Engineering structures of concrete are generally recognized to be rarely fully water-saturated. The water transportation process in unsaturated cementitious materials offers therefore a relevant problem the understanding of which can be crucial in assessing concrete's degradation and failure mechanisms. In recent years, the number of published papers on this topic is significantly increased. This review presents the latest advancements in determining water permeability of unsaturated cement-based materials by experimental methods and numerical modelling. The effects are summarized of water-cement ratio (w/c), curing age, particle size distribution, interfacial transition zone (ITZ) and supplementary cementitious materials (SCMs) on the permeability of partially saturated cement-based materials. Next, the underlying relationship between relative water permeability and pore structure is presented and discussed. Additionally, an insight into water transport mechanism of unsaturated concrete is proposed. Finally, some evaluative conclusions are drawn that can be instrumental for setting up future studies.

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Permeability estimates obtained by physical experiments and by simulations differ quite significantly. When biases at the experimental side would be eliminated, the expected modest gap could be bridged by surface layer modifications of the hardened cement paste, discussed herein. This involves the formation of a fractal-like nano-particle structure in the outer hydration layer, instead of the smooth-surfaced layer obtained by the vector approach. This study firstly applies a DLA method for simulating the fractal structure of nodules in a low-density 2D setting of mono-size cement particles. Herewith it is confirmed that density of the outer hydration layer will diminish almost linearly away from the inner one, inevitably leading to permeability decline. This approach yielded also a realistic range of modifications for the outer layer, i.e., a 0.1 to 0.5 μm increased thickness. Therefore, in the normal 3D set up, the smooth vector-based hydration layer is given a stepwise thickness increase in this range, whereupon the consequences for pore geometry and topology, as well as for permeability can be investigated. The outcomes of this study are laid down in a separate publication. When further structural information on nano level will become available in the near future, the simulations can be appropriately adapted. This paper specifically proposes as a practical methodology to slightly step-wise enlarge at the packing simulation stage the fresh cement grains in proportion to their respective sizes. The herein introduced standard methodology for porosimetry and permeability estimation can readily be employed for simulating these cases. This is demonstrated for cement paste with w/c = 0.5, whereby packing density is increased by about 1% per step. This can be associated with a fictitious reduction in w/c from 0.49 to 0.45. It could be demonstrated this way that a permeability decline of one order of magnitude can be realized, i.e., at least enough to bridge the modest gap with corrected experimental permeability data. So, the final solution can be expected in this range.@en

Research on cementitious materials can provide geometric data on structural topics of interest. Such structural data should be subjected to a process called “geometric averaging” to be coupled on the engineering level with properties like strength, stiffness or permeability. The prime purpose of this work is to demonstrate that the mathematics underlying the process of going from the materials structure to engineering properties is governed by simple stereology-based constants. Particularly, Cauchy concepts are referred to for expressions relating the length of a curved line in a plane or in space, alternatively of a curved surface in space, to extensions of total projections on lines, respectively planes, in random directions. The two parameters due to Cauchy, i.e., 2/π and 1/2 will be demonstrated dominantly governing the geometric averaging process. The stereological methodology to assess the geometric material parameters and the engineering application of the outcomes are also briefly touched upon in the paper.@en

Cauchy paved the way for constructing models in concrete technology, and elsewhere. He determined the (non-flat) surface area in 3D by measuring random total projections. Analogously, he determined the length of a curved line in 2D by way of measuring the total projections. The paper will present the mathematical expressions, because in many branches of concrete technology, modelling is found based on such Cauchy concepts. These branches - fractography in compression, tension or shear, fibre reinforcement and permeability estimation - will briefly be mentioned to demonstrate this. It has been found that, for the discussed fields of engineering relevance, major model parameters for cementitious materials are similar to those developed by Cauchy in the 19th century. In the paper some previous investigations concerning fractography, fibre reinforcement and fracture roughness will be summarized but basically a new development on porosimetry will be presented. Particularly a new achievement of successful implementation of the methodology (also based on Cauchy) for optimizing permeability estimation will be discussed.@en

A survey of a methodology for estimating material properties of cementitious systems on the basis of computermade concrete/cement paste (compucrete) is presented. This computer model of the cementitious material is based on a sequence of modules that are shortly reviewed in this paper. Each one is important because of fulfilling a different role. However, the most crucial one is the underlying foundation of the particle packing system. Contrary to general practice in concrete technology, the discrete element model (DEM) should be selected for this purpose. The other modules, which are built on experiences, are either updated (like the hydration simulation module) or they are selected from other fields of materials science (DRaMuTS from robotics and SVM from life science experimental practice) and upgraded for the present purpose. Relevant references are provided@en

This chapter deals with the issues related to packing of particles in nature - aggregate in the first place - and in cementitious materials. Many of these topics are extensively discussed in the international literature, so will only be briefly introduced, while additionally giving a restricted number of references. Relatively new developments, such as producing the realcrete by computer, yielding compucrete, will receive more explicit attention. The way to do this properly by DEM (discrete element method) instead of by popular RSA (random sequential addition) is stressed. Modern dynamic DEM renders possible simulating aggregate of fluvial origin as well as of crushed rock. Similarity of simulating particle packing on mesolevel (aggregate) and on microlevel (binder) was the argument to sketch modern developments in the latter field, because they provide information on permeability and is thus of paramount important for sustainability. A phenomenon receiving recently attention in the literature is Brazil Nut Effect. It is part of nature and it can significantly influence the compacted particle structure of aggregate or binder alike. Some relevant information as to cementitious materials will be provided. @en

Four topics of high engineering relevance in which we were involved are introduced herein. Aggregate packing in concrete is of obvious relevance: denser packings lead to reduced cement demands, while modern developments in the (super) high performance range of cementitious materials are based on particle packing. Fiber reinforcement efficiency in concrete that we have studied extensively offers a relatively simple stereological problem for which Cauchy laid down the fundament. In the third problem of damage analysis the dispersion of small cracks in concrete is at issue. Insight into damage characteristics would be relevant in all (fracture) mechanical experiments. This topic can equally be linked to Cauchy. In both cases, the data acquisition by stereological methods is indicated. The fourth topic is of high actual relevance. It involves porosimetry in computer-simulated (virtual) cementitious materials, ultimately aiming permeability estimation. The stereological problems involved are indicated, and - again – Cauchy can be linked to finding solutions. Finally, new, mostly yet unpublished developments are indicated aiming for more economic procedures as well as improving reliability of permeability estimates by nano-packing of globules, so that ultimately this methodology could replace the laborious and expensive (and biased) experimental route.@en

Various systems for simulating particulate matter are developed and used in concrete technology for producing virtual cementitious materials on the different levels of the microstructure. Basically, the systems can be classified as two distinct families, namely random sequential addition systems (RSAs) and discrete element methods (DEMs). The first type is hardly being used for this purpose outside concrete technology, but became popular among concrete technologists. Hence, it is of utmost relevance to compare the two families in their capabilities, so that the reliability of produced data can be estimated. This paper pursues to do this on the basis of earlier published material of work performed by a succession of PhD students in the group of the second author. Limited references will be given to external sources.@en

Finds and ideas with a surprising element similar to the playful inventions of Heron of Alexandria, after whom this journal is named@en

To assess the pore size of virtual cementitious materials, the star volume method (SVM) can be considered an effective tool. Unfortunately, the SVM requires a large number of plane sections in each of the very large number of random points, resulting in a time-consuming and expensive operation. As a more economical alternative, this paper presents a stereology-based contracted method, which uses a well-known theoretical concept proposed by Cauchy. This method completed pore size measurements in a shorter period of time (reductions as high as 85%) while demonstrating reliability to be maintained at the same level.

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In this study, a numerical approach developed in our group is used to assess the permeability of partially saturated cement paste based on a discrete element modelling (DEM) technique. The relationship between saturation degree and permeability is found to be in good agreement with experimental observations. Also, outcomes of a systematic study of the effects of technological parameters (i.e., hydration period, water/cement ratio and cement particle size range) on the permeability of partially saturated specimens follow expected trends. Moreover, permeability is found to be correlated to effective porosity. This is a sound basis for investigating the impact of the interfacial transition zone on water and gas permeability. Effects of partial saturation are demonstrated different for water and gas transport. Possible mechanisms underlying these permeability characteristics are discussed in this paper.

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The solution of a technical problem is in many cases potentially available however probably somewhat hidden in the literature. At least, research engineers in concrete technology have the tendency not to search for it but to come up with their own ideas. Unfortunately, not always of the same standard as guaranteed by the original source. Interestingly, many powerful theoretical concepts relevant for concrete technology are of stereological nature, although in many cases (much) older than stereology itself (Stroeven and Hu, 2006; Stroeven et al., 2009). With the development of stereology as a science since the foundation of the society for stereology in 1963, old roots became apparent: stereology avant la lettre. As a concrete technologist the second author of this fountain enjoyed several playful discoveries over the years that in some cases constituted old but reliable milestones along the route to solving popular problems in our field. Baron Augustin-Louis Cauchy (21 August 1789 – 23 May 1857) formed such a milestone. He was a French mathematician reputed as a pioneer of analysis. He was one of the first to state and prove theorems of calculus rigorously. Of the extensive oeuvre of Cauchy, two formulas – almost two centuries old – are of significance for concrete technology (and other branches of science) (Cauchy, 1882; Stroeven and Hu, 2006) @en

Realistically simulating fresh and hardening cementitious materials renders possible understanding controversial issues existing in the field of concrete technology. The experimental studies on the impact of the interfacial transition zone (ITZ) on permeability of concrete reveal two controversial results. The first involves the concept of promoting the permeability by increasing the aggregate fraction of concrete that will lead to (more) ITZ percolation. This is supported by some experiments reported in the literature. However, contradictory data are also published by other researchers. This paper aims at explaining by an advanced modelling technique why these conflictive observations are experimentally obtained.@en

The interfacial transition zones (ITZs) are supposed to promote fluid transport through concrete. As a consequence, one would expect an increase in permeability with an increasing aggregate fraction. This has been shown in some experiments, however, the opposite effect is observed as well. The permeability ratio of ITZ to matrix seems to be a key parameter in interpreting this controversial phenomenon. A higher ratio favors the flow of water through the interface zone. This work aims at studying this ratio at various conditions (i.e., hydration degree, water/cement ratio, particle size range and water saturation degree) using a numerical model, so that the influence of the ITZ on the permeability of cementitious composites can be better understood. The findings presented in this paper can provide a new perspective on controversial experimental results as to the effect of the ITZ on transport capacity.

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Although an earlier developed numerical methodology for permeability estimation of cement pastes can provide satisfactory results in comparison with experiments, it would be of engineering interest to find a simpler way to perform the same task. This method referred to by “the shorter approach” is presented in this paper. In the approach, water permeability is only correlated to the water-filled porosity of the specimen. A mathematical model is proposed to approximately calculate the water permeability using the water-filled porosity as the only input parameter. The confidence limit is found to yield an appropriate level of reliability. To better understand the proposed mathematical relationship, pore throat size and connectivity of the capillary pores are separately shown as a function of the water-filled porosity. Their respective and successive impacts on permeability is illustrated in this way.

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A quick approach to estimate water permeability of virtual cement paste is outlined in this paper. Although the computational models developed by the authors are able to provide satisfactory results in comparison with experimental data, it is still interesting and meaningful to further limit the efforts. This paper therefore presents a simple mathematical model for permeability assessment. Only one parameter, i.e. waterfilled porosity, is required for the proposed model. The results from the presented mathematical model are compared with data obtained by other approaches. A good agreement can be observed, validating the presented method. Additionally, median pore throat size and connectivity of the capillary pores are plotted as a function of water-filled porosity to help understand the permeability changes in structural terms. @en