671017.pdf

Pl

ast

ic

vi

scosi

ty

(mPas)

200

180

160

140

120

100

80

60

40

20

0

Time (min)

0 100 200 300 400 500 600

w/c=5 : 1

w/c=3 : 1

w/c=2 : 1

w/c=1 : 1

w/c=0. 7 : 1

w/c=0. 5 : 1

(a) Plastic viscosity of grout

w/c=5 : 1

w/c=3 : 1

w/c=2 : 1

w/c=1 : 1

w/c=0. 7 : 1

w/c=0. 5 : 1

Yi

eldi

ng

st

ren gt

h

(Pa)

140

120

100

80

60

40

20

0

Time (min)

0 100 200 300 400 500 600

(b) Yielding strength of grout

Figure 1: Time variation curves of the rheological parameters for cement grouts at different ratios (푤/푐is the water-cement ratio of grout).

fractures and shares some internal relations with the mechan-
ical opening2푏푚. Renshaw (1995) deduced the following
equationbasedontheprobabilityandstatisticstheory[ 20 ]:

푏ℎ

푏푚

=[(

휎푏

푏푚

)

2

+1]

−1/2

=[

exp휎^2 퐵⋅(exp휎퐵^2 −1)

[exp(휎^2 퐵/2)]

2 +1]

−1/2

,

(6)

where휎푏and휎퐵are the standard deviation of the opening
andthestandarddeviationoftheopeningtothevalues,
respectively.

(2)Change of the Fracture Opening due to the Precipitation of
Cement Particles.The analysis of the instable grout in frac-
tured rock showed that the fracture filled with grout material
is mainly caused by the cement particle precipitation. There
is a critical velocity value,푉kp, in the flow process of cement
grout. When the velocity of grout diffusion is less than푉kp,
the cement particles begin to precipitate, the sediment at
the bottom of the fractured wall gradually increases, and
the effective opening of the fracture gradually decreases. The
reduction of the fracture opening will further slow the grout
flow down. The particles will continue to precipitate until the
fracture opening becomes less than 0.2 mm, when the cement
particles cannot pass through the fractures, and thus the grout
seepage channel is regarded to be blocked. The semiempirical
formula for the critical velocity value is [ 21 ]

푉kp=푘(푔훿)0.5[

푉^2 (휌푇−휌퐵)휎푚

6푓푔푑cp휌퐵

]

3/7

, (7)

where푘is the correction coefficient;푔is the gravitational
acceleration;Vis the sinking velocity of cement particles in
water;훿is the fracture opening;휌푇and휌퐵are the density of
the cement particles and water, respectively;휎is the content
of solid particles in solution;푓is the resistance coefficient

u 0

u 1 u 2

h h

ABdx

(w/c) 1 (w/c) 0 (w/c) 2

Figure 2: Change of the water-cement ratio after the cement

particles precipitation.

of water in the fracture;푑cpis the feature size of the cement

particle;푚is the empirical indicators.

The sinking velocity of cement particles in water푉can

be approximately regarded as obeying the Stokes’ law for free

settling [ 14 ]:

푉=

푑^2 (휌푇−휌퐵)푔

18휂

, (8)

where푑isthemeansizeofthecementparticlesand휂is the

viscosity of the liquid medium or grout.

To understand the cement particles precipitation phe-

nomenon from another angle, it is also a process of the

increase of the water-cement ratio caused by free water

separating out of grout, leading to the change of rheological

parameters of grout. The flow and precipitation process was

shown inFigure 2.

According to the conservation of cement mass, the

following formula can be obtained:

(

푤

푐

)

0

=ℎ⋅

0.316 +(푤/푐) 1

푢 0 푡 + ℎ − 1.5푊 1

− 0.316, (9)

where(푤/푐) 1 is the initial water-cement ratio of the grout;

(푤/푐) 0 is the water-cement ratio of the grout after precipita-

tion;푡is the settling time started from the precipitation;푢 0