Predicting water permeability and relative gas permeability of unsaturated cement-based material from hydraulic diffusivity
Introduction
Durability of concrete material is mostly determined by the coupled action of physical and chemical processes, in which the transport of ingressive agents plays a central role. As an indicator of transport performance, permeability is the most crucial parameter of concern to quantify durability of cement-based materials [1], [2]. Modern concrete materials with low water to cement ratio, high density are weakly permeable. Indirect estimation of permeability is not trivial in order to evaluate this central transport property. Furthermore, concrete materials in use are commonly unsaturated. To quantitatively describe concerned mass transport process in unsaturated concrete material, the relative permeability to water and gas is of great importance.
In the case of weakly permeable cement-based material, indirect assessment of unsaturated water permeability is more preferable than direct experimental measurement. It is widely recognized that direct measurement of water permeability faces great practical difficulty for high-quality concrete [3], though some advanced experimental devices were proposed [4], [5], [6], [7]. Indirect assessment, either from micro-structural parameters or some other simple experiments that are easy to perform, is more attractive. Katz–Thompson model [8], based on percolation theory, has been proven useful in providing good estimates of permeability for sedimentary rock from mercury intrusion porosimetry (MIP) data [9], [5]. When it is extended to cement-based materials, the validity of Katz–Thompson model for cement-based material is still questionable [5], [10]. In addition, some rapid methods like beam bending and thermopermeametry, originally developed for soft gels, were further applied to cement-based materials but restrict to cement pastes [11], [12]. Another powerful indirect method deriving water and gas permeability inversely from drying isotherm was also developed and successfully applied to cement-based materials with various mix-compositions [13], [14]. However, the total gas pressure is assumed to remain constant as the atmosphere pressure during drying in this model [13]. Considering the existence of capillary pressure, this assumption is still of question. Besides, although the intrinsic permeability is theoretically independent of permeating fluid, the intrinsic permeability of cement-based material to active water and neutral gas may be not true, which have been experimentally observed for various cement-based materials [6] but recently argued from a thorough 3D lattice Boltzmann modeling [15].
The influence of water saturation degree on permeability to water or gas is important when modeling transport process in unsaturated porous materials. Burdine model and Mualem model, originally proposed by Burdine and Mualem in soil science [16], [17], give the relative permeability to water and gas from only water vapor adsorption or desorption isotherms. These two conceptual models form the basis of some indirect methods, and are further employed to study cementitious materials recently [13], [18], [19]. Many efforts were also made to validate the model of relative water permeability from relative gas permeability of observable variability [19], [20], which is easier to measure experimentally but vulnerable to the microstructural change possibly involved by prior drying preparation or other treatments [21], [22]. It is indicated that Burdine or Mualem model has good potential to fit for cement-based materials only if reasonable tortuosity function of liquid and gas phases is adopted for unsaturated material. However, the tortuosity function is very hard to determine with high accuracy since it is an empirical parameter without clear physical significance. This makes the estimation of unsaturated permeability to water and gas very difficult.
This paper is devoted to predicting the water permeability and relative gas permeability of unsaturated cement-based materials, from which the influence of saturation degree on relative water and gas permeability can be given out clearly. The water permeability for unsaturated cement-based materials is assessed from the cross-property relationship between hydraulic diffusivity and permeability. Furthermore, the relative gas permeability is also deduced from water permeability through their relationship. As relative gas permeability is easy to obtain, the proposed model is validated by measured relative gas permeability of cement-based materials.
Section snippets
The relationship between water permeability and hydraulic diffusivity
It is well-known that water volume content θ (−) has remarkable influence on many transport properties including permeability, diffusivity and sorptivity etc. To facilitate the analysis about the relationship between water volume content and transport properties, the water saturation degree Θ (−) is first introduced aswhere θr,s are the residual and saturated water volume contents, respectively. In unsaturated flow theory, the physics of water flow is expressed in the extended
Relationship between relative permeabilities to water and gas
For unsaturated porous material in equilibrium moisture state, water always occupies the small pores while gas phase exists in the other pore space. The transport paths and space of water, gas phases in unsaturated material are always complementary to each other, which determines the relationship between relative permeabilities to water and gas.
Burdine model [16] (further developed by Brooks and Corey [50]) and Mualem model [17], from which the relationship between relative water and gas
Verification of water retention curve model
To strictly satisfy the three restrictions on WRC model for cement-based materials, the Zhou model is proposed in Section 2.3. Considering the fitting ability of the Brutsaert model and the similarity between power term and exponential term, it is expected that the proposed Zhou model can very well characterize the water retention data of cement-based materials. In literature there are many groups of measured water retention data [54], [55], [56], [57], [58], which are used herein to verify the
Conclusions
- •
The unsaturated water and gas permeability are key parameters for the characterization of mass transport in cement-based materials. In this paper, a new approach to measuring unsaturated water permeability indirectly from hydraulic diffusivity is proposed. The relative gas permeability is further derived from the relationship between relative water permeability and relative gas permeability given by either Burdine model or Mualem model. The predicted relative gas permeability is compared to
Acknowledgment
The financial supports from the National Natural Science Foundation of China (No. 51208153), Key Projects in the National Science & Technology Pillar Program During the Twelve Five-year Plan Period (No. 2013BAJ12B03), the National Science Foundation for Post-doctoral Scientists of China (No. 2012 M510092), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20122302120083) and the open fund of State Key Laboratory of Silicate Materials for Architectures (Wuhan
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