R. GAO et al.: RESEARCH OF THE MECHANISMS OF BACKFILL FORMATION AND DAMAGE
163–169
RESEARCH OF THE MECHANISMS OF BACKFILL FORMATION
AND DAMAGE
RAZISKAVA MEHANIZMOV OBLIKOVANJA IN PO[KODOVANJA
ZASUTJA
Rugao Gao, Keping Zhou, Jielin Li
Central South University, College of Resources and Safety Engineering, Hunan Changsha 410083, China
gaorgcsu@163.com
Prejem rokopisa – received: 2017-06-09; sprejem za objavo – accepted for publication: 2017-07-28
doi:10.17222/mit.2017.070
This work aims to improve the research method relating to the formation and destruction of the mechanical properties of a
backfill. The hydration and pore-distribution characteristics of a backfill were examined with an AniMR-150 nuclear-magnetic-
resonance instrument and MIRA3 scanning electron microscopy. Microscopic studies show that the porosity change of the
backfill tends to be stable after 7 d, and the formation of chemically bound water is the main reason for a dense microstructure
of the backfill with a high cement-tailing ratio. Based on the principle of the Lemaitre strain equivalence, non-linear constitutive
equations of backfill damage were proposed and validated, revealing the stress-strain characteristics of the process of backfill
damage. The work introduces a micro-physical mechanism into the backfill-property analysis, which provides a new scientific
basis for the preparation and application of an appropriate design of a frame filling.
Keywords: cemented-tailing backfill, nuclear magnetic resonance, hydration characteristics, mechanical properties
Namen tega dela je izbolj{ati raziskovalno metodo pri nastajanju in uni~evanju mehanskih lastnosti zapolnjevanja. Karakte-
ristike za hidratacijo in porazdelitev por so bile preizku{ene z instrumentom za jedrsko magnetno resonanco AniME-150 in z
elektronsko mikroskopijo. Mikroskopske {tudije ka`ejo, da je sprememba poroznosti v 7 d stabilna in da je nastanek kemi~no
vezane vode glavni razlog za gosto mikrostrukturo polnila z visokim cementnim razmerjem. Na podlagi principa ekvivalence
sevov po Lemaitreu, so bile predlagane in validirane nelinearne konstitutivne ena~be defektov, ki nastanejo pri povratnem
polnjenju, kar ka`e na zna~ilnosti napetostne sile defektov v zapolnitvenem procesu. Delo uvaja mikrofizikalni mehanizem pri
analizi lastnosti samozapolnjevanja, ki omogo~a novo znanstveno osnovo za pripravo in aplikacijo ustreznega dizajna in okvir-
nega polnila.
Klju~ne besede: cementno polnilo, nuklearno-magnetna resonanca, karakteristike hidratacije, mehanske lastnosti
1 INTRODUCTION
Backfill-mining technology plays a significant role in
environmental protection and the prevention of water-
resource pollution.1,2 Therefore, it is being widely and
intensively employed in the global mining industry.
Various types of research on the mechanical properties of
the backfills were conducted in order to reduce the ore
dilution and loss during pillar robbing. Distinguished by
concrete, backfill is a kind of a multiphase composite
material with fractures, cracks, bubbles and cavities, and
a low intensity. The deformation of a backfill medium is
not only due to its brittleness.3,4 Therefore, research of
backfill-material mechanical properties changed from
classical-macroscale to mesoscopic-scale research.
In backfill slurry, water is attached to the pores
between the material surface and the particles; the mo-
lecular movement of the moisture is limited. The limiting
effect of solid-pore walls on the surface adsorption of
water and the paramagnetic ions on the surface of the
cement particles can lead to additional surface-relaxation
mechanisms. The distribution of the internal pore-bound
water hydrogen nuclei in a saturated slurry was carried
out with nuclear magnetic resonance. The T2 relaxation
time of the slurry in different curing periods was deter-
mined with the CPMG method. The internal
microstructural evolution behavior of the backfill was
tested with these methods, and the test results were
verified with electron microscopy.
Backfills with different cement-tailing ratios were
tested to obtain the necessary mechanical parameters and
the stress-strain curve. Deformation and failure charac-
teristics of the backfills were analyzed to derive the
damage-constitutive equation, then the reliability was
validated. Damage analyses of the backfills with
different ratios based on the Lemaitre strain equivalent
hypothesis were carried out,5 then a constitutive model of
a backfill based on continuum-damage mechanics was
established.
2 EXPERIMENTAL PART
2.1 Hardening test of the filling slurry based on nuc-
lear magnetic resonance
Backfilling slurries with cement-tailing ratios of
0.333:1, 0.200:1 and 0.125:1 were compounded of un-
classified tailings and 325# Portland cement. An
electronic balance with an accuracy of 0.01 g was used
Materiali in tehnologije / Materials and technology 52 (2018) 2, 163–169 163
UDK 620.1:620.172.2:621.742.48 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 52(2)163(2018)
for weighing. During the stirring process, the cement and
the tailings were mixed uniformly and then water was
poured into the mixing bucket. Finally, the mixed cement
and the tailings were added into the mixing bucket to be
stirred for 10 min. After the mixing, the prepared
filling-slurry samples were put into an AniMR-150
nuclear-magnetic-resonance instrument for a CPMG test,
with the probe-coil diameter being 15 mm. The room
temperature of the test was adjusted to 26 °C using air
conditioning.
In the CPMG experiment, the transverse relaxation
time (T2) was collected for the first time 5 min after the
start of the stirring with water, and the T2 data was
collected at intervals.
The early hydration of Portland cement took place
about 3 h after the water addition, so the total time for all
the signals collected was controlled within 200 min.
2.2 Mechanical test of the cemented-tailing backfills
Backfill specimens with cement-tailing ratios of
0.250:1, 0.167:0, 0.125:1, 0.100:1 and 0.083:1 were
compounded of classified tailings and 325 # Portland
cement (five pieces per group). The specimens were cut
into 70-mm cubes with an unevenness of the bearing
surface of not more than 0.05 mm per 100 mm. After
being kept in a curing room for 28 d and at 26 °C, the
specimens were subjected to a uniaxial compression test
with an electro-hydraulic servo-testing machine.
3 RESULTS AND DISCUSSION
3.1 Formation characteristics of the cemented-tailing
backfill
The spin-echo series recorded by the CPMG sequen-
ce (transverse relaxation measurement) is not the
attenuation of a single T2 value, but the distribution of
T2 values. The relationship between different levels of
porosity in a porous medium and the spin-echo series are
shown in Figure 2.
The distribution of the T2 spectrum during the hard-
ening process of the filling slurries with different
cement-tailing ratios are shown in Figure 3. It can be
seen from the figure that the T2 distributions of the
filling slurries with different ratios contain one main
peak and one or two secondary peaks. The peak area of
the main peak occupies more than 96 %. The T2 distri-
butions of the filling slurries with different ratios are
mainly concentrated at 0.2-10 ms.
With the hydration reaction proceeding, the T2 distri-
butions of the three kinds of backfilling slurry move to
the left. The left-shift speed of the filling slurry is rela-
tively fast; after 3–7 d, the left-shift speed is relatively
slow; after 7 d, the distribution of the main-peak area and
T2 value of the filling slurry is very slow and the
left-shift phenomenon is not obvious. The leftward-shift
velocity of the T2 distribution of the filling slurry can
reflect the hydration-reaction rate in the filling slurry.
The displacement of T2 showed that the hydration rate
was the fastest in the first three days and it decreased
from the third day to the seventh day as the hydration
reaction proceeded slowly.
The weighted average T2-weighted values of the
slurries with cement-tailing ratios of 0.333:1, 0.200:1
and 0.125:1 were (3.51, 4.04 and 4.64) ms, respectively.
The 0.200:1 and 0.125:1 filled slurries had weighted
average pore sizes of 1.15 times and 1.32 times the
weighted average pore diameter of the 0.333:1 filled
slurry. After 3 d, the weighted average T2 main peaks of
0.333:1, 0.200:1 and 0.125:1 were (1.75, 2.01 and 3.05)
ms, respectively. The 0.200:1 and 0.125:1 filled slurries
had weighted average pore sizes of 1.15 and 1.74 times
R. GAO et al.: RESEARCH OF THE MECHANISMS OF BACKFILL FORMATION AND DAMAGE
164 Materiali in tehnologije / Materials and technology 52 (2018) 2, 163–169
Figure 1: CPMG sequence
Figure 2: Magnetic resonance monitoring: a) peak decay curve of
CPMG signal, b) correspondence between the attenuation of spin
echoes and the distribution of porosity in porous media
the weighted average pore size of the 0.333:1 filled
slurry. After 7 d, the weighted average T2 value of the
main peak of the filling slurry with a different ratio of
lime to sand tended to be stable. The weighted average
T2 values of the main peaks of the filling slurry were
1.32, 1.75 and 2.31 ms after 21 d, respectively. The
0.200:1 and 0.125:1 filled slurries had weighted average
pore sizes of 1.33 and 1.75 times the weighted average
pore diameter of the 0.333:1 filled slurry.
As shown in Figure 4, the higher the filling-slurry
ratio, the smaller is the T2 peak value, which means that
the higher the cement-tailing ratio, the smaller is the
overall pore size of the backfilling slurry. With a diffe-
rent cement-tailing ratio, the amount of hydration
product is different and so is the original pore density of
the backfill. The higher the proportion of the backfilling
slurry, the more hydration products there are, resulting in
more tailings, a decreased filling-slurry porosity and
pore diameter, and a good hardening effect.
When the Ca2+ ion component in the cement is sub-
stantially converted to Ca(OH)2 and equilibrated, the
slurry loses its fluidity and changes from viscoplastic to
R. GAO et al.: RESEARCH OF THE MECHANISMS OF BACKFILL FORMATION AND DAMAGE
Materiali in tehnologije / Materials and technology 52 (2018) 2, 163–169 165
Figure 3: T2 spectrum characteristics of backfills with different ratios
at different ages: a) sample with a cement-tailing ratio of 0.333:1,
b) sample with a cement-tailing ratio of 0.200:1, c) sample with a
cement-tailing ratio of 0.125:1
Figure 5: Electron-microscopy images of the slurry cured for 7 d:
a) sample with a cement-tailing ratio of 0.125:1, b) sample with a
cement-tailing ratio of 0.200:1, c) sample with a cement-tailing ratio
of 0.333:1
Figure 4: Weighted average T2 main-peak value of the filling slurry
with a different cement-tailing ratio
viscoelastic. The tailings are attacked by alkaline
brackets, in which silicate anions and Ca2+ start to form a
C-S-H gel (hydrated calcium silicate) on the surfaces of
the particles. It can be seen from Figure 5 that in the
case of a higher cement-tailing ratio, the whole tailing is
filled with more needle-like C-S-H gel volume, forming
a compact structure and resulting in a higher backfill
strength. The scanned images validate the accuracy of
the NMR test. The main water absorption by the filling
slurry takes place during the first seven days; in this
period, the porosity is significantly reduced with the
increased bleeding and drainage work needs to be done.
3.2 Damage characteristics of the cement-tailing back-
fill
A deformation and failure process involving a cement
backfill under uniaxial loading can be divided into four
stages according to the stress-strain curves obtained from
the experiment (Figure 6):
Stage 1: Initial deformation stage (curve OA section in
Figure 6). The compression of fissures occurs inside
the specimen.
Stage 2: Linear deformation stage (curve AB section in
Figure 6). The curve is approximately a straight line;
the curve of the backfill with a larger elastic modulus
is steeper.
Stage 3: Yield stage (curve BC section in Figure 6).
Stress grows slowly and eventually reaches the peak;
the higher the cement-tailing ratio, the more distinct
is the yielding process of deformation and the higher
is the yielding stress.
Stage 4: Failure stage (curve CD section in Figure 6).
The stress value declines gradually and cracks occur
in the specimen; the compressive capacity of the
backfill is rapidly reduced.
To summarize from the stress and strain regularity, it
is evident that the peak stress of backfill is reduced with
the cement-tailing ratio, while the strength variation
tends towards stability when the ratio is reduced to a
certain extent; after the peak stress, the lower the
cement-tailing ratio, the smaller is the deformation and
the more abrupt is the occurrence of failure.
3.3 Damage-constitutive equations of backfills with
different cement-tailing ratios
As the main basis of describing mechanical-property
changes, the backfill damage degradation is divided into
three stages: deformation, damage and fracture. Macro-
scopic fractures of backfills are caused by an internal
damage accumulation, so the deformation can be
primarily analyzed with the constitutive-relation research
of damage evolution. According to the principle of
Lemaitre’s strain equivalence, it can be concluded that
when the backfill is regarded as an isotropic continuum6
 = −E D( )1 (1)
where  is the effective stress; E is the elastic modulus;
 is the strain; D is the damage value.
When D = 0, the backfill is in no-damage state; when
D = 1, the backfill is in the course of absolute damage or
failure.
Loland derived a stress-strain curve containing a
damage variable based on the strain-equivalence prin-
ciple; he deduced damage law by assuming the equation
of the expressions of effective stress and strain:7
D D C= +0 
 (2)
where D is the damage value; D0 is the initial damage
value; C and  are undetermined constants.
Loland’s model assumed a linear relationship bet-
ween the effective stress and strain; however, as the
effective stress is a constant value, it does not change
with the strain. There are differences between an
assumption and engineering practice. The micro-unit
strength of materials obeys the Weibull distribution of
the statistical-damage theory, where a damage variable is
the probability-density cumulative-distribution function
of the material fracture strength. The statistical-distri-
bution equation of damage parameters was determined as
the fracture strength of backfills and analyzed in
accordance with the Weibull distribution:
D
n
= − = − −⎛⎝
⎜ ⎞
⎠
⎟
⎡
⎣⎢
⎤
⎦⎥
1 1

exp
m
(3)
where m is the shape parameter of the Weibull distri-
bution; n is the scale parameter (m, n  0).
Inserting Equation (3) into Equation (1), Equation (1)
can be written in the following form:
  

= − = −⎛⎝
⎜ ⎞
⎠
⎟
⎡
⎣⎢
⎤
⎦⎥
E D E
n
( )1
m
(4)
Taking the derivative of  from Equation (1), accord-
ing to the boundary conditions based on the experiment
results, Equation (5) can be derived:
R. GAO et al.: RESEARCH OF THE MECHANISMS OF BACKFILL FORMATION AND DAMAGE
166 Materiali in tehnologije / Materials and technology 52 (2018) 2, 163–169
Figure 6: Compressive stress-strain curves for the backfill (real lines
1, 2, 3,4 and 5 stand for cement-tailing ratios of 0.250:1, 0.167:1,
0.125:1, 0.100:1 and 0.083:1, respectively)
0 1= −
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥⋅ −
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥E n
m
n

 
exp
p
m
p
m
(5)
Equation (5) is used only if
1 0−
⎛
⎝
⎜
⎞
⎠
⎟ =m
n
p
m
then the scale parameter of the Weibull distribution can
be written in the following form:
n
m
=
p
1 /m( / )1
(6)
Inserting Equation (6) into Equation (3), we can
describe the damage value D as:
D
m
= − −
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥1
1
exp

p
m
(7)
Before the peak stress, the damage-constitutive
equation of the backfills under uniaxial loading can be
written as:
 


= ⋅ −
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥E
m
exp
1
p
m
(8)
After the peak stress, where   p u< ≤ (u is the
ultimate strain), the stress-strain relationship coincides
with the Mazars model of concrete, in which the stress
drops exponentially with the increase in the strain. This
description fits well with the elastic damage of the
backfill under uniaxial test conditions. Therefore, at this
stage, the damage value D is described as:
[ ]D D B= + − − −p p1 exp ( )  (9)
where Dp is the damage value when the stress reaches
its peak value (D mp = − −1 1exp( / )) and B is the damage
parameter of the backfill.
Combining Equation (1) with Equation (9), the
damage-constitutive equation of the backfill after the
peak stress can described as:
[ ]    = − + − −ED E Bp pexp ( ) (10)
Inserting the results obtained with the experiment
such as the stress-strain curves, elastic modulus and peak
R. GAO et al.: RESEARCH OF THE MECHANISMS OF BACKFILL FORMATION AND DAMAGE
Materiali in tehnologije / Materials and technology 52 (2018) 2, 163–169 167
Table 1: Damage parameter for different backfills
Cement-tailing
ratio
Elastic modulus
(E/MPa)
Peak stress
(p/MPa)
Strain at peak
stress (p)
Damage at peak
stress (Dp)
Damage parameter
(m 1/m B)
0.250:1
0.167:1
0.125:1
0.100:1
0.083:1
565
384
263
151
98
3.95
2.92
2.13
1.29
0.89
0.0109
0.0114
0.0115
0.0118
0.0124
0.3592
0.3341
0.2963
0.2776
0.2659
2.2473
2.4593
2.8457
3.0749
3.2351
0.4450
0.4066
0.3514
0.3252
0.3091
66.49
86.32
110.58
149.01
254.74
Table 2: Damage-constitutive equations for different backfills
Cement-tailing ratio
Damage-constitutive equation
Before the peak stress After the peak stress
0.250:1

 

≤
= − ⎛
⎝
⎜ ⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥
⎧
0 0109
565 0 4450
0 0109
2 2473
.
exp .
.
.
⎨
⎪
⎩⎪
⎫
⎬
⎪
⎭⎪
[ ]{ }

  
≥
= − + −
0 0109
565 0 3592 66 49
.
. exp . (
0.167:1

 

≤
= − ⎛
⎝
⎜ ⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥
⎧
0 0114
384 0 4066
0 0114
2 4593
.
exp .
.
.
⎨
⎪
⎩⎪
⎫
⎬
⎪
⎭⎪
[ ]{ }

  
≥
= − + −
0 0114
384 0 3341 86 32
.
. exp . (
0.125:1

 

≤
= − ⎛
⎝
⎜ ⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥
⎧
0 0115
263 0 3514
0 0115
2 8457
.
exp .
.
.
⎨
⎪
⎩⎪
⎫
⎬
⎪
⎭⎪
[ ]{ }

  
≥
= − + −
0 0115
263 0 2963 110 58
.
. exp . (
0.100:1

 

≤
= − ⎛
⎝
⎜ ⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥
⎧
0 0118
151 0 3252
0 0118
3 0749
.
exp .
.
.
⎨
⎪
⎩⎪
⎫
⎬
⎪
⎭⎪
[ ]{ }

  
≥
= − + −
0 0118
151 0 2776 149 01
.
. exp . (
0.083:1

 

≤
= − ⎛
⎝
⎜ ⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥
⎧
⎨
0 0124
98 0 3091
0 0124
3 2351
.
exp .
.
.⎪
⎩⎪
⎫
⎬
⎪
⎭⎪
[ ]{ }

  
≥
= − + −
0 0124
98 0 2659 254 74
.
. exp . (
strain into Equation (1) and Equation (8), we can obtain
the values of m:
m
E
=
⎛
⎝
⎜
⎞
⎠
⎟1/ ln


p
p
(11)
We can also obtain boundary conditions from the
theoretical curve speculation and experiment results:
 
  
 
 
 
=
=
=
=
=
=
⎧
⎨
⎪
⎩
⎪
p
p
p
p
d d 0
1D
(12)
When solving Equation (12), we have:
B D= − −ln / ( )p u p  (13)
Based on the experimental data and solutions of
Equation (11) and Equation (13), we can obtain the
damage parameters (Table 1) and damage-constitutive
equations (Table 2) for different backfills.
By calculating these equations, we can obtain the
stress-strain curves of the backfills with different ratios
(dashed lines of Figure 6). Compared with the experi-
mental curves, the calculated results agree well with the
experimental data.
It is clearly observed from Table 1 that the damage
values for different backfills range from 0.26 to 0.35 as
the stress reaches its peak. The damage-strain curves of
the backfills with different ratios of 0.250:1, 0.167:1,
0.125:1, 0.100:1 and 0.083:1 can be traced with the cal-
culations of the damage-constitutive equations (Fig-
ure 7). In Figure 7, we can see that the damage-growth
rate reaches its maximum at the peak stress, and that the
lower the cement-tailing ratio, the more slightly the
damage value increases. However, after the peak stress,
the damage values go up steeply with the increase in the
strain and the damage values get increasingly large with
a decreasing ratio.
The damage-constitutive model established in this
paper is in good agreement with the measured full
stress-strain curve, which can be used to fit the tensile
curve. It is shown that the established damage-consti-
tutive model is reliable and has a certain reference value
for engineering.
4 CONCLUSIONS
1) The process of hydration and pore evolution during
the hardening process of a filling slurry is complex,
and its dynamic evolution cannot be studied with
conventional detection methods. NMR allows an
extraordinary method as it has unique non-destructive
and non-disruptive features such as dynamic
observation of the filling-slurry hydration and pore
evolution.
2) The filling-slurry hydration is mainly observed in the
first seven days, which is an important period for
drainage in the project. The effect of a high slurry
cementation is more obvious with a lower porosity
and a more compact structure. The results show that
the effect of the chemical bonding with water has a
significant impact on the solidification of the filling.
3) From the perspective of damage rules, the damage rate
of a backfill reaches its peak at the peak stress. The
higher the cement-tailing ratio, the larger is the
damage value before the stress reaches its peak. By
contrast, the deformation becomes increasingly large
after the peak stress. The theoretical curve simulated
by the constitutive equation is in good agreement
with the experimental curve, and the model can des-
cribe the uniaxial compression damage of backfills
with different cement-tailing ratios.
4) This paper was written based on laboratory experi-
ments and theoretical modeling; the results and
achievements can be accurately used in a backfill
design and production. This method can reduce the
dependence on large-scale experiments and industrial
verification, and it also provides for reference values
supporting underground mining. Based on further
development of the software language, a combination
of a numerical simulation and experiments is feas-
ible. These methods will allow us to analyze the paste
filling and coarse-aggregate filling on the micro-
scopic scale. Further research is expected to allow
more possibilities for backfilling transportation.
Acknowledgments
The authors would like to acknowledge that the work
was supported by the National Natural Science
Foundation of China (grant no. 51474252).
R. GAO et al.: RESEARCH OF THE MECHANISMS OF BACKFILL FORMATION AND DAMAGE
168 Materiali in tehnologije / Materials and technology 52 (2018) 2, 163–169
Figure 7: Relationship between damage value (D) and strain
Conflict of interests
The authors declare that there is no conflict of
interests regarding the publication of this paper.
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