Self-Sensing concrete: A data-driven approach to comprehensive analysis and review

Abstract

Structural health monitoring of civil infrastructure is vital in ensuring a safe and functional built environment. Self-sensing cementitious materials have emerged as a promising alternative in the field of concrete monitoring due to their pronounced sensing potential. Research into this field has been ongoing for decades, with new sensor designs being constantly proposed. It is therefore fundamental to review recent advancements to stay up to date with the current state-of-the-art. This review examines the sensing performance of self-sensing cementitious materials and presents a data-driven analysis based on 121 peer-reviewed sources. From the analysis, it was found that the gauge factor (GF) of these materials varies according to the number, type and concentration of conductive filler, type of cementitious matrix, mechanical testing method, and the type and number of electrodes. Most reported gauge factors were below 1000, with single-filler composites producing higher values under compression and multi-filler composites yielding higher values under tension and flexure. Nickel powder was found to result in the highest GF as a single filler, while the combination of carbon black and carbon fibre displayed the highest GF for multiple fillers. Combining fillers with different dimensional properties (e.g., 0D with 1D) can significantly enhance sensing performance by creating a more stable conductive network. In terms of concrete type, paste and mortar result in higher GFs compared to concrete and ultra-high-performance concrete. Regarding probe configurations, the two-probe method results in higher data variability compared to the four-probe method, with GFs exceeding 3000 and therefore, its reliability should be reconsidered. Combining data from different electrode configurations can also misrepresent results, highlighting the need to consider probe design when interpreting the sensing response. Overall, the findings of this paper underscore the need for standardised protocols to enable meaningful comparisons and reproducible results, thereby advancing our understanding of self-sensing cementitious materials.

Introduction

The aging and degradation of civil infrastructure have led to the annual expenditure of millions of dollars and substantial CO_2eq emissions for rehabilitation and maintenance. ¹ The poor condition of structures is often a consequence of a lack of regular upkeep and delayed decision-making. Structural health monitoring (SHM) revolves around the acquisition of data from structures with the use of sensors to make informed decisions on the condition of infrastructure and thus allow for proactive maintenance to take place. Typically data acquisition is conducted via electronic sensors such as displacement sensors, ² strain gauges, ³ fiber optic sensors, ⁴ piezoelectric transducers ⁵ and sensing sheets. ⁶ Despite their widespread use, these types of sensors often experience some degree of failure during their lifespan due to the harsh environments they are exposed to as well as poor compatibility with the cementitious matrix. ⁷ In turn, this could lead to issues such as poor readings and the need for redeployment and reinstallation of sensors. A solution to this problem involves the use of cementitious materials with self-sensing properties to monitor the condition of structures. These are traditional cementitious materials that incorporate electrically conductive additives. Over the years self-sensing cementitious materials have gained growing interest and have become a focal point in the field of civil engineering and structural health monitoring due to their high monitoring potential compared to electronic sensors.

Since their initial conception in the 1990s,^8–10 research into the field of self-sensing cementitious materials has expanded significantly. Diverse applications have been conducted and novel experimental protocols and procedures have been introduced that have led to the advancement and maturity of this technology throughout the years. Research is carried out at a high pace, with over 100 research articles being published annually in recent years (Figure 1). As such review articles and state-of-the-art reports are published to keep up with the latest findings, providing the current understanding of these materials.^12–18 As research into this field expands, it will become increasingly difficult to compile and analyse the available literature to provide comprehensive and critical reviews of self-sensing materials. With the advancement of computational power, it is possible to work with larger datasets to build data-driven models from the available literature to deepen our understanding of the behaviour and performance of these materials and overcome hurdles commonly associated with their use.

Figure 1.

Number of research articles (excluding reviews) on ‘self-sensing’ or ‘piezoresistive’ in combination with ‘cement’ or ‘paste’ or ‘mortar’ or ‘concrete’ or ‘cementitious’ ¹¹ from 2014 to 2024.

This review focuses on understanding the performance of self-sensing cementitious materials through a data-driven approach. An exhaustive dataset was compiled by reviewing 121 peer-reviewed literature sources, covering a broad spectrum of parameters related to self-sensing cementitious materials.^19–139 These parameters include information on the type of cementitious systems e.g., paste, mortar, concrete and ultra-high performance concrete, the types and properties of conductive fillers, mix design, curing conditions, electrical probe materials and layout, loading type, compressive strength and sensing coefficients. The dataset provides the foundation for in-depth analysis and a better understanding of self-sensing materials as it accounts for diverse experimental setups, materials and methods. The data were subsequently processed with the use of statistical and visualisation techniques. However, the analysis does not represent the final output. Rather than relying solely on the output of data processing, this review uses it as a starting point for interpreting the results, identifying influential factors, exploring emerging trends, and critically discussing performance-related issues. The findings are examined through the lens of engineering insight and contextual knowledge, aiming to guide future work and bridge the gap between raw data and practical application.

This paper begins with an overview of self-sensing cementitious materials covering the theory and technical background of mix design and sensing performance in Section 2, sensor design in Section 3, and sensing mechanisms, sensing response, data acquisition and analysis methods employed in Section 4. An analysis and evaluation of existing trends in this field follows and the data-driven results are then illustrated and analysed in Section 5. Recommendations for future research in this field are then made in Section 6. Lastly the main points and contributions of this review paper are summarised in the conclusions section in Section 7. An Appendix is also included which explores further facets of self-sensing materials.

Self-Sensing cementitious materials – materials, sensing behaviour & mix design

Overview of self-sensing cementitious materials

Self-sensing cementitious materials are electrically conductive cementitious materials that are used for monitoring purposes. Conductive filler is typically added to a cementitious matrix to form a conductive network, instilling sensing capabilities. External factors such as loads or environmental conditions can alter the composite's network connectivity in the matrix leading to changes in the material's electrical properties. ¹⁴ This has allowed the use of these materials in strain,^140–143 moisture, ¹⁴⁴ humidity, ⁴⁵ temperature ¹⁴⁵ and chloride ¹⁴⁶ sensing applications. Outside of monitoring, electrically conductive cementitious composites have also been used for energy storage ¹⁴⁷ and energy harvesting^148,149 purposes.

Types of electrically conductive filler

Conductive fillers can be broadly categorised into two types based on their composition, a) carbon-based conductive fillers ¹⁵⁰ e.g., graphene, graphene oxide, graphene nanoplatelets (GNP), graphite, expanded graphite, carbon nanotubes (CNT), multi-walled carbon nanotubes (MWCNT), carbon fiber, carbon black, shungite, and b) metal-based conductive fillers ⁷⁷ (e.g., brass fiber, steel fiber, nickel powder, steel wires).

Carbon-based conductive fillers

Carbon-based fillers are typically found in the form of particles, single/multi-layers tubes or sheets, and fibres; depending on their form, the size of carbon filler can vary from a few nanometers to less than 100 microns. Powders are individual particles with approximately equal dimensions which are regarded as 0D. Fibres are elongated thread-like materials with a length much greater than their width constituting them as 1D materials. Graphene varies to a greater extent as it is dependent on the number of layers and its arrangement. A single layer of graphene is a 2D element, graphene obtains a 3D structure when its layers are stacked, which is then referred to as graphite. Graphene can also be folded in the form of a tube which is then denoted as a carbon nanotube. Based on the structure carbon nanotubes can be either single wall or multi-walled, similar to fibres, these materials are also regarded as 1D elements.^15,151–154

Even though the carbon nanomaterials vary in their microstructure, they provide very high specific surface area due to their smaller size and hence more conduction pathways per unit volume compared to conventional metal-based conductive fillers and are therefore more efficient in improving electrical and sensing properties. The main obstacle in using conductive fillers is achieving sufficient dispersion, poor dispersion could affect both the electrical and mechanical properties of the material due to the formation of macro-defects (agglomeration) in the cementitious matrix.

Metal-based conductive filler

Metal-based conductive fillers employed in cementitious matrices are mainly made of steel, nickel, copper and brass, with steel being the most common.^24,39,85,88 Steel-based fillers including fibres and wires are commonly used in ultra-high-performance concrete (UHPC).^63,77,95 One of the benefits of steel filler is that it can be easily dispersed with minimal treatment. Steel filler presents high conductivity compared to carbon filler. Despite their good conductivity properties though, they often result in low sensing capabilities as their larger dimensions compared to carbon-based fillers prevent them from easily forming a uniform conductive network in the cementitious matrix. As a result, additional carbon fillers are used in tandem with steel fillers to improve sensing capabilities.^27,95 However, this can lead to increased production costs and complexities in the mixing process. Lastly, steel fibre concrete has also been demonstrated to be susceptible to rapid corrosion in the presence of small amounts of NaCl. ¹⁵⁵

Self-sensing behaviour of cementitious composites

To characterise the self-sensing response of the cementitious materials, the resistivity, ρ, is quantified by Eq. 1 and the fractional change in electrical resistivity, often denoted as FCR, under loading is calculated using Eq. 2.

$$\rho ={\displaystyle \frac{RA}{l}}$$

(1)

where R is the resistance of the sample, A is the contact area of the electrodes in the material and l is the length between the electrodes.

$$FCR={\displaystyle \frac{{\rho }_i-{\rho }_0}{{\rho }_0}}$$

(2)

where ρ_i is the resistivity of the sample at a given point and ρ₀ is the initial resistivity.

The self-sensing behaviour of cementitious materials depends on the type of loading applied i.e., compressive, tensile, flexural. Under uniaxial compression, the FCR decreases due to the reduced distance between conductive fillers. In tensile loading, the FCR increases due to increase in distance between conductive fillers. Flexural loading presents a more complex behaviour due to the presence of both compression and tension within the material. Depending on the region monitored, either an increase or decrease in FCR can be observed.^13,14,91,156

The response of self-sensing cementitious materials under loading, or their piezoresistivity, is examined through the strain sensitivity coefficient, more commonly known as the gauge factor (GF). The GF, often quoted as λ or k, is the fractional change in resistance per unit strain and can be calculated using Eq. 3.^43,157,158

$$\lambda ={\displaystyle \frac{{\displaystyle \frac{dR}{R}}}{\epsilon }={\displaystyle \frac{{\displaystyle \frac{d\rho }{\rho }}}{\epsilon }+(1+2v)}}$$

(3)

where R is the initial resistance in a non-deformed state, ρ the initial resistivity in a non-deformed state, dR is the change in resistance under load at a given point, dρ is the change in resistivity under load at a given point ε is the applied strain and v is Poisson's ratio.

The component (dρ/ρ)/ε represents the piezoresistive effect and the component (1 + 2v) is the geometric effect of the sensing material. In cases, Eq. 3 is further simplified to Eq. 4.

$$\lambda ={\displaystyle \frac{{\displaystyle \frac{dR}{R}}}{\epsilon }\approx {\displaystyle \frac{{\displaystyle \frac{d\rho }{\rho }}}{\epsilon }}}$$

(4)

The GF can be determined from the slope of the linear region in the FCR–strain plot. GF values for cementitious materials range quite considerably depending on factors such as the type of conductive filler,^150,154 the concentration of filler,^13,159 geometric factors,^61,160 and sensor design. ¹⁶¹

Alternative methods of characterizing the sensing response include the stress-sensing coefficient (SSC) which depicts the fractional change in resistance per unit stress as displayed in Eq. 5.

$$SSC={\displaystyle \frac{{\displaystyle \frac{dR}{R}}}{\sigma }\approx {\displaystyle \frac{{\displaystyle \frac{d\rho }{\rho }}}{\sigma }}}$$

(5)

where σ is the applied stress.

The reader is referred to the Appendix for further information on the sensing behaviour of cementitious materials.

Mix design and dispersion techniques

Mix design

Self-sensing cementitious materials involve Portland cement, a supplementary cementitious material (typically fly ash, blast furnace slag or silica fume), aggregate, electrically conductive filler (which may include more than one type) and superplasticizer.^13,17,162 The proportions of the mix design are based on the type of system employed i.e., paste, mortar, concrete and UHPC and the percolation threshold of a given conductive filler. Due to the lack of standards, mix designs and mixing procedures are typically based on accepted experimental procedures within this field which are often based on a trial-and-error basis and numerical modelling.

Dispersion of filler

One of the hurdles in incorporating conductive fillers in a cementitious matrix is achieving a homogeneous dispersion which is an essential step toward high-quality sensing properties. ²² The addition of conductive fillers can lead to aggregation and agglomeration. For instance, graphene-related materials are hydrophobic in nature and tend to agglomerate due to attractive Van der Waals π-π stacking interactions. ¹⁶³ Graphite particles are characterised by a greater contact angle than cement which makes them difficult to wet and thus tend to agglomerate. This results in mixing water being entrapped in the clustered graphite reducing dispersion efficacy. ¹⁶³

Dispersion techniques are typically based on mechanical and chemical means and are employed depending on the type of filler used. Examples of mechanical dispersion include the use of high-shear mixers, ¹⁶⁴ magnetic stirring, and ultrasonic bath ¹⁶⁵ ; examples of chemical treatment include ozone, ¹⁶⁶ and silane, ¹⁶⁷ usage of supplementary cementitious materials, and the addition of chemical admixtures such as polycarboxylate-based high-range water reducers.^165,168 The effectiveness of these techniques can be measured via visual inspection, ζ-potential, by Fourier Transform Infrared Spectroscopy and image analysis.

As mentioned, mechanical dispersion relies on high-speed shear mixing, dry mixing, magnetic stirring, and sonication. ¹⁶⁹ High-shear mixing is based on the dispersion of one phase into a liquid through a rotor that mixes the composite. Dry mixing refers to the addition of filler to dry binders which are mixed without the presence of any liquid. Alternatively, magnetic stirring exploits the rotation of a spinning magnet which homogenizes all different phases. Typically, mixing and magnetic stirring are executed in combination with sonication, which is widely regarded in the literature as the most effective method for dispersing carbon nanomaterials in cementitious composites, as it prevents any alteration to the systems. ¹⁵⁴ By placing the material in a bath sonicator and applying ultrasonic frequencies, the particles are agitated to disperse nanomaterials in liquids evenly. To provide an example, as graphene nanoplatelets (GNP) cannot be adequately dispersed through dry mixing alone; they are added to water and sonicated for more efficient dispersion before being mixed with cement. In this case, the water entrapped in the clusters gets released after sonication, thus achieving good fluidity. A minimum of 60 min was found to achieve a stable suspension of GNPs in a water solution in which the material did not agglomerate and did not precipitate at the bottom of the solution after 24 h. ¹⁷⁰ However, it was found that sonication beyond 2 h did not provide significant improvement. The combination of chemical and mechanical mixing also leads to good homogeneity.^171,172 Du and Pang ¹⁷⁰ investigated the effect of the different amounts of dispersant and different sonication times concerning varying GNP quantities. In this instance, sonication allows the dispersant to be better adsorbed on the nanoplatelets’ surface, increasing the repulsion between various elements.

In terms of chemical dispersion, the use of covalent/non-covalent functionalization with chemical/mineral additives has been reported to result in good dispersion. ¹⁷³ Mineral additives, such as silica fume have also been used to improve dispersion and mixing of filler.^174,175 Waqar et al. ¹⁷⁶ suggest that the concurrent usage of carbon fibre (CF) and silica fume in a cementitious mix disrupts the CF agglomerations and enhances mechanical properties. Moreover, it was mentioned by Ashraf et al. ¹⁷⁷ that silica fume has a synergistic effect as apart from improving carbon fibre dispersion, due to its pozzolanic nature, C-S-H gel develops in the matrix improving density and the bond between the binder and the carbon fibres. Carboxylic and hydrophilic groups are also used as dispersant alternatives by creating a better bridging network between C-S-H gel phases and carbon-based particles. ¹⁶³ The hydrophobic tails can attract the hydrophobic surface of the filler, while the hydrophilic heads can create hydrogen bonds with water. Moreover, being negatively charged, hydrophilic groups can apply electrostatic repulsion between adjacent particles and avoid agglomerate formation. Furthermore, superplasticizers have also been used to decrease the aggregation between graphene-based particles. Sodium dodecylbenzene, ¹⁷⁸ melamine, ²³ and naphthalene sulphonate ¹⁷⁹ have been used as surfactants to efficiently separate nucleotides of graphene particles within a cementitious system. ¹⁸⁰ Tao et al. ²³ achieved good stability of the water-graphene solution for more than 4 h and a 70% reduced GNP size using a melamine dispersant. Wang et al. ¹⁶³ demonstrated that surfactants (dodecyl dimethyl betaine, sodium dodecyl sulfate and sodium laurylsulphonate) could improve the fluidity of graphite-cement composites due to their favourable adsorption and dispersion effect in the system. The use of polycarboxylate and lignosulphonate superplasticizers has also been employed due to their steric hindrance and electrostatic repulsion nature thereby providing excellent homogeneity to the system.^89,181,182 However, an excess of dispersant use might result in the formation of multiple adsorption layers on the nanomaterials interface. ¹⁷⁰ Furthermore, the manner the fillers are prepared can lead to improved and simpler dispersion approaches. For instance, surface treatment with silane has also been reported to improve the wettability of CF. This is a multi-step procedure, which involves preparing a solution of silane + solvent (ethyl acetate or acetone). ¹⁸³ Then, the CFs are immersed in the solution at a moderately high temperature (∼75 °C) and stirred. After filtration and washing off the solvent, the fibres are oven-dried and ready to use. Xu and Chung ¹⁸⁴ reported that the mortar with silane-treated CF demonstrated a lower air void content and a higher tensile modulus when compared to as-received CF. This suggests an improvement in the cement and fiber surface bond, which could be attributed to the hydrophilic nature of silane. Moreover, it is hypothesised that the formation of a polysiloxane network on the fibre surface leads to a stronger bond between the cement matrix and the fiber.^185,186 Ding et al. ¹⁸⁷ developed a carbon based conductive filler by growing CNTs on the surface of CF. This involved a multi-step process that included oxidation, catalyst impregnation and chemical vapor deposition. This enabled the homogeneous distribution of CNTs in the cementitious matrix. Through this procedure, the resulting filler led to simpler dispersion i.e., mechanical mixing, while at the same time enhancing interfacial bond between the filler and cement and the synergic and spatially morphological effects of CF-CNT.

Overall, various dispersion methods exist that could be employed in cementitious systems. Not all methods apply to every type of filler though and therefore proper assessment is required depending on the application. Moreover, alternative dispersion methods are being constantly sought out. For example, Guo et al. ⁹¹ used polypropylene fibers as a means to improve carbon black dispersion – carbon black is adsorbed on the surface of the fibers due to the hydrophobic reaction in an aqueous environment. Gupta et al. ¹⁸⁸ sprayed CNT inks on dry aggregates and cement powder as a simpler and cost-effective way of filler dispersion in the matrix.

Shotcrete and additive manufacturing applications

Apart from traditional casting methods, self-sensing materials containing conductive filler have also been fabricated with the use of 3D printing and spraying.^{102,189–197} Compared to mould cast applications though, additive manufacturing of self-sensing materials is quite limited. Difficulties in extrusion-based applications involve ensuring adequate pumpability, extrudability, and buildability of a mix while simultaneously maintaining satisfactory filler dispersion and electrical properties.^195,196 If not properly tailored, issues such as under-extrusion, segregation of filler from the slurry, or complete blockage of the nozzle or printhead could occur during printing. ¹⁹⁷

In contrast to mould casting, 3D concrete printing (3DCP) causes anisotropy due to its layered structure. ¹⁹⁰ 3DCP leads to air voids in the printed filaments due to the extrusion of stiff materials, which results in higher porosity and weaker mechanical properties.^198,199 Recent studies have demonstrated that 3D printed concrete is comprised of distinct filaments with varying material properties at the core and interface of each filament that are linked to shearing and deposition during printing. As a result, anisotropy remains a distinct property of 3DCP even if mitigation methods are applied. ²⁰⁰ Consequently, all these factors can impact the electrical conductivity and sensing response of 3D-printed materials. It has been shown that samples tested in the longitudinal direction have higher conductivity due to a denser structure, resulting in an easier formation of the conductive path. Similarly, greater sensing performance is observed when the printed layers are parallel to the load applied, as filler is aligned and the conductive path can be easily formed in this direction.^193,195,201 The alignment of fillers could be viewed as a distinct advantage of additive manufacturing as it is able to bypass experimental setup and scaling difficulties found in other alignment methods such as magnetic fields^85,86 that have been employed in self-sensing applications. Furthermore, layer-by-layer deposition of the material is an attribute of 3DCP that has significant potential in self-sensing concrete. For the purpose of structural health monitoring, strategic employment of self-sensing material in critical zones is possible via 3DCP. For instance, in members under flexural loading such as beams, the loading effect is concentrated the most on the lower (tension) and upper (compression) surfaces. Therefore, substituting only the lower region undergoing tension with self-sensing concrete is a more cost-effective way of achieving self-sensing.

In terms of sensing behaviour, additive manufacturing generally results in lower sensing sensitivity compared to mould-based applications. This has been commonly associated with the layered structure and increased porosity. For example, Liu et al. ¹⁹⁴ found that 3D printed UHPC specimens with graphite and carbon fibre exhibited lower gauge factors compared to cast specimens, ranging from 380–540 to 310–400, respectively, and in some cases, lower linearity (and therefore higher noise). This was attributed to the weaker bonding between layers, which led to poorer strain transfer and limited electrical continuity when layers were perpendicular to the load. In a different study, Liu et al. ¹⁸⁹ employed carbon fibres and graphite in 3D printing of cementitious composites. The 3D printed specimens displayed lower gauge factors than mould applications (from 60–225 to 20–118). This reduction was attributed to the increased porosity in the 3D printed composites. In a study by Wang et al. ¹⁹³ on fibre-based cement 3D printing, samples demonstrated lower piezoresistivity when layers were perpendicular to the load due to the lack of filler connecting the adjacent layers. In contrast, when the load was parallel to the layers, an adequate piezoresistive response was observed due to fibre alignment, thus establishing a better conductive path. The addition of powder-based filler alongside fibres can improve the sensing response in this orientation, as the powder is better distributed within the layers, thereby improving layer connectivity and forming a shorter conductive path. However, this does not have the same effect when tested in the parallel direction, which led to reduced sensing behaviour. Moreover, in a spray-based application by Lu et al., ¹⁹⁰ it was found that samples tested with layers parallel to the load yielded higher sensing performance compared to the perpendicular direction, i.e., 0.45%/MPa in the former and 0.30%/MPa in the latter. The performance in the perpendicular direction also exhibited greater variability in the results, which was attributed to the cold joints leading to higher resistivity. Compared to 3D printing applications, lower anisotropy was observed. It could be hypothesised that this is due to the greater material dispersion achieved with spraying.

Although additive manufacturing offers numerous potential advantages for realizing the vision of future infrastructure construction, the current studies showed that additively manufactured samples exhibit reduced sensing sensitivity compared to mould applications. Therefore, strategies related to this method must be comprehensively studied within the context of self-sensing materials to ensure effective implementation. As research into this field expands, further improvements in the performance and design of 3D printed self-sensing composites could be anticipated. However, due to the variability and complex nature of 3D printed concrete compared to mould cast specimens, such applications will not be considered in the data-driven analysis.

Sensor fabrication

Specimen details

Types of self-sensing materials

Self-sensing materials could be used in several ways to monitor infrastructure. Figure 2 summarises the typical forms of self-sensing concrete commonly found in the literature. Namely, these are referred to as bulk, coating, sandwich, bonded and embedded. The bulk form represents both the structural element and sensing material e.g., beam or column. For the coating, a self-sensing composite is applied as a surface layer onto a substrate. The case in which two self-sensing layers are applied to both the top and bottom surfaces of a substrate is classified as a sandwich form. When it pertains to bonded and embedded applications, these refer to prefabricated small-size self-sensing composites that are either attached to a structure with adhesives (bonded form) or embedded in a structure during casting (embedded form).^14,150

Figure 2.

Typical application forms of self-sensing concrete: in (a) bulk, (b) coating, (c) sandwich, (d) embedded, (e) bonded form.

All forms of self-sensing materials can achieve stable and repeatable sensing performance. Among these, the bulk application is the most widely investigated due to its straightforward design and testing method. The other forms of self-sensing materials may likely be more practical monitoring solutions in the field due to their lower construction costs and reduced manual handling. Self-sensing layers (coatings and sandwich forms) present high versatility as they can monitor both newly fabricated and existing structures.^202,203 That said, proper design is necessary to ensure good bonding and strain transfer between the substrate and the sensing layer.^156,204 Similarly, bonded sensors can also be used to monitor new and existing infrastructure. Compared to sensing layers, bonded sensors present a simpler deployment method as they are prefabricated units that can be installed on site with adhesives. ²⁰⁵ In contrast, embedded sensors primarily target new structures as they are installed during casting. One of the disadvantages of embedded and bonded sensors is their rather localised monitoring capabilities compared to the bulk and layered self-sensing materials which can monitor larger areas. For greater area coverage, additional sensors will be required, however, this requires greater planning for deployment and can also lead to a long processing time for real-time data monitoring. ²⁰⁶

Geometry of specimens

The shapes of self-sensing materials in bulk applications are typically cubes, rectangular prisms, cylinders, and dog bone specimens. Cubes, prisms and cylindrical specimens are used for compressive tests, prisms are used for bending tests and dog bone and cylindrical specimens are used for tensile tests. The maximum dimensions typically encountered for most laboratory scale tests are 100 mm for cubes, 200 mm for the length prisms, 200 mm in height for cylinders, and 150 mm for dog bone specimens. Large-scale applications are also common and are typically conducted on beams in which their length could span up to 2 m. Overall, the size and shape are important factors to take into consideration in strain-sensing applications as they can impact the sensing properties of self-sensing materials.^61,164

Steel reinforcement

While steel reinforcement is commonly used to improve the tensile behaviour of concrete particularly in bending applications, studies involving steel reinforcement in self-sensing composites are quite narrow. For example, Wen and Chung ²⁰⁷ investigated the performance of reinforced and unreinforced carbon fibre (CF) cement-based beams. It was found that the presence of embedded steel reinforcement enhanced the self-sensing capability of the beams by increasing their sensitivity due to current penetration into the steel and greater localised deformation resulting in larger resistance changes. The fractional change in surface electrical resistance increased by 40% on the tension face and 70% on the compression face due to the steel reinforcement. Celik et al. ²⁰⁸ investigated the sensing performance of large-scale carbon nanotube (CNT) and CF reinforced beams. It was reported that steel reinforcement did not adversely impact the sensing capabilities of the composites. This was explained as the increased levels of deflection override the current penetration into the steel rebars. It was also mentioned that the increased strain capacity due to the steel reinforcement led to abrupt changes in resistivity which was attributed to the pull-out and breakage of the filler at high strain values. It should be pointed out though that unreinforced samples were not tested and therefore the exact impact of reinforcement (positive or negative) cannot be drawn from this study alone. Cholker and Tantray ⁹⁰ examined the sensing performance of CF beams under bending for steel reinforcement ratios between 0.92–1.43%. It was reported that the ratio of steel reinforcement did not have a significant impact on the sensing performance of the beams with gauge factors ranging between 196–219 in tension and 57–63 in compression. It should be mentioned though that the carbon fibres were congregated around the midspan of the beam in both the tension and compressive zones resulting in a quasi-embedded application. Similarly, tests on unreinforced beams were not conducted and therefore a definitive claim on the presence of steel reinforcement cannot be made.

While the applications are limited, the literature suggests that steel reinforcement does not negatively impact the sensing performance of cementitious composites. A clear trend on whether the influence is positive or negligible is difficult to make with the available applications at hand. In general, the sensing response of these materials is dependent on the interaction between the reinforcement and the current flow which is related to the electrode layout. Therefore, more investigations are warranted to conclusively understand the role of steel reinforcement in the self-sensing capabilities of reinforced conductive cementitious composites. This can help us design better specimens in the future to avoid stray currents and other noise in measurements.

Electrode configuration

Two-probe and four-probe methods

To generate and exploit electric signals throughout a cementitious system, electrical probes are used to measure the electrical properties of the cementitious materials. Common electrode configurations involve the use of a symmetrical serial arrangement of two or four electrodes. An illustration of the two-probe and four-probe methods is provided in Figures 3(a) and 3(b) respectively. In the two-probe arrangement, both electrodes are used to apply and measure voltage and current whereas in the four-probe arrangement, the current is typically applied at the outer two electrodes and the voltage is measured in the inner two electrodes. The equivalent electrical resistance in both cases is determined by Ohm's law. Therefore, the resistance in a 2D system of an isotropic material can be defined by Eq. 6.

$$R={\displaystyle \frac{V}{I}}$$

(6)

where V is the voltage drop between two electrodes and I is the applied current through two electrodes (Ohm's law).

Figure 3.

Schematics of (a) 2-probe and (b) 4-probe method (adapted from Reference ²⁰⁹ , Licensed under CC BY 3.0).

Figure 4.

Qualitative graph of electrical resistivity and filler concentration (adapted from Reference ¹⁴ , with permission from Elsevier. © 2015 Elsevier). ¹⁴

When comparing these two probe arrangements, the two-probe method can lead to lower reliability due to contact resistance and its sensitivity to probe geometry.^209,210 As the voltage measurement occurs at the location of the probes, the actual resistance of the sample will be connected in series to the contact resistance of the probes. ⁸⁹ The four-probe method is able to eliminate both these phenomena and as a result, is preferred particularly in laboratory settings. Both these methods are widely used in the literature, while the four-probe method is more reliable, the two-probe method is often used due to its simpler setup and its alleged tolerable and constant error. ²¹¹ That said, the reliability of the two-probe method can be questionable at times; contact resistance may exceed the sample's resistance and can vary significantly from sample to sample. ¹⁵⁷ It is therefore recommended to quantify the contact resistance before sensing characterisation if this method is used.

Apart from the serial arrangements, other electrode arrangements used, while not as common, include the Van der Pauw method in which the electrodes are positioned in a rectangular arrangement through the entire surface of the specimen (e.g., four corners in the case of a rectangular cross-section). ²¹² This method allows for average resistance measurements across the entire surface of a specimen while also reducing stress concentrations that occur near the electrodes. ²¹³

Types of electrical probes and applications

Electrodes commonly used in cementitious composites are mainly made of stainless steel ²¹ or copper. ²⁰ Stainless steel electrodes are typically preferred over copper electrodes due to their higher corrosion resistance. The most common shapes of electrodes employed in sensing applications are meshes,^39,45 plates^48,52 and pins. ²⁰² The shape of the electrode used is usually dependent on the application and size of the specimen. For example, plate electrodes could be less favorable in bending applications as they could act as a point of weakness causing failure to occur within that region. ¹⁵⁶ In addition, pins may be preferred in coatings and applications where more than four electrodes are used, as they can reduce tensile stresses and thus cracking in the composite. ²⁰²

Electrical probes can be embedded in self-sensing materials or attached to their surface once cured. Embedding electrodes is commonly employed due to higher accuracy and reliability; typically, plates, mesh and pins are used for such applications. ¹⁴ Plate and wire electrodes are mainly used for the attachment method; the electrodes are bonded on the surface of the specimen with silver paint.^37,41,214 Attaching electrodes though can lead to higher resistivity values, it was reported by Demircilioğlu et al. ²⁰ that electrons have difficulty entering the material conductive network compared to the embedded method in which the electrodes can transport the electrons directly through the cross-section. Moreover, attaching electrodes can lead to a longer polarization time when direct current is used ⁶³ and a higher contact resistance. ¹⁴ However, attaching electrodes has been widely used in capacitance-based applications.^215–217 Adhesives are used to attach the electrodes to the concrete surface, which also act as dielectric films to increase the system's resistance, allowing for capacitance measurements to be made. This approach is beneficial as it can be applied to existing structures and does not require the use of conductive fillers.^216,217

Overall, both methods have been successfully employed in self-sensing applications. While embedding electrodes can lead to more reliable results, the attachment method also has its merits; it can be used as an alternative, particularly in field applications in the case of electrode failure or debonding.

Sensing mechanisms – theory behind the conductivity

Ionic and electronic conduction

Sensing in cementitious materials is a result of ionic and electronic conduction in the cementitious matrix. Ionic conduction of cementitious materials is associated with the mobility of free ions in the pore solution, primarily Ca²⁺, K⁺, Na⁺, Si⁴⁺, Fe²⁺, Al³⁺ and OH−. ²¹⁸ In Portland cement systems, ionic conductivity is attributed to the movement of the Ca²⁺ and OH− ions in the pore solution. This form of ionic conduction is dependent on the amount of free water in the matrix and as a result, Portland cement binders present low sensing capabilities when completely dried.^219,220

Electronic conduction refers to the movement of electrons within the electrically conductive filler in the cementitious matrix. The type of electronic conduction depends on the distance and contact between conductive fillers. If a continuous network of fillers inside the material is formed, then electronic conduction is the result of the movement of electrons within the conductive path. If the conductive filler is not in direct contact but within a certain range, sensing is still possible and is a result of electron hopping (tunneling effect) between the filler. ²²¹ Changes in the distance between filler particles affect the dominant conduction mechanism and overall conductivity. ²²² In both cases, as load is applied, the path the electrical current follows changes, thus impacting the electrical response of the composite. ¹⁴

It should be noted that both ionic and electronic conduction could be present in self-sensing concrete. Such situations include concrete with conductive fillers under elevated moisture conditions. Characterising self-sensing concrete under these conditions could lead to compromised results as ionic conduction can override the effects of electronic conduction. ⁷⁴ It is therefore recommended to characterise self-sensing materials in a dry state and under ambient conditions to attribute the electrical and sensing properties exclusively to the presence of filler and thus electronic conduction. The reader is referred to the Appendix for further information on the influence of both ionic and electronic conduction in sensing applications.

Percolation theory

The piezoresistive behaviour of self-sensing cementitious composites (SSCC) relies on the formation of conductive particles and paths in the matrix. This is described through the percolation theory in which the electrical conductivity of concrete is depicted as a function of filler concentration. The conductivity and sensing performance of SSCC are dependent on the amount of filler added.^13,18,150 An explanation of the percolation theory follows.

Conductive filler is required to convert a cementitious matrix from an insulating material into a semiconductor and/or conductor with sensing capabilities. Numerous studies have investigated the impact of conductive filler on the conductivity of cementitious composites.^223–225 Through these investigations, three zones have been identified; depending on the filler concentration, these are the insulation zone, the percolation zone and the conduction zone.^13,14 In the insulation zone the main form of conduction is ionic, in the percolation zone the main form of conduction is a combination of ionic conduction and electronic conduction primarily through the tunneling effect. In the conduction zone, the main form of conduction is electronic conduction through direct contact.^13,14 A qualitative graph of the percolative behaviour of cement-based composites as a function of filler concentration is illustrated in Figure 4. The curve is divided into the three different conductive zones previously introduced, and is defined by Eq. 7 ²²⁶ :

$$\delta ={\delta }_f{\left({\displaystyle \frac{\varphi -{\varphi }_c}{1-{\varphi }_c}}\right)}^{\gamma }$$

(7)

where ϕ is the additive quantity, ϕ_c is the percolation threshold, δ_f is the filler conductivity, and γ represents the universal critical exponent.

For sensing purposes, the insulation zone relies entirely on ionic conduction and is characterised by the electric behaviour based on free water. This zone is not sufficiently conductive on its own and presents an insulating behaviour when dried. The addition of conductive filler at low quantities has a negligible effect in this region as it can inhibit polarization-related charge carriers. ²²⁷ The percolation zone presents the optimum content of functional filler in achieving sensing properties as the quantity of additives in this zone is sufficient to produce an electrical network. ¹⁴ Therefore, the percolating behaviour of the composite is based on tunnelling and partial contact conduction mechanisms. The conduction zone is characterised by the lowest resistivity and leads to the most stable network. Excessive filler within this zone can lead to less sensitive materials to induced strain or stress, therefore leading to poor sensing abilities. ¹³

Optimal sensing performance has been stated to occur around the ‘percolation threshold’ of the composite.^79,158 The percolation threshold, which is situated in the percolation zone, is defined as the critical concentration of filler at which conductivity increases by several orders of magnitude and the composite transitions from an insulator to a semiconductor. ¹⁴ The percolation threshold varies depending on the type and size of filler used. Fibre based filler with high aspect ratio has been stated to require lower concentrations to impact conductivity compared to spherical filler. ¹³ In certain cases, the percolation threshold has also been defined as the point of maximum conductivity gains (e.g., towards the end of the percolation zone) in which further addition of conductive filler is excessive as the benefits in conductivity are minimal.^31,79 While the percolation threshold is often a key factor in cementitious materials containing electrically conductive fillers and provides valuable insights into the sensing composite, it has been demonstrated that high sensing performance can take place at concentration values other than the percolation threshold and within the percolation zone.^21,158

Evaluation of experimental testing and data processing methods

One of the challenges that the field of self-sensing cementitious materials faces is the evaluation of the data collection process and analysis methods followed to characterise the sensing materials. In most cases, the gauge factor or the stress sensing coefficient is calculated to evaluate and compare the results between other self-sensing materials and commercial sensors. However, how data have been collected and analysed could influence the results and the reported sensor characteristics.

Sensing coefficients

Self-sensing materials are typically characterised in their elastic region where linear trends in mechanical and electrical properties are expected. However, nonlinear responses are rather common in experimental investigations. ²²⁸ This could be attributed to factors such as artefacts in the experimental setup, loading rate, ⁸³ low loading amplitude in which nonlinear behaviour can be expected, ²²⁹ and compromised mechanical performance of the specimen due to the presence of the electrodes. ¹⁵⁶ In cases where nonlinear behaviour is observed, the linear regions, where possible, should be identified (as in Reference ⁸³ ) and the GF should be calculated within the strain range that provides the highest coefficient of determination of the linear fit. Linear models with low regression values could lead to skewed results that do not accurately portray the sensing capabilities of a given material. In turn, this could lead to sensor characteristics that cannot be easily interpreted or properly evaluated against similar sensing options.

Moreover, a sensing material is characterised under cyclic loading once a stable sensing response has been established. ¹⁵⁷ It is common at times though that monotonic loading is employed for characterisation as well. However, different GF values have been reported for the same material between cyclic and monotonic loading.^26,52,69,109 At first glance, this can be rather contradictory and can suggest two things – a) the GF in both loading cases was not calculated for the same strain region and b) monotonic loading was not able to account for plastic deformation that accrues over repeated loading which can lead to a different sensing response. To ensure proper comparisons between the two loading schemes, the GF should be evaluated for the same strain region and the material should be primed under similar conditions before characterisation, i.e., the sensor should be subjected to the same number of loading cycles even if it were to be tested under monotonic loading.

Sensing coefficients may be more complicated to assess in bending applications due to the presence of both compression and tension in the material. Different GFs are usually calculated to account for the compressive and tensile zones of the beam. ¹¹⁰ The electrode layout plays a significant role in distinguishing the response associated with these two regions due to current penetration. ¹⁵⁶ Furthermore, due to the strain development under flexural testing, the stress-sensing coefficient may not be a suitable indicator to characterise the sensing performance under these circumstances.

In tension and particularly strain hardening applications for fibre reinforced concrete, different GFs could be identified depending on the strain condition e.g., pre and post strain hardening or the presence of cracks.^{56,63,75,91,214} Similarly, in this case, the correct region must be used to evaluate the materials.

Further inconsistencies in data evaluation involve the use of the maximum FCR to evaluate sensing performance. This value on its own provides limited information on the nature of the response, e.g., linear or nonlinear. The sole use of the maximum FCR could be more useful in damage-sensing applications in which massive jumps in FCR could be observed in the presence of cracks or damage. ²³⁰

Strain acquisition

In most applications, strain is measured with the use of external sensing devices such as commercial strain gauges, linear variable differential transformers (LVDT) or cameras for digital image correlation. While widely used, these methods are also susceptible to imprecision and erroneous readings, thus requiring frequent calibration.^42,231 As a result, the strain acquisition and therefore the calculation of the GF are highly dependent on the accuracy and precision of the strain and displacement sensors used. While displacement values can also be acquired from the load cells or calculated through the material's stress-strain relationship, the addition of experimental artefacts in the experimental setup, e.g., plastic sheets for insulation, may result in strain loss, which is not accounted for, and thus lead to misconstrued strain values. ²³² In instances where strain is not available, the stress sensitivity coefficient may be calculated. However, direct correlations between SSC and GF cannot always be made, e.g., uneven changes could occur in one coefficient than the other.^58,109

Electrical testing and sensor parameters

Aside from data analytics, the size and design of self-sensing materials may impact the response of self-sensing materials. In a study conducted by D’Alessandro et al., ⁶¹ significantly different GFs were reported for carbon fibre cementitious materials of the same mix design for various sizes under compression. The literature is rather conflicting as increasing the specimen size has reportedly led to both an increase ⁶¹ and a decrease ¹⁶⁴ in GFs. It was stated by Demircilioğlu et al. ¹⁶⁴ that the electrical interrogator's settings may need to be adjusted when testing larger samples to achieve similar performance between different-sized samples. The impact of electrical settings has been acknowledged in the literature. For example, Birgin et al.^42,43 stated that altering the voltage from 10 V to 2 V reduced noise and minimised drift in measurements. Hou et al. ⁴⁹ reported that AC voltage can lead to lower noise in measurements and lower resistivity values as it can travel through the interface between filler and matrix to form new electrical conduction pathways.

Lastly, sensor design and in particular the gauge length can also impact the response of cementitious materials as it is linked to the current penetration depth into the material.^156,233 Small gauge lengths could lead to errors due to the distortion of voltage as a result of limited spacing. ²³⁴

Environmental conditions and compensation

The performance of self-sensing cementitious materials is sensitive to temperature,^37,235 moisture^130,144 and humidity ²³⁶ conditions. It is pertinent that these factors are controlled when characterising these materials to ensure consistency and agreement in measurements and apply proper calibrations when required. To provide an example, studies have reported laboratory temperatures ranging between 20°C ³⁰ and 32°C. ⁶⁵ In these cases, unless the results are temperature compensated, the experimental findings could not be directly compared due to the temperature effect on sensing. Furthermore, as previously stated, specimens are typically dried before testing to eliminate the moisture effect in the readings. However, the duration and temperatures employed in studies often differ, which may impact the exact moisture conditions in the samples. For example, Suchorzewski et al. ¹⁹ dried multi-wall carbon nanotubes self-sensing concrete samples at 65% RH and 20 °C for 28 days, Tao et al. ²³ dried graphene nanoplatelets cementitious samples at 80 °C for 24 h, while Frąc et al. ⁴¹ dried graphite-cement composites at 60°C until a constant mass was reached. As different approaches are available, it is recommended that weight measurements be taken, or desiccators be used to ensure consistent moisture content. It should also be noted that in the case of oven drying, excessively high temperatures may lead to cracks in the samples which in turn may impact their electrical and mechanical behaviour. ³⁷ Therefore, proper temperature and duration should be selected depending on the nature of the materials. A more detailed account of the impact of temperature, moisture and humidity on the sensing performance of self-sensing cementitious materials is provided in the Appendix.

Data-Driven approach

Comprehensive data collection from literature

A dataset was compiled by reviewing 121 peer-reviewed literature sources (up to 2023) with a total of 701 data points collected, covering a broad spectrum of parameters related to self-sensing bulk cementitious systems. Only bulk and mould-cast applications were considered due to their wider data availability, representing the simplest form of self-sensing materials. This approach allows for clearer conclusions to be made and also lays the groundwork for future investigations into more complex self-sensing composites. The dataset provides information on the types of cementitious materials, such as paste, mortar, concrete, and ultra-high performance concrete, the types and properties of conductive fillers, mix design, curing conditions, electric probe materials, loading types, compressive strength, and gauge factors. Gathering data from a wide array of studies ensures that the analysis is more robust and reliable, accounting for various experimental setups, materials, and methods employed in the field. The main focus of this analysis was to identify parameters that impact the sensing performance of self-sensing concrete. An excerpt of the dataset is provided in Table 1 for demonstrative purposes. A systematic screening process was used during dataset compilation to ensure its reliability. The experimental procedures, including material preparation, testing setups, and loading protocols, were assessed for consistency with established practices. In terms of material response, the specimens were required to follow expected trends, for example, a decrease in resistance under compression and an increase under tension. For cyclic loading tests, the change in resistance at loading peaks was required to be repeatable across cycles. For monotonic loading tests, and more broadly when the gauge factor was determined from fractional change in resistance versus strain, the coefficient of determination (R²) was examined; data with R² values below 0.8 were excluded. Sources that did not satisfy these criteria were omitted to maintain both the integrity of the dataset and the validity of the subsequent analysis.

Table 1.

Excerpt of self-sensing dataset.

Type of material	Filler 1	Dosage a	Filler 2	Dosage a	Type of test	Gauge factor	Stress sensitivity%MPa	Reference
Mortar	Graphite	2 wt%	–	–	Compression	77	0.39	41
Mortar	Graphite	3 wt%	–	–	Compression	65	0.34	41
Mortar	Graphite	4 wt%	–	–	Compression	51	0.30	41
Mortar	Carbon black	0.6 vol%	Carbon fibre	1 vol%	Compression	165.48	–	52
Mortar	Carbon black	0.6 vol%	Carbon fibre	1 vol%	Tension	14.71	–	52

^a

By weight of cement or volume of composite.

Data cleaning

The collected dataset consists of a mix of both numeric and string data types, necessitating a rigorous and systematic data cleaning and preprocessing approach. Data cleaning ensures that the dataset is free from inconsistencies, errors, and missing values, providing a solid foundation for subsequent analysis.

Data visualisation and meta-analysis techniques

By employing state-of-the-art data visualisation techniques, the distribution and trends within the dataset were systematically analysed and explored, allowing for the identification of patterns, correlations, and relationships between different variables. A meta-analysis was then conducted to delve deeper into the performance of self-sensing cementitious materials and allow for more reliable and generalisable conclusions to be made. In addition, it assisted in pinpointing areas where further improvements and innovations can be made, providing avenues for further exploration and development.

Multiple types of conductive fillers (e.g., carbon fibres, carbon black, carbon nanotubes, graphite, steel fibres) are commonly used to enhance the sensing performance of cementitious materials. The inclusion of different fillers can lead to a synergistic interaction, creating a more effective and tenable conductive network within the cementitious matrix. Figure 5(a) displays the distribution of samples based on the number of active conductive fillers used. As it can be seen, the majority of samples (over 400) contain only one active filler, about 150 samples used 2 fillers, and only a minimal number of samples were identified that employed over 3 fillers. Figure 5(b) presents a contour plot mapping the relationship between the gauge factor and the number of conductive fillers, along with the corresponding frequency distribution. The densest region is observed at 1 and 2 fillers with the gauge factor below 1000, indicating this range is most common. While isolated peaks at higher gauge factors are presented in the figure, their underlying methodology and reproducibility remain uncertain and warrant further investigation before being considered reliable.

Figure 5.

Number of conductive fillers in self-sensing materials. a) Distribution of samples by the number of active conductive fillers b) Contour plot of gauge factor (FCR/ε) versus the number of conductive fillers and the corresponding frequency distribution. The frequency distribution in the horizontal direction on top of the graph indicates the number of conductive fillers. The frequency distribution in the vertical direction to the right of the graph indicates the gauge factor.

Figure 6 illustrates the gauge factors associated with various combinations of conductive fillers in cementitious composites. Furthermore, a distinction has been made between the data obtained from the 2-probe and 4-probe testing methods. Figure 6(a) highlights the performance of single active fillers, where nickel powder and used foundry sand exhibit notably high gauge factors. On average, though, carbon-based fillers display higher gauge factors when compared to metal-based fillers, indicating their effectiveness in enhancing the strain sensitivity of the composites. Figure 6(b) expands on the interactions between two active fillers, revealing that those combinations, such as carbon fibre with carbon black (carbon-carbon based fillers), CNT with nickel fibre or steel fibre (carbon-metallic based fillers) lead to significant improvements in the gauge factor suggesting synergistic effects. Figure 6(c) explores the influence of three active fillers, with combinations such as carbon fibre, CNT, and magnetite aggregates demonstrating substantial gauge factor increases, indicating a favourable interaction between one-dimension (fibre) and three-dimension (aggregates) fillers that could be harnessed to increase the surface area of fillers for high-performance sensing applications. Overall, based on the results presented in Figure 6(b) and 6(c) it could be deduced that due to their longer length, fibre-based filler can bridge gaps within the matrix, therefore creating a more stable conductive network. ²³⁷ These results underscore the potential of optimising filler combinations to tailor the strain-sensing properties of cementitious materials.

Figure 6.

Gauge factor (FCR/ε) for various combinations of active conductive fillers. a) Single Active Conductive Fillers b) Double Active Conductive Fillers c) Triple Active Conductive Fillers d) Dimensional categorisation of conductive filler combinations tested with the 2-probe method. e) Dimensional categorisation of conductive filler combinations tested with the 4-probe method. Cross-hatching pattern indicates probe method.

To explore the synergistic effect of filler dimension on sensing performance, Figure 6(d) and 6(e) present box plots illustrating the influence of various combinations of conductive fillers on the gauge factor. The conductive fillers were categorised based on their dimensions (shape). Fillers such as carbon black, TiO₂, and gasification char are considered 0D; CNT, carbon fibre, and steel fibre are 1D; graphene, graphite, and GNP are 2D; and conductive aggregate is 3D. The combinations of various conductive fillers result in a wide range of effects on strain sensitivity. As observed, single conductive fillers of 0D and 1D display median GF values of 100 and 40, respectively. The incorporation of additional conductive fillers alongside 1D fillers, apart from the case of 0D and 1D, generally leads to enhanced sensitivity values and improved data distribution within the 75th percentile. The combination of 1D and 3D filler leads to the highest and most consistent sensing performance, albeit with limited applications, likely due to the workability and strength compromises associated with 3D aggregate fillers. ²³⁸ It has been stated that the inclusion of fillers with diverse shapes and sizes can enhance the conductive network within the matrix, thereby improving its sensing performance.^34,194 As additional filler is added to the matrix, the main conduction method changes from tunnelling to contact conduction. ²³⁷ While the combination of 0D and 1D also results in increased gauge factors compared to the 1D samples, a significant number of outliers are present. This may be attributed to the challenges of adequately dispersing these materials. ²³⁹ It should also be noted that the exclusive use of 0D filler demonstrates comparable sensing performance to other filler combinations. Based on sensing merit alone, it could be a viable option for reducing production complexity. In terms of probe method, it can be observed that the two-probe configuration generally led to higher standard deviations and considerable outliers compared to the four-probe method, with gauge factors exceeding 3000 and reaching values up to 6500. This is also viewed in Figure 6(a) and 6(b), in which the two-probe and four-probe methods led to different gauge factor ranges, with the two-probe method yielding higher values for most conductive fillers. This behaviour is likely due to the contact resistance of the electrodes affecting the electrical measurements. ¹⁵⁷ This analysis suggests that the four-probe method provides a more reliable approach for evaluating self-sensing materials.

Overall, it could be observed that incorporating multiple fillers, especially of different types, can improve the sensing performance of cementitious composites. Apart from filler type, the scale of filler (nano, micro and macro) also influences sensing performance.^238,240 This highlights the need for further research to optimise filler selection based on specific applications. Factors such as ease of material fabrication and mechanical strength should also be considered when selecting conductive fillers. Additionally, the probe configuration can influence gauge factor values, and in the case of the two-probe method, this can lead to overestimation and should therefore be considered when designing self-sensing materials.

Figure 7 provides insights into the effects of mechanical testing types—compression, flexural, and tension—on the gauge factor in cementitious composites containing one or two active conductive fillers. Figure 7(a) indicates that when only one filler is used, the gauge factor is significantly higher in compression tests, with notable outliers reaching values above 3000; flexural and tension tests result in lower, more consistent gauge factors. Figure 7(b) illustrates that the introduction of a second active filler leads to a substantial increase in the gauge factor, particularly under tensile testing, where values exceed 6000. The use of multiple fillers can increase the surface area of the conductive particles and the contact points of the conductive path within the cementitious matrix, which in turn can improve the sensing performance of the composite.^34,194 The addition of fillers can also enhance bending and tensile behaviour, improve cracking resistance, and increase toughness. These mechanical improvements likely influence the material's microscale response, which in turn affects its electrical properties and overall sensing behaviour. These results highlight the critical role of both filler content and the type of mechanical loading in understanding the expected self-sensing performance of cementitious composites under various scenarios.

Figure 7.

Gauge factor (FCR/ε) distribution by testing type. (a) Single Active Conductive Fillers (b) Two Active Conductive Fillers.

Figure 8 provides a detailed analysis of the relationship between gauge factor and compressive strength for various cementitious materials, including paste, mortar, concrete, and UHPC for both 2-probe and 4-probe methods. Figure 8(a) presents a comprehensive scatter plot that captures the wide distribution of gauge factors across different strength levels. The data reveal that most gauge factors fall below 1000 for strengths up to 175 MPa, significant outliers though can be observed for UHPC and paste samples with GFs exceeding 3000. Figure 8(b) is an Ashby plot that categorises this relationship by material type, illustrating the distinct performance envelopes for each. Paste and mortar samples exhibit a broad range of gauge factors within lower strength domains, while UHPC dominates the high-strength region with moderate gauge factors.

Figure 8.

Relationship between gauge factor and strength across different cementitious materials. a) Comprehensive scatter plot b) Ashby plot. Marker outline indicates probe method, no outline refers to 2-probe and solid outline refers to 4-probe.

Regarding the probe methods, as seen in Figure 8(a) it is evident that the two-probe method led to significant outliers surpassing GFs of 3000. For GFs below 1000, as depicted in Figure 8(b), both methods displayed comparable results, with most GFs concentrated around 200. Some discrepancies were observed for mortar samples in the two-probe method, with GFs exceeding 700. Similar to what was previously mentioned, these differences could be attributed to the presence of contact resistance in the measurements that lead to inflated values. Based on these graphs, this further demonstrates the liability of the two-probe method and therefore the four-probe method should be preferred for more reliable results.

The Ashby plots in Figure 9(a) and 9(b) present the relationship between gauge factor and compressive strength for cementitious composites incorporating different carbon-based fillers under 2-probe and 4-probe testing configurations, respectively. The plot categorises the fillers into three types based on their dimensionality: 0D (zero-dimensional), 1D (one-dimensional), and 2D (two-dimensional). The data reveals that 2D fillers, such as graphene nanoplatelets (GNP) and graphite, generally result in higher gauge factors, particularly in the strength range of 40 to 70 MPa. In contrast, 0D fillers, like carbon black, are associated with lower gauge factors but are effective across a wider range of strengths, up to 160 MPa depending on the type of cementitious materials as Figure 8 illustrates. 1D fillers, including CNT and carbon fibres, show moderate gauge factors, bridging the performance characteristics between 0D and 2D fillers. This plot underscores the importance of materials selection and filler dimensionality in tailoring the mechanical and sensing properties of cementitious composites allowing for efficient and targeted design of self-sensing. For instance, graphite proves to be more suitable for applications requiring strength above 60 MPa compared to fillers such as GNP, carbon fibre and carbon nanotubes. Furthermore, the combination of fillers e.g., 0D with 1D or 2D fillers, can improve sensing performance. 0D fillers can be distributed within the cementitious matrix, bridging smaller gaps, whereas fillers with a larger aspect ratio are able to connect larger distances within the matrix. ²³⁷ This synergistic effect has been shown to lead to increased gauge factors, as displayed in Figures 6 and 7.

Figure 9.

Ashby plot of gauge factor versus strength for cementitious composites with carbon-based fillers. a) 2-probe method b) 4-probe method. Markers are grouped according to filler type.

Figure 10 presents the p-values from one-way analysis of variance (ANOVA) tests assessing the influence of eight categorical variables on the gauge factor across three datasets: the full dataset, a subset including only 2-probe measurements, and a subset including only 4-probe measurements. The y-axis is shown on a logarithmic scale to capture a wide range of p-values, and a red dashed line marks the 0.05 threshold for statistical significance. The outliers identified through the box plot analysis in Figure 6(d) and 6(e) were excluded to ensure the integrity of the dataset. When analysed separately, both the 2-probe and 4-probe datasets exhibit highly significant effects of concrete type, with p-values well below 0.05; this is also emphasised in Figure 8 where paste and mortar samples led to higher GFs compared to concrete and UHPC. However, this effect disappears in the combined dataset, where the p-value exceeds 0.05, suggesting that aggregating across probe designs introduces heterogeneity that obscures the effect. A similar pattern is observed for the number and concentration of conductive fillers: both factors are highly significant in the 4-probe subset but not in the 2-probe subset, indicating probe-dependent effects. In the combined dataset, the number of fillers remains significant, whereas concentration does not. Conversely, the material and shape of probe electrodes consistently influence both probe configurations, maintaining significance when combined. This has been brought up in the literature, where studies have reported varying measurements for electrodes made from different materials and shapes.^241–244 Testing type and number of probes yield p-values above 0.05 in all analyses, indicating no measurable effect. It is worth noting that AC/DC voltage is significant only in the full dataset, suggesting its influence emerges when the entire range of probe configurations is considered. It should be noted, though, that for the 4-probe subset, the type of concrete and the type and number of fillers were found to be statistically significant, which is consistent with our current understanding of self-sensing materials,^13,151,159 thereby reinforcing the notion that four-probe measurements provide more reliable data compared to the two-probe method. Collectively, these results demonstrate that the apparent significance of each factor depends on how the data are stratified and emphasise the need to account for probe design when interpreting gauge factors.

Figure 10.

One-way ANOVA p-values for categorical variables influencing the gauge factor. Cross-hatching pattern indicates probe dataset.

To address the confounding effects of probe design and measurement mode, a multi-factor ANOVA was conducted, modelling the gauge factor as a function of: (a) concrete type, (b) number of electrode probes, and (c) measurement mode (AC/DC), while including all two-way and three-way interaction terms (Figure 11). Multi-factor ANOVA controls for probe design and AC/DC and focuses on a subset of the data, which reduces the unexplained variance and reveals a clearer effect of concrete type. The analysis reveals significant main effects for both concrete type (p = 0.0291) and AC/DC mode (p = 0.0444), but not for probe design alone (p = 0.301). Critically, all interaction terms, including (a) × (b), (a) × (c), (b) × (c), and (a) × (b) × (c), are statistically significant, with several p-values below 10⁻⁶. This indicates strong interdependence among the factors: for instance, the effect of concrete type varies not only between AC and DC modes but also across 2- and 4-probe systems. The significant three-way interaction (p = 0.000416) underscores the importance of modelling these complex interdependencies. These results explain the inconsistencies observed in the one-way ANOVA: pooling data without accounting for such interactions masks real effects. Overall, the findings highlight the need for multifactorial statistical approaches when evaluating self-sensing performance in heterogeneous experimental setups, particularly when probe configuration and measurement protocols vary.

Figure 11.

Multi-way ANOVA p-values for categorical variables influencing the gauge factor.

Recommendations and future work

Durability of self-sensing materials

While one of the main advantages of self-sensing cementitious materials is their greater durability compared to electronic sensors,^78,159,245 the performance of these materials under harsh conditions and long-term performance is seldom considered. ²⁴⁶ To properly and safely deploy these sensors into the field, it must be ensured that they can withstand the environmental conditions they will be exposed to e.g., nuclear plants and saline environments. However, it is currently unclear how most sensing materials would perform under such conditions. As such, further research is required to understand the behaviour of cementitious sensing materials outside of laboratory settings. By assessing the durability, these materials could be properly categorised and deployed depending on their intended use and characteristics.

Open-source dataset platform

Creating an open-source dataset platform for self-sensing materials would be of great benefit by providing unrestricted access to a comprehensive and up-to-date dataset. The platform should feature a clean, intuitive, and user-friendly interface, robust and scalable data storage and management systems, and rigorous data curation and quality control processes. By integrating various data visualisation and analysis tools, as well as collaboration and community features, the platform can facilitate knowledge sharing, innovation, and a dynamic research environment in the field. Such a platform has the potential to accelerate the advancement of knowledge and technology in the vital area of self-sensing materials, fostering collaboration and supporting the development of innovative solutions for civil infrastructure.

Graphical user interface for the data processing

The development of a user-friendly Graphical User Interface (GUI) for data processing and analysis of self-sensing materials is highly warranted. Currently, data processing and analysis can be a complicated and time-consuming processes. By streamlining the data processing workflow, the GUI will facilitate the efficient exploration and visualisation of the data, enabling users to make better-informed decisions and draw meaningful insights. Additionally, the GUI can be designed to integrate various data processing tools and algorithms, along with access to datasets, making it a comprehensive and versatile platform for the analysis of self-sensing materials.

Standardisation of electrical characterisation

A recurring theme in the field of self-sensing cementitious materials is the establishment of a standardised framework for data collection, processing, and analysis. Due to the wide range of experimental setups and methods employed, the reported performance of self-sensing concrete can vary significantly. Standardisation of testing protocols and guidelines for data reporting, experimental procedures, and performance metrics will not only improve the consistency and reliability of the results but also allow for straightforward evaluation and comparison of findings from different studies.

Field applications

Currently, field applications for self-sensing cementitious materials are quite limited. ⁵³ As research into this field has progressed significantly over the years, the next steps should involve seeing these materials being utilised in field settings. This would allow us to understand their technology readiness level and at the same time provide valuable lessons learned for future improvements. Some considerations to be made for field applications include measurement compensations due to environmental conditions, impermeabilization of the materials for greater stability, low-cost electrical interrogators for large scale deployment and automated data processing algorithms.

Conclusions

This paper provides a holistic review of self-sensing cementitious materials by reviewing the available literature and applying a data-driven analysis based on a dataset compiled from 121 peer-reviewed sources. The review aimed at providing an overview and general understanding of self-sensing concrete while also identifying common practices and key challenges within this field. The purpose of the data-driven analysis was to distinguish trends in the performance of self-sensing materials by applying statistical methods and data visualisation techniques. The key outcomes of this review and analysis are outlined below:

Gauge factors

The strain sensing sensitivity of cementitious materials varies based on numerous factors, such as the number, type and concentration of conductive filler, cementitious matrix, type and number of electrodes, and mechanical testing method. The most common range of GF values is below 1000. However, some outliers have been recorded with values exceeding 3000 in compression and 6000 in tension. The reproducibility of such tests still needs to be validated. These elevated values may stem from specific experimental conditions and require further scrutiny before being considered broadly reliable.

Filler type and concentration

Filler type and concentration are significant factors that influence sensing behaviour. Optimal sensing performance is typically achieved near the percolation threshold which marks the critical concentration at which a continuous conductive network forms and the composite transitions from insulating to semiconducting behaviour. High sensitivity has also been reported within the broader percolation zone, although exceeding the percolation threshold can lead to reduced sensitivity. Nickel powder was found to lead to the highest GF as a single filler. However, on average, carbon-based filler led to a higher sensing response compared to metal-based filler. This reinforces the need for precise control and tailoring of filler dosage based on filler type, geometry, and interaction.

Optimal Filler Combinations

Most investigations on self-sensing materials have focused on the use of single conductive fillers, particularly for compression-based tests. However, incorporating multiple conductive fillers, especially those with different geometries, can significantly enhance sensing performance. Hybrid-dimensional filler systems can overcome the limitations of individual fillers, resulting in improved sensitivity, especially under tensile and flexural loading. 0D fillers can increase contact points, while 1D fillers can bridge gaps within the cementitious matrix, promoting stable and well-connected conductive networks. The combination of carbon black and carbon fibre was found to yield the highest GF among double active fillers. Although these combinations may pose challenges in terms of workability or mechanical integrity, the performance benefits justify further optimisation and targeted mix design.

Influence of Material Type and Loading Conditions

The sensing response is strongly influenced by both the type of cementitious matrix and the applied mechanical loading. Paste and mortar-based composites consistently exhibited higher gauge factors than concrete and UHPC. Moreover, the response of self-sensing materials is generally higher under compression than under tension or flexure for single-filler systems. However, the sensitivity under tensile and flexural loading is greater when incorporating multiple fillers.

Electrode Configuration

The two-probe and four-probe electrode configurations are widely used in the field of self-sensing materials. However, based on the analysis conducted, it was found that they could lead to significant differences in sensing response. Compared to the four-probe method, the two-probe method generally led to higher gauge factors for the same type of conductive filler and resulted in greater data variability, with outliers exceeding 3000 and therefore, its robustness is questionable. Consequently, the four-probe method remains a more reliable approach for the characterization of self-sensing materials.

ANOVA

An analysis of variance was performed across multiple testing parameters, using the full dataset and subsets separated by two-probe and four-probe configurations. The full dataset and the two-probe subset produced inconsistent results, whereas the four-probe dataset proved more reliable. Specifically, the type of concrete, filler concentration, number of conductive fillers, and electrode type and shape were all statistically significant when determining the gauge factor for the four-probe configuration. These findings emphasise the importance of structuring datasets under comparable testing conditions, as combining divergent data can lead to misleading conclusions. Furthermore, a multiway ANOVA was conducted on parameters that were significant for one probe configuration but not the other. This analysis revealed that concrete type, number of probes, and voltage type remained statistically significant when considered simultaneously but not individually. This highlights the importance of accounting for complex interdependencies in the analysis of self-sensing materials and their effect on sensing response.

Together, these findings offer a clear roadmap for designing more targeted and fit-for-purpose self-sensing cementitious composites. By strategically selecting filler combinations, refining mix designs, and optimising electrode configurations, future research and applications can result in significantly improved sensing capabilities. It is envisioned that the dataset can serve as the basis for further data-driven and machine learning analyses, enabling improved performance prediction. As our understanding of self-sensing concrete matures, the potential for field implementation increases, allowing for the widespread use of this technology in structural health monitoring.

CRediT authorship contribution statement

Christos Vlachakis: Conceptualization, Data curation, Formal Analysis, Investigation, Methodology, Validation, Writing – original draft, Writing – review & editing. Yen-Fang Su: Conceptualization, Formal Analysis, Funding Acquisition, Investigation, Methodology, Software, Visualization, Writing – original draft. Sripriya Rengaraju: Conceptualization, Data curation, Investigation, Writing – original draft, Writing – review & editing. Xueying Wang: Data curation, Investigation, Visualization, Writing – original draft, Writing – review & editing. Gabriele Milone: Data curation, Investigation, Visualization, Writing – original draft, Writing – review & editing. Khalilullah Taj: Formal Analysis, Investigation, Software, Visualization, Writing – original draft. Abir Al-Tabbaa: Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Validation, Writing – review & editing.

Supplemental Material

sj-docx-1-inr-10.1177_09506608251391873 - Supplemental material for Self-Sensing concrete: A data-driven approach to comprehensive analysis and review

Supplemental material, sj-docx-1-inr-10.1177_09506608251391873 for Self-Sensing concrete: A data-driven approach to comprehensive analysis and review by Christos Vlachakis, Yen-Fang Su, Sripriya Rengaraju, Xueying Wang, Gabriele Milone, Khalilullah Taj and Abir Al-Tabbaa in International Materials Reviews