Abstract

1. Introduction

Structural health monitoring (SHM) techniques can provide increasing service life and construction safety, from early detection of strain, failures and damages¹1 Sofi A, Regita JJ, Rane B, Lau HH. Structural health monitoring using wireless smart sensor network: an overview. Mech Syst Signal Process. 2022;163:108113.^,22 Tian Z, Li Y, Zheng J, Wang S. A state-of-the-art on self-sensing concrete: materials, fabrication and properties. Compos, Part B Eng. 2019;177:107437.. However, continuous and wide-ranging monitoring may require high-cost investments due to the need for numerous sensors throughout the structure. So, using materials to be able to self-monitoring can be a solution to some problems with the use of sensors¹1 Sofi A, Regita JJ, Rane B, Lau HH. Structural health monitoring using wireless smart sensor network: an overview. Mech Syst Signal Process. 2022;163:108113.^,33 Al-Bahrani M, Bouaissi A, Cree A. Mechanical and electrical behaviors of self-sensing nanocomposite-based MWCNTs material when subjected to twist shear load. Mech Adv Mater Struct. 2021;28(14):1488-97.. These materials can be created from a variety of matrices, such as polymers, asphalts, and cements⁴4 Liu Z, Zeng M, Wang H, Wang X, Li Y, Zeng C. Toward flexible piezoelectrets with high environmental stability: a hybrid approach. es materials and manufacturing. ES Mater Manuf. 2022;17:73-82. 5 Saxena P, Shukla P. A comprehensive review on fundamental properties and applications of poly(vinylidene fluoride) (PVDF). Adv Compos Hybrid Mater. 2021;4(1):8-26. 6 Wang H, Li Y, Wang X, Liu Z, Ahmed M, Zeng C. Preparation and characterization of piezoelectric foams based on cyclic olefin copolymer. Eng Sci. 2021;16:203-10. 7 Liu X, Wu S. Study on the graphite and carbon fiber modified asphalt concrete. Constr Build Mater. 2011;25(4):1807-11. 8 Ahmad M, Al-Dala’ien RNS, Beddu S, Itam ZB. Thermo-physical properties of graphite powder and polyethylene modified asphalt concrete. Eng Sci. 2022;17:121-32.^-99 Chen J, Zhu Y, Guo Z, Nasibulin AG. Recent progress on thermo-electrical properties of conductive polymer composites and their application in temperature sensors. Eng Sci. 2020;12:13-22.. The built-in sensors can make heterogeneity in the structure, which may cause some damage to the structure. While self-sensing composites make homogeneity to the structure²2 Tian Z, Li Y, Zheng J, Wang S. A state-of-the-art on self-sensing concrete: materials, fabrication and properties. Compos, Part B Eng. 2019;177:107437..

For the monitoring without using coupled or embedded sensors, the concrete structures need self-sensing cementitious composites in their manufacture to be able to detect changes in mechanical stress. Several electrical effects are the object of study for the application of self-sensing in materials, such as piezoresistivity. The piezoresistive effect allows the detection of mechanical strain and stress changes, as a result of the monitored electrical resistance change¹⁰10 Scholle P, Sinapius M. A review on the usage of continuous carbon fibers for piezoresistive self strain sensing fiber reinforced plastics. J Compos Sci. 2021;5(4):96.^,1111 Chung DDL. A critical review of piezoresistivity and its application in electrical-resistance-based strain sensing. J Mater Sci. 2020;55(32):15367-96.. Further on the piezoresistivity, piezoelectric effect, capacitance and impedance are also used in self-sensing materials and sensor’s manufacture and mechanism¹²12 Han G, Su YF, Ma S, Nantung T, Lu N. In situ rheological properties monitoring of cementitious materials through the Piezoelectric-based Electromechanical Impedance (EMI) Approach. Eng Sci. 2021;16:259-68. 13 Su YF, Han G, Kong Z, Nantung T, Lu N. Embeddable piezoelectric sensors for strength gain monitoring of cementitious materials: the influence of coating materials. Eng Sci. 2020;11:66-75. 14 Dong W, Li W, Vessalas K, Wang K. Mechanical and conductive properties of smart cementitious composites with conductive rubber crumbs. ES Mater Manuf. 2020;7:51-63. 15 Chung DDL. Self-sensing concrete: from resistance-based sensing to capacitance-based sensing. Int J Smart Nano Mater. 2021;12(1):1-19.^-1616 Mishra S, Chaudhary P, Yadav BC, Umar A, Lohia P, Dwivedi DK. Fabrication and characterization of an ultrasensitive humidity sensor based on chalcogenide glassy alloy thin films. Eng Sci. 2021;15:138-47.. Also used in sensors and sensing platforms are nanomaterials, which are another large field of research that is growing¹⁷17 Rohilla D, Chaudhary S, Umar A. An overview of advanced nanomaterials for sensor applications. Eng Sci. 2021;16:47-70. 18 Huang K, Wu Y, Liu J, Chang G, Pan X, Weng X, et al. A double-layer carbon nanotubes/polyvinyl alcohol hydrogel with high stretchability and compressibility for human motion detection. Eng Sci. 2022;17:319-27. 19 Huang Y, Luo Y, Liu H, Lu X, Zhao J, Lei Y. A subcutaneously injected SERS nanosensor enabled long-term in vivo glucose tracking. Eng Sci. 2021;14:59-68.^-2020 Gijare M, Chaudhari S, Ekar S, Garje A. Reduced graphene oxide based electrochemical nonenzymatic human serum glucose sensor. ES Mater Manuf. 2021;14:110-9..

Regular concrete and mortar exhibit a few piezoresistive responses when under loads, that is not enough to consider as self-sensing materials²¹21 Frąc M, Pichór W. Piezoresistive properties of cement composites with expanded graphite. Compos Commun. 2020;19:99-102.. At least up to a certain point, piezoresistive composites offer a certain electrical conductivity for concretes and mortars. This conductivity cannot be too low to be considered the composite almost insulating, or too high to the offer almost no electrical resistivity, as this would impede the measurement of the piezoresistive effect¹¹11 Chung DDL. A critical review of piezoresistivity and its application in electrical-resistance-based strain sensing. J Mater Sci. 2020;55(32):15367-96.. In other words, for the composite to be able to self-monitoring, a minimum conductive filler needs to be used, but not without prejudice to the highest possible electrical conductivity. This limit is called the "percolation threshold" as shown in Figure 1 ²³23 Al-Dahawi A, Sarwary MH, Öztürk O, Yıldırım G, Akın A, Sahmaran M, et al. Electrical percolation threshold of cementitious compositespossessing self-sensing functionality incorporating different carbon-basedmaterials. Smart Mater Struct. 2016;25(10):105005..

Figure 1
Schematic description of percolation theory. In Zone A, there is no conductive network. In Zone B, the resistivity is reduced abruptly, with few additions of fillers. Lastly, in Zone C, there is no significance in the reduction of resistivity when more fillers are added²²22 Wang L, Aslani F. Development of self-sensing cementitious composites incorporating CNF and hybrid CNF/CF. Constr Build Mater. 2021;273:121659..

As shown in Figure 2, as the self-sensing composite is compressed, the electrical resistivity decreases, as well as it is tensioned, it increases. In other words, this effect is what characterizes piezoresistivity, as a relationship between mechanical forces and the change in resistivity of the material. This change happens because conductive fillers move closer together or further apart, with compression or tension, thus altering the conductive paths. The change occurs linearly in the elastic regime of the composite, that is, up to a certain point in this relationship, as shown in Figure 3 ¹¹11 Chung DDL. A critical review of piezoresistivity and its application in electrical-resistance-based strain sensing. J Mater Sci. 2020;55(32):15367-96., and the reversible strain happens in the elastic regime. As cracks appear after the elastic regime, the continuous paths are interrupted and the resistivity increases again²2 Tian Z, Li Y, Zheng J, Wang S. A state-of-the-art on self-sensing concrete: materials, fabrication and properties. Compos, Part B Eng. 2019;177:107437..

Figure 2
Conductive microstructure scheme in self-sensing cementitious (based on²⁴24 Lee SY, Le HV, Kim DJ. Self-stress sensing smart concrete containing fine steel slag aggregates and steel fibers under high compressive stress. Constr Build Mater. 2019;220:149-60.).

Figure 3
Graphic relationship between electrical resistivity and mechanical effort in a self-sensing composite (adapted from²⁵25 Vlachakis C, Perry M, Biondi L. Self-sensing alkali-activated materials: a review. Minerals. 2019;10(10):885.).

However, challenges must be overcome so that it is possible to use self-sensing composite to monitoring real structures, for example, to mitigate and reduce the influence of external environmental issues, which affect the performance of self-sensing²⁶26 Han J, Pan J, Cai J, Li X. A review on carbon-based self-sensing cementitious composites. Constr Build Mater. 2020;265:120764.. In this way, it could be useful to use Pearson's correlation analysis (r) to see how the piezoresistivity effect works in a cementitious composite.

Pearson's correlation analysis (r) makes it possible to quantify the degree of association between two linear variables in a sample. This association has been described as a level of assessment of intensity and direction between the two compared variables. The correlation is great when the coefficient is 1 (one) or -1 (negative one) and unsatisfactory when it approaches zero. This method of correlation, which today has the name of its author, was developed in 1985, by Karl Pearson, and is obtained by Equation 1, where “x” and “y” are the variables, “x̄” and “ӯ” the means, and "n" the number of variable pairs²⁷27 Baak M, Koopman R, Snoek H, Klous S. A new correlation coefficient between categorical, ordinal and interval variables with Pearson characteristics. Comput Stat Data Anal. 2020;152:107043..

There are some limitations to Pearson's method, such as the need for analyzed data to have a bivariate normal distribution and a linear relationship between them. Although the samples analyzed are significantly large in relation to the population, no more than two decimal places of the coefficient should be considered if the sample size <500, not even more than one decimal place, if the value of the coefficient is very small. For three decimal places, should be considered more than 100,000 the sample size²⁸28 Armstrong RA. Should Pearson’s correlation coefficient be avoided? Ophthalmic Physiol Opt. 2019;39(5):316-27.^,2929 Bedeian AG, Sturman MC, Streiner DL. Decimal dust, significant digits, and the search for stars. Organ Res Methods. 2009;12(4):687-94..

Researchers from different areas of science usually give names to the levels of Pearson's coefficient intervals used to rank their results, such as “moderate correlation” between 0.6 and 0.7. However, like the classification for this range, it is also called otherwise by other researchers who consider it strong and not moderate. That is to say, the interpretation of the coefficients varies substantially between the different areas of scientific research, and thus the use of classification nomenclature should be avoided, given the lack of absolute rules for interpreting the correlation between the variables³⁰30 Akoglu H. User’s guide to correlation coefficients. Turk J Emerg Med. 2018;18(3):91-3..

Even though researchers²¹21 Frąc M, Pichór W. Piezoresistive properties of cement composites with expanded graphite. Compos Commun. 2020;19:99-102.^,2222 Wang L, Aslani F. Development of self-sensing cementitious composites incorporating CNF and hybrid CNF/CF. Constr Build Mater. 2021;273:121659.^,3131 D’Alessandro A, Tiecco M, Meoni A, Ubertini F. Improved strain sensing properties of cement-based sensors through enhanced carbon nanotube dispersion. Cement Concr Compos. 2021;115:103842. 32 Ding S, Wang YW, Ni YQ, Han B. Structural modal identification and health monitoring of building structures using self-sensing cementitious composites. Smart Mater Struct. 2020;29(5):055013. 33 Rovnaník P, Kusák I, Bayer P, Schmid P, Fiala L. Electrical and self-sensing properties of alkali-activated slag composite with graphite filler. Materials. 2019;12(10):1616. 34 Kim TU, Le HV, Park JW, Eock SK, Jang Y, Kim DJ. Development of a smart concrete block with an eccentric load sensing capacity. Constr Build Mater. 2021;306:124881. 35 Suchorzewski J, Prieto M, Mueller U. An experimental study of self-sensing concrete enhanced with multi-wall carbon nanotubes in wedge splitting test and DIC. Constr Build Mater. 2020;262:120871. 36 Ferdiansyah T, Turatsinze A, Balayssac JP. Design and characterization of self-sensing steel fiber reinforced concrete. MATEC Web Conf. 2018;199:11008. 37 Dong W, Li W, Wang K, Luo Z, Sheng D. Self-sensing capabilities of cement-based sensor with layer-distributed conductive rubber fibres. Sens Actuators A Phys. 2020;301:111763. 38 Frąc M, Szudek W, Szołdra P, Pichór W. The applicability of shungite as an electrically conductive additive in cement composites. J Build Eng. 2022;45:103469. 39 Konkanov M, Salem T, Jiao P, Niyazbekova R, Lajnef N. Environment-friendly, self-sensing concrete blended with byproduct wastes. Sensors. 2020;20(7):1925. 40 Monteiro AO, Cachim PB, Costa PMFJ. Self-sensing piezoresistive cement composite loaded with carbon black particles. Cement Concr Compos. 2017;81:59-65.^-4141 Del Moral B, Baeza FJ, Navarro R, Galao O, Zornoza E, Vera J, et al. Temperature and humidity influence on the strain sensing performance of hybrid carbon nanotubes and graphite cement composites. Constr Build Mater. 2021;284:122786. have been working to analyze self-sensing behavior in cement composites, they have used only the coefficient of determination (R²) or graphic comparisons. However, this work does not aim to evaluate the mechanical properties of the cementitious composite but to use the Pearson’s correlation to analyze the piezoresistive effect of self-sensing cement, which is why only graphite was used in the composite. Carbon-based materials have good electrical conductivity, so they are the materials most commonly used nowadays to make self-sensing cement composites⁴²42 Luo T, Wang Q. Effects of graphite on electrically conductive cementitious composite properties: a review. Materials. 2021;14(17):4798.. Graphite is used, in a wide range of composites and materials, including smart structures, electromagnetic shielding, building, electric power, road engineering, aircraft parts, and thermal management⁸8 Ahmad M, Al-Dala’ien RNS, Beddu S, Itam ZB. Thermo-physical properties of graphite powder and polyethylene modified asphalt concrete. Eng Sci. 2022;17:121-32.^,4242 Luo T, Wang Q. Effects of graphite on electrically conductive cementitious composite properties: a review. Materials. 2021;14(17):4798.

43 Holle MJ, Misak HE, Malik RA, Alarifi IM, Asmatulu R. Structural analysis and wear behavior of different graphite-based brushes for aircraft starter generator application. Adv Compos Hybrid Mater. 2021;4(1):162-72.^-4444 Hu X, Wu H, Lu X, Liu S, Qu J. Improving thermal conductivity of ethylene propylene diene monomer/paraffin/expanded graphite shape-stabilized phase change materials with great thermal management potential via green steam explosion. Adv Compos Hybrid Mater. 2021;4(3):478-91.. Graphite powder was chosen because it is a low-cost material when compared with nanomaterials.

2. Materials and Methods

2.1. Materials

Following the literature⁴⁵45 Loamrat K, Sappakittipakorn M, Sukontasukkul P. Application of cement-based sensor on compressive strain monitoring in concrete members. Adv Mat Res. 2014;931–932:446-50.

46 Chen M, Gao P, Geng F, Zhang L, Liu H. Mechanical and smart properties of carbon fiber and graphite conductive concrete for internal damage monitoring of structure. Constr Build Mater. 2017;142:320-7.^-4747 Tao J, Wang X, Wang Z, Zeng Q. Graphene nanoplatelets as an effective additive to tune the microstructures and piezoresistive properties of cement-based composites. Constr Build Mater. 2019;209:665-78. four mortar specimens were prepared for the piezoresistive test, in cubic shape samples with a 40 mm edge, dimensions recommended in NBR 16868-2⁴⁸48 ABNT: Associação Brasileira de Normas Técnicas. ABNT NBR 16868-2: structural masonry - part 2: execution and site control. Rio de Janeiro: ABNT; 2020. for compression test. The mortar mix rate was made in the following proportions of cement, sand, and graphite: T1C=1:4:0; T2C=1:4:0.125; T3C=1:4:0.250; and T4C=1:4:0.375, in proportions to the cement mass, and these graphite proportions are within the range (0-0.4) used by⁴⁹49 Papanikolaou I, Litina C, Zomorodian A, Al-Tabbaa A. Effect of natural graphite fineness on the performance and electrical conductivity of cement paste mixes for self-sensing structures. Materials. 2020;13(24):5833..

The water/cement ratio (w/c) of 0.50 used in the T1C mix could not be maintained in the other mixes, in which the following w/c ratios were used: T2C=0.75; T3C=1.05; and T4C=1.40, to get the consistency for molding the samples.

The specifications of the materials, according to the manufacturers, are: Portland cement, marketed by the company Votorantim Cimentos – Classification CP-II-F-32, 75% - 89% by mass of clinker + gypsum; 11% - 25% carbonate material; The quartz sand has a Fineness Modulus 2,03 according to NBR 7211⁵⁰50 ABNT: Associação Brasileira de Normas Técnicas – ABNT. ABNT NBR 7211: aggregates for concrete: specification. Rio de Janeiro: ABNT; 2009.. The powdered graphite, marketed by Wonder - Carbon (Loss to Fire) >72%; Ash a maximum of 28%; maximum moisture 0.5%. In the Figure 4, the granulometric of sand and graphite are shown.

Figure 4
The granulometric curves of the sand (a) and graphite (b) samples.

During the molding of the sample’s specimens, 4 electrodes (aluminum plates) with a size of 35 x 20 x 0.1 mm were inserted, spaced 10 mm between each other and with 25 mm embedded in the mortar, as shown in Figure 5.

Figure 5
Cubic specimens with electrodes

Although graphite improves the electrical conductivity of the cementitious composite, it generally causes a reduction in the composite's compressive strength. Much research reports the use of graphite with other fillers, such as polymer fibers or carbon, to improve the mechanical strength⁴⁶46 Chen M, Gao P, Geng F, Zhang L, Liu H. Mechanical and smart properties of carbon fiber and graphite conductive concrete for internal damage monitoring of structure. Constr Build Mater. 2017;142:320-7.^,4949 Papanikolaou I, Litina C, Zomorodian A, Al-Tabbaa A. Effect of natural graphite fineness on the performance and electrical conductivity of cement paste mixes for self-sensing structures. Materials. 2020;13(24):5833.^,5151 Cordon HCF, Tadini FB, Akiyama GA, Andrade VO, Silva RC. Development of electrically conductive concrete. Rev Cerâmica. 2020;66(377):88-92..

2.2. Methods

The samples were tested by compression in a manual press, for three repetitions of each sample⁴⁵45 Loamrat K, Sappakittipakorn M, Sukontasukkul P. Application of cement-based sensor on compressive strain monitoring in concrete members. Adv Mat Res. 2014;931–932:446-50.^,5252 Han BG, Han BZ, Ou JP. Experimental study on use of nickel powder-filled Portland cement-based composite for fabrication of piezoresistive sensors with high sensitivity. Sens Actuators A Phys. 2009;149(1):51-5., with a maximum load of nearly 2 kN³¹31 D’Alessandro A, Tiecco M, Meoni A, Ubertini F. Improved strain sensing properties of cement-based sensors through enhanced carbon nanotube dispersion. Cement Concr Compos. 2021;115:103842.^,3232 Ding S, Wang YW, Ni YQ, Han B. Structural modal identification and health monitoring of building structures using self-sensing cementitious composites. Smart Mater Struct. 2020;29(5):055013., since this load would not cause rupture of the samples, because it is a non-destructive test. The voltage (U) changes and force (compression) applied were recorded synchronously at a sampling rate of 10 Hz, using the scheme in Figure 6, which had a data acquisition system (DAQ) model 8000-8-SM (Micro-Measurements), a load cell, and a laptop.

Figure 6
Data acquisition scheme of the experiment.

The electrical resistance was obtained from Ohm’s law⁴¹41 Del Moral B, Baeza FJ, Navarro R, Galao O, Zornoza E, Vera J, et al. Temperature and humidity influence on the strain sensing performance of hybrid carbon nanotubes and graphite cement composites. Constr Build Mater. 2021;284:122786. and, through the electrical circuit in Figure 7, it was possible to determine the electrical resistance (R_s) of the composite by Equation 2 (adapted from⁵³53 Monteiro AO, Loredo A, Costa PMFJ, Oeser M, Cachim PB. A pressure-sensitive carbon black cement composite for traffic monitoring. Constr Build Mater. 2017;154:1079-86.). A DAQ system was used to obtain the voltages in the sample (U_s) and in the circuit supply (U_in), with the use of a reference resistor (R_ref) 1000 Ω³⁴34 Kim TU, Le HV, Park JW, Eock SK, Jang Y, Kim DJ. Development of a smart concrete block with an eccentric load sensing capacity. Constr Build Mater. 2021;306:124881.^,5454 Lima GES, Nalon GH, Santos RF, Ribeiro JCL, Carvalho JMF, Pedroti LG, et al. Microstructural investigation of the effects of carbon black nanoparticles on hydration mechanisms, mechanical and piezoresistive properties of cement mortars. Mater Res. 2021;24(4):e20200539.^,5555 Nalon GH, Ribeiro JCL, Araújo END, Pedroti LG, Carvalho JMF, Santos RF, et al. Effects of different kinds of carbon black nanoparticles on the piezoresistive and mechanical properties of cement-based composites. J Build Eng. 2020;32:101724.. The data from voltages in the sample (Us) corresponds to the wires green and yellow in Figure 6.

Figure 7
Electrical circuit for measuring electrical resistance (adapted from⁵³53 Monteiro AO, Loredo A, Costa PMFJ, Oeser M, Cachim PB. A pressure-sensitive carbon black cement composite for traffic monitoring. Constr Build Mater. 2017;154:1079-86.).

The electrical resistivity (ρ) was calculated by Equation 3 ⁵¹51 Cordon HCF, Tadini FB, Akiyama GA, Andrade VO, Silva RC. Development of electrically conductive concrete. Rev Cerâmica. 2020;66(377):88-92.^,5656 Birgin HB, D’Alessandro A, Laflamme S, Ubertini F. Smart graphite-cement composite for roadway-integrated weigh-in-motion sensing. Sensors. 2020;20(16):4518., where the distance (L) between the central electrodes and their contact area (A) with the composite are known values, while the fractional change in resistivity (FCR) was calculated using Equation 4 ²2 Tian Z, Li Y, Zheng J, Wang S. A state-of-the-art on self-sensing concrete: materials, fabrication and properties. Compos, Part B Eng. 2019;177:107437..

Among the ways indicated in the literature, the sensitivity²²22 Wang L, Aslani F. Development of self-sensing cementitious composites incorporating CNF and hybrid CNF/CF. Constr Build Mater. 2021;273:121659. of the piezoresistive composite was determined from the fractional change of resistivity per unit stress (σ), using Equation 5 ³⁴34 Kim TU, Le HV, Park JW, Eock SK, Jang Y, Kim DJ. Development of a smart concrete block with an eccentric load sensing capacity. Constr Build Mater. 2021;306:124881.^,3737 Dong W, Li W, Wang K, Luo Z, Sheng D. Self-sensing capabilities of cement-based sensor with layer-distributed conductive rubber fibres. Sens Actuators A Phys. 2020;301:111763.

38 Frąc M, Szudek W, Szołdra P, Pichór W. The applicability of shungite as an electrically conductive additive in cement composites. J Build Eng. 2022;45:103469.

39 Konkanov M, Salem T, Jiao P, Niyazbekova R, Lajnef N. Environment-friendly, self-sensing concrete blended with byproduct wastes. Sensors. 2020;20(7):1925.^-4040 Monteiro AO, Cachim PB, Costa PMFJ. Self-sensing piezoresistive cement composite loaded with carbon black particles. Cement Concr Compos. 2017;81:59-65..

In other words, the sensitivity is the relationship between mechanical and electrical effects for the evaluation of piezoresistivity, when the resistivity can be affected by stress amplitude³⁷37 Dong W, Li W, Wang K, Luo Z, Sheng D. Self-sensing capabilities of cement-based sensor with layer-distributed conductive rubber fibres. Sens Actuators A Phys. 2020;301:111763.

38 Frąc M, Szudek W, Szołdra P, Pichór W. The applicability of shungite as an electrically conductive additive in cement composites. J Build Eng. 2022;45:103469.^-3939 Konkanov M, Salem T, Jiao P, Niyazbekova R, Lajnef N. Environment-friendly, self-sensing concrete blended with byproduct wastes. Sensors. 2020;20(7):1925..

Pearson's correlation (r), coefficient of determination (R²) and other statistical parameters were determined using OriginLab Pro software, version 2021b.

3. Results and Discussion

According to literature³³33 Rovnaník P, Kusák I, Bayer P, Schmid P, Fiala L. Electrical and self-sensing properties of alkali-activated slag composite with graphite filler. Materials. 2019;12(10):1616.

34 Kim TU, Le HV, Park JW, Eock SK, Jang Y, Kim DJ. Development of a smart concrete block with an eccentric load sensing capacity. Constr Build Mater. 2021;306:124881.

35 Suchorzewski J, Prieto M, Mueller U. An experimental study of self-sensing concrete enhanced with multi-wall carbon nanotubes in wedge splitting test and DIC. Constr Build Mater. 2020;262:120871.^-3636 Ferdiansyah T, Turatsinze A, Balayssac JP. Design and characterization of self-sensing steel fiber reinforced concrete. MATEC Web Conf. 2018;199:11008. the applied force (compression) values and the fractional change in resistivity (FCR) obtained in the experiment are compared in the graphs of Figure 8, for each of the samples and repetitions, and a visual correlation analysis would be very subjective for qualifying the results, which is why a preliminary sensitivity analysis of the piezoresistive effect was performed.

Figure 8
Compressive force values and the FCR in each mix and repetition test for T1C (a, b, c), T2C (d, e, f), T3C (g, h, i) and T4C (j, k, l).

The sensitivity analysis was made from the relationship between the peak values of the compression force and the FCR, using Equation 5, as shown in Table 1.

Through the sensitivity relationship, it was possible to verify that the T2C and T3C samples had better results compared to the other samples. This is even clearer when presented graphically in Figure 9, with shows the mean values and their standard deviations (SD).

Figure 9
Mean sensitivity and standard deviations (SD) of samples.

Even though the sensitivity relationship analysis shows a better response of the T2C and T3C samples, it also makes evident the accentuated variations between repetitions. This is especially true for the T3C sample, with has a high standard deviation compared to the other samples.

In a preliminary linearity analysis, the graphs of Figure 10 were plotted, which visually show better results for the T2C and T3C samples, but also possible to the subjectivity of their interpretation.

Figure 10
Graphical relationship between FCR and compression force, with linear regression (line in red) in each mix and repetition test for T1C (a, b, c), T2C (d, e, f), T3C (g, h, i) and T4C (j, k, l).

The Pearson’s correlation values (r), based on the data in the graphs in Figure 8, and the coefficients of determination (R²) based on the data in the graphs in Figure 10, are shown in the graph in Figure 11. Although both coefficients (r and R²) have been plotted on the same graph, the direct comparison between them cannot be adequate because the first express values from -1 to 1, and the second from 0 (zero) to 1.

Figure 11
Pearson (r) and determination (R²) coefficients per sample.

The means and standard deviations of each coefficient (r and R²) for the samples tested are shown in the graphs in Figure 12, where again the best results for samples T2C and T3C are shown.

Figure 12
Mean and standard deviation per sample for each type of coefficient (r and R²).

The R² values obtained for the T2C and T3C samples are close to those found in the literature avaliable⁴⁶46 Chen M, Gao P, Geng F, Zhang L, Liu H. Mechanical and smart properties of carbon fiber and graphite conductive concrete for internal damage monitoring of structure. Constr Build Mater. 2017;142:320-7., while the low correlation of the T1C sample is justified by the absence of graphite and that of the T4C sample by the excess of graphite, which is also valid to justify the results obtained with the Pearson analysis.

For the final visualization of the results, each sample was ranked for each of the analyzes performed according to the table in Figure 13a, and each sample was spatialized according to the values of each parameter obtained, as shown in the graph in Figure 13b.

Figure 13
Ranking table of the results per sample for each analysis parameter (a); spatialization of the results of each parameter in each sample (b).

With the ranking shown (Figure 13a), the proportionality between the Pearson and determination coefficients becomes even more evident. Although they have different purposes, there is a quadratic relationship⁵⁷57 Realini TDA. Prospective, randomized, investigator-masked evaluation of the monocular trial in ocular hypertension or open-angle glaucoma. Ophthalmology. 2009;116(7):1237-42.^,5858 Martins M. Coeficiente de correlação amostral. Rev Cienc Elem. 2014;2(2):42. between them. This relationship is shown in Figure 14, which exposes the analytical values of Pearson starting in 0.01 and moving forward in centesimal fractions to 1.00. Then, the quadratic value of Pearson that corresponds to R², for each centesimal fraction, is plotted (Pearson versus R²). The experimental values of Pearson and R² of tested samples are plotted in the same graph (Figure 14), and are the same as the quadratic relationship analytical.

Figure 14
Analytical values (continuous line) and tested samples' values (dashed line) of Pearson versus R² and the difference between them; maximum difference (red line).

On the other hand, the graphic spatialization (Figure 13b) visually supported the best results obtained for T2C and T3C.

4. Conclusions

Based on the results obtained, it can be considered that for the conditions and cases analyzed, the Pearson’s coefficient has the potential to be used in the analysis of the correlation between changes in electrical resistivity and mechanical forces (or stress and strain) to verify the piezoresistive effect in self-sensing cementitious composites, although more studies are required to extrapolate these considerations to other cases and conditions.

We also saw that the higher the sensitivity, the standard deviation was higher too, which indicates that the repeatability was affected. But, in contrast to this, the correlation from Pearson (r) and determination (R²) coefficients did not show that the repeatability was affected, because the higher the coefficients, the smaller the standard deviation.

It is also possible to pronounce that:

1. 1

   The evaluation of piezoresistive effect should not be limited only to graphical analysis of the values of electrical and mechanical parameters. Although it is important, this may lead to subjective or even mistaken interpretations, when not compared to numerical analysis;

2. 2

   The correlation analysis by Pearson must be limited to the linear behavior range of the study otherwise, other methods must be used;

3. 3

   The use of the Pearson correlation method should not exempt analysis by the coefficient of determination (R²) method, because they have different purposes. But, the first does not have the influence of a quadratic relationship in the results. The quadratic relationship makes the difference between the coefficients be minimum when approaching 0 (zero) or 1 (one) and maximum, when approaching 0.5 (half), as shown in Figure 14.

Determination of sensitivity, a relationship between FCR and stress, is also an important way of evaluating the self-sensing composite, although it has been observed (Figure 13) that few the sensitivity of the T4C-1 sample did not directly impact the bivariate correlation, as this sample obtained the 3rd position in the ranking of the Pearson and determination (R²) coefficients.

Lastly, both graphic and numerical evaluations (sensitivity and correlation coefficient) must be present in the analysis of the piezoresistive effect in self-sensing cementitious composites because, together, they allow a better interpretation of this effect.

5. Acknowledgments

CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), Brasil - Financing Code 001; CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) - Prof. Luísa Andréia Gachet (310375/2020-7; 406234/2018-3) e Prof. Rosa Cristina Cecche Lintz (310376/2020-3).

6. References

Publication Dates

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