**2. Overview of the Coordinate System**

As standard with coordinate systems, the one developed for games in [JS1] can be adjusted to meet other needs. The choice given here [JS2] reflects central features of potential games.

Consider an arbitrary 2 × 2 game G (Table 1), where each agent's strategies are labeled +1 and −1 (cells also will be denoted by TL (top-left), BR (bottom-right), etc.).

**Table 1.** Arbitrary Game G in Normal-Form.

A weakness of this representation is captured by the Table 2 game. Information about which strategy each player prefers, whether they do, or do not want to coordinate with the other player, and where to find group opportunities is packed into the entries. Yet, in general, this structure is not readily available from the Table 2 form.

The coordinate system described here significantly demystifies a game by unpacking its valued behavioral information. This is done by decomposing a game into four orthogonal components, where each captures a specified essential trait: individual preference, individual coordinative pressures, pure externality (or Behavioral), and kernel components (see Table 3) (the orthogonality comment follows by identifying games with vectors). The original game is the sum of the four parts.

**Table 3.** The Four Components of a 2 × 2 Game.

To associate these components with behavioral traits of any 2 × 2 game, the individual preference component identifies an agent's inherent preference for strategy +1 or −1. If *αi* > 0, then agent *i* prefers strategy +1 to −1 *independent* of what the other agent plays. In turn, *αi* < 0 means that agent *i*'s individual preference is for strategy −1. The Table 2 values will turn out to be *α*1 = 2, *α*2 = 3, which indicates that both players prefer +1 (or TL).

The coordinative pressure component *γj* reflects a conforming stress a game imposes on agent *j*. Independent of the *αi* sign, a *γj* > 0 value rewards agent *j* a positive payoff by conforming with agent *i*'s preferred *αi* choice. Conversely, when *γj* < 0, agent *j*'s payoff is improved by playing a strategy different than what agent *i* wants. With Table 2, *γ*1 = −3 while *γ*2 = −1, so neither player is strategically supportive of personally reinforcing the other agent's preferred choice.

The pure externality component represents consequences that an agent's action imposes on the other agent.3 If agent *i* plays +1, for instance, then, independent of what agent *j* does, agent *j* receives an extra *βj* payoff! Acting alone, however, agent *j* is powerless to change this portion of the payoff. To see why this statement is true, should Column select L in Table 3c, then no matter what strategy Row chooses, this extra advantage remains *β*1. The sign of *βj* indicates which of agent *i*'s strategies contributes to, or detracts from, agent *j*'s payoff. In Table 2, the *β*1 = −3, *β*2 = 2 values convert TR into a potential *group* opportunity.

A subtle but important behavioral distinction is reflected by the *γ* and *β* terms. The *γj* values capture whether, in seeking a personally preferred (Nash) outcome, an agent should, or should not, coordinate with the other agent's preferred interests. In contrast, the *βj* values identify externalities and opportunities to encourage both to cooperate. For a supporting story, suppose the strategies are to take highway 1 or −1 to drive to a desired location. A *γ*1 < 0 value indicates the first agent's personal preference to avoid being on the same highway as the second. However, it should it be winter time, then the second agent, who always has a truck with a plow when driving on highway 1, creates a positive externality that can be captured with a *β* value.

The final component is the kernel, which for Table 2 is *κ*1 = 1, *κ*2 = 3. This can be treated as an inflationary term that adds the same *κi* value to each of the *ith* agent's payoffs. Methods that compare payoffs cancel the kernel value, so, as in this paper, the kernel can be ignored.

It is important to point out that the individual and coordinative pressure components contain all information from a game that is needed to compute the Nash equilibrium and to analyze related strategic solution concepts [JS1]. To appreciate why this is so, recall that the Nash information relies on payoff comparisons with unilateral deviations. But with the pure externality and kernel components, all unilateral payoff differences equal zero, so they contain no Nash information. This also means that "best response" solutions and methods ignore, and are not affected by the wealth of a game's *β* information (for explicit examples, see [11]).

By involving eight orthogonal directions and independent variables, these components span the eight-dimensional space of all 2 × 2 games. Consequently, any 2 × 2 game can be expressed and analyzed in terms of these eight coordinates. The equations converting a game into this form are

$$\begin{array}{llll} \alpha\_{1} = \frac{1}{4}[(a\_{1} + a\_{3}) - (a\_{2} + a\_{4})], & \alpha\_{2} = \frac{1}{4}[(b\_{1} + b\_{3}) - (b\_{2} + b\_{4})], & \gamma\_{1} = \frac{1}{4}[(a\_{1} + a\_{4}) - (a\_{2} + a\_{3})],\\ \gamma\_{2} = \frac{1}{4}[(b\_{1} + b\_{4}) - (b\_{2} + b\_{3})], & \kappa\_{1} = \frac{1}{4}[a\_{1} + a\_{2} + a\_{3} + a\_{4}], & \kappa\_{2} = \frac{1}{4}[b\_{1} + b\_{2} + b\_{3} + b\_{4}],\\ \beta\_{1} = \frac{1}{2}[a\_{1} + a\_{2}] - \kappa\_{1}, & \beta\_{2} = \frac{1}{2}[b\_{1} + b\_{2}] - \kappa\_{2}. \end{array}$$

For interpretations, *κj* is agent *j*'s average payoff, *βj* is agent *j*'s average payoff should the other agent play 1 minus the inflationary *κj* value, *αj* is half the difference of agent *j*'s average payoff if the other agent plays 1 and the average if the other agent plays −1, and *γj* is half the difference of the *jth* agent's average TL, BR payoff, and average BL and TR payoff.

To illustrate the derivation of Equation (1), the *α*1 value of the Table 4a game is computed. All that is needed is a standard vector analysis to find how much of game G is in the *α*1 coordinate direction, which is denoted by G*α*1 , where *α*1 = 1 and *α*2 = 0. The sum of the squares of the G*α*1 entries (which in the following notation equals [G*α*1 , G*α*1 ]) is 12 + 02 + 12 + 02 + (−1)2 + 02 + (−1)2 + 02 = 4, so, according to vector analysis, *α*1 = 1 4 [G, G*α*1 ]. Here, [G, G*α*1 ] is the sum of the products of

3 This is the behavioral component in [JS1].

corresponding entries from each cell. (Identifying a game's payoffs with components of a vector in R8, [G1, G2] is the scalar product of the vectors.) In this example, [G, G*α*1 ]=(12)(1)+(10)(0)+(2)(1) + (2)(0)+(0)(−1)+(4)(0)+(6)(−1)+(0)(0) = 8,, so *α*1 = 1 4 [G, G*α*1 ] = 2.. Similarly, by defining a corresponding G*α*2 , G*γ*1 , ... ,, the remaining values are *α*2 = 3, *γ*1 = 4, *γ*2 = 1, *β*1 = 1, *β*2 = 2, *κ*1 = 5, and *κ*2 = 4. The Equation (1) expressions can be recovered in this manner.

This decomposition simplifies the analysis by extracting the portion from each payoff that contributes to these different attributes of a game. Illustrating with Table 1, rather than handling each entry separately, behavior can be analyzed with the separated impact of the components. For instance, the *a*1 entry is *a*1 = *α*1 + *γ*1 + *β*1 + *κ*1, which, for Table 2, is *a*1 = −3 = 2 − 3 − 3 + 1.

To connect this notation with [JS1], [JS2], a game's Nash component, denoted by G*N*, is the sum of the individual preference and coordinative pressure components as given in Table 5.

**Table 5.** The G*N* Nash component.

Principal facts about 2 × 2 games follow.4 As a reminder, a game is a potential game if there exists a global payoff function that aggregates the unilateral incentive structure of the game. More precisely, the payoff difference obtained by an agent unilaterally deviating is reflected in the change of the potential function. Potential games are often called "common interest" games. *Coordination games* have pure strategy Nash equilibria precisely where the agents play the same strategy (i.e., the strategy profiles (+1, +1) and (−1, −1)). On the other hand, *anti-coordination games* have pure strategy Nash equilibria when the agents play different strategies (i.e., the strategy profiles (+1, −1) and (−1, +1)).

**Theorem 1.** *Generically (that is, all* G*N and βj entries are nonzero), the following hold for* 2 × 2 *normal form games* G*.*

$$
\pi\_1(t\_1, t\_2) = a\_1 t\_1 + \gamma\_1 t\_1 t\_2 + \beta\_1 t\_2 + \kappa\_1 \text{ and } \pi\_2(t\_1, t\_2) = a\_2 t\_2 + \gamma\_2 t\_1 t\_2 + \beta\_2 t\_1 + \kappa\_2 t\_2
$$

*where t*1 *and t*2 *represent the strategy choice (either* +1 *or* −1*) of agents 1 and 2,*

*5. A potential function for a game with components described in Table 3 can be transformed into*

$$P(t\_1, t\_2) = a\_1 t\_1 + a\_2 t\_2 + \gamma t\_1 t\_{2\prime} \text{ where } \gamma = \gamma\_1 = \gamma\_2. \tag{2}$$

4 All of these results extend to 2 × ... × 2 games.


**2. Materials and methods**

#### **2.1 Collection of samples**

Blood samples of 80 colon cancer patients (aged 40–80 years) who attend the Teaching Oncology Hospital at the City of Medicine and the National Center for Oncology, Baghdad for the period (18-2-2018 to 28-2-2019), were obtained.

A total of 50 blood samples were collected from apparently healthy individuals as a control group (aged 40–80 years). The samples were collected by drawing blood from the vein (5 mL) using a syringe and placing the blood in a gel tube.

The tubes were placed in the centrifuge at 1252 g for 10 minutes to obtain serum. The serum was kept by Eppendorf tube in deep-freeze at 20°C until testing.

#### **2.2 Measuring the LOX activity in blood serum**

The method of measuring the activity of the LOX enzyme [24] is based on stimulating the oxygen reaction with the unsaturated fatty acids containing (cis, cis 1.4-pentadiene). It consists of a sequential system of double bonds that increase absorption at a wavelength of 234 nm where the absorption intensity is directly proportional to the concentration of the enzyme [25]. The unit of enzyme is defined as the amount of enzyme that changes in absorbance by 0.001 / sec at wavelength 234 nm under ideal conditions.

#### **2.3 Estimation protein concentration**

The biuret method was used to estimate the concentration of the protein in the samples [26].

#### **2.4 Separation and purification of LOX from serum patients of colon cancer**

LOX is purified using the following steps:


*1.2. Approaches of Thermal Image-Based Canopy Extraction*

Canopy extraction approaches incorporating thermal imagery include methods that use a single thermal infrared image (1-source) and other methods that use a thermal infrared image and additional remotely sensed images, usually RGB (multi-source). One-source methods include purely threshold-based statistical analysis on the one hand and coupled statistical and spatial analyses on the other hand. Statistical analysis of a temperature histogram to identify canopy pixels within a thermal image has been performed in orchards [11,12] where canopy can be distinguished from soil. In such cases, temperature histograms are characterized by a bimodal distribution, where the canopy and soil pixels are represented by cooler and warmer peaks, respectively. Mixed pixels, which include combinations of canopy, soil, weeds, foreign objects, and shade in a single pixel, are generally composed of a "saddle" area between the two peaks. Depending on the crop architecture, the distance between plants, the degree of complexity, and pixel resolution, there can be significant overlap between mixed pixels, pure-canopy pixels, and pure-soil pixels, creating a challenge in identifying pure-canopy pixels. Additionally, water-stressed trees may have higher canopy temperatures and could be misidentified as mixed or soil pixels [13].

An additional group of 1-source methods incorporates statistical and spatial analyses of a single thermal image. Spatial watershed segmentation has been coupled with binary thresholding to extract pure-canopy pixels in palm trees [14] and in vineyards [15]. Camino et al. [16] incorporated watershed segmentation and quartile histogram analysis in an almond orchard. Superpixel algorithms are used to differentiate meaningful regions of interest in an image [17], such as tree crowns in a forest system [18] and fruit detection in orchards [19]. In peach orchards, one technique involved thresholding to remove noncanopy pixels and then morphological erosion to remove mixed pixels and to extract pure-canopy pixels [20]. A second method used edge detection algorithms followed by morphological dilation to remove mixed pixels [21]. Additional methods include delineation of regions of interest of a single canopy [2] as well as pure edge detection analysis [22]. The incorporation of two types of analyses, statistical and spatial, on thermal images alone has been claimed to improve the quality of canopy extraction in comparison to merely statistical-based analysis [23].

In general, multi-source methods are based on statistical analysis of a visible (RGB) or multispectral image to extract canopy pixels, which is then used as a binary mask that is superimposed on a thermal image. This technique has been implemented in crops including potato [9], mint [24], and grape [25]. Additional feature layers, such as maps of irrigation pipes, can be incorporated to improve canopy extraction [26]. However, poor overlap of RGB and thermal images can cause misidentification of canopy pixels.

Currently, there are many methods of canopy extraction, but, to the best of our knowledge, there is no comprehensive quantitative comparison of canopy extraction methods in the context of orchard water status estimation. Thus, the decision of which canopy extraction method to incorporate and how to calculate canopy temperature may be arbitrary and not based on experimental data. Accurate canopy extraction and temperature calculations are crucial to minimizing inaccuracies in thermal image-based estimation of orchard water status that may directly affect irrigation decisions. This study tested the hypothesis that thermal image-based orchard water status estimation is significantly sensitive to the canopy extraction quality and to the temperature calculation approach. The objective was to determine the sensitivity of thermal image-based orchard water status estimation to canopy extraction methodology and quality. Four canopy extraction methods were evaluated. Three methods followed the 1-source approach (thermal images), incorporating both statistical and spatial analyses: (1) 2-pixel erosion (2PE), where non-canopy pixels were removed by thresholding followed by morphological erosion; (2) edge detection (ED), where edges were identified and then morphologically dilated; and (3) vegetation segmentation (VS) using statistical analysis of the temperature histogram followed by spatial watershed segmentation. A fourth method, denoted RGB-BM, followed the multi-source approach and used an RGB image to statistically extract a binary canopy layer to mask the thermal image. Additionally, two approaches to canopy temperature calculation were assessed by calculating the following: (1) the average of 100% of canopy pixels (T100%), and the average of the coolest 33% of canopy pixels (T33%).

#### **2. Materials and Methods**

#### *2.1. Research Area*

A field experiment was conducted during the 2019 season in a 4 ha commercial lateharvest peach orchard (Prunus persica cv. 1881) located near Mishmar Hayarden, Israel (33.01◦N; 35.60◦E) (Figure 1). The elevation of the orchard ranges from 171 to 188 m above sea level, the average slope is 5% to the northwest, and within the orchard, the slope ranges from 0 to 11.3%. The orchard was planted in 2007 with spacing of 2.6 m and 5 m between trees and rows, respectively, and was divided into 22 management cells (MC) of 35 m × 35 m to monitor various orchard parameters, including canopy area and SWP. A precision drip irrigation regime was implemented in the north subplot (MC 1–11), while the south subplot (MC 12–22) was uniformly irrigated. A detailed description of the irrigation design of the entire orchard and the decision-making process in the north subplot using thermal image-based tree water status estimation following the 2PE canopy extraction method is reported in [27]. The experiment was conducted during stage III of

fruit development, which is the primary stage of fruit growth and period when most of the annual irrigation is applied.

**Figure 1.** Mishmar Hayarden peach orchard (green line) divided into 22 management cells (MC) (black dashed squares).

The major steps of data acquisition and analysis are presented as a flow chart in Figure 2.


*3.2. FTIR Spectera*

The infrared analysis spectra of the applied fly ash are shown in Figure 2. The figure shows several peaks at 428 cm−1, 532.64 cm−1, 733.22 cm−1, 1253.53 cm−1, 1663.95 cm−1, 3222.98 cm−1, and 3782 cm−1. Absorption bands at 733.22 cm−1, 532.64 cm−1, and 428.59 cm−1 were labelled as O Si O links in quartz, and Si O and Al O bonds in zeolite frameworks, and the band surrounding 1000−960 cm−1 represents bonds of Si–O–T (T is tetrahedral Si or Al) of the geopolymer gel. Absorption bands at regions at 450 cm−1 can represent Si–O–Al linkage; Si O bond characterizes to bending vibration at 400−500 cm−1, and the stretching vibration at 800−1000 cm−1. Although, absorption bands in regions at 980 cm−1 can be related to O–Si–O bond bending vibration, or symmetric stretching vibrations of the Si–O–Si (Al) bridge [15,16].

**Figure 2.** FTIR spectrum of fly ash.

The asymmetric stretching vibrations of the silicon tetrahedral (SiO4-4) found in the chain structure of the Si-O terminal bonds can also be attributed to several additional bands found in regions around 1253.53 cm−1 [17]. Meanwhile, the stretching vibration of O-H and H-O-H due to water and silanol group occurs within a range of 3222.98 cm−1 to 3782 cm−1. This indicates a stretching vibration of O-H and H-O-H from 82 water molecules which are weakly bonded that appear at the surface, or are trapped in a large cavity inside the geopolymer sample. In addition, a wavenumber of 1664.95 cm−1 represents bending vibration of H-O-H.

Meanwhile, infrared analysis spectra for the geopolymer concrete are illustrated in Figure 3. The result shows observation at peak 3775.37 cm−1, 3454.07 cm−1, 1638.68 cm−1, 1544.29 cm−1, 1411.56 cm−1, 1062.90 cm−1, and 671.18 cm−1.

**Figure 3.** FTIR spectrum of geopolymers.

The intensity of absorption bands at 671.18 cm−1 is connected to the stretching vibration of the Si-O-Si symmetry and the bending vibration of the O-Si-O bonds (Al) [17]. The size of these bands is due to the material being amorphous. There is also a vibration band for the stretching of Si-O-A at 1062.90 cm−1. The Si-O-Al was determined by the peaks found between 700 and 1100 cm−1 [18]. In the peak from 1400 to 1450 cm−1 it was noticed the temperature rose to 1000 ◦C. As the peak shifted to 1411.56 cm−1, the strength of the composite decreased. The band at 1411.56 cm−1 displays the feature of the asymmetric O-C-O stretching mode, which shows the existence of sodium carbonate due to the interaction between too much sodium and ambient carbon dioxide [19].

Three bands located at 1638.68 cm−1, 3375.37 cm−1, and 3454.07 cm−1 were associated with the water molecules. As a result of the inclusion of nanoparticles, the overall spectra also demonstrated an increase in the intensity of the Si-O-Al band, suggesting a rise in the quantity of N-A-S-H gel [20]. Simultaneously, the frequency moved to a higher wavenumber at 1544.29 cm−1 as rising solid/liquid ratios, which suggested calcite vibration. Calcite and amorphous silica were produced when tobermorite decalcified, which caused the wavenumber to change [21]. Peak calcium-based component intensity demonstrated the dominance of high strength geopolymer structure.

## *3.3. Compressive Strength*

Fiber reinforced geopolymers at 28 days, as well as Geopolymer concrete with nylon66 fiber (NF) reinforcement's compressive strength for both samples at 28 and 90 days. The compressive strength of geopolymer concrete appears to increase with plastic fiber addition, up to a maximum value at 0.50% of fiber addition. This is because nylon66 fibers, which restrict cracks from spreading during compression loads, and linked interlocking plastic beads act as reinforcing agents by interlocking with each other in the aggregate skeleton. The main strategy used in this study is to fill the spaces between the fine and coarse aggregate with beads to give them an interlocking strength using a linked plastic system, as illustrated in the schematic picture in Figure 4. The weak interfacial connection between the matrix and the fiber caused by hydrophobic surface characteristics was significantly improved by the linked interlocking plastic beads. As a result of the nylon66 fibers' contribution, the geopolymer binder slid out of the nylon66 fibers' diamond-shaped ends with greater resistance than the straight fiber without anchorage.

**Figure 4.** The chained interlocking plastic beads schematic diagram illustrated.

The compressive strength of geopolymers with fiber addition is depicted in Figure 5. The results demonstrate that fly ash geopolymers without nylon66 fiber addition have higher strengths, and the strength starts to decrease with the inclusion of nylon66 fiber. Even though the reduction in strength is about 35% at 0.50v% fiber addition, the strength obtained is still notably higher (35.59 MPa). According to the results, adding nylon66 fiber or linked interlocking plastic beads did not improve the compressive strength properties of geopolymers. The interfacial connection between the matrix and fiber is believed to be weak due to the smooth or hydrophobic surfaces of the polymers, and the fiber cannot inhibit the spread of cracks in geopolymers. However, some regions in the geopolymer matrix that include nylon66 fibers are believed to fill the voids between fly ash particles with beads to give them an interlocking strength and contribute to good strength. Insertion of fiber greater than 0.50% disturbs the CASH bonding in the geopolymer matrix and diminishes its compressive strength. According Patrycya et al. [22], the optimum result obtained on geopolymers reinforced with hooked-end steel fiber and melamine fiber was circa 0.5% amount of fiber by weight. The result shows that plain GPC is 40 MPa; steel fiber 0.5% is 40 MPa, and 1.0% is 39 MPa; and melamine fiber 0.5% is 50 MPa, and 1.0% is 45 MPa. Melamine fiber has better resistance to force. Based on the research, fiber shape gave an effect to the compressive strength on geopolymers; hooked-end type steel fiber held the matrix with greater force during crack propagation [23]. The schematic function of fiber that was used in this study for the geopolymer concrete was illustrated previously in Figure 4. The addition of nylon66 fibers' (ICPB) diamond shape on reinforced geopolymers was intended to investigate the effect on the compressive strength between GP and GPC.

Figure 6a depicts the compressive strength of Nylon66 Fiber Reinforced Geopolymer Concrete (NFRGC) after 28 days of room temperature curing. It was discovered that adding 0.5% of fiber resulted in a higher compressive strength with a value of 67.6 MPa, which then decreased to 53.3 MPa with the addition of fiber at 2.0%. Geopolymer concrete has a high compressive strength, and suitable fiber addition as well as fiber type were discovered to increase properties depending on the application. Chained interlocking plastic-bead fibers increase the strength of NFRGC as compared to geopolymers. This is due to the capacity of Nylon66 fibers to delay the spread of cracks during compression loads. This can be attributed to RTS fiber's high stiffness and hydrophilicity, which allow it to absorb more energy and form a strong fiber-matrix interaction [23,24].

**Figure 5.** Compressive strength of geopolymers.

**Figure 6.** (**a**) Compressive strength of NFRGC for 30 days and (**b**) Compressive strength of NFRGC for 90 days.

Since Nylon66 fiber has a lower young modulus than steel fiber, increasing fiber addition in geopolymers results in a negative trend in concrete. As additional fiber is added, the compressive strength decreases while the toughness increases due to the higher elasticity of nylon66 fiber over geopolymer concrete. Fiber length influences compressive strength or toughness strength, and research has shown that short fiber is ideal for these qualities as well as to avoid microcrack propagation. Composites with an irregular internal structure resulted in reduced compressive strengths and variable compressive behaviour. As a result, the incorporation of metallic fibers could improve the mechanical properties of GPC, whilst the high fraction of nylon66 fibers in GPC could lower its mechanical performance. The substantial standard deviations of the findings of the hybrid replacement series with more fiber made this apparent. Meanwhile, Figure 6b illustrates the NFRGC's compressive strength after 90 days.

The compressive strength of NFRGC is affected by the curing period. After 90 days, the compressive strength of the NFRGC has increased in comparison to 28 days. After 90 days, the compressive strength increased to 70.13 MPa, from 67.6 MPa at 28 days, with the addition of 0.5% fiber. However, once the fiber inclusion exceeds 0.5%, the compressive strength of geopolymers decreases. When the NF volume exceeds 0.5%, the decrease in compressive strength is primarily due to the difficulty of fiber distribution, especially in large volume fractions, which is caused by poor workability and inadequate compaction. In contrast, NFRGC with the lowest nylon66 fiber concentration achieved the highest compressive strength, owing to the mechanical properties of nylon66 fiber. The fibers in concrete contributed to energy dissipation via the bridging effect of their shape and mechanical properties. The frictional bonding that develops as a result of the resistance to pulling out the nylon66 fibers, caused by friction between the fibers and the geopolymer matrix, contribute to the NFRGC's high strength [25].

In addition, as the fiber content increased to 1%, compressive strength decreased substantially from 70.13 to 57.5 MPa. This is believed to be attributed to the material's poor compaction and significant voids. Due to the material's high degree of flexibility, high volume fractions of Nylon66 fiber make compaction difficult, resulting in a loose and porous geopolymer matrix. The relative density of fiber-reinforced geopolymer composites, on the other hand, was decreased by adding more fibers. This is due to the fact that the air bubbles caused by imperfect vibration in the composite products caused the relative density to increase. This condition hinders the consolidation of the fresh mixture, and even the long exterior vibrations are ineffective at compacting the concrete. As observed, an increase in fiber content above 2% has a negative impact on composite density.

The compressive strength of fiber reinforced concrete increased initially and subsequently declined as the nylon66 fiber content grew from 0% to 2%, with a 0.5% optimal point where the internal structure of geopolymer concrete was considerably enhanced. The main factor causing the decline in compressive strength when the NF percentages are more than 0.5% is the difficulty in dispersing fiber, especially in large volume fractions, which contributes to poor workability and insufficient compaction [26].

Judging by previous work, there are no studies focusing on Nylon as fiber in concrete. However, other types of fiber such as PP and PF were the guidance in this research. According to Wang et al. [27] the compressive strength of polypropylene (PP) fiber reinforced geopolymer concrete with fiber length of 12 mm was observed to be slightly higher than that of 3 mm. The fiber type was straight fibers. Longer fibers performed better in terms of bridge effects because of the increased contact area between them and the geopolymer concrete, which led to a greater frictional force. In comparison to shorter strands, longer fiber could connect more air spaces. This research shows that effect of length contributes to the contact area and helps improve the bonding of polymer fibers and geopolymers. Compared to our study using long fiber, short fiber can also be improved by size and shape.

Piti et al.'s [2] study used the PF crimped type in fiber reinforced geopolymers, based on the compressive strength result that 0.5% fiber content is the optimum result. The plain geopolymer's strength was 40.08 MPa, and the strength improved to 47.0 MPa after being reinforced by fibers at 0.5%. This illustrated that the trend of compressive strength was decreased to 34.49 MPa at 1.0% and so on.

According to Ranjbar et al.'s [15] investigation on the mechanisms of interfacial bond in steel and polypropylene reinforced geopolymer composite, after curing PF reinforced geopolymers for 56 days, the compressive strength of the plain geopolymers was the highest compared to others with fiber added. They illustrated that 0.5% content was the best, with 45 MPa compressive strength, compared with 1%, 2%, 3%, and 4% contents.

The compression results between 28 and 90 days followed the same pattern as the optimal result, indicating that a fiber content of 0.5% is the best result. The 90-day outcome was somewhat enhanced due to the geopolymers themselves. Curing time and temperature are significant factors in the hydration process of geopolymerization, with higher temperatures accelerating the hydration process and contributing to the geopolymer's high strength. An extended curing period, however, influences the performance of geopolymers. In this instance, curing time enhances the compressive strength of geopolymers. The addition of NF reinforced in fly ash-based geopolymers progressively causes a geopolymer bonding reaction in the NFRGC, and the interlocking between the fiber, aggregate, and geopolymer matrix gets better with time.

The failure mode of the NFRGC cube when compressed is shown in Figure 7. All NFRGC specimens maintained their forms with little debris even after compressioninduced failure, which is often characterized by evident large fissures.

Figure 7a shows the geopolymer concrete breaks into parts due to the brittle properties of geopolymer concrete. The fibers provided greater energy for resisting tensile tension in the cube, which prevented tensile fracture growth. Without fiber, geopolymer concrete can withstand the high load of energy. Addition of nylon66 fibers make the major crack propagation directly occur without displaying signs of crack growth prior to breakage.

In comparison to geopolymer concrete without fiber addition, 0.5% has the highest compressive strength of all results, despite having significant fracture propagation. The addition of fiber improves geopolymers' ability to absorb energy, and the interlocking plastic beads aid in limiting crack propagation, resulting in the major crack spreading from the minor crack after 0.5% fiber was added. The inclusion of more fibers reduces compressive strength; however, crack propagation was decreased from major to minor due to the energy supplied into the fibers during the compression test to slow or stop the crack growth. The tensile strength was only slightly different from the value reported in the work of Arsalan et al. [25], which included NF as a fiber addition to the concrete mix. In addition to selecting the proper fiber fraction, geopolymer concrete must also have equally distributed fibers in order to achieve the desired amount of strength.

During the compressive test, the greater fiber volume controlled the development of cracks. Geopolymer density decreases as fiber volume increases, whereas compressive strength and toughness increase. With the interlocking chain fiber, it is feasible to reduce energy transmission from the geopolymer concrete itself. It exchanges energy with the fiber to slow the spread of cracks. Nylon66 fiber can restrict the spread of cracks in geopolymer concrete, as shown in Figure 7e. It exhibits the symptoms of material breakdown as the crack spreads.

**Figure 7.** Crack pattern of geopolymer concrete (**a**) without fiber, (**b**) 0.5%, (**c**) 1.0%, (**d**) 1.5%, and 2.0% (**e**) with a schematic of failure mode.