Electrical tomography for characterizing transport properties in cement-based materials: A review

Highlights

• Review of ET for characterizing transport properties in cementitious materials.

• Contextualization of ET among contemporary imaging modalities.

• Overview of the future opportunities afforded by ET.

Abstract

The ability to spatially and temporally quantify the state and distribution of moisture and ions is of central importance to understanding the durability of cement-based materials and structures. Owing to the heterogeneous nature of concrete and challenges associated with using point-based measurements in accomplishing such a task, the use of two- and three-dimensional tomography for quantifying transport properties has become the source of much research interest. Distinct from electromagnetic radiation-based modalities – Electrical Tomography (ET), including Electrical Resistance Tomography, Electrical Impedance Tomography, and Electrical Capacitance Tomography, has emerged as a viable means for characterizing transport in cement-based materials. In this work, we provide a technical overview of ET and the nature of ET inverse problems. We also review historical challenges and successes of ET for imaging transport properties in cement-based materials. Based on realizations from the review, challenges and opportunities afforded by ET for characterizing transport properties are provided and discussed.

Introduction

In the context of global climate change, cement production contributes approximately 5–8% of the total CO₂ emissions [1]. It is therefore imperative that researchers and industry are invested in developing sustainable cement binder systems and alternative cementitious materials [2], [3], [4], [5], [6]. All the while, it is important to (i) extend the service life of concrete structures thereby reducing the long-term demand for traditional cementitious binders and (ii) continually improve our understanding of the durability and transport mechanisms in novel cementitious materials [7].

Central in the discussion of a concrete structure’s durability is moisture distribution and transport. This is because many degradation processes in concrete structures, such as reinforcement corrosion [8] and ASR [9], take place in the presence of moisture. Moreover, the transport of corrosion-promoting ions, such as chloride, is facilitated by moisture [10], [11]. Inasmuch, it is logical to use moisture transport properties, such as permeability or hydraulic conductivity, as metrics for concrete durability [12], [13], [14], [15].

Concrete is, however, a highly heterogeneous material, rarely fully saturated, and often has some level of distributed cracking when exposed to environmental conditions [16], [17], [18]. As such, endeavoring to quantify the durability characteristics of an unsaturated, heterogeneous, and possibly damaged cement-based material by interpreting data from point-based measurements – alone – often leads to results that are highly variable and/or painfully frustrating to decipher. Moreover, the use of such parameters can lead to significant errors in numerical models [19] and life-cycle estimations using such models [20].

These realizations have encouraged researchers to adopt measurement regimes acquiring data from more than two points. Broadly speaking, these methods include direct and inverse methods. In direct methods, the user directly interprets a suite of measurements to gain information on the transport phenomenon of interest. The advantages of these methods are their speed, broad usage, and well-documented behavior. Within this family, multi-point resistivity methods using, e.g. Wenner probes, have proven useful in characterizing water content, pore fluid resistivity, and properties related to the pore-space tortuosity of cement-based materials [21]. One challenge in using such a method is that calibration using numerical models and precise knowledge of the samples’ mix design and condition may be required to attain accurate quantitative results [22]. In the case of Wenner probes, an “apparent” resistivity (not the true concrete resistivity, but one affected by reinforcement, contact impedance, etc.) is calculated from the measurements using knowledge of the sample geometry, injected current, and assuming that the sample is homogeneous and semi-infinite [23], [24], [25], [26], [27]. A significant body of research has addressed challenges associated with the calibration of direct electrical methods used in characterizing durability properties of cement-based materials and structures. For example, the effects of geometry [24], reinforcement [25], air content [28], temperature [29], and curing [30] – among numerous other variables – has been considered. Meanwhile, other researchers have focused on the development of new measuring apparatuses, including, e.g. multi-ring devices [31], embedded sensors [32], [33], and near-surface electrode grids [34]. As a whole, this body of research has significantly improved the robustness of direct methods to the point that direct methods have become standard in field and laboratory characterization of cement-based materials [35].

Tomographic methods are an alternative to direct methods, wherein researchers aim to gain spatial and/or temporal information on transport properties by solving an inverse problem using distributed data. In general, tomographic methods use input data to reconstruct properties such as moisture distribution, flow rates, ingress, and conductivity [36], [37]. The use of tomography for characterizing transport properties and transport-related properties in cement-based material is extensive. Broadly speaking, these methods have included radiation-based modalities such as X-ray [38], [39], [40] and $\gamma$-ray [41] tomography, neutron imaging [42], [43], [44], magnetic resonance imaging [45], [46], and electrical tomography (ET) [47].

Of the tomographic modalities, each have their respective strengths and weaknesses for characterizing transport properties and transport-related properties of cement-based materials. For example, X-ray tomography is often considered the modality of choice for characterizing the solid pore space of cement-based materials, while neutron tomography is arguably better suited for characterizing unsaturated flow [48]. It is important to recognize that the imaging capabilities of X-ray and neutron tomography are driven by the underlying physics of each modality. As it pertains to this work, the physical differences lie in the X-ray and neutron cross sections of hydrogen [49]. Since hydrogen has a large neutron cross section, neutron tomography is well-suite for characterizing water ingress. On the other hand, hydrogen has a small X-ray cross section, therefore X-ray tomography is not ideal for imaging water ingress. In contrast, while X-ray and neutron tomography are based on measurements from beams passing through a sample more-or-less linearly, electrical-based modalities rely on diffusive electric fields flowing through the cementitious medium [50]. As such, ET may be categorized as “diffusive” [50].

We may then conclude that the use of ET for characterizing transport properties in cement-based materials results in fundamentally different imaging characteristics compared to the aforementioned radiation-based modalities. The primary differences between ET and radiation-based modalities derive from (i) the diffusive nature on electrical fields in porous media and (ii) the contrasting behaviors of electrical and radiation-based inverse problems [51]. In principle, (i) and (ii) are relatively straightforward to conceptualize; in practice these differences result in fundamentally different abilities of electrical- and radiation-based modalities for characterizing transport in cement-based materials. To summarize, rather qualitatively, the tomographic features of popular modalities used for characterizing transport in cement-based materials are provided in Table 1.

The summary shown in Table 1 generally indicates that electromagnetic radiation-based modalities are powerful tools for characterizing transport properties at high resolution when the sample is small. The small-medium sample size range required for high-resolution imaging¹ using electromagnetic radiation-based tomography results from the high attenuation of concrete [58], which has been shown experimentally in e.g. [59]. In other words, the distinguishability of electromagnetic radiation-based measurements decrease significantly as sample size increases, which is of course proportional to the loss in resolution. On the other hand, electrical-based modalities are shown to be effective for imaging large specimens at the cost of resolution, which is fundamentally linked to the diffusive nature of electrical tomography. In either case, both electromagnetic radiation- and electric-based modalities both have implementation limitations that should be noted. For example, radiation-based tomography requires a radiation source, i.e. a reactor, synchrotron, etc. which usually requires a dedicated facility. Meanwhile, electrical-based tomography is relatively easy to implement, but quantitative interpretation of results can be difficult and prior knowledge of the electrical-transport properties of interest may be required. Nonetheless, the purpose of this article is not to contrast the performance of electrical- and electromagnetic radiation-based tomographic modalities. Indeed, each modality has its strengths and weaknesses – therefore the use of a given modality should be selected based on application-specific criteria.

In this paper, we provide a first review of ET applications used for characterizing transport properties in cement-based materials. Here, we distinguish between “transport” in the holistic sense and “transport properties,” where we refer to “transport properties” as physical phenomena directly or indirectly related to the spatial–temporal movement and evolution of water, ions, etc. in the pore space of cement-based materials. Additionally, we discuss some challenges and opportunities in using for ET for investigating transport-related processes in cement-based materials. We begin by providing a necessary technical background highlighting ET imaging regimes and their corresponding inverse problems. Following, we overview applications of two- and three-dimensional ET for investigating and characterizing transport properties in cement-based materials. Lastly, a discussion of the challenges and opportunities remaining in this field is provided.