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Proc. Int. Symp. „Brittle Matrix Composites 11”
A.M.Brandt, J.Olek, M.A.Glinicki, C.K.Y.Leung, J.Lis, eds.
Warsaw, September 28-30, 2015
Institute of Fundamental Technological Research
LIQUID WATER PERMEABILITY OF PARTIALLY SATURATED CEMENT
PASTE ASSESSED BY DEM-BASED METHODOLOGY
Kai LI*, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS
Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1
2628 CN Delft, the Netherlands, *e-mail: [email protected]
ABSTRACT
Permeability of virtual cement seems to exceed experimental data by several orders of magnitude. The
differences may actually not be that dramatic, since experimental samples are in practice not always fully
saturated as generally assumed. This paper demonstrates that this has enormous effects on permeability. A
numerical study is conducted on water permeability of partially saturated cement paste based on simulated
microstructures. During drying, larger pores empty first according to the Kelvin-Laplace law, leading to a
significant decline in water permeability. The results in terms of relative water permeability have been validated
against lattice Boltzmann simulations and experimental data, respectively. A satisfactory agreement is found.
Both the pore size distribution and pore connectivity are shown to have an important influence on the overall
permeability. The effects of technological parameters, such as hydration age and water-to-cement ratio, have also
been discussed.
Keywords
Cement paste, water permeability, water saturation degree, pore network, DEM, particle
simulation
INTRODUCTION
The durability of concrete depends on its ability to prevent the ingress of aggressive agents,
such as carbon dioxide (CO2) or chlorides. Permeability, defined as the movement of the
agent (liquid or gas) through the porous cement paste under an applied pressure, is therefore
the most important property of concrete governing its long-term behaviour [1]. However,
permeability values obtained from numerical analyses differ significantly from values in
experimental tests. The origin for those differences could be found in the commonly neglected
humidity level. Although the specimens used for these experiments were assumed to be fully
saturated in order to compare them with numerical experiments, the reality is that humidity
fluctuations in the cement paste are unavoidable. Full saturation is difficult if not virtually
impossible to establish and maintain. In fact, air pockets are inherent features and have a
significant effect on the local transport properties as will demonstrated. Thus, the saturation
degree should not be ignored when measuring the intrinsic permeability especially when
comparing numerical results with experimental ones. In fact, a series of publications deal with
experimental studies on the impact of the degree of saturation on permeability [2-6]. Hereby,
the degree of water saturation is defined as the volume fraction of the pores filled with water.
Unfortunately, experimental approaches are usually laborious, time-consuming and thus
expensive. The modelling of fluid flow through a realistic virtual representation of the cement
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paste’s microstructure can therefore be considered an attractive alternative. For that purpose,
network models [7-9] and discrete models [10-12] can be used. The latter, voxel-based ones
pursue solving the equations of flow by numerical methods such as the lattice Boltzmann
method. Although the lattice Boltzmann method became recently quite popular due to its low
demand for computing resources, the actual pore structure is not considered, which can be
considered a significant disadvantage. The permeability by methods in the first category is
determined from a network of cylindrical tubes that are derived from the underlying actual
pore network. Each tube represents a local pore. Next, the equations of laminar flow inside
this tube network are solved to obtain the intrinsic permeability. Network models heavily
depend on the proper description of the pore structure, which determines the permeability.
Since we are interested in the relationship between pore structure and permeability, this
method is selected in this paper. Pignat et al. [7], Ye et al. [9] and Nghi et al. [13] have
conducted earlier studies following this approach. However, these earlier studies only
addressed the case of fully saturated porosity conditions and cannot be compared to waterbased experiments with saturation levels lower than 100%.
In this paper, the methodology is outlined for simulating the permeability of a partially
saturated pore structure of hydrated cement. Discrete element method (DEM) is used instead
of random sequential addition (RSA) to realistically distribute the individual cement grains in
the container. For more details on DEM versus RSA, see [14-16]. The pore microstructure is
obtained after hydration simulation. Thereupon, pore characteristics in the fully and partly
saturated specimens are assessed by a novel methodology and associated water permeability
values can be determined. As the saturation degree is reduced, the calculated water
permeability decreases significantly, spanning the major part of the experimental range of
data. Our simulation results, in terms of relative permeability (defined as the ratio of intrinsic
water permeability at a certain degree of saturation to the intrinsic water permeability
measured in the fully saturated state), are compared with estimates obtained by a lattice
Boltzmann approach and with physical experiments. A satisfactory agreement is observed,
validating the presented methodology. Pore size distribution and pore connectivity are
investigated to explain the changes of permeability data at various degrees of saturation.
Moreover, the influences of hydration age and water-to-cement ratio (w/c) on the estimated
permeability are also discussed.
METHODOLOGY
The complete methodology of our computational technique consists of four stages. In the first
stage, cement grains packing is modelled by a DEM simulation. Then, the packed structure is
an input for hydration simulation by XIPKM (eXtended Integrated Particle Kinetics Method).
Once the hydration simulation is done, porosimetry of hydrated paste can be assessed by
DRaMuTS (Double Random Multiple Tree Structuring system) and SVM (Star Volume
Measuring). Finally, the tube network model is used for permeability estimation. Interested
readers can find all relevant details in [13]. The method as described in [13] only applies to
fully saturated specimens. Therefore, a new “empty” algorithm for modelling the
microstructure of a partially saturated paste and thus to calculate permeability has been
developed and will be outlined in this paper. In general, the pore space of mature paste for
permeability estimation is assumed 100% water-filled. This hypothesis is equivalent to the
ideal underwater curing whereby the sample is supposedly fully saturated, and thus the water
saturation degree is 100%. As the relative humidity declines, the structure starts loosing water
by evaporation from the pores. An empty pore acts as a barrier for water transport; this
phenomenon is mimicked in our simulation by positioning solid objects in the presumed
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water permeability of partially saturated cement paste assessed...
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empty pores, as illustrated in Fig. 1. According to the Kelvin-Laplace equation [17], larger
pores easier loose water and become empty first. Thus, the “empty” algorithm starts from the
largest pores in our simulation. Once the pore structure is determined, water is sequentially
removed by positioning solid sphere at the calculated centre of the pore to represent the
partially saturated state.
(a)
(b)
(c)
Fig. 1. Illustration of the “empty” algorithm in 2D; (a) fully saturated state; (b) positioning of
a solid circle in water-filled pore; (c) partially saturated sate. The position and size of the
virtual red circle (in 3D: solid sphere) is obtained by DRaMuTS.
A network structure consisting of cylindrical tubes was thereupon constructed to
represent the pore channels. The main trunks represent the direct paths through pore space
from the bottom to the top of the sample. In contrast to isolated paths and dead-end branches,
the main trunks play a key role in the transport process. They can be extracted from the
system and then used for permeability calculations, while the other pores are neglected. The
diameters of the tubes along the main trunks were taken equal to the size of the underlying
pore structure. For the estimation of the pore size, a star volume method (SVM) was used. A
pressure gradient is applied between inlet and outlet nodes located at the bottom and top
surfaces of the specimen. The intrinsic permeability ĸ, in m2, can be calculated by Darcy’s
equation [18],
(1)
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Kai LI, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS
where L (m) and A (m2) are the length and cross sectional area of a test sample through which
a fluid flow Q (m3/s) is driven by applying an external pressure gradient P (Pa). The
parameter µ (Pa·s) represents the dynamic viscosity of the fluid. The influence of the actual
shape of the pores on conductivity is explicitly taken care of, whereby reference [13] gives all
details.
Virtual cement pastes were generated in a cube (100 µm in size) with an initial w/c of
0.4. The phase composition of the cement clinker was 61% C3S, 20% C2S, 8% C3A, 11%
C4AF by volume. The Rosin Rammler function represented the particle size distribution,
ranging from 1 to 30 µm. The samples were at an age of 28 days subjected to the earlier
sketched methodology. The results will be discussed in the next section.
RESULTS AND DISCUSSION
Evolution of water permeability with the degree of saturation
As a first result, the evolution of the measured intrinsic water permeability with the degree of
saturation obtained by our numerical simulation approach is shown in Fig. 2. To avoid systematic bias due to the computation, multiple structures (8 samples) were analysed. The
standard deviations of our simulation data are also displayed in Fig. 2. As the small standard
deviation suggests, reliable results at any given saturation degree can be obtained from a
single structure. In general, as the water saturation degree decreases, the number of connected
pores filled by water declines, resulting in a reduction of the available paths for water
transport in the system. Hence, the system is de-percolating. Moreover, the large pores dry-up
first, additionally contributing to a lower permeability. When the water saturation degree
reaches a value around 0.25, the remaining fully water-filled pores is mostly disconnected,
thus, leading to a permeability approaching to zero.
Although a limited number of experimental studies on liquid water permeability of
partially saturated cement paste are available, Kameche et al. [19] recently published a paper
in this field that is focusing on concrete. This is the latest and according to our knowledge
probably also the only available data dealing with water permeability in partially saturated
cementitious samples. Even though the experiments concern concrete, the tendency should be
similar between concrete and cement paste since both belong to cement-based materials. The
relative permeability (instead of intrinsic permeability) allow direct comparison between
different cementitious materials, such as concrete and cement paste in this case. In addition to
the experimental data, the permeability results of cement paste from the 3D LatticeBoltzmann (LB) modelling by Zalzale et al. [17] are also used for comparison reasons. The
outcomes are shown in Fig. 3. A satisfactory agreement is observed between our simulation
data and both other results, validating our methodology.
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water permeability of partially saturated cement paste assessed...
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Fig. 2. Standard deviation of water permeability data pertaining to virtual cement pastes.
Fig. 3. Validation of our simulation results by comparing them with experimental data and the
values obtained by the LB method.
Porosimetry analysis
Pore size distribution (PoSD) and connected pore fraction are two of the key factors affecting
the transport process in cementitious materials. In this paper, these two parameters were
investigated to link the variations in water permeability of cement paste at five different water
saturation levels (100%, 75%, 61%, 54%, 39%) to its internal structural changes. In Fig. 4, we
can see that the volume-based pore size distribution curve of water-filled pores shifts to the
left as the capillary water saturation decreases. Note that empty pores are no longer
considered on the pore size distribution estimation. As water was progressively removed from
the largest pores according to the Kelvin-Laplace equation, this causes the PoSD to shift to
the left for lower degrees of saturation. Fig. 5 reveals an almost linear decline in median pore
size with diminishing degree of water saturation in the pores. The calculated median pore size
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Kai LI, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS
is also volume-based instead of number-based, as already shown in Fig. 4. So, the PoSD of
water filled pores and hence its related permeability is very sensitive to the degree of water
saturation.
The other important parameter, pore connectivity in mature cement paste, was studied
as well. DRaMuTS is based on a system of randomly distributed points, so the accuracy of the
method depends strongly on the number of points. A large number of points increases
accuracy, but makes the computations more expensive. Although the PoSD also depends on
these numbers, the sensitivity is larger with structure-sensitive parameters such as the
connectivity. Therefore, a sensitivity analysis of the connected pore fraction (= number of
pores directly related to the pore path connecting the top and bottom of the specimen divided
by the total number of pores) at various degrees of water saturation was carried out first. The
results are plotted in Fig. 6. It shows the connected pore fraction to increase sharply as the
number of points distributed in the remaining water-filled pores increases. The curves seem to
gradually approach a plateau value indicating the measurement to approach the real value.
The number of points used in the remainder of the examples was set to 105 to limit the
computation time without a significant loss of accuracy.
Fig. 4. Pore size distribution of samples at various degrees of water saturation.
Fig. 5. Almost linear reduction in volume-based median pore size with declining degree
of water saturation in the capillary pore network structure.
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water permeability of partially saturated cement paste assessed...
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Fig. 6. Sensitivity analysis of connected pore fraction by the number of measurement points
distributed in the pore volume for a variety of water saturation degrees.
Fig. 7. Connected pore fraction as a function of capillary water saturation.
The connected pore fraction as a function of the capillary water saturation is plotted in
Fig. 7. With a decreasing capillary water saturation, the initially fully water-filled pores
gradually become empty, leading to a reduced fraction of connected pores. A smaller number
of connected pores involves a lower water permeability. The reductions in pore size and pore
connectivity explain the structural changes of cement paste under different water saturation
degrees. Both factors play a key role in interpreting the decrease of water permeability at
lower saturation degrees.
Influence of technological parameters on permeability
The influence of two technological parameters (hydration age and w/c) on permeability have
been studied as well.
Firstly, specimens at four different hydration ages (3 days, 7 days, 28 days and 4 months)
but identical w/c of 0.4 were selected to study the influence of this parameter on water
permeability of samples with various degrees of water saturation. The results are plotted in
Fig. 8. For the different hydration ages, a pattern of slightly curved almost parallel lines is
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Kai LI, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS
obtained for water saturation versus intrinsic water permeability. This can easily be explained
by the increasing density in the hydrate structure and as a result reduced pore space. The latter
involves both smaller pores and more advanced pore depercolation, both leading to reduced
permeability.
Secondly, specimens with w/c = 0.3, 0.4 and 0.5 at 28 days of hydration were selected
for the permeability analysis. The results are illustrated in Fig. 9. For different values of w/c, a
pattern of slightly curved almost parallel lines is obtained for water saturation versus intrinsic
water permeability. An increasing w/c actually means that the volume of cement in the
container space is declining, leading to a lower packing density and thus to higher porosities.
This, in turn, leads to an increased permeability.
Fig. 8. Influence of hydration age on water permeability of partially saturated cement pastes.
Fig. 9. Influence of w/c on water permeability of partially saturated cement pastes.
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water permeability of partially saturated cement paste assessed...
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CONCLUSIONS
In this paper, a new methodology (XIPKM-DRaMuTS-SVM-Empty algorithm-Tube network
modelling) has been developed to determine the permeability of partially saturated pastes,
reference [20] gives all details. It is found that the intrinsic water permeability strongly
depends on the degree of water saturation. In general, water permeability reduces with
decreasing water saturation. Pore size distribution and pore connectivity are investigated to
understand the underlying modification related to pore structure. Specifically, large pores are
blocked in the “empty” procedure leading to a leftwards shift of the pore size distribution
curve. This also reduces the pore connectivity in the structures since the transport paths for
water are blocked. Both factors result in lower permeability data.
The effects on permeability of two technological parameters, i.e., hydration age and w/c,
have been discussed as well. As hydration age increases, the structure of hydrated paste
becomes denser since pore space is gradually filled up with hydration products. Therefore, the
calculated permeability declines at prolonged hydration duration. An upward trend can be
observed in the permeability curves by increasing w/c. This is because at higher w/c the
density of the hydrate structure is reduced, yielding lager pore space for water transport, and
thus higher permeability. Moreover, the curves almost remain “parallel” in Fig. 8 and Fig. 9
which is an interesting observation. The influence of the investigated parameters seems to just
shift the curves to a certain extent.
ACKNOWLEDGEMENTS
The first author would like to thank the China Scholarship Council (CSC) for the financial
support to this work.
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