG(2), Huatang SHI(2)and Miao WANG(3)(1) State Key Laboratory of Geomechanics and Geotechnical Engineering
Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China
E-mail: zqhan@whrsm.ac.cn(2) Changjiang Institute of Survey, Planning, Design and Research, Wuhan, China(3) CCCC Second Highway Consultant Co. Ltd, Wuhan, China
Abstract
Digital Borehole Camera Technology is an advanced method for engineering
geologic investigation, which can identify a large number of subsurface rock discontinuities
and calculate the geometric parameters. With the characteristics of big number, accurate
and deep buried, these parameters reveal the spatial distribution and combination form. A
new mathematics description method is proposed based on discontinuities characteristic
points which include information of occurrence and depth. Then, this method is used forresearch in connectivity of discontinuities and gets some innovative research results. This
research provides new ideas for stability evaluation of rock mass based on discontinuities
geometrical characteristics.
Keywords: structural plane, Digital Borehole Camera Technology, discontinuity characteristic
points1.

Introduction
Rock mass is a geologic body composed of rockblocks and structural plane which split rock (Alsoknown as discontinuity). The distribution andcombining form of structural planes in space formed
the structure of rock masses, which is the criticalfactor of engineering geological characteristics andmechanical property of rock masses. Only a few
structural planes developed in rock masses can beseen from outcrop rock area or artificial excavation
face, however, more of the structural planes are in theinterior of rock masses and very difficult to beobserved directly. [2-4] Digital Borehole Camera
Technology provides a new method to explore
structural planes in the interior of rock masses. It can
go deep into rock masses through borehole, identify
the structural plane and calculate the geometricparameters. By this technology, greater number andmore accurate data will be given for the research on
statistical regularities of structural plane. [5-6]
There are many differences between structuralplane data obtained from outcrop rock and borehole.
For example, the former data contains information of
trace length but does not contain information of
depth; however, the latter contains information of

depth but does not contain information of trace length.
So the traditional analytical methods used in outcrop
rock data are not applicable to the data from borehole.
In view of the above considerations, this paper put
forward a new method suitable for the structuralplane data obtained from borehole. This method
transforms the structural plane geometric parameters
into coordinate point, and every coordinate point is
the comprehensive performance of geometricparameters. It makes structural plane data more
numerical and easier to carry out statistical analysis.

[7-8]

2.

Characterization of Discontinuity
in Borehole

2.1 Basic assumption
Geometric feature of structural plane is thefoundation to research mechanical properties of rockmasses. The most basic geometric parameters include
occurrence, width, space, trace length etc. In order totransform and analyze these geometric parameters,
we firstly make the following assumptions:(1) The structural plane is a space plane ofunlimited extension;1

10th Asian Regional Conference of IAEG (2015)
X c  Rz  cos   sin   cos (2) Using the right hand rule of 3D Descartes
coordinate system.

Z c  Rz  cos   cos 

2.2 Discontinuity characteristic point under local
coordinate system
To establish local coordinate system, we choose
the center of borehole orifice to be the base point of
coordinate system. The positive X axis points to theEast, the positive Y axis points to the North and thepositive Z axis points to Vertical.
Describing
thestructuralplane
inthree-dimensional space with a point, we call thispoint structural plane characteristic point and denote
it by Pc defined as the crossover point between
structural plane and normal vector (i.e. plane normal)of structural plane from base point of coordinate
system. There are one to one corresponding featuresof structural plane and structural plane characteristic
point, reflecting the space form and space position of
structural plane.
Setting Pc coordinate as (Xc, Yc, Zc), theequation described by this point is:
X c  ( x  X c )  Yc  ( y  Yc )  Zc  ( z  Zc )  0

Through the above conversion formula, thegeometric parameters (dip, dip direction and depth)
will be converted into characteristic point coordinates
under the local space coordinate system.
2.3 Discontinuity characteristic point under global
coordinate system
To establish global coordinate system, we choose
orifice of the borehole at center of area or
representative borehole to be the base point of
coordinate system. The positive X axis points to theEast, the positive Y axis points to the North and thepositive Z axis points to Vertical.
Information of discontinuity characteristic point
obtained in the previous section is calculated under
the respective local coordinate system. In order toestablish the relationship between different
characteristic points, these information neednormalization processing under global coordinate
system. Supposing the origin point of local coordinate(2.1)

Also can be expressed as:system is PLO ( X LO , YLO , Z LO ) under global coordinate

X c  x  Yc  y  Z c  z  ( X c 2  Yc 2  Z c 2 )  0 (2.2)

system,

z

Z

y

the

discontinuity

PCL ( X CL , YCL , Z CL )

x

o

(2.4)

Yc  Rz  cos   sin   sin characteristic

point

under local coordinate system will








be transformed into PCL ( X CL , YCL , Z CL ) under global
Characteristic
pointsDiscontinuity
plane

coordinate system. The conversion equations are as
below:X CL  X LO  X CLYYCL  YLO  YCLXOZ CL  Z LO  Z CL

Fig.1 Schematic description of structural plane characteristic point

Setting the dip direction of structural plane
described by characteristic point as  , the dip as 

( PLO  PCL )( P  PCL )  0

and the crossover point between Z axis and structuralplane asYc
Xc

X  Yc  arctan( c
)
Zc
2

2

(2.6)

Hereinto, the point P is any point in global
coordinate system OXYZ.
In addition, unit normal vector of structural planeis the same, as below:

Rz , the equations of these parameters are:  arctan(2.5)

The equation of structural plane under global
coordinate system OXYZ is as below:n  ( X CL / root , YCL / root , ZCL / root )(2.3)

Hereinto,

X 2  Yc 2  Z c 2
Rz  cZc

Or as below:

2root  X CL 2  YCL 2  ZCL 2(2.7)

10th Asian Regional Conference of IAEG (2015)

characteristic
P2 ( x2 , y2 , z2 )pointscoordinate

P1 ( x1 , y1 , z1 ),. The distance between two characteristic

points can be expressed as below:
P1 P2  ( x1  x2 )2  ( y1  y2 ) 2  ( z1  z2 ) 2
Fig.2 Discontinuity characteristic point under global coordinate system

Z

Therefore, coordinate value of any point P(X, Y,Z) at the normal of structural plane from origin pointof global coordinate system OXYZ is as below:
X  t  X CL / rootY  t  YCL / root

Fracture 2
Fracture 1(2.8)

Two points
coincideZ  t  ZCL / root

YX

Hereinto, t is arbitrary value.
Take this formula 2.8 into formula 2.1, the valueof t can be calculated as below:

Fig.3 Sketch map of discontinuity connectivity analysis

Every fracture has the only corresponding
characteristic point coordinate under global
coordinate system. Under ideal condition, if the
distance of two characteristic points is zero (namely
the two points coincided), these two fractures may bebelong to the same structural plane (namely they haveconnectivity), as shown in Fig.3. But in the actual
situation, due to the measurement precision and error
limit, the two points are impossible to completely
coincide. Therefore, a minimum is setting as thecriterion whether they have connectivity and theformula is as below:t  root  (1  ( X CL  X LO  YCL  YLO  Z CL  Z LO )) (2.9)

The insertion point between normal of structuralplane (discontinuity) from origin point and structuralplane under global coordinate system OXYZ can beobtained. The coordinate of this point Pc ( X c , Yc , Z c )
will

be

calculated

PCL ( X CL , YCL , ZCL )bycharacteristicpoint

and origin point PLO ( X LO , YLO , Z LO )under local coordinate system.
X c  X CL  (1 
Yc  YCL  (1  P1 P2   P1 P2  (2.10)X CL  X LO  YCL  YLO  Z CL  Z LO)
X CL 2  YCL 2  Z CL 2

Z c  Z CL  (1 

3.

X CL  X LO  YCL  YLO  Z CL  Z LO)
X CL 2  YCL 2  Z CL 2

(2.11)

P1、P2 have connectivity
P1、P2 not have connectivity(2.12)The value of  will be setting based onrequired computational accuracy.
|P1P2| is the distance between two fracturescharacteristic points. If the value of |P1P2| is lessthan  , the two fractures may be belong to thesame structural plane. With the further analysis
on rock feature up and down the structural plane,
the result will be confirmed. If the value of|P1P2| is greater than  , the two fractures are noton the same plane.

X CL  X LO  YCL  YLO  Z CL  Z LO)
X CL 2  YCL 2  Z CL 2

Discontinuity Connectivity
Analysis Based on Characteristic
Point

3.1 Introduction
In the engineering geological survey, in order to
identify the geological conditions of a region, several
boreholes need to be drilled. Structural plane is ageological interface with a certain size, which may be
penetrated by more than one borehole. Therefore,
when using borehole camera technology to detection
discontinuities, different cutting trace of the same
discontinuity may be seen in adjacent boreholes. The
above is the principle of discontinuity connectivity
analysis. [1]Under global coordinate system, two fractures P1,P2 in adjacent boreholes are indicated by

3.2 Case analysis
Taking boreholes of a hydropower station dam
foundation grouting test as an example, connectivity
analysis between adjacent boreholes is carried out
based on the above method. The location of boreholes
in this engineering field is shown as Fig.4. The origin
point of local coordinate system is setting at the3

10th Asian Regional Conference of IAEG (2015)

center of every borehole orifice. According to theprinciple of middle construction, the origin point of
global coordinate system is setting at the center ofborehole DJ-1 orifice. The positive X axis points tothe East, the positive Y axis points to the North andthe positive Z axis points to Vertical.

1.25m

2.5m

2.5m

According to the particularity of structural planein borehole, a new mathematical description method
is proposed based on characteristic point and theconversion formula for transforming geometricparameters into characteristic point coordinate isderived. This method is applied to fracturesconnectivity analysis and the connectivity condition
is developed. Though the case analysis, this method
is proved correct and feasible.

1.25m

Acknowledgements
This study is subsidized by National Natural
Science Foundation of China (No.41402278) and by
Strategic Research Program of the Chinese Academyof Sciences (XDB10030200).

Fig.4 Location of boreholes

Fracture P1 is located in borehole DW-1 with dip
direction of SW238.5°, dip of 50°and depth of
2.164m. Fracture P2 is located in borehole DJ-3 with
dip direction of SW228.4°, dip of 55.3°and depthof 1.316m. Transforming the parameter information
into characteristic point under local coordinate system,
we can get the coordinates are P1CL (0.908, 0.557,-0.894), P2CL (0.461, 0.409, -0.426). Then we can get
the normalized coordinates P1 (-1.874, -2.518, 1.845),
P2 (-1.832, -2.514. 1.842) through transforming underglobal coordinate system.
The distance of the two points P1P2 is as below:

References[1] Han Zengqiang, Wang Chuanying (2013).
Research on connectivity of deep ore-lodes based on
digital borehole camera [J]. Disaster Advances, 6(8):41-46[2] Huang Runqiu et al (2004). Complicated rockmass structure elaboration and its engineering
application [M]. Beijing, Science Press.
[3] Jia Hongbiao, Tang Huiming. Three dimensional
network simulation of rock mass structure theory
and engineering application [M]. Science Press,
2008[4] Prensky S. E. (1999), Advances in borehole
imaging technology and application, Borehole
Imaging: Applications and Case Histories, London,
Geological Society, pp.1-43[5] Wang Chuan-ying, Ge Xiu-run, Bai Shi-wei(2001). The digital panoramic borehole camera
system and its application, Rock and Soil
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(2009): Study of connectivity of discontinuities ofborehole based on digital borehole images [J].
Chinese Journal of Rock Mechanics andEngineering, 28(12): 2405-2410[7] Wang Xiaogang, Jia Zhixin. The simulation ofrock joint network and its application [M]. China
WaterPower Press, 2010[8] Wu faquan. Principles of statistical mechanics ofrock masses [M]. China University of Geosciences
Press, 1993

PP
( 1.874  1.832) 2  ( 2.518  2.514)2  (1.845  1.842)2  0.042
1 2 

Assuming the judgment standard of connectivity
is  =0.1, the distance of the two points P1P2 is lessthan this standard. Therefore, we can initiallydetermine that these two fractures may belong to asame discontinuity. Through observing the rockfeature around the fractures, they are both gray rock,the lithology is very similar and the width are
7.13mm and 7.26mm. In the end, through the above
analysis, we can basically determine that these two
fractures have connectivity and belong to a same
discontinuity. The images of these two fractures areas below:

Fracture 1 in DW-1

Fracture 2 in DJ-3

Fig.5 The two connected fractures in adjacent boreholes

4.

Conclusions

4