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Mechanical behavior of cement paste and alterations of
hydrates under high-pressure triaxial testing
Yuya
Sakai
,
Masao
Nakatani
Akihiro
Takeuchi
,
,
Yoji
Omorai
Journal of Advanced Concrete Technology,
volume ( ), pp.
14
2016
1-12
Toshiharu
Kishi
,
Correlation between Permeability of Concrete and Threshold Pore Size Obtained with Epoxy-coated
Sample
Yuya
Sakai
,
Choji
Nakamura
Toshiharu
Kishi
,
Journal of Advanced Concrete Technology,
volume ( ), pp.
11
2013
189-195
Change of the Coefficient of Thermal Expansion of Mortar Due to Damage by Freeze Thaw Cycles
Evdon
Sicat
,
Fuyuan
Gong
Dawei
Zhang
,
,
Tamon
Ueda
Journal of Advanced Concrete Technology,
volume ( ), pp.
11
2013
333-346
Micromechanical study of the interface properties in concrete repair systems
Mladena
Lukovic
,
Branko
Savija
Hua
Dong
,
,
Erik
Schlangen*XDQJ<H
Journal of Advanced Concrete Technology,
volume ( ), pp.
12
2014
320-339
Journal of Advanced Concrete Technolog y Vol. 14, 1-12 Janua ry 2016 / Copyright © 2016 Japan Concrete Institute 1
Scientific paper
Mechanical Behavior of Cement Paste and Alterations of Hydrates under
High-Pressure Triaxial Testing
Yuya Sakai1*, Masao Nakatani 2, Akihiro Takeuchi3, Yoji Omorai4and Toshiharu Kishi5
Received 22 September 2015, accepted 7 January 2016 doi:10.3151/jact.14. 1
Abstract
High confining pressure works on concrete under various conditions such as concrete structures deep underground/sea,
the lower floors of an extremely tall building and on the foundation concrete piles of an enormous structure such as dam.
Understanding the performance of concrete and the deformation mechanism under high confining pressure is important
for avoiding unexpected risks and for rationalization of design. A high-pressure triaxial test was conducted on cement
paste to understand the mechanism of mechanical performance of concrete under a high confining pressure. The devia-
toric stress-axial strain relationship of cement paste was independent of confining pressure during ductile deformation
under confining pressures greater than 30 MPa. Ion-milled cross-sections of specimens were examined by scanning
electron microscopy, and the obtained backscattered electron images were darker after the test. This darkening may in-
dicate the alteration of hydrates at the molecular level caused by deformation involving crystal plasticity. Furthermore, the
pore volume of the sample tested at 400 MPa was drastically reduced.
1. Introduction
Application of concrete is becoming more extensive
because of new social demand and technology devel-
opment. For example, high-level nuclear waste is dis-
posed of underground at depths of more than 300 m,
where concrete is expected to serve as both structural and
water-sealing material (Owada et al. 2008). Another plan
involves development of a city using concrete under the
ocean at a depth of 3000 to 4000 m, which is expected to
become technically feasible around 2030 (McCurry
2014). At this depth, water pressure is 30 to 40 MPa.
These two examples share a common condition in which
concrete is subjected to high confining pressure (Pc). In
other examples, high pressure can act on the concrete in
the lower floors of an extremely tall building and on the
foundation piles of an enormous structure such as dam.
When concrete is used with large quantities of expansive
additive under strong confinement, e.g., by a steel pipe,
large confining stress works on the concrete. A calcula-
tion based on the strain in the steel pipe indicated that the
pressure was about 6 MPa (Nishigori 1977). Furthermore,
impact loading can cause large triaxial stress. When an
object of 2.3 kg collides with concrete at 315 m/s, it can
cause a mean stress of 150 MPa according to a simulation
in which necessary parameters were validated by ex-
periments (Gran and Frew 1997). As shown above, high
Pc works on concrete in a wide variety of applications.
Understanding the performance of concrete and the
mechanism under such conditions is important for
avoiding unexpected risks and for rationalization of
design. Currently, an enormous amount of concrete is
produced and disposed of all over the world. In Japan,
over 90% of concrete waste is recycled, most of which is
filled underground as base-course material. In the long
run, buried concrete waste accumulates on the earth’s
surface and gradually becomes a component of the crust.
Therefore, as well as natural rocks, it is important to
understand how concrete behaves underground. In the
future, the effects of weathering or leaching need to be
studied by taking aging into account.
Many studies have investigated the performance of
hardened concrete (HC) under high Pc (Gabet and
Daudeville 2008; Malecot et al. 2010; Poinard et al.
2010). For example, the effects of cement paste volume,
aggregate size (Vu et al. 2011) and shape (Poinard 2012),
saturation degree (Vu et al. 2009), and loading rate (Zeng
et al. 2013) have been investigated. These studies have
revealed that the fracture style of HC changes depending
on Pc (Sfer et al. 2002) (Fig. 1), where an increase in Pc
reduces the effects of the cement paste volume (Poinard
et al. 2012) while increasing the effects of the saturation
ratio (Vu et al. 2009). Changes in the pores were also
observed, and the relationship of confinement-induced
microcracking and porosity reduction to the mechanical
performance was discussed (Poinard et al. 2012). Al-
though the changes in porosity and mechanical per-
formance have been studied, the mineralogical changes
in hydrates are not well known, possibly because they are
1Assistant Professor, Institute of Industrial Science, The
University of Tokyo, Tokyo, Japan.
*Corresponding author, E-mail: ysakai@iis.u-tokyo.ac.jp
2Associate Professor, Earthquake Research Institute, The
University of Tokyo, Tokyo, Japan.
3Engineer, Earthquake Research Institute, The University
of Tokyo, Tokyo, Japan.
4Graduate Student, Graduate School of Engineering and
Design, Hosei University, Tokyo, Japan.
5Professor, Institute of Industrial Science, The University
of Tokyo, Tokyo, Japan.
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 2
difficult to evaluate. In concrete, the volume ratio of
cement paste is about 30%, existing as interstitial filler
between the aggregates of various sizes that occupy
majority of the volume. Consequently, the observation of
hydrates is difficult. In addition, we could not find any
studies on the mechanical performance of cement paste
under high pressure.
In the present study, a high-pressure triaxial test was
conducted on hardened cement paste (HCP) to under-
stand its mechanical performance under high Pc and the
mechanism involved. To examine the altered hydrates,
cross sections of the samples were prepared using an
ion-milling method, and back-scattered electron images
(BEIs) were captured. Porosimetry was used to evaluate
any change in porosity. The obtained results were dis-
cussed through comparison with literature on HC and
natural rocks with compositions or properties similar to
HCP, such as limestone, marble, and porous rocks.
2. Experimental
2.1. Specimen preparation
In this study, we used HCP with a water-cement ratio
(W/C) of 40%. The properties of the Ordinary Portland
cement are presented in Tab le 1 . The mixing procedure
was based on JIS R 5201; the paste was first mixed for 60
sec at low speed (orbital rotation: 62±5 rpm, planetary
rotation: 140±5 rpm). The mixer was stopped for 30 sec
to 60 sec to scrape off cement paste on the side of the
mixing bowl and the paddle. Then the paste was mixed
for 90 sec at high speed (orbital rotation: 125±5 rpm,
planetary rotation: 285±5 rpm).The mixed paste was cast
in a steel prism mold of 10 × 10 × 40 cm and sealed. It
was demolded 24 h after casting and then kept under
water for 28 days. The temperature of the room and water
was 20°C. After curing, eight cylinders of φ2 × 4 cm
were cored from the prism HCP. Only the part deeper
than 2 cm from the surface was used to avoid the effect of
bleeding. Both ends of the cylinder were ground to
achieve a parallelism of 0.005 and surface roughness of
0.25 μm. The prepared cylinders were immersed in ace-
tone for 3 days to stop the hydration reaction and reduce
capillary suction in the subsequent drying period. To
eliminate the possible effects of pore pressure during the
triaxial test, the cylinders were dried for two weeks at
40 °C and 10% relative humidity. The water content was
7.5% after drying, which was obtained from the weight
loss during further drying at 105 °C for 24 h. Since HCP
had been immersed in acetone, the 7.5% residual fluid
was a mixture of water and acetone. Carbonation depth
of a sample which had been kept in a sealed container
(20 °C and 10% relative humidity) for one month after
the drying at 40 °C was measured with 1% solution of
phenolphthalein in ethyl alcohol. The sample was split
horizontally with a chisel at the middle and the solution
applied on the fracture surface indicated a carbonation
depth of 0.3 mm (Fig. 2), meaning 97% of the
cross-sectional area was not carbonated. The mixed paste
was also placed in three plastic cylindrical molds (φ50 ×
100 mm) and sealed. They were demolded 24 h after
casting and kept under water until the uniaxial compres-
sion test (based on JIS R 5201) at 28-day age.
2.2. High-pressure triaxial test
A high-pressure triaxial test was executed to study HCP
under high Pc. The test apparatus is shown in Fig. 3. The
steel spherical tank, located at the center of the loading
frame, was filled with silicon oil (density: 0.935 g/cm3,
kinetic viscosity at 25 °C: 10 mm2/s), the confining me-
a
b
c
d
e
f
Fig. 1 Fracture style of HC at different confining pressure
σL. With permission of ASCE, from (Sfer et al. 2002).
Table 1 Cement property.
Chemical composition (%) Density Fineness (Blaine)
Ig. Loss MgO SO3Na2Oeq Cl- g/cm3 m
2/kg
2.00 1.45 1.95 0.58 0.020 3.15 335
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 3
dium in the test (Fig. 4). The schematic view of the
loading system is shown in Fig. 5. A specimen was as-
sembled with tungsten carbide spacers and molybdenum
sheets (55 μm in thickness), which was used to avoid
cracking due to stress concentration at the sharp corner of
the spacers. Laboratory atmosphere was led to the end
face of the HCP sample through small center holes of the
spacers and pistons to avoid pore pressure being gener-
ated during experiments. The entire assembly was placed
on the tip of the piston (Fig. 6). The sample, spacers, and
the tip of the bottom piston were enclosed with a
heat-shrinkable FEP (Fluorinated ethylene propylene)
tube which sealed the sample from the confining medium
while securing the assembly to the bottom piston. The
tube was heated up from the outside with a heat gun for
shrinkage. To check the temperature of HCP specimen
during heat treatment on the tube, a hole of 2 mm in
diameter was prepared on a HCP sample and the tem-
perature in the hole was measured using a needle probe
thermometer. The distance from the sample surface to the
hole was 2 mm. A heat-shrinkable FEP tube was placed
over the HCP sample and heated until the tube touched
the sample completely. The obtained maximum tem-
perature reached was 46 °C, so we do not worry about the
effect of this procedure. After fixing, the entire assembly
was inserted into the tank shown in Fig. 4. A Teflon sheet
of 0.5 mm thick was inserted into the contact point be-
tween the top face of the assembly and the tip of the top
piston inside the tank to reduce lateral friction. Friction
on the molybdenum sheets are higher, so lateral dis-
placement that might occur as a result of the large
asymmetric deformation of the HCP sample is taken by
the sliding between the top piston and the top end piece,
keeping the other parts (except inside the sample) cen-
tered to each other. Pcs of 30, 100, or 400 MPa were
applied to the samples by pressurizing the oil with an
intensifier. Only one specimen was tested under each Pc.
Axial load (for differential stress) was then applied by
moving the top and bottom pistons (Fig. 4) toward each
other at a rate of 0.1 mm/min. The load was measured by
the load cells on the pistons. If the tube was broken
during the test, the oil would leak through the holes in the
spacers. However, such leakage was not observed, and
we concluded that the samples remained sealed
throughout experiments. After the triaxial tests, the
Fig. 2 Carbonation depth of HCP measured one month after drying at 40 °C (One tick of the scale in the figure is 1 mm).
0.3 mm
Fig. 3 Triaxial testing machine.
Fig. 4 Closeup of steel tank. Top and bottom pistons were
used to apply axial load to the specimen. Two horizontal
pistons equipped for true-triaxial tests were not used and
kept away from the specimen assembly.
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 4
samples were removed and inspected by the naked eye
while still in the tubes.
2.3. Scanning electron microscopy (SEM) ob-
servation inside the specimens
After each high-pressure triaxial test, the samples were
removed from the steel tank. Following visual inspection,
small (2 × 5 × 10 mm) pieces were taken out from the
center of the samples. These pieces were washed with
n-hexane to remove the silicon oil, embedded in resin
and cut. Their cross-sections were milled with ion beam
(Brodusch et al. 2013) to obtain flat surfaces at a mo-
lecular scale. We did not employ ordinary mechanical
polishing to avoid deformation and scratch of the sample
by abrasives. In ion milling, hardly any physical stress is
induced (Brodusch et al. 2013). Platinum was spattered
on the sample surface for conduction. The BEIs were
then captured using an accelerating voltage of 10 kV. We
also took a small piece from a virgin sample of the same
age, embedded it (without washing) in resin, cut it and
smoothed its cut surface using argon beam ion milling.
To obtain quantitative information from the BEIs, a his-
togram with 256 grayscale levels was prepared.
2.4. Porosity analysis
Using the rest of the samples from the SEM observation,
mercury intrusion porosimetry (MIP) was conducted to
evaluate their porosity. Several cubes with edges meas-
uring 3 mm (1.5 g) were taken from random locations of
the sample and washed with n-hexane. The pieces were
then immersed in acetone for 24 h, D-dried for 24 h, and
analyzed. We followed the same procedure for the virgin
sample but without washing.
3. Results
3.1. High-pressure triaxial test
The obtained deviatoric stress-nominal axial strain (SS)
curves for tests under different Pcs are shown in Fig. 7.
The deviatoric stress (σd) was calculated by dividing the
difference between the measured load and the load due to
oil pressure by the sample’s cross-sectional area. The
nominal axial strain (εa) was calculated by dividing the
relative displacement of the top and bottom pistons by
the sample length. This included elastic deformation of
the pistons and spacers, which was not important in the
present study where much greater inelastic deformation
of the sample was concerned. Also, the piston and spacer
deformation was much less than the elastic deformation
of our sample with low Young’s modulus. In Fig. 7,
measured data up to the point just before the start of the
unloading operation are shown. The broken line in the
figure indicates the average uniaxial compressive
strength (78.1 MPa). All the three curves show similar
linear trends up to εa = 0.5% and σd = 100 MPa, indi-
cating a linear elastic stage. After that, σd increases with a
reduced slope in all cases, an indication of ductile de-
formation. The yielding point was clear and almost the
same (εa = 0.5% and σd = 100 MPa) for Pc = 30 and 400
MPa. The yielding for Pc = 100 MPa was gradual, but
starting at more or less the same strain. The
strain-hardening slope is similar for the three tests. Duc-
Fig. 5 Schematic view of the loading system. Note the lef
t
and right pistons were not used for any active purpose in
the present experiments. They never touched the sample
assembly.
Fig. 6 Sample assembly.
Sample
Lower piston
Spacer
End piece
Fig. 7 Deviatoric stress-nominal axial strain response for
different confining pressures.
Deviatoric stress σd (MPa)
Nominal axial strain εa (%)
400 MPa
100 MPa
30 MPa
Uniaxial compressive strength: 78.1 MPa
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 5
tile deformation lasted longest at the highest Pc of 400
MPa, up until εa = 3.5%, where a small sudden stress
drop occurred. Here, ‘ductile deformation' doesn’t con-
tain the stress descending portion. For Pc = 30 and 100
MPa, similar sudden stress drops occurred at an earlier
strain of εa = 2 to 2.5%. As the result of the long-
est-lasting ductile stage with strain-hardening, the test at
Pc = 400 MPa showed the highest peak strength. On the
other hand, the strain-hardening curves of the three tests
do not show a systematic dependence on Pc. As we will
discuss in §4.3, this may imply that the ductile strength
was mainly limited by crystal plasticity, rather than fric-
tional cataclastic flow (Paterson and Wong, 2005), at all
the tested levels of Pc (30 to 400 MPa).
In Fig. 8, tubed samples after the test are shown. With
30 MPa of confinement, single macroscopic shear plane
developed at an angle of about 30° off the most com-
pressive principal stress axis. This faulting style is uni-
versally seen in triaxial compressive tests in brittle re-
gime but with significant confinement to suppress the
splitting mode of failure typical of zero or very low Pc
(Hatanaka et al. 1987; Sfer et al. 2002; Paterson 1958)
(Fig. 9). Under a Pc of 100 MPa, the middle of the sample
bulged locally. There were several axial cracks of 0.3 mm
wide on the sample surface and axial and circumferential
cracks at the bulge, but these were all thin hair-line
cracks and shear displacement in them appeared nil. At
Pc = 400 MPa, the sample was thinned laterally as if it
had been squeezed by Pc. The diameter decreased by
10% and one horizontal macrocrack was observed. At the
middle of the sample, there were creases in the tube
horizontally and at an angle of 20° from the horizontal
plane. On the other hand, lateral bulging occurred only at
the top end of the sample.
3.2 SEM observation inside the specimens
The cross sections of the pieces taken from the virgin and
tested samples were observed using SEM. The BEIs of
the ion-milled surface are shown in Fig. 10. They are
also shown in Fig. 11 as a histogram of gray-scale inte-
gers that range from 0 (black) to 255 (white). In Fig. 10,
compared with the virgin sample, the area of voids
(a) 30 MPa (b) 100 MPa (c) 400 MPa
Fig. 8 Samples after triaxial test (Numbers below figures indicate confining pressures).
a
b
d
c
e
Fig. 9 Failure style of Wombeyan marble at different Pc From left to right, Pc = 0, 3.5, 28, 46 and 100 MPa. Published with
permission of Geological Society of America, from (Paterson 1958).
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 6
(shown in black) is reduced as the Pc increases. However,
in the sample tested with a Pc of 400 MPa, many micro-
cracks are observed in multiple directions. These voids
and microcracks have a gray value of around 0 and the
magnified figure in Fig. 10 demonstrates the reduction of
their area. Note that pores smaller than 0.1 μm in di-
ameter (§3.3), which was smaller than the resolution of
Fig. 10, 1 μm, contributes a lot to the total porosity
shown in Fig. 13. In all SEM photos, fairly large white
isolated clasts up to about 30 µm are buried in the gray
matrix. In the virgin sample, the entire gray matrix is
uniform in tone. Fig. 11 shows this graphically, there is a
narrow peak with its center at the gray value of 160. At a
closer look, there are few small darker gray phenocrysts,
but the amount is so minor that it is not recognized in the
histogram. After testing with Pcs of 30 and 100 MPa, the
dark gray area increases so as to surround the light gray
area. In Fig. 11, the change appears as an asymmetric
widening of the distribution toward darker, lower gray
values. In the case of Pc = 400 MPa, many small spots of
Fig. 11 Histogram of gray value of images in Fig. 7.
Gray value
400 MPa
100 MPa
30 MPa
Not tested
Black White
Frequency
Frequency
Gray value
(a) Not tested (b) 30 MPa
(c) 100 MPa (d) 400 MPa
Fig. 10 Reflected electron images of samples after ion beam milling. (Numbers below figures indicate confining pressures)
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 7
further darker (~90) gray appear in the matrix. In Fig. 11,
the peak of the distribution shifts to the left, and the
frequency at a gray value of around 90 increases three-
fold compared with the others. Additional observations
were made while tilting the sample, but no change was
observed by doing this.
After small pieces were taken from the specimens for
the SEM observation, the FEP tubes were removed (Fig.
12). The sample tested under a Pc of 30 MPa split into
two parts, and no small fragments were found. On the
other hand, for Pc = 100 and 400 MPa, after the removal
of the tubes, the specimens collapsed into fragments and
powders. The fine powders were about 1 and 0.1 mm in
diameter in the cases of 100 and 400 MPa, respectively.
3.3. Porosity measurement of the specimens
The cumulative pore volume measured by MIP is shown
in Fig. 13. Compared with the virgin sample, the others
had much less porosity after the triaxial test. Especially,
the sample after testing at Pc = 400 MPa had very few
pores, even the smallest ones. The cumulative pore
volume at 3 nm pore diameter was about 18% before the
test. However, it decreased to less than 1% after the test
at Pc = 400 MPa.
4. Discussion
4.1 Macroscopic fracture pattern
Here, we focus on the macroscopic fracture style. As
shown in Fig. 8 and Fig. 12, fracture patterns differed
depending on the Pc. At 30 MPa (Fig. 8a, Fig. 12a),
single oblique macroscopic shear fracture surface was
formed. This pattern is known to occur in brittle regime
under moderate confinement. A similar pattern was re-
ported in the case of Wombeyan marble at 3.5 MPa
(Paterson 1958) and in the case of HC at 9 MPa (Sfer et
al. 2002). When the Pc was increased to 100 MPa, our
HCP sample deformed by bulging laterally without
forming a distinct macroscopic fracture surface (Fig. 8b).
The Wombeyan marble showed similar deformation
when the Pc was increased above 30 MPa (Paterson
1958). In HC (Sfer et al. 2002), macroscopic fracture
occurred up to their highest Pc of 60 MPa, though the
fracture geometry at 30 and 60 MPa was clearly not of
shear-faulting type. So, it appears that the range of Pc
exhibiting a macroscopic shear fracture surface or lateral
bulging (distributed deformation) depends on the mate-
rial and the testing condition. At Pc = 400 MPa, the sam-
ple became thinner as if it had been squeezed laterally,
and horizontal-subhorizontal (20°) creases occurred on
the tube (Fig. 8c). The squeezing and crease indicate
shortening of the sample in the radial and axial directions,
respectively. The horizontal crease may have been
caused by a local compaction band, which is reported for
HC (Malecot et al. 2010), porous sandstone (Wong and
Baud 2012), and so on, all under very high Pcs. In Fig. 13,
the porosity decreased drastically in the 400 MPa case
compared with the 100 MPa case. In porous rock, a
sudden volume decrease due to the collapse of pores at
certain very high pressures was reported (Curran and
Carroll 1979; Wong and Baud 2012). In HCP, sudden
pore collapse might take place between Pc = 100 and 400
MPa and this collapse could be one of the reasons for the
pulverization shown in Fig. 12.
As shown above, failure properties of HCP were ba-
sically similar to those of carbonate rocks but there are
Fig. 13 Pore size distribution.
Cumulative pore volume (%)
Pore diameter (nm)
400 MPa
100 MPa
30 MPa Not tested
(a) 30 MPa (b) 100 MPa (c) 400 MPa
Fig. 12 Samples after removal of tube. (Numbers below figures indicate confining pressures)
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 8
some differences. These differences are likely to be at-
tributable to material properties such as chemical com-
position, porosity (Vajdova et al. 2004), or grain size, but
possible effects from sample preparation and test method,
such as aspect ratio and friction at the ends of the samples
(Paterson 2005), cannot be ruled out at this point. In the
future, with HCP, the effects of the aspect ratio and fric-
tion at the sample ends need to be examined. Nonetheless,
we can say that the range of Pc from 30 to 400 MPa has
turned out to be sufficient to create different fracture
styles for HCP, namely, brittle faulting, distributed duc-
tile fattening, and pore collapse/pulverization.
4.2 Brittleness and ductility in the deviatoric
stress-nominal axial strain curve
As mentioned earlier, elastic limit of the tested HCP was
about εa = 0.5%, in the all tested Pcs of 30, 100, and 400
MPa (Fig. 7). Significant ductile deformation followed
in every case, but the duration of ductile stage differed.
At Pc = 30 and 100 MPa, peak stress was shortly fol-
lowed by an abrupt stress drop of a few tens of MPa that
occurred at εa = 1.8 to 2.5%, marking the end of ductile
deformation, while a similar stress drop occurred sig-
nificantly later at εa = 3.5% under Pc = 400 MPa, mean-
ing greater ductility. The general increasing trend of
ductility (in terms of SS curves) with Pc is well known
for rocks (Heard 1960; Edmond and Paterson 1972;
Va j do v a et al. 2004; Paterson and Wong 2005) and HCs
(Sfer et al. 2002), however, correspondence to the frac-
ture pattern differs as we discuss in detail below.
We begin by comparison with the brittle-ductile tran-
sition of rocks, where certain systematic trends have
been established after many years of research (Paterson
and Wong, 2005). Especially, carbonate rocks are struc-
turally close to HCP in that they are aggregates of soft
minerals with relatively sorted grain size.
The distinct fracture surface, 30° off the maximum
principal stress, seen as in our 30 MPa test (Fig. 8a, Fig.
12a), is a typical ‘brittle’ failure style of rocks (Paterson
1958). For hard silicate rocks at room temperature, such
brittle faulting is not preceded by significant ductile
deformation (Paterson and Wong 2005). In contrast,
faulting in the present test at 30 MPa most likely oc-
curred concurrently with an abrupt stress drop at εa =
2.5%, so was preceded by ductile strain of about 2%.
This, actually, is quite common for carbonate rocks,
whose constituent minerals are much softer than tecto-
silicates. Examples include coarse-grained Wombeyan
marble at Pc = 3.5 to 14 MPa (Paterson 1958). Heard
(1960) found similar behaviors for fine-grained Solen-
hofen limestone at higher Pc of 40 to 75 MPa but only at
raised temperatures of 150 to 400°C. At room tempera-
ture, brittle faulting of the limestone was not preceded by
significant ductile deformation. Fine-grain carbonate
rocks require a much higher Pc to exhibit ductility than
coarse-grained carbonate rocks (Fredrich et al. 1990).
Our HCP sample is definitely ‘fine-grained,’ but the
results rather resembled to the coarse-grain marble,
showing significant ductility at Pc as low as 30 MPa. This
is presumably attributable to inherent low plastic
strength of the constituent minerals (hydrates), compared
with calcite.
The SS curve of our HCP at Pc = 100 MPa showed an
abrupt stress drop at εa = 2%, similarly to the 30 MPa
case (This is slightly earlier than the Pc = 30 MPa case,
contrary to the expectation, but with limited number of
experimental runs, this may well be a matter of experi-
mental reproducibility.) However, a macroscopic fracture
surface did not occur in the 100 MPa test (Fig. 8b),
suggesting enhanced ductility compared with the 30 MPa
test. Instead, the sample exhibited a localized bulging,
which resembles a band of distributed plastic shear de-
formation, commonly seen in ductile deformation of
carbonate rocks (Paterson 1958). They ideally occur at
45° off the maximum principal stress, i.e., on the plane of
maximum shear stress because plastic strength of crystals
does not depend on the normal stress to the crystalo-
graphic slip plane. Our bulged zone seems to be inclined
at about 45°, indeed.
Abrupt stress drop in tests with a servo-controlled
axial displacement means rapid shortening of the sample.
In literature, we do not find the cases where abrupt stress
drop occurred without forming some sort of macroscopic
fracture surface. We speculate two possibilities to ex-
plain this contradiction. First possibility is the unstable
acceleration of plastic deformation in the ductile shear
band. Though plastic deformation is generally deemed to
be a slow process, spatial localization implies the oc-
currence of strain weakening in the band as required for
positive feedback in localization. Second possibility is
hinted by the observation that the post-experimental
sample was pulverized (Fig. 12). Though we do not
know at what timing the pulverization occurred, this
could be the cause of the abrupt stress drop at εa = 2.5%.
Pulverization was seen in HCP tested at 400 MPa as well,
where, again, no macroscopic fracture surface occured,
while the SS curve had an abrupt stress drop at εa = 3.5%.
This stress drop event could be associated with the for-
mation of subhorizontal compaction bands. Further ex-
periments including AE monitoring might be useful to
identify the reason for this perplexing phenomenon of
stress drop without forming a macroscopic fracture sur-
face.
Setting aside the reason for the strength drop event, it
is important to note that the sample behavior signifi-
cantly changed upon this event. In both 100 and 400 MPa
tests, the strain-hardening trend was terminated upon the
event. Hence, we tentatively surmise that the strain at
which the abrupt stress drop occurred marks the end of
ductile deformation of HCP.
The present HCP test at Pc = 400 MPa showed the
greatest ductility as expected. However, the deformation
style is far from the typical ductile deformation known
from rocks. Lateral bulging, the icon of ductile defor-
mation, is only seen at the contact with the end piece; for
most part the sample diameter rather decreased! Fur-
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 9
thermore, the 3.5% of εa to the stress drop is unusually
low for the Pc. Both marble and limestone take up more
than 10% ductile εa at such a high Pc (Paterson 1958;
Heard 1960). Thus, although the low plastic yield
strength of cement hydrates allowed the onset of ductility
at a fairly low Pc for the small grain size, macroscopic
ductility of HCP is fairly limited even at the very high Pc
of 400 MPa. In § 4.4, on the basis of microscopic sample
observation, we propose that the resultant pulverization
is a critical factor in the very high Pc regime. Note that
ductile deformation tests with rocks are typically done
with low-porosity specimens.
We now compare the present results with that of HC,
mainly with the results reported by Sfer et al. (2002) at Pc
= 0 to 60 MPa (Fig. 1, Fig. 15). In their tests, distinct
brittle shear faulting occurred only at a very limited
condition of Pc = 9 MPa. In this test, however, axial stress
peaks at εa = 0.5% and then decreased gradually up to εa
= 10% without causing an abrupt stress drop. Actually,
abrupt stress drop was seen in his HC tests only at 0 ≤ Pc
≤ 4.5 MPa, where axial splitting and/or distributed axial
cracking of visible sizes played a major role, as univer-
sally seen in uniaxial compression tests of almost any
rock. Therefore, while the SS curve at Pc = 9 MPa does
not look brittle, it is not appropriate to take the disap-
pearance of the abrupt stress drop at Pc = 9 MPa as the
manifestation of brittle-ductile transition of the defor-
mation mechanism of HC. As evidenced by the distinct
shear fracture surface 30° off the maximum principal
stress, Sfer et al.’s test at Pc = 9 MPa resulted in typical
brittle faulting at εa as small as 0.5%; the gentle strain
weakening after the peak would be rather ascribed to the
frictional sliding on the rough fracture surface involving
deep interlocking between large, hard gravels (Maekawa
et al. 2003) and also deep plowing of the soft matrix
made of cement and sand by the large gravels, that would
cause gradual wear-induced weakening over a long slip
distance. Such distinction has some practical implication.
For example, HC under Pc = 9 MPa would lose its sealing
capability at 0.5% strain while it still supports a fair
amount of shear load up to several % strain.
At highest Pcs of 30 and 60 MPa, Sfer et al.’s HC
showed continuous strain hardening up to εa = 10%,
where the differential stress abruptly dropped by 90% or
more. Their post-experimental sample showed a few
thoroughgoing, curved and kinked macroscopic fracture
surfaces including a major part subparallel to the maxi-
mum principal stress, rather than the typical shear frac-
ture surface by brittle faulting, which runs 30 degree off
the most compressive principal stress axis. However, the
broken pieces bound by those few macrofractures re-
tained good mechanical integrity. This fracture style
contrasts with our HCP tests at 100 and 400 MPa (Fig.
12), where the sample lost integrity everywhere by per-
vasive pulverization without forming any macroscopic
fracture surfaces. It is interesting that, despite these dif-
ferences, the SS curves from our HCP tests and their HC
tests commonly exhibited similar ductile looks accom-
panied by considerable strain hardening. Although the
timing of macroscopic fracture in Sfer et al.’s experi-
ments is not known, the authors inferred that the mac-
roscipic cracking (if not thoroughgoing) occurred early
on and the subsequent apparently very ductile SS curves
reflect the slip-hardening friction between interlocking
pieces. If so, HC’s ductile behavior at 30 and 60 MPa is
also apparent, as we suggested for their HC result at 9
MPa.
4.3 Confining pressure dependence during
ductile deformation
We here focus on the absolute levels of SS curves of
HCPs (cylindrical shape of φ20 × 40 mm and dried at
40 °C for two weeks) obtained at different Pcs. One re-
markable feature of our HCP tests is that SS curves at
different Pcs overlap each other during both initial elastic
portion (0 < εa = 0.5%) and following ductile portion
(0.5% < εa < stress drop event). In typical brittle-ductile
transition experiments of carbonate rocks, two system-
atic Pc dependences are usually observed. Firstly, dif-
ferential strength during ductile deformation is positively
dependent on Pc. Secondly, as a result of this, change
from elastic to ductile deformation curves, indicated by
the steep-to-gentle change of SS-curves slope, occurs at a
greater strain and differential stress for higher Pc. These
results from rocks suggest that their ductile deformation
mechanism is not the pure crystal plasticity whose
strength should be independent of Pc. Indeed, at ex-
tremely high Pcs, e.g., about 600 MPa in Fig. 14 of Ed-
mond and Paterson (1972), and/or high temperatures,
400°C for Solenhofen limestone of Heard (1960), both
dependences are lost for rocks as well. Thus, it is gener-
ally accepted that brittle-ductile transition in rocks has a
broad intermediate regime where both crystal plasticity
and frictional-cataclastic processes play a role in ductile
deformation. In light of this understanding, the presently
observed Pc-independent SS curves for HCP suggest that
ductile deformation was almost purely governed by the
low plastic strength of cement hydrates. Although the
fracture pattern that involves intensive pulverization at
100 and 400 MPa indicates that cataclastic processes
could accommodate much strain, the strength during
ductile deformation seems to have been strongly limited
by crystal plasticity.
Such easy transition to fully plastic behavior is not
seen in HC (Fig. 15). For example, Malecot et al. (2010)
found clear increase of ductile strength up to Pc = 400
MPa. This is probably because much of the shear
strength of HC is supported by the strong gravel
framework, whose plastic flow would require extreme
conditions.
In addition, we note that there is a tendency known
that ductile SS curves of high-porosity carbonate rocks
tend to lose Pc dependence above certain levels of Pc. For
example, Solnhofen limestone (Paterson 2005), Tavel
limestone, and Indiana limestone (Vajdova et al. 2004)
have porosities of 3%, 10% and 15.6%, respectively.
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 10
They showed less dependence when the Pc exceeded 200,
100, and 20 MPa, respectively. Our HCP sample had high,
18% initial porosity, and exhibit pulverization at higher
Pcs of 100 and 400 MPa, similarly to porous rocks sub-
jected to high Pcs (Wong and Baud 2012). So, phe-
nomenology resonates definitely. However, it is not es-
tablished why of this phenomenon, given that cataclastic
flow expected of pulverized sample is an inherently
pressure-sensitive frictional process. One speculation
may be that free grain rotation enabled by the pulveriza-
tion help each grain align to the crystalographic orienta-
tion compatible with macroscopic deformation, provid-
ing the environment for crystal plasticity to contribute
efficiently to the macroscopic deformation. Note that
calcite, the constituent minerals of limestones and mar-
bles, is a relatively soft mineral well known for the easy
appearance of anisotropic crystal plasticity such as
twinning at room temperature (Turner et al. 1954).
Limestone and marble are known to show ductile de-
formation under low Pcs (Vajdova et al. 2004; Paterson
and Wong 2005). In marble, before the macroscopic
fracturing took place, local yielding was confirmed to
occur in the crystal particles (Paterson and Wong 2005;
Sakaguchi et al. 2011).
4.4. Pervasive microfractures due to high con-
fining pressure
In general, as the Pc increases, the elastic limit, both in
stress and strain, increases. However, they can decrease
in porous rock (Baud et al. 2000; Vajdova et al. 2004;
Paterson and Wong 2005), likely due to distributed mi-
crofracturing induced by hydrostatic loading. As shown
in Fig. 12, when the samples tested under Pc of 100 and
400 MPa were taken out of the tubes, they collapsed into
small pieces. In general, when the crystal plasticity takes
place evenly, the sample does not show macroscopic
fracturing. The coexistence of pulverization and full
plasticity could be explained by assuming that the crystal
plasticity of each grain occurred in different directions
due to the random variation of crystallographic orienta-
tions or that the pressure required for crystal plasticity
was very different among grains. This is, we propose,
why the sample could behave full-plastically, as a whole,
while pervasively microcracked due to local incompati-
bility between neighboring grains. However, it is re-
ported for HC (Poinard et al. 2012) and rocks (Paterson
2005) that microfracturing can be introduced not only by
applying Pc and load but also by unloading. Therefore, in
future, to properly understand the deformation mecha-
nism, further examination is required to identify when
pervasive fracturing was introduced to the samples.
4.5. Alteration of hydrates
Finally, we will discuss the change in hydrates due to the
high-pressure triaxial test. As shown in Figs. 10 and 11,
the BEIs became darker after testing at any Pc. The gray
value in Fig. 11 can vary depending on the SEM obser-
vation condition, which is not completely-consistent
from sample to sample. However, even if the curves are
shifted relatively to correct the difference coming from
the observation condition using the large white spots in
Fig. 10 as a common reference, which is seen at gray
values of around 200 and 220, the samples after testing
are still darker than the one before testing. BEI brightness
changes according to the atomic number, surface
roughness, and molecular structure of the material
(Lloyd 1987; Shimizi et al. 2006). In the field of metal-
lurgy, BEIs are used to observe dislocations
(Gutierrez-Urrutia et al. 2009). In our case, the atomic
number could not change, and the prepared surfaces were
smooth at a molecular scale. Reduction in porosity can-
not be the reason of darker BEIs under higher confining
pressure because denser material becomes brighter in
Fig. 15 Stress-strain curves of HC at different confining
pressure σL. With permission of ASCE, from (Sfer et al.
2002).
Fig. 14 Stress-strain curves in ductile deformation of
Carrara marble at different Pc (kb). With permission of
Elsevier, from (Edmond and Paterson 1972).
Y. Sakai, M. Nakatani, A. Takeuchi, Y. Om orai and T. Kishi / Journal of Advanced C oncrete Technology Vol. 14, 1-12, 2016 11
BEI, which is opposite to our results. Thus, the change in
BEI brightness is likely due to a structural change at a
molecular scale. As discussed in § 4.3, given that
Pc-insensitive ductility is the manifestation of crystal
plasticity due to intragranular slip or twinning, HCP
likely suffered molecular-scale changes in its hydrates.
The yielding strength of 100 MPa, commonly seen in
tests at Pc = 30 to 400 MPa, indicates the low level of
differential stress for such processes to operate. Addi-
tional experiments will be conducted in the future for
validation purposes because, at this point, we cannot rule
out the possibility that the alteration of hydrates occurred
already by hydrostatic loading.
5. Conclusion
Triaxial tests of HCP, with 18% initial porosity, were
conducted under Pcs of 30, 100, and 400 MPa. The re-
sults covered three representative failure styles previ-
ously known in triaxial tests of porous carbonate rocks
composed of relatively soft minerals: the oblique brittle
faulting, the distributed ductile deformation, and the pore
collapse and resultant pulverization.
Typical oblique brittle faulting occurred only at Pc =
30 MPa, but the macroscopic failure by faulting was
preceded by a significant ductile phase. At Pc = 100 MPa,
bulging occurred as the sample exhibited a modestly
strain-hardening ductile SS curve. Role of crystal plas-
ticity was suggested by BEIs of the post-experimental
samples where much of the matrix hydrates seems to
have suffered molecular-scale alterations during tests.
No macroscopic fracture surface was formed even after a
small sudden stress drop occurred at 2.5% strain. Abrupt
stress drop without a macroscopic fracture surface is
probably not reported in previous literature, and we are
not sure of the cause. Post-experimental samples of the
present tests at Pc = 100 and 400 MPa were pulverized
throughout, similar to the pore collapse phenomenon of
porous rocks under very high Pcs. Consistently, sample
porosity became lower after the tests; especially the
sample tested at Pc = 400 MPa had a porosity of only 1%.
Formation of compaction bands is suggested by visual
inspection of the sample after this test.
Interestingly, SS curves at different Pcs overlapped
each other, though the experiment (and ductile phase)
lasted to a greater strain at a higher Pc. This implies that
the strength during the ductile phase (from yield point at
0.5% strain to the small abrupt stress drop) was governed
by the pressure-insensitive plastic strength of the hy-
drates, notwithstanding that the sample was totally pul-
verized in the tests at Pc = 100 and 400 MPa. This result
contrasts with rocks and HC, where the ductile (-looking)
SS curves have a positive dependence on Pc, suggesting
that their ductile strength is partially controlled by fric-
tional cataclasis. We propose that the low inherent plastic
strength of cement hydrates is the reason for the differ-
ence, as supported by intensive alteration captured by
BEIs. We argue that the occurrence of pulverization can
coexist with the easy flow of the hydrates, if we presume
the crystallographic anisotropy of plastic strength and/or
their inhomogeneity.
Overall, from the present experiments that cover a
wide range of Pc, though clearly insufficient to propose
anything quantitative, we surmise that HCP behavior
under confinement seems to well compare to rocks, es-
pecially carbonate rocks, whereas some differences exist
that are probably attributable to the extreme weakness of
the HCP’s hydrates compared with rock-forming miner-
als.
On the other hand, by comparing the fracture style and
the SS curves of HC from literature, we note that be-
havior of HC under confining pressures are not
straightforwardly compared with HCP and rocks. What
makes HC intractable is that the appearance of SS curves
does not correspond well to the fracture pattern in the
regular way expected from rock experiments under high
Pc. Notably, very rough irregular fracture surfaces, that
almost look like a splitting failure in unconfined tests of
rocks, occur even under a fairly high Pc. This is pre-
sumably a result of the large size of gravel stones com-
pared to the specimen size, bound together by weak
cement paste, which may be deemed as a flowable ma-
terial under some confinement as we saw in the present
experiments. Although such is the very structure that
gives the HC the exceptional usefulness as structural
material, in order to evaluate, understand, and predict
HC’s properties under high pressure, starting with less
formidable HCP may be an approach worth considering.
Systematic studies on HCP including the effects of po-
rosity, cement type, etc. may be prerequisite to begin the
comprehensive studies of HC under confinement.
Acknowledgment
This study was supported by the Earthquake Research
Institute Cooperative Research Program (2015-F3-03)
and JSPS KAKENHI Grant Number 25709034.
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