Behavior of Macro-Synthetic Fiber-Reinforced High-Strength Concrete Beams Incorporating Bacillus subtilis Bacteria

High-strength concrete incorporating macro-fiber combines high compressive strength of the matrix, strain-hardening, and multiple crack characteristics. Also, calcite sediment remediation bacterial techniques can enhance the mechanical properties, reduce concrete deterioration, and prevent corrosion of steel reinforcement in both the short-term and long-term. In this paper, The Bacillus subtilis bacteria at an optimum dosage of 10 5 cells/ml of mixing water was incorporated into M60 and M80 concrete strengthened with 0.5% macro synthetic-fiber content. The performance of 32 simply supported reinforced concrete beams with rectangular-section were evaluated numerically using ANSYS. In this study, the properties of matrix components are considered for different geometric sizes as slender and short beams with different longitudinal reinforcement ratios. The results showed that the bacterial participation in fibrous concrete beams had more significant enhancement in the initial cracking load, ultimate load, moment capacity ratio, ductility ratio, and flexural toughness compared to associated conventional concrete. Software and Formal anlysis, A Ghoniem; Investigation, A Ghoniem and L Aboul-Nour; Writing - original draft, A Ghoniem; Writing - review & editing, A Ghoniem; Visualization, A Ghoniem; Supervision, H Hassan and L Aboul-Nour.


INTRODUCTION
The cracks in concrete structures are predictable due to deterioration throughout their service life through various load combination factors. For that reason, there is a need for a product that generates multiple micro cracks and repairs it to prevent the cracks from propagating. This article deals with the Fiber-Reinforced Bacterial Concrete (FRBC), which is defined as fiber-reinforced concrete self-repaired by bacteria. The produced FRBC presents a further step development of construction materials with both performance and sustainable service life (Karimi and Mostofinejad, 2020). Adopting the self-repairing mechanism produces smart infrastructure systems. Smart structures can provide a unique response of sensing and action that make concrete sustainable, durable, and protected against any aggressive environments without expensive maintenance (Li et al., 2019;Zhang et al., 2020). Also, the crack treatment affects the behavior of Fiber-Reinforced Concrete (FRC) beams due to improved adhesion between the fiber and the matrix. The increased frictional shear stress during the pull-out allows the full fiber anchorage utilization without the fiber rupture (Di Maida et al., 2018). The short macro-fiber distributed randomly in the matrix can bridge the crack width and also improve both fresh and hardened mechanical properties (Alberti et al., 2020).
The carbonate participation technique can regain original mechanical that enhances strength and durability properties in the short-term and long-term (Hizami Abdullah et al., 2018). However, the fiber could affect the concrete tensile strength only, bacterial self-repairing can enhance both compressive and tensile strength of Bacterial Concrete (BC). The CaCO 3 bacterial participation can heal both micro/macro-cracks of the cracked section and voids of the uncracked section by reducing the ingress of moisture and aggressive elements, which eventually lead to concrete deterioration (Micelli et al., 2019;Griño et al., 2020). Bacterial self-repairing can enhance the early-age concrete compressive and tensile strengths. The compressive strength of concrete was optimized at the B. subtilis bacteria cell concentration of 10 5 cells/ml of mixing water (increased by an average value of 23% at age 28 days). Moreover, the split tensile strength improved in a range of (13.7 -25.3%) (Ghoneim et al., 2020).
Conventional Concrete (CC) becomes more brittle and has very low flexure or shear capacities when its compressive strength increases. To reduce these side effects, FRC has arisen as an Engineering Cementitious Composites (ECC). The higher fiber content may cause accumulation in the concrete. Therefore, the moderate fiber content should be less than 4% to make sure an adequate balance between obtaining post cracking behavior and the workability of fresh concrete benefits (Hasan et al., 2019). Both the Microbially Induced Calcite Precipitation (MICP) and fibers have no side effects on the cement specimen containing admixtures (Termkhajornkit et al., 2009;Athiyamaan and Ganesh, 2017). For improving self-healing capacity, the combination of fibers with cement replacement is recommended (Guerini et al., 2018). High Strength Concrete (HSC) with a strength more than 60 MPa could be produced through the addition of cement replacements frequently as Silica Fume (SF), fly ash, Ground Granulated Blast Furnace Slag (GGBS), limestone powder, and metakaolin (MK). HSC can reduce structural member size, enhance density and permeability, but its durability and serviceability enhancement need more requirements to resist sulfate, freeze-thaw, abrasion, low alkali-aggregate reactions, and embedded steel corrosion (Ayub et al., 2014).
Coupled effects of macro fibers and bacteria on early-age characteristics of concrete are mentioned in the literature (Feng et al., 2019;Ganesh et al., 2019). However, studies on the short-term performance of concrete beams made with bacteria and different fiber admixtures are very scarce. The authors believe that this fusion generates the development of HSC mechanical properties and structural behavior by achieving high strength, strain hardening, and multiple microcracking characteristics. The 32 admixtures were carried out to judge the properties of the FRBC beams with higher concrete grade (M60 & M80) and investigate its performance, initial cracking, and failure behavior.

STUDY PROCEDURE
There is a multiscale modeling issue ranging from the fiber with a few micrometers in diameter to the structural dimension in meters. The link between the length scales using either the hierarchical approach or the homogenization approach eliminates the scale problem in the Finite Element (FE) modeling. Although the evaluation of organisms curing condition is difficult numerically, the crack opening width ζ for fibrous concrete should stay within an ever-experienced limit of B. subtilis rehabilitation incorporated to close cracks up to 0.46 mm (Wiktor and Jonkers, 2011).

Samples Description
The beams proposed with varying geometry are tested under a monotonic three-point loading system as shown in Figure 1. The rectangular beam sections configured with no stirrups by different geometrical parameters such as; clear span length l n , shear-span to depth ratio a/d (the shear-span a is half of the beam span l n in a three-point loading setup), width b, height h, depth d, and flexure singly reinforcement ratio ρ.
Beams with shear-span to depth ratios a/d from 1.0 to 2.5 are referred to as "short", while those with a/d from 2.5 to about 6.0 are referred to as "slender" (a slender beam geometry has reduced beam height, increased span length, or both) (MacGregor and Wight, 2012). To consider the influence of beams size on the results, two major types of beams in terms of slenderness were selected to be investigated in this study since they have different failure mechanisms (slender beams fail due to the propagation of flexure-shear cracks while short beams fail more due to the propagation of webshear cracks). Table 1 presents the details of the four geometry model types L1, L2, Sh1, and Sh2. In the notation used for the beam titles, the letter 'L' denotes long and is used for slender beams (a/d = 3.5) while 'Sh' represents short (a/d = 2.3). Numbers 1 and 2 indicate the first phase and second phase with flexural reinforcement ratio ρ equals 2.15% and 3.18%, respectively.  The steel bars idealized to have compressive and tensile elastic perfectly plastic behavior with a modulus of elasticity E s equals 2.1×10 5 MPa, Poisson's ratio ν equals 0.3, and yield stress f y equals 420 MPa. The modeled beam load (500 kN) and the hinged roller restraints are represented in Figure 2. The 32 full-scale reinforced concrete (RC) beams were analyzed under a monotonic three-point loading system. The study classified the beams into three matrix types (fiber-reinforced concrete FRC, bacterial concrete BC, fiber-reinforced bacterial concrete FRBC). The scheme of specimen sets is outlined in Figure 3.

Material Properties
To provide reliable inputs for the study, the properties of matrix integrated materials are considered based on previous experimental literature. For both high strength M60 & M80 concrete grades, the matrix properties are characterized by early-age concrete properties after 28 days as mentioned by Rao et al., 2017. For the present study, Bacillus subtilis JC3 is distinguished as aerobic alkaliphilic spore-forming bacteria. The growth medium used is based on peptone, NaCl, yeast extract (Rao et al., 2017).
The straight macro synthetic fiber has unit diameter d f equals 433 µm, aspect ratio AR f = l f / d f equals 90, specific gravity equals 0.97 g/cm 3 , elastic modulus E equals 73000 MPa, Poisson's ratio ν equals 0.422, and ultimate tensile strength equals 2580 MPa. The fiber was incorporated into the concrete mixture with 0.5% fiber content and the optimum cell concentration of B. subtilis equals 10 5 cells/ml of mixing water. The uniaxial crushing stress set in the fibrous concrete is similar to the non-fibrous concrete pre peak compressive stress f cu as shown in Table 2. The effective Young's modulus and the Poisson's ratio of composites could be computed using the properties of their integrated materials. This could be performed through the ANSYS Material Designer as an integrated component system in the ANSYS package using the homogenization or unit cell approach. The unit cell is a repeated cell or a typical Representative Volume Element (RVE) proposed in Figure 4 for predicting the equivalent homogeneous material properties.   The concrete linear isotropic ANSYS input data properties are valid for each beam geometry group L1, L2, Sh1, and Sh2 as illustrated in Table 2, where the target sample notation is "Matrix Type -Concrete Grade". However, the elastic modulus and Poisson's ratio of fibrous composites are the homogenized RVE characteristics, the total tensile stress ft determined by the literature approach in Eq. (1).
Both the Variable Engagement Model (VEM) and the Simplified Diverse Embedment Model (SDEM) are the recommended models to determine the total FRC tensile stress f t (Carnovale, 2013). The total FRC tensile stress mentioned in Eq. (1) consists of three terms, as follows: (i) the frictional bond stress in the macro synthetic fiber f f presented by modifying SDEM has given in Eq. (2), (ii) the mechanical anchorage stress f eh (the smooth straight fiber has no mechanical anchorage component), and (iii) the matrix tensile cracking strength f ct . The crack opening width ζ should stay within an ever-experienced limit of B. subtilis rehabilitation incorporated to close cracks up to 0.46 mm as recommended in the literature (Wiktor and Jonkers, 2011).
In these expressions; V f is the fiber content (%), l f is the fiber length (mm), d f is the fiber diameter (mm), τ f, max is the fiber maximum bond strength constant (equals 0.6 of the concrete matrix (Won et al., 2006)), and α f is the fiber orientation factor as a function of member thickness b and height h in Eq. (3) (Oh, 2011 For surveying the after-cracking behavior, two stages are considered with the K st coefficient: (i) early-stage 1 for the elastic fiber behavior at a small crack width; and (ii) latterly stage 2 for the plastic fiber behavior at large crack width. This coefficient in Eq. (4) is a function of the straight fiber slip S f at τ f, max that was consistently equal to 0.01 mm. 0. 087 For the non-fibrous concrete, the uniaxial tensile cracking stress f t is set into the investigated values in the literature (Rao et al., 2017). While the addition of smooth macro synthetic fiber increases the tensile cracking strength f t as in Table  2. According to the SDEM, Eqs. (1) to (4) implies the formulations for both stage 1 (ζ > 0.01 mm) and stage 2 (ζ ≥ 0.01 mm). The K st coefficients are equal to 0.2 and 0.885 for stage 1 and stage 2, respectively. The member geometry has little effect on the fiber orientation factor α f and equals 0.52.
The multilinear isotropic stress-strain material properties of the compressive models based on the experiments are depicted in Figure 5. The study selects some of the expressions as Carreira andChu model, 1985 (Carreira andChu, 1985) and Lu andZhao model, 2010 (Lu andZhao, 2010)  In addition, the inelastic plasticity is defined using the Willam and Warnke model by constants such as the typical shear transfer coefficients for an open crack β t and a closed crack β c . For the non-fibrous concrete, the β t and β c coefficients were set to 0.25 and 0.7, respectively. For the fibrous concrete, the shear transfer at the cracks depends on the pull-out mechanism in the matrix-fiber interaction. For V f = 0.5%, the β t and β c coefficients were set by linear interpolation as 0.31 and 0.73, respectively, based on the previous investigations (Thomas and Ramaswamy, 2006;Thomas and Ramaswamy, 2007

RESULTS
For providing an in-depth understanding of the combined effect of bacteria and fibers on the behavior of simple RC beams, an extensive parametric study was designed. The numerical modeling results of the concrete beam specimen at both fiber elasticity-plasticity stages are shown in Table 3, these two stage results are as follows: (i) Stage 1, the elastic fiber behavior at a small crack width was used for determining the fiber elastic initial cracking load P cr, e , the mid-span flexure M cr, e that occurs from the existing forces with neglecting the own weight of beams, and the deflection δ cr, e .
(ii) Stage 2, the plastic fiber behavior at large crack width led to determine the fiber plastic ultimate load P u, p , the mid-span flexure M u, p , the maximum nodal XY shear strength ν fc , and the flexural toughness (the area under the flexural load deflection curve obtained from a specimen static test up to a specified deflection) as an indication of the material energy absorption capability, and the deflection δ u, p . Hence, the ductility ratio (DR = δ u, p / δ cr, e ) and the moment capacity ratio (RM = M u, p / M cr, e ) could be calculated.

Cracking Patterns
Multi-cracks were observed in the presence of fibers and bacterial additions. The propagated flexure cracks at midspan of the L1, L2, Sh1, and Sh2 beams are represented in Figure 6, Figure 7, Figure 8, and Figure 9, respectively. The crack propagation for both slender and short beams observed at mid-span where all beams tend to fail due to the flexural. The orientations of the cracks were vertical in the mid-span bottom region and lightly inclined outward, in which the steel reinforcements will distribute cracks along the damage zone. The FRC beams did exhibit distributed flexural cracking before the first diagonal shear crack propagation due to the increased confining of the fibers around the steel bars. These results are broadly consistent with the major trends of experimental observations in the literature (Furlan Jr and de Hanai, 1997).
Incorporating bacillus subtilis bacteria at optimum dosage into M60 and M80 concrete strengthened with macro synthetic fiber transforms the unstable crack propagation into a controlled crack growth with more warning signs than conventional concrete. Also, the sudden failure could be eliminated by combining the macro synthetic fiber and bacteria as an internal reinforcement self-repairing technique. Hence, the enhancement of structural behavior such as flexural strength, deformation capacity, and ductility could be achieved for concrete structures.     Figure 10 shows the value of mid-span vertical crack length at the ultimate load and the average crack length value for the different study specimens. For both fibrous M60 and M80 concrete, the FRBC average crack length at the ultimate load is more than that of FRC. This longer crack length with a bigger ultimate load means the more consumed amount of energy before failure. As a mutual benefit status, the reduced crack widths by fibers require fewer healing products to fill. Also, the healed crack by bacterial participation on the micro-scale increases the fiber embedment length. Consequently, the remarkable enhancement of the FRBC performance could be achieved among all fibers bridging cross cracks on the macro-scale of the composite. This observation is broadly consistent with the literature trend (Nili and Afroughsabet, 2010;Di Maida et al., 2018;Vijay and Murmu, 2019).

Bacterial Self-Repairing Influence
Moreover, the significance level was determined using the statistical analysis of variance (ANOVA) method to compare means and study parameters effect on the performance. The enhancement percentage related to associated CC in the target mechanical performance of different matrix types FRC, BC, and FRBC is illustrated in Figure 11. The relative change results showed that the influence of bacterial participation in fibrous concrete was more pronounced than the individual addition of bacteria or fibers in beams. The results of the test hypothesis, including a 95% confidence interval, showed that the FRBC had more mean significant enhancement in the initial cracking load P cr , the ultimate load P u , and the moment capacity ratio RM with a range of (6-21%), (20-42%), and (8-23%), respectively. Also, the relative enhancements in shear stress and toughness for FRC beams are more pronounced than BC beams. This confirms that fiber incorporation plays a bigger influence in improving concrete shear performance up to 80% as shown in Figure 11. These results are broadly consistent with the major trends of experimental observations in the literature. The macro fibers made remarkable improvements in beam shear strength by 30% (Altoubat et al., 2009;Li et al., 1992) and reach 65% using new generation macro synthetic fibers (Hasan et al., 2011;Kirsanov and Stolyarov, 2018).

Geometrical Parameters Influence
The enhancement percentage related to associated CC in the target mechanical performance of different model types L1, L2, Sh1, and Sh2 is as shown in Figure 12. The relative change results showed that the influence of fiber and bacteria addition in the slender beams was more pronounced than the short beams. The results of the test hypothesis including all matrix types showed that the L1 had more significant enhancement in the maximum shear strength ν fc . Figure 13 illustrates the enhancement percentage related to associated CC in the target mechanical performance of M60 and M80 concrete grade. The relative change results showed that the influence of fiber and bacteria addition in the M80 was more pronounced than in M60. The moment capacity ratio RM and the ductility ratio DR of M80 had more significant enhancement with a range of (5-18%) and (12-44%), respectively.

Concrete Grade Influence
The addition of low modulus synthetic fiber and bacteria increased flexure strength, toughness, and residual loadcarrying capacity due to high crack widths. However, the initial cracking load, ultimate load, and flexural toughness do not follow the trend of gradually increasing with the increased concrete grade. The results of the test hypothesis showed that the M60 had more mean significant enhancement in the initial cracking load, the ultimate load, and the flexural toughness with a range of (11-27%), (20-37%), and (47-130%), respectively. However, a dual-component improver has a higher synergistic effect, this improvement could not treat the high brittleness of the M80 concrete grade.