The relative humidity dependence of the permeability of cement paste measured using GARField NMR profiling
Introduction
A factor common to nearly all forms of degradation of concrete materials is water transport into, and out of, the solid matrix and in particular the binder phase, cement. In consequence, characterisation of the porosity of cement, and of properties related to water transport within it, are seen as valuable indicators of durability. Intrinsic permeability is one such indicator. Intrinsic permeability, K, is the macroscopic property that relates volume liquid flow through the matrix, Q, to the driving pressure P according to Darcy's law,where A is the cross sectional area of a test sample of length L and μ is the dynamic fluid viscosity. The intrinsic permeability relates to a fully saturated system.
The intrinsic permeability of cement paste is unusually low compared to many other porous media. This makes its measurement extremely difficult since, at moderate pressures, the flux of liquid through a representative volume is extremely slow. Literature reports a very wide range of experimental values from 10− 17 m2 measured using O2 gas as the permeating fluid [1] through to values in the range 10− 20 down to 10− 22 m2 using liquid water [2], [3]. Clearly, these values are not fluid independent. The most likely hypothesis, advanced previously [4], [5], [6], is that these discrepancies may be explained if it is appreciated that in almost all, if not all, measurements the fluid does not fully saturate the system. In the case of O2 gas measurements, the C–S–H gel phase that percolates the paste is not normally completely dehydrated while in the case of liquid water measurements, self-desiccation of larger pores invariably causes the capillary network to be partially desaturated. Hence, a combination of both liquid water and vapour/air fills the pore space.
In the case of partially saturated media with liquid and vapour flow, the relative permeability of the liquid and vapour should be considered. Moreover, it is then necessary to measure the permeability as a function of saturation. This is not possible with most conventional methodologies where a macroscopic sample is exposed to a pressure gradient as in, for instance, a so-called “cup-test” without making many measurements that each span different small ranges of RH and hence saturation — a difficult and time consuming process. Imaging is required to overcome this difficulty. NMR imaging (MRI) has previously been used to measure water concentration, ingress and drying profiles in cement based materials [7], [8], [9], [10]. However, in general, MRI has only visualised the water in the larger pores with long spin–spin lattice relaxation times, T2. A lack of full T2 resolution coupled with spatial resolution has limited the analyses. Lesser known NMR methods that do access less mobile water with much shorter T2 in more confined spaces as well as water in larger pores are known and have been used. These include so called single-point imaging (SPI) methods [11], [12]. However, SPI lacks discrimination between water in different environments, as only a single relaxation decay time, albeit short, is interrogated unless the experiment is repeated for different interrogation times [13], [14]. Stray field imaging (STRAFI) techniques have also been used [15], [16]. In this case the observed relaxation time bridges between T2 and T1ρ, the so-called spin lattice relaxation time in the rotating frame. STRAFI is closely analogous to GARField NMR as used in this work.
This paper reports measurements of the permeability of cement paste to water transport as a function of the degree of saturation obtained using magnetic resonance profiling. The profiles are recorded with a GARField MR magnet that affords an unusually high magnetic field gradient so as to allow sufficiently short magnetic resonance echo times to see signals from short T2 liquid fractions.1 As a result, it is possible to quantify the capillary pore, C–S–H gel pore and C–S–H interlayer water of the sample. Moreover, the method has sufficiently high spatial resolution (sub millimetre) so as to use samples that are small enough to equilibrate relatively quickly. The profile intensities are calibrated through recent advances in the understanding of NMR relaxation experiments applied to cement pastes and by cross reference to a saturated packed sand sample of known porosity. Finally, the pore type specific desorption isotherm of cement paste is taken from the recent work of Muller et al. [18] in order to link water saturation to RH in the calculation of permeability.
The data is analysed in three ways. First, the simple macroscopic permeability as would result from a conventional test is calculated. Second, the effective water permeability as a function of RH or saturation is calculated, making no attempt to separate liquid and vapour. Third, the data is fit to a model of coupled liquid and vapour transport in cement materials due to Baroghel-Bouny et al. [19].
Section snippets
Theory
The NMR experiment yields the (calibrated, and pore-type resolved) dynamic equilibrium profile of water saturation across a cement paste sample, S(z)where z is the space coordinate exposed to a spatial gradient of the RH. Darcy's law, Eq. (1), can be written in terms of the reciprocal of the profile gradient aswhere φ(z) is the local (external) RH that would yield the local (internal, equilibrium) saturation, S; P is the corresponding vapour pressure; and J = Q/A is the water
Cement pastes
Short lengths of thin walled, 10 mm outer diameter, glass NMR tubes were cut so as to be open at both ends. The cut ends were ground flat and “square on”. The tubes were cleaned using dilute hydrochloric acid. Having sample tubes open at both ends, allowed samples to be exposed subsequently to an RH gradient. The cleaning procedure greatly facilitated the adhesion of the paste to the tube wall so preventing wicking of water up the outside of the paste cylinders. The sealing procedure was found
The desorption isotherm and paste porosity
The desorption isotherm for an identical paste to that used in this work has been measured previously using NMR [18]. As shown in Fig. 1 of reference [18], it is pore type resolved and includes the water bound in crystalline Ca(OH)2. In that earlier work, it was pointed out that the interlayer and solid water signals apparently increase as the gel water is removed. This is due to the shorter relaxation time of residual surface water layers in dry pores, compared to the relaxation time of the
Profile results and analysis
Fig. 3 shows the profile of the sample as originally hydrated (i.e. aged 28 days) and again aged 609 days, after exposure to a RH gradient from 98% at the right hand end of the sample to 15% at the left. The sample is 22.5 mm long. The data is reconstructed from the sum of the echoes recorded at each position. This presentation dramatically over-weights the contribution of long T2 components such as capillary water. However, it serves to illustrate well the spatial uniformity of the sample
Effective permeability
The permeability calculated using Eq. (1) is 4.5 × 10− 21 m2. This result takes account only of the pressure difference across the whole sample and assumes single fluid, liquid water, flow. The analysis replicates standard measurements and the result is very much in accord with previous estimates for water permeability of cement paste published elsewhere. It gives confidence that the sample preparation and procedures are working as expected.
An effective permeability as a function of relative
Conclusion
It has been shown that GARField NMR profiling is a suitable means to obtain profiles in small cement paste samples with high spatial resolution that separately quantitate water in C–S–H interlayer, gel pore and capillary pore environments. As a result, this methodology goes further than earlier MRI studies that have largely accessed water in only the larger pore environments. We have shown that the data can be used to evaluate models of cement permeability with a good degree of accuracy, beyond
Acknowledgements
SZ thanks the Kwan Trust for financial support. This work was funded by the UK Engineering and Physical Sciences Research Council (Grant No. EP/H033343/1).
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