Underground Construction - January 2022 - 34

CIGMAT Report
to 1.11 Ωm, also four times the amount of SBR added.
Hence, initial resistivity could be adopted as a quality control
measure in the fi eld to determine the amount of SBR added and
also the quality of mixing.
During the curing process, the resistivity rapidly changed with the
time, suggesting several parameters be used in monitoring the curing
(or hardening) process: initial resistivity (ρo
(ρmin
), time to reach the minimum resistivity (tmin
24 hours of curing (ρ24
resistivity (Resistivity Index) [RI24hr
), minimum resistivity
), resistivity after
), and percentage of maximum change in
= (ρ24
- ρmin ) / ρmin
] × 100].
After initial mixing, the electrical resistivity reduced to a
minimum value (ρmin
), and then gradually increased. Time to reach
minimum resistivity, tmin, can be used as an index of speed of
chemical reactions and cement set times.
With the formation of large amounts of solid hydration products
in the cement matrix, blocking the path, electrical resistivity
increased sharply with curing time.
Finally, a relatively stable increase in trend was reached by the
ions' diff usion control of the hydration process, and resistivity
increased steadily for up to 24 hours, reaching a value of ρ24hr
.
Change in the electrical resistivity with respect to minimum
resistivity quantifi es the formation of solid hydration products,
which leads to a decrease in porosity and, hence, the cement's
strength development.
Th e following observed trends (as summarized in
TABLE 1) clearly indicate the sensitivity of resistivity to the changes
occurring in the curing of cement:
* Time to reach minimum resistivity (tmin
* Minimum resistivity (ρmin
) increased by 12 percent
and 38 percent when SBR polymer content was 1 percent and
3 percent, respectively.
) of smart cement with 0 percent,
1 percent and 3 percent SBR polymers was 0.97 Ω-m, 1.00 Ω-m
and 1.05 Ω-m, respectively, an increase of 3 percent and
8 percent in minimum electrical resistivity.
* Resistivity index (RI24hr
) for smart cement with 0 percent,
1 percent and 3 percent of SBR polymer was 259 percent,
307 percent and 341 percent, respectively, increasing with
polymer content.
Based on experimental results, a theoretical model proposed by
Vipulanandan and Paul (1990) was modifi ed and used to predict
the electrical resistivity of smart cement during hydration, up to
28 days of curing, as shown in FIGURE 2.
Th e Vipulanandan p-q curing model (Vipulanandan et al. 2015) is
defi ned as follows:
⎛
1
=
ρ
⎛
⎜⎝
1
ρmin
⎞
⎟⎠
⎜
⎜
⎜
⎜
⎜⎜
⎝
q1 + 1−p1 −q1 ) ×
(
⎛
⎜⎝
⎛
⎜⎝
t + to
tmin + to
t + to
tmin + to
⎞
⎟⎠
⎞
⎟⎠
+p1 ×
⎛
⎜⎝
t + to
tmin + to
where ρ: electrical resistivity (Ω-m); t is the curing time
(minutes); ρmin
corresponding to minimum electrical resistivity (ρmin
to and q1 are model parameters (TABLE 1).
⎞
⎟⎠
is minimum electrical resistivity (Ω-m); tmin
q1+p1
p1
⎞
⎟
⎟
⎟
⎟
⎟⎟
⎠
), and p1
TABLE 2. Piezoresistive model parameters for smart cement
without and with SBR polymer
FIGURE 2: Variation of resistivity with curing time for smart cement
without and with SBR
Mix Type
SBR = 0%
SBR = 1%
SBR = 3%
p2
0.12
0.43
q2
1.25
0.301
0.467
Max Change in
Resistivity (%)
171
125
104
Compressive
Strength, (σc psi)
1400
1650
1850
R2
0.99
0.96
0.99
TABLE 3. Vipulanandan Gas Flow Model parameters for the smart
cement without and with SBR polymer
Darcy's Law
k
(m/sec)
1-hour Curing
2.34
2.04
24 Hour Curing
0.69
FIGURE 3: Piezoresistive behavior of smart cement without and with SBR
34 JANUARY 2022 | UCONonline.com
0.51
R2
0.99
0.99
0.99
0.99
RMSE
(mm/s)
3.23
4.67
1.56
0.43
Vipulanandan Fluid Flow Model
M
N
MPa.sec/m2
0.47
0.63
1.05
1.81
sec/m R2
-0.001
-0.003
0.010
0.003
0.99
0.99
0.99
0.99
RMSE
(mm/s)
2.72
2.34
0.90
0.38
is time
,
(3)
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