3rd China-Japan Joint Seminar for the Graduate Students1 Laws for Coupled Analysis of Seepage Flow...

3rd China-Japan Joint Seminar for the Graduate Students 1

Laws for Coupled Analysis of Seepage Flow in Soft Rock

Li Peng Li Yan

[email protected]


Content

• Introduction of soft rock and present research state• Characteristics of seepage deformation of soft rock• Characteristics of seepage flow coupling of soft rock• FEM soft for coupling analysis based on MATLAB


Introduction of soft rock

• Widely distributed around the world

• Mainly made up of mud-stone and cleaving-stone

• Including sedimentary deposit, weak interlayer, joint plane, discontinuous fracture face, array of particles and agglomerations, micro-pore and micro-fracture etc.

• Obvious variability and anisotropy

• Greatly influenced by water

• Exist in railway, highway, mine, hydraulic power engineering etc.


Present research state of seepage flow coupling analysisPorous media seepage flow

• In the 1970s, Biot’s theory was widely used for the porous rock

• Zhujiang Shen (1977) firstly studied consolidation through FEM based on Biot’s consolidation theory

• Rock stress coupling research was made by Noorishad (1982 1990)

• Curran (1987) made a study of porous media consolidation through BEM displacement discontinuous model

• Elastic porous media seepage flow coupling control equations denoted as:

2 02

0

j ijii

j j i j i j

i

i w i i

uu pG G F

x x x x x x

uK p pn

x x t t x


Fracture media seepage flow Single fracture face seepage flow• Cube law• Lomize and Louis’s experiment through imitated natural fracture

Fracture net seepage flow• Double media model Snow (1968), Oda (1986), Yuxing Xiao (1997 1999)• Non-double media model (Equivalent continuous media model & Discrete fractu

re media model) Wilson&Witherspoon (1974), Noorishad (1985), Enzhi Wang (1998), Xiaoming

Ji (2003)

3max

CQ bH


Characteristics of seepage deformation of soft rockInfluencing factor

Rock and structural surface character

• Worotnicki (1993) divided rocks as follows:

1) quartz-feldspathic-rocks (Granite, Quartzy-sandstone, Granulite etc.)

2) lithic-rocks (Lithic-sandstone, Amphibolite etc.)

3) pelitic-rocks (Mud-stone, Slate, Phyllite etc.)

4) carbonate rocks (Lime-stone, Dolomite etc.)

According to 200 groups tests, pelitic-rocks represent the most anisotropic properties.


a) quartz-feldspathic-rocks & carbonate rocks b) pelitic-rocks c) carbonate rocks


• Man-chao He (2002) made single axle compression test of siltstone and got a result of mechanical index alteration correlated with the included angle of compression stress and structural face direction


Rock environmental field

• Stress field, seepage flow field and temperature field

• Zhi-jun Feng (2005) made triaxial tests of three typical soft rock and got a resul

t of Young’s modulus considering of natural and saturated moisture content with

different confining pressure


Rock materialsNatural (MPa) Saturated (MPa)

Confining pressure Young’s modulus Confining pressure Young’s modulus

Sand stone

0.0 3632.3 0.0 818.1

1.0 3709.7 0.5 2160.7

2.0 7600.7 1.0 3394.8

3.0 8425.3 3.0 5728.8

Mud stone

0.0 1143.1 0.0 660.6

0.5 1133.7 1.0 823.9

1.0 1621.4 2.0 1231.8

2.0 2122.9 3.0 1630.2

Silt stone

0.0 548.9 0.0 496.5

0.5 1411.6 0.5 1041.9

1.0 1903.9 1.0 1655.5

2.0 6270.7 3.0 1663.2


Equivalent transverse isotropic model• Goodman (1968) introduced this model to simulate regular joint rock

(a) Basic element

(b) Shearing performance

(c) Compressing performance


• For the complex joints, assume three groups different direction joints which parallel n, s, t axis ( , , axis)① ② ③

• According to displacement equivalent law

• Rock constitutive equations

1 1 1

i ni iE E k s

1 1 1 1

ij si i sj jG G k s k s

D

1 2D D D

(i=1,2,3 or n,s,t)

(i, j=1,2,3 or n,s,t)


1

10 0 0

10 0 0

10 0 0

10 0 0 0 0

10 0 0 0 0

10 0 0 0 0

sn tn

n s t

sn ts

s s t

tn ts

t t t

st

nt

ns

E E E

E E E

E E ED

G

G

G

1 1

2 2

3 32

2 2 3 3

1 1 3 3

1 1 2 2

10 0 0 0 0

10 0 0 0 0

10 0 0 0 0

1 10 0 0 0 0

1 10 0 0 0 0

1 10 0 0 0 0

n

n

n

s s

s s

s s

k s

k s

k sD

k s k s

k s k s

k s k s


Young’s modulus• Affects from different confining pressure

• Affects from stratification plane direction

Brown-red mudstone full stress-strain curve under different confining pressures

Brown-red mudstone stress-strain curve of vertical&parallel stratification plane

3 5Mpa

vertical

parallel


Characteristics of seepage flow coupling of soft rockAnisotropy seepage flow properties

• Basic equations:

• Tensor transformation

x xx xy xz x

y xy yy yz y

z xz yz zz z

v K K K i

v K K K i

v K K K i

1

23 3

3

0 0

0 0

0 0

K

K K

K

22 231 2

1 2 3

coscos cos1

ijK K K K


Seepage flow-stress coupling control equations• Coupling representation

or

• Empirical equations

Louis (1974)

Gale (1982)

Yuan-tian Zhou (1998)

• Indirect equations

Baton (1985)

K f K f

0 ( )ak k e h a

fT 3 12f nT gb

10 naS bK

2 220

2.5 2.50

(1 )m m nn

m no

b bb

b kJRC JRC


Principle stress and permeability directions

• Kozeny theory & Timoshenko method

• Principle stress and permeability directions coincide

21

2 32 2

0

9 111 2 2

k

k E

21

2 323 2

1,0

9 111 2 2

ij

j j ii

k

k

3

1,

1i i j

j j iE

(i=1,2,3)

(i=1,2,3)


• Principle stress and permeability directions mismatch

212 32

2

0

9 111 2 2

xy

x

k

k

212 32

2

0

9 111 2 2

yx

y

k

k

11 1 cos 2

2y x y x yE

11 1 cos 2

2y x y x yE


Experimental investigation

• Quantitative analysis based on the subject study tests

• Principle permeability directions assumed as the tangential directions of the joint surface

• Larger difference of confining pressure and axial pressure, greater affects to permeability considering of the joint surface included angle

• Test materials from highway tunnel sites, in Yun Nan province

mud-siltstone and brown-red-mudstone

test samples taken from rock mass which cross or parallel the joint surfaces

cylinder test with a diameter of 50mm and height of 80~84mm


Permeability coefficient—included angle of stratification face curve considering of

different confining pressure

Permeability coefficient—included angle of stratification face curve considering of

different axis pressure


Rock materials Relation between permeability directions & joint surface

Serial number

Range of coefficient of permeability (ms-1)

Mud-siltstone

parallel

70 （ 1.06 ～ 1.39 ） ×10-9

85 （ 0.95 ～ 1.50 ） ×10 － 9

95 （ 1.09 ～ 2.51 ） ×10 － 9

vertical

101 （ 2.25 ～ 3.47 ） ×10 － 9

102 （ 1.16 ～ 3.83 ） ×10 － 9

110 （ 1.86 ～ 3.85 ） ×10 － 9

Brown-red-mudstone

parallel

164 （ 0.98 ～ 2.82 ） ×10 － 13

166 （ 0.28 ～ 1.57 ） ×10 － 13

168 （ 0.27 ～ 0.69 ） ×10 － 13

vertival

173 （ 0.73 ～ 1.82 ） ×10 － 13

175 （ 0.83 ～ 3.21 ） ×10 － 13

177 （ 0.20 ～ 0.91 ） ×10 － 13


Mud-siltstone parallel joint

&

curve

K


Mud-siltstone vertical joint

&

curve

K


Brown-red mudstone parallel joint

&

curve

K


Brown-red mudstone vertical joint

&

curve

K


FEM soft for coupling analysis based on MATLABIterative coupling method

Input

Output Input

OutputSeepage flow field module

Seepage flow boundary

Dis-field module

Form dis-field body forceCoupling module


Analysis example

• Manxie No.2 tunnel, multiple arch tunnel, with a length of 225m

Tunnel cross-section

Geologic section


• Mother rock mainly made up of slightly weathered silty-sand rock and highly weathered sandy-mud rock

• Fault above the tunnel

• Embedded depth 32m according to the calculation profile

• In the finite element method analysis, 2468 nodes and 2502 elements

Calculation model Calculation meshes


First w

ork step

water

pressure distribu

tionL

ast work

step w

ater pressure d

istribution

Fifth w

ork step

w

ater pressure

distribution

Ultim

ate seepage qu

antity vector


Nephogram of

X-dis

Y-dis

sgmx sgmy

sgmxy

of last work step


Contour line of

X-dis sgmx sgmy

Y-dis sgmxy

of last work step

(solid lines represent non-coupling analysis results

dashed lines represent coupling analysis results)


Interpretation of the results

• Differences between non-coupling and coupling analysis results

• Comparison according to monitoring result

Items x-direction displacement

y-direction displacement

x-direction stress

y-direction stress

Shear stress

flux Water pressure

D-value 1.3mm 4.1mm 767.8KPa 578.7KPa 390.5KPa 1.334e-7m/s

8.6mm

Left-hole circumferential nodes K3+490 section vault monitor

monitor


Fifth work step left hole circumferential nodes displacement contrast

Non-coupling

Coupling

Fifth work step left hole vault displacement contrast

Non-coupling

Coupling

Monitoring results


Nodes Non-coupling Coupling

1 -1097.4 -5352.2 -1698.1 -1179.9 -5767.7 -1848.2

2 -1552.5 -3385.9 -2101.3 -1700.8 -3671.2 -2292.7

3 -1682.3 -2131.2 -1873.7 -1858.1 -2291.5 -2035.5

4 -1152.8 -1279 -1168.9 -1357.9 -1372.6 -1293.5

5 -574.5 -623.18 -759.04 -876.16 -670.05 -854.65

6 256.56 3.1387 -363.51 -106.72 -5.6044 -362.6

7 448.56 151.46 -102.43 57.991 104.34 15.479

8 82.571 -240.73 416.38 -278.97 -396.02 635.29

9 -248.84 -1608.9 1123.9 -536.35 -1891.3 1378.3

10 -406.09 -3178.7 1338.8 -588.87 -3514.6 1550.9

11 -5082.3 -1952.2 -3159.1 -5761 -2168 -3537.5

12 -1603.5 -934.04 -2341.3 -2277.3 -1047 -2640

13 174.26 155.93 -766.35 -532.22 105.25 -956.99

14 1711.7 154.25 -167.12 1022.7 141.14 -244.34

15 2634.9 -41.471 -188.82 1993.9 -53.603 -163.47

16 2690.9 -180.2 -327.4 2118.2 -222.53 -209.55

x xy yxy xy


Conclusions

• when the water pressure is very high, seepage flow may have great effects on

the host rock and the structure

• coupling process has little effect on water pressure distribution of seepage field

• under different operating modes, coupling has different effects on the

displacement field

• according to the FEM procedure based on MATLAB, the rapidity of

convergence is very fast


Thank you for your kind attentionThank you for your kind attention

Glimpses on seepage flow

coupling problemsa brief report by Li Peng

Date post:	15-Dec-2015
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3rd China-Japan Joint Seminar for the Graduate Students1 Laws for Coupled Analysis of Seepage Flow...

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