671017.pdf

H=hb1

H=hb2

V=0 V=0

M

M

N

N

Figure 6: Fracture network schematic diagram in seepage area.
MNandM耠N耠are the constant head boundaries with the hydraulic
head ofℎ푏1andℎ푏2respectively;MM耠andNN耠are the impervious
boundaries with flow푉of zero.

degrade and the Young’s modulus of the damaged element is
defined as follows [ 34 ]:

퐸=퐸 0 (1−퐷), (5)

whereDrepresents the damage variable andEand퐸 0 are

the elastic moduli of the damaged and intact rock samples,

respectively. In this equation, all parameters are scalar.

With the geometric information of the fracture sample,

the damage tensor [ 35 ] could be defined as

퐷푖푗=

푙

푉

푁

∑

푘=1

훼(푘)(푛(푘)⊗푛(푘)), (푖,푗 = 1,2,3), (6)

whereNisthenumberofjoints,lis the minimum spacing

between joints,Vis the volume of rock mass,n(푘)is the

normal vector of thekth joint, anda(푘)is the trace length of

thekth joint (for 2 dimensions).

According to the principal of energy equivalence [ 36 ], the

flexibility matrix for the jointed rock sample can be obtained

as

푆耠푖푗=(1−퐷푖)

−1

푆푖푗(1 − 퐷푗)

−1

, (7)

where푆푖푗is the flexibility matrix for intact rock;퐷푖and퐷푗are

the principal damage values in푖and푗directions, respectively.

For plane strain geometric problem, the constitutive relation,

where the coordinates and principal damage have the same

direction, could be expressed as follows:

[

[

휎 11

휎 22

휎 12

]

]

=

[[

[

[

[[

[

[

[

[

[

퐸 0 (V 0 −1)(퐷 1 −1)

2

2 V^20 +V 0 −1

−퐸 0 V 0 (퐷 1 −1)(퐷 2 −1)

2 V^20 +V 0 −1

0

−퐸 0 V 0 (퐷 1 −1)(퐷 2 −1)

2 V^20 +V 0 −1

퐸 0 (V 0 −1)(퐷 2 −1)

2

2 V^20 +V 0 −1

0

00

퐸 0 (퐷 1 −1)(퐷 2 −1)

2(1+V 0 )

]]

]

]

]]

]

]

]

]

]

[

[

휀 11

휀 22

휀 12

]

]

, (8)

where퐸 0 is the Young’s modulus of intact rock andV 0 is
Poisson’s ratio for intact rock.
The parameters could be easily captured by laboratory
tests. Equation ( 7 ) gives the principal damage values퐷 1 and
퐷 2. Based on geometrical damage mechanics, all elements
in this matrix could be obtained by the method mentioned
previously, and the anisotropic constitutive relation of jointed
rock sample could finally be confirmed.

3.2. Seepage Analysis.The seepage parameters of rock mass
arequantizedformofpermeabilityandalsoarethebasis
to solve seepage field of equivalent continuous medium.
Basedontheattributeoffracturedrockmassandbytaking
engineering design into account, fractured rock mass is often
considered to be anisotropic continuous medium. In the
fracture network shown inFigure 6,atotalnumberof푁cross

points or water heads and푀line elements are contained.

Parameters can be obtained with the model such as water

head, the related line elements, equivalent mechanical fissure

width,seepagecoefficient,andsoon.Thecorresponding

coordinates of each point could be acquired. For a fluid flow

analysisbasedonthelawofmassconservation,thefluid

equations on a certain water head take the form [ 37 ]

(

푁耠

∑

푗=1

푞푗)

푖

+푄푖=0, (푖=1,2,...,푁), (9)

where푞푗is the quantity of flow from line element푗to water

head푖,푁耠is the total number of line elements intersect ati,

and푄푖isthefluidsourceterm.Inthejointnetwork,eachline

element would be assigned a length푙푗and fissure width푏푗to

investigate the permeability.