*3.3. Rheological Measurements*

The rheological properties were characterized by using Rheometer MCR302 (Anton-Paar) while Rheoplus software was used to monitor and analyze the data points. To determine the rheological characteristics of the GNP–cement paste, smooth parallel plates with a gap thickness of 0.6 mm were used. At first, approximately 15 mL of GNP–cement paste was added on the plate having diameter 25 mm at a fixed temperature of 25 ◦C. The cement paste was held at rest and after 10 min it was pre-sheared at a shear rate of 100 s<sup>−</sup><sup>1</sup> for 60 s. This was done to re-homogenize the sample, as cement paste has thixotropic character [25]. Then, after 5 min, shear rate was applied from 0.6 s<sup>−</sup><sup>1</sup> to 100 s<sup>−</sup><sup>1</sup> and then back from 100 s<sup>−</sup><sup>1</sup> to 0.06 s<sup>−</sup><sup>1</sup> in 20 decreasing steps. The downslope curve data was used for calculation of rheological parameters. Similarly, GNP–cement paste was also run for two different shear rates cycles, i.e., from 200 s<sup>−</sup>1–0.6 s<sup>−</sup><sup>1</sup> with 40 steps and 300 s<sup>−</sup>1–0.6 s<sup>−</sup><sup>1</sup> with 60 steps. The flow properties were also determined at different time interval, i.e., 0 min, 30 min and 60 min. For 30 and 60 min resting time, the samples were manually stirred for 15 s before measuring the rheological data. It is pertinent to mention here that the effect of graphene and its content on the rheology of cement paste was investigated by using mix M0, GM3, GM5 and GM10, while to examine the influence of different shear rate cycle range (100–0.6 s<sup>−</sup>1, 200–06 s<sup>−</sup><sup>1</sup> and 300–0.6 s<sup>−</sup><sup>1</sup> represented by symbols a, b and c respectively) and different resting times (0, 30 and 60 min time between sample preparation and casting) on rheological properties, only M0 and GM3 mix were used. The detailed description about the shear rate cycle range and resting time of various samples for measuring rheological data is given in Table 3. All measurements were repeated with identical samples for three times and averaged. The apparent viscosity, shear stress and shear rate of GNP–cement paste with different proportions were measured by the rheometer while the yield stress and plastic viscosity of the GNP–cement paste was determined by using the Bingham, Modified Bingham, Herschel–Bulkley and Casson models.


#### *3.4. Test Setup for Electrical Properties*

The four-probe method was used to determine the piezo-resistive properties of the GNP–cement composite specimens. Four-probe method involves four electrical contact points in which voltage is measured through the inner two electrical contacts while the current is measured using outer two electrical contacts. [26] Four-probe method is better than the two- probe method because measured resistance does not include the contact resistance [27]. According to Han et al. [27], the space between the current pole and voltage pole is very important. However, its influence is marginal if space is more than 7.5 mm. Various researchers used different spacing in their experimental work. Li et al. [28] used the spacing of 10 mm while Le et al. [29] used 40 mm spacing between current and voltage measuring probes. Similarly, the distance between the two voltage measuring probes is not fixed and its value varies. Li et al. [28] used the 40 mm gap between two measuring probes while Le et al. [29] used 80 mm gap. As resistivity values remain unaffected provided that the spacing is above threshold value [27], in this research, we used 40 mm spacing between the current measuring probe and voltage measuring probes and 60 mm between two voltage measuring probes. Pang et al. [30] explored the effect of percentage of graphene nanoplatelets on the strain and damage sensing of the composites. They found that with increase in the percentage of graphene nanoplatelets in cement based composite, the fractional change in resistance values was also increasing. Therefore, based on the study of Pang et al. [30], only M0 and GM3 specimens were considered to explore the electric resistivity of cement based composite materials.

The setup for measuring the electrical resistivity consist of Instron 600 kN machine used for applying a compressive load, TDS-530 data logger to record the voltage measurements, a DC power supply and 10-ohm resistance. Specimens were placed in Instron machine and a constant voltage of 15 V through DC power supply was applied to the samples (Figure 1a). Inner wire meshes were connected to the data logger and measures the voltage drop in V. Meanwhile, one of the outer wire meshes was connected to the negative terminal of the power supply and the remaining outer wire mesh was connected to the resistor followed by the connection to the second channel of the data logger and positive terminal of the power supply forming a series circuit. Finally, the practical application of these GNP–cement composite specimen was investigated by testing the reinforced concrete (RC) beam having cross-sectional dimension 200 × 300 (mm) and span length 3200 mm. For this purpose, GM3 specimen was placed inside the beam in center at the time of beam casting as shown in Figure 1b,c. The beam was tested under flexural loading using Instron 600 kN and response of the GNP–cement composite specimen was recorded using 15 V DC power supply and TDS 530 data logger. The test setup is shown in Figure 2c.

**Figure 2.** Measurement of electrical properties (**a**) The overall set up for the four-probe method for the electrical properties testing; (**b**) placing of the specimen into the Instron 600 kN machine; (**c**) sample failure under compression; and (**d**) propagation of cracks in failed sample.

## **4. Results and Discussion**

#### *4.1. Rheological Characteristics of GNP–Cement Composite*

Variation in rheological characteristics of both cement paste and graphene–cement paste were observed, which originates due to mix composition of the paste, shear rate cycle, resting time and rheological model. As these rheological methods determine the flow property values from statistical trials, several values can be obtained. However, in this research, best curve fitting and minimizing the standard error was considered in determining the rheological flow values. The effect of mix composition mainly includes water to cement ratio, admixture, mixing and testing technique [31]. As these parameters were studied in detail [9,31], all these factors were kept constant and only effect of graphene/cement ratio, shear rate range, and resting time was investigated. Moreover, the parallel plates, whose results are close to reality, were used to determine the rheological characteristics of cement based composites [2]. However, particle sedimentation or "creaming" occurs more in the parallel plate, which may contribute to increase the viscosity [32].
