Mechanical properties optimization using response surface methodology (RSM) of a bio-mortar manufactured based on sisal fibers

Mechanical properties optimization using response surface methodology (RSM) of a bio-mortar manufactured based on sisal fibers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Mechanical properties optimization using response surface methodology (RSM) of a bio-mortar manufactured based on sisal fibers Hocine Khelifa, Abderrezak Bezazi, Haithem Boumediri, Gilberto Garcia delPino, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5844500/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 May, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted 5 You are reading this latest preprint version Abstract The application of lignocellulosic fibers to reinforce mortars with cementitious matrices was investigated for possible use in non-structural applications. A Box-Behnken design L29 (BBDL29) experimental design, using the response surface method (RSM), was used to obtain the combination that maximizes the bending stress and modulus. Four input parameters were evaluated for this purpose: fiber content percentage in the mortar, fiber length, NaOH concentration percentage, and immersion duration. Subsequently, different bio-mortars were produced and tested after 28 days of drying in compression and 3-point bending mode. The results showed that the reinforcement of mortars with sisal fibers allows reductions or increases in mechanical properties, while in literature it generally decreases. In comparison to the reference mortar, the optimal combination exhibited a substantial enhancement of 66.3% and 82.8% in compressive stress and modulus, respectively, while in bending, the increases were 34.8% and 21.5%. The RSM analysis of the mechanical outcomes facilitated the development of a quadratic regression model exhibiting a high correlation coefficients (𝑅2) value. Furthermore, the desirability function was employed in multi-objective optimization to generate ten ideal combinations, yielding results that closely aligned with those obtained experimentally for compressive and bending stresses. Sisal fiber Bio-mortar RSM methodology Bending and Compression Mechanical properties Desirability function Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1 Introduction The effectiveness of composite materials that use cementitious matrices, such as mortars and concrete, lies in their high compressive strength and acceptable flexural strength, associated with good structural durability. In the case of reinforced concrete, and depending on its applications, it may be necessary to add metallic reinforcements to increase tensile and flexural strength [ 1 , 2 ]. However, although the mechanical properties of these metallic constituents can be improved by using precisely controlled temperature, heating, and cooling rates [ 3 ], these procedures must be carried out before they are combined with the matrices, because any increase in temperature provides greater evaporation of the mixing water and its hardening is much faster, leading to the occurrence of cracks and other adverse effects on mechanical performance [ 4 ].For the same reasons, the effect of the increase in ambient temperature that has been affecting the Earth should not be excluded. Therefore, it is crucial to develop more ecological, economical and efficient infrastructures to achieve a balance between environmental sustainability and the durability of construction materials. For this purpose, several researchers have proposed the insertion of cellulose-based natural fibers as a reinforcing element in cement-based construction materials to improve their strength, durability as well as thermal insulation and/or phonic [ 5 – 8 ]. Furthermore, the advantages attributed to the use of natural fibers to reinforce cementitious composites, known as fiber-cement [ 4 ], include biodegradability, relatively low cost, the availability of raw materials from renewable sources, low density, and thermal conductivity, resulting in minimal environmental impact [ 9 – 15 ].As a consequence of all these benefits, the incorporation of natural fibers in the building sector has increased by around 13% in the last decade [ 4 ] and, given the wide variety of existing natural fibers, it is not surprising that the literature reports several studies focused on their applications and optimization of the mechanical properties [ 16 – 19 ]. Many of them analyze the incorporation of lignocellulosic fibers into earth bricks, coatings for buildings walls when associated with a mineral matrix or even in transformed materials (steel/vegetable fiber, Portland cement) [ 20 – 22 ]. In the latter case, for example, the use of concrete/mortar coupled with various fibers stands out [ 23 ]. Akhzeroun et al [ 24 ] proposed novel low-cost compressed earth blocks (CEB) reinforced with date palm stems (DPS) capable of satisfying the masonry requirements of green earthen constructions. The results showed that for CEB reinforced with 2% DPS raw with 0.5 mm of length treated by immersion and those treated by autoclaving led to increases in bending strength by 25.71% and 20.00%, respectively, and compressive strength by 12.82% and 22.71%, respectively, compared to unreinforced blocks. Amziane and Arnaud [ 25 ] even suggested a construction process using agricultural raw materials (Canosmose procedure) to build houses entirely out of hemp. Currently, sisal fibers are the most widely used in the construction sector because they are widely cultivated and relatively cheap, providing a very economical material for reinforcement. This interest arose due to the fact that they present mechanical properties very similar to those of polypropylene fibers [ 26 ], and there is a growing desire to materialize them as a reinforcement element in construction composites with a cementitious matrix [ 27 – 30 ]. After six months of hardening, for example, cementitious composites reinforced with short sisal fibers present 83.3% of their initial strength and a slight reduction in toughness [ 31 ]. However, compared to unreinforced cement mortars, the compressive strength of those reinforced with sisal fibers having lengths of 25 and 45 mm showed reductions of around 11% and 22%, respectively [ 32 ]. Wei and Meyer [ 33 ] investigated the impact of incorporating rice husk ash into sisal fiber-reinforced cement composites and found that the flexural strength of these composites decreased by 25%, 68%, and 87% after undergoing 5, 15, and 30 wetting and drying cycles, respectively, compared to the initial value (control group). According to the author, this can be explained by the aging of sisal fiber and the deterioration of the interfacial bonding strength between the fiber and the cement matrix, while the addition of rice ash improved the flexural properties by around 18%and the durability to exposure to wetting and drying cycles. Izquierdo et al [ 34 ] performed experimental compression tests and numerical studies to evaluate the mechanical response of brickwork reinforced with 1 wt.% sisal fibers, finding that both the compressive strength and modulus decreased by about 25% and 61%, respectively. Klerk et al [ 35 ] studied the flexural strength of a cementitious matrix reinforced with sisal fibers, and in particular the effect of its treatment with NaOH using different concentrations (2%, 6%, 10%, 20%, and 30%), having observed only slight increases of 8.8% and 9.2%, compared to the reference mortar, when they were treated with 2% and 6%NaOH, respectively. However, the studies reported in the literature are essentially limited to the analysis of one or two parameters used to develop bio-mortars reinforced with sisal fibers and the respective maximization of the mechanical properties in both compression and bending. Most of them report reductions of up to 25% and 61% in terms of strength and modulus, respectively, or slight increases with a maximum value of 9%.In this context, this work aims to optimize different parameters in order to maximize the mechanical properties of Portland cement-based mortars reinforced with sisal fibers to values higher than those reported in the literature. For this purpose, four criteria will be considered, i.e., the percentage of fiber incorporated, fiber length, the percentage of alkali (NaOH) used in the chemical treatment, and the immersion time of the fibers in the chemical solution. The mechanical properties evaluated will be strength and modulus in both bend and compression, to obtain environmentally friendly, resistant and good quality mortars for application in the construction sector. The response surface method (RSM) will be used, combining the four parameters mentioned above, each with three levels, which leads to an experimental design of 29 types of bio-mortar tests. Therefore, it is possible to optimize the production conditions, reduce the number of samples and the test time of this study without losing its efficiency. In fact, RSM is a method used by several researchers in various fields, including the bio-composites [ 36 , 37 ], construction materials [ 38 ], and optimization of experimental conditions [ 39 ]. 2 Experimental methodologies 2.1 Fiber preparation For this study, sisal fibers were chosen due to their availability, good mechanical, thermal and acoustic properties, reasons that explain the huge interest from the construction sector. The fibers have a beige hue and possess an average diameter of around 200 µm in their raw state (see Fig. 1 ), which were obtained commercially by the Laboratory of Mechanics of New Materials (LMNM) of the University 8 May 1945 from Guelma. Sisal fibers were used in their raw state and chemically treated with sodium hydroxide (NaOH) at different concentrations (1%, 3% and 5%) and for different immersion times (2h, 8h, 14h) to increase fiber/matrix interfacial adhesion and provide better fiber resistance to moisture by reducing the surface energy. Subsequently, after being extracted from the chemical solution, they were immersed in sulfuric acid for 5 min, washed with tap water and, finally, submerged in distilled water for 15 minutes to equilibrate the pH. The fibers were dried, cut into pieces of 5, 10, and 15 mm long, and stored in airtight bags for later use. 2.2 Experimental design and statistical analysis The different bio-mortar types produced were optimized by Response Surface Methodology (RSM) to examine the influence of individual development factors and their combinations on mechanical performance in compression and bending modes. The four development parameters are symbolized by: the percentage of fiber reinforcement (A), fiber length (B), percentage of alkaline element (C), and immersion time (D). Therefore, the experimental plan was designed using Design Expert 12 software, employing the Box-Behnken design (BBD) with three levels for each parameter to establish the Design of Experiments (DOE) based on the L29 orthogonal array (Table 1 ).The use of the BBD design assumes that all design parameters are continuous, quantifiable, and experimentally controllable with minimal errors [ 36 , 40 ], comprising the central point (0) and the extreme points (+ 1 and − 1), as shown in Table 1 . Table 2 delineates the experimental plan for the various parameters for the bio-mortar developed according to the Box-Behnken design L29. 2.3 Production of the bio-mortar samples The bio-mortars samples involving cementitious matrix reinforced with sisal fibers were developed from the BBD L29 experimental plan (see Table 2 ), according to European Standard NF-EN 196-1[ 41 ]. To properly reinforce the mortar, the mass quantities of sisal fibers were added gradually from the beginning of the sand, cement, and water mixture. The binder consists of Portland cement, the sand was dried at 105°C for 24 hours and sieved before usage, and the water utilized is tap water. The mortar was dozed according to the following protocol: four parts sand, one part cement, and half a part water. In this case, to produce four specimens with a volume of 125 cm 3 each, the following contents were used: 1172 ± 5 g of sand, 293 ± 2 g of cement, and 146.5 ± 1 g of water. All of them were mixed with different amounts of sisal fibers randomly distributed. Stainless steel molds were used to produce the specimens, and their dimensions for the bending and compression tests followed the recommendations of the ASTM C293.2010 [ 42 ] and ASTM C 109/C 109M–02 [ 43 ] standards, respectively. Following a 24-hour drying period, all specimens were extracted from the mold and subjected to curing at ambient temperature for 28 days before being tested (see Figs. 2 ). 2.4 Mechanical test methods This study evaluates the mechanical performance of bio-mortars reinforced with sisal fibers by analyzing stress and Young's modulus under both loading regimes (bending and compression). For this purpose, three-point bending (3PB) and compression tests were carried out at room temperature using a Walter & Bai universal test machine, with a displacement rate of 2 mm/min and a span of 100 mm for the 3PB tests. 3 Results and discussion 3.1 Mechanical characteristics using ANOVA approach From the bending and compression tests, the mechanical responses were analyzed in terms of stress and Young's modulus, whose experimental values are shown in Table 3 . It is possible to observe that the incorporation of sisal fibers in the mortars both improves and decreases the mechanical performance in relation to control specimens. In fact, finding a compromise between the different factors to maximize mechanical properties is a complex operation, but to highlight the influence of each factor it is enough to establish comparisons between the formulations shown in Table 3 , keeping three factors constant and one variable. In this case, the following four comparisons can be made for bending: (a) The comparison between formulations 24 and 11, with fiber contents of 1% and 5%, respectively, leads to bending stresses of 4.5 MPa and 2.1 MPa, i.e., the increase in fiber content promotes a stress reduction of 53.33%; (b) Considering formulations 4 and 24, whose fiber lengths are 5 mm and 15 mm, respectively, the bending stress is 4.98 MPa and 4.5 MPa, which means that increasing the fiber length leads to a reduction of 9.64%; (c) Formulations 12 and 23, which compare the responses of fiber-reinforced mortars treated with 1% and 5% NaOH, respectively, led to bending stresses of 5.39 MPa and 4.27 MPa, representing a reduction of around 20.78%; (d) Finally, formulations 3 and 7 compare treatment times of 2 hours and 14 hours, respectively, promoting bending stresses of 1.97 MPa and 2.11 MPa, i.e., a slight increase of 7.11%.Therefore, it is possible to conclude that the fiber content is the parameter that has the highest influence on the bending stress(which can lead to gains of 53.33%), followed by the NaOH concentration(with gains of up to 20.78%), while the fiber length and immersion time provided marginal benefits (around 9.64% and 7.11%, respectively). Regarding the compression performance, and based on the same comparative analysis established previously, it is observed that between formulations 24 and 11 there is now an increase in compression strength of around 19.73% (from 23.57 MPa to 28.22 MPa), while formulations 4 and 24 lead to a decrease of 30.16% (from 33.75 MPa to 23.57 MPa). Finally, comparing formulations 12 and 23, a decrease of around 34.95% is observed (from 34.94 MPa to 22.73 MPa), as well as for formulations 3 and 7 of about 43.53% (from 29.52 MPa to 16.67 MPa). In this case, it is clear that the parameters affect the mechanical properties of the mortars differently, whose response to compression is positively affected in decreasing order by the immersion time (with gains of up to 43.53%), NaOH concentration (up to 34.95%), fiber length (up to 30.16%) and fiber content (up to 19.73%). It should also be noted that, for example, the bio-mortar with the lowest compressive strength (14.92 MPa) was obtained with parameters of 3% fiber fraction, 10 mm length, 3% NaOH and 8 hours of immersion. These values compared with the previous ones show that there may be a neutral/critical zone, where none of the parameters are optimized to maximize the mechanical properties. On the other hand, when comparing these parameters with those that led to the production of the mortar with the highest compressive strength (line 12 of Table 3 ), it is noted that both the fibers fraction and the alkali content decreased (in both cases from 3–1%). Therefore, it is possible to conclude that the values of the parameters involved in the manufacture of mortars should not be considered in isolation to maximize the mechanical properties but rather analyzed to establish an interdependent balance between them. Therefore, the effect of short sisal fibers randomly incorporated into mortars can be summarized in Fig. 3 for clarity. From Fig. 3 a, it can be observed that, compared to the control mortar, the configuration that showed the best bending results (1% fiber fraction, 10 mm length, 1% NaOH and 8 hours of immersion) presented improvements of 34.8% in stiffness and 21.5% in strength, while one of the worst configurations (5% fiber fraction, 10 mm length, 3% NaOH and 14 hours of immersion) promoted decreases of around 47.3% and 86.9%, respectively. The same comparison for the compression properties based on Fig. 3 b shows that the best mortar (1% fiber fraction, 10 mm length, 1% NaOH and 8 hours of immersion) has compressive strength and stiffness about 66.3% and 82.8% higher than the control, while one of the worst configurations(3% fiber fraction, 10 mm length, 3% NaOH and 8 hours of immersion) led to reductions of 29% in terms of stress and an increase of 11.6% in terms of stiffness, respectively. This ambiguity of benefits related to the parameters involved in the manufacturing processes is in line with the literature. For example, Arsène et al. [ 44 ] studied the bending response of a mortar reinforced with banana trunk fibers and sugarcane residues with different contents (1%, 2%, and 5%) and treatments (sulfuric acid and calcium hydroxide) at a concentration of 5% for one hour. The authors found that untreated banana fibers led to an increase in bending strength of 33.6%, 25.8%, and 6.5% for contents of 1%, 2%, and 5%, respectively, but when the fibers were treated with sulfuric acid and calcium hydroxide led to a decrease of 22.6% and 25.8%, respectively. Furthermore, as described/observed above, the different parameters involved in the mortar manufacturing process affected their response to bending and compression differently, due to the damage mechanisms intrinsic to each loading mode. To substantiate this evidence, the damage mechanisms for the different bio-mortars analyzed are shown in Figs. 4 and 5 for the bending and compression modes, respectively. In the first case, the control specimens (see Fig. 4a) evidence the initiation of a crack, approximately halfway between the supports and in the lower region subject to tensile stresses, which propagates very fast towards the point of load’s application, causing a sudden rupture typically associated with a brittle fracture. On the other hand, this brittle fracture changes to ductile behavior when the bio-mortar is reinforced with sisal fibers, reaching its maximum value at 5% of reinforcement (see Fig. 4c). In this case, not only does the crack propagate more slowly, but also the distance between the two cracks faces is much smaller and, in some cases, almost unnoticeable (see Figs. 4a and 4c). As can be seen in the SEM images, when sisal fibers are incorporated, they act as reinforcement, absorbing and distributing stress more effectively. When a crack forms, the fibers can bridge the gap, preventing the crack from spreading rapidly. In addition, the fibers can help to stop the crack at their interfaces, forcing it to change direction or become more diffuse. In this context, the sisal fibers absorb part of the energy and reduce the rapid propagation of cracks, resulting in ductile behavior. In terms of length, longer fibers are generally more effective in delaying crack propagation, because they provide better crack-bridging, crack deflection, and toughness, contributing to improved durability and performance of the bio-mortars under stress. However, effectiveness depends on their alignment, which is quite difficult to guarantee during the manufacturing process adopted, and on the fiber-mortar bonding. In the latter case, the fiber content is crucial, because its increase leads to the appearance of defects and, consequently, stress concentration points, or promotes voids/air pockets in the mortars due to insufficient filling of the spaces between the fibers. Moreover, although the strain at maximum load was the highest, the bending stress and Young’s modulus were the lowest due to the higher porosity rate. Nevertheless, as porosity decreases, it is expected that these values may be slightly higher. Regarding the failure damage observed in compression (see Fig. 5), the control specimen exhibit brittle behavior with a single dominant vertical crack along the entire length of the specimen (from top to bottom as shown in Fig. 5a). This behavior is similar to that observed in bending and which was described in detail above. However, the introduction and corresponding increase in fiber reinforcement leads to a reduction in dominant cracks and an increase in micro- and macro-cracks due to the increase in mortar/fiber interfaces, which are characterized by their weak interfacial strength. For example, for the mortar reinforced with 1% of sisal fibers, characterized by the highest values of stress and Young's modulus in compression, it was possible to observe multiple micro- and macro-cracks, but when the reinforcement was 5%, they increased much more due to the compaction evidenced by the increase in the modulus. Subsequently, the experimental results were analyzed using the ANOVA analysis to determine the primary determinants affecting the mechanical characteristics of the manufactured bio-mortars (see Table 1 ). Polynomial regression analysis models were used for each response, namely: the linear model, two-factor interaction (2FI) model, quadratic model, and cubic model (see Table 4 ). However, only one regression model should be selected from the four proposed. For this purpose, the selection criteria are duly reported by several authors [ 45 , 46 ], where the significance of each model derives from the existence of the highest correlation coefficients R 2 , Adjusted R 2 and Predicted R 2 . In this study, the two quadratic and cubic regression models established for the two responses and each test is highly significant compared to the Linear and 2FI models. On the other hand, according to the response surface approach, the cubic model should be aliased its configuration, because evaluating all its aspects independently necessitates multiple elevated design points, thus resulting in erroneous and disturbed images [ 23 ].This suggests the use of the quadratic model, selected to develop the response surface in a later optimization procedure. Consequently, to assess the precision of the chosen quadratic regression model, ANOVA was employed once more to analyze the ultimate stress and Young's modulus for the bending and compression tests, as presented in Tables 5 and 6 , respectively. The development factor codes A, B, C and D are considered, as well as their combinations. Three indices for assessing the reliability and accuracy of the quadratic polynomial model for the significance of the bio-mortar development factors are quantified, namely: F-value, R 2 , and the probabilistic parameter P-value. The postulated hypothesis considers that if the P-values are less than 0.05, the factors used to develop bio-mortars are considered significant. This means that, for the two mechanical responses (bending stress and Young's modulus), the independent parameters A, B, and C are significant, while the parameter D is considered insignificant. On the other hand, the AC and BC combinations for the bending stress, as well as the AC, AB, BC, and CD combinations for the bending modulus are considered significant. This hypothesis is also applied to identify the significance of the development parameters for the compression tests. All independent terms A, B, C, and D with the combinations AB, AC, AD, BD, and CD are significant for the compressive stresses, while for Young's modulus, the independent terms A, C, and D with the AD, BC, and CD combinations are also significant. All significant parameters of the two responses obtained for each test were employed to derive the ultimate formulation of the most suitable mathematical model, and the Design-Expert 12 software was applied to fit a multi-parameter quadratic polynomial that brings together all the significant factors (independent or combined). Therefore, based on Tables 5 and 6 , the following mathematical equations are obtained, which allow the mechanical properties under study to be optimized/maximized: Y 1 (σ f ) = 2.926–1.3155×A − 0.20725×B − 0.441583×C + 0.0318333×D + 0.118×AB + 0.3195×AC + 0.2×AD + 0.9365×BC − 0.08575×BD + 0.17675×CD + 0.21425×A2 + 0.349125×B2 + 0.329625×C2 + 0.2095×D2 (1) Y 2 (E f ) = 0.591–0.394417×A − 0.0825833×B − 0.0939167×C − 0.0175833×D + 0.07375×AB + 0.082×AC − 0.0335×AD + 0.15775×BC + 0.03075×BD + 0.1145×CD − 0.00358333×A2 -0.0690833×B2–0.0213333×C2–0.0375833×D2 (2) Y 3 (σ c ) = 14.927–2.55658×A − 1.14142×B − 2.96275×C − 2.40892×D + 3.99875×AB + 2.526×AC -4.0325×AD − 0.2355×BC- 2.748×BD + 2.37475×CD + 7.44621×A2 + 4.66496×B2 + 3.57496×C2 + 4.01171×D2 (3) Y 4 (E c ) = 29.836–10.6943×A + 0.524333×B + 2.59942×C + 7.31358×D + 0.15475×AB + 1.2725×AC − 4.40425×AD + 2.582×BC − 1.93925×BD − 3.24675×CD − 2.27425×A2–14.209×B2–8.00887×C2–3.54987×D2 (4) The quadratic regression models established by equations (1) to (4) concern the bending stress Y 1 (σ f ), bending modulus Y 2 (E f ), compressive stress Y 3 (σ c ), and compressive modulus Y 4 (E c ). Figure 6 shows the graphical representation of the efficiency obtained for each model based on the ANOVA hypothesis. Essentially, the relationship between the normal probability distribution and the internal residuals is established, as well as the relationship between the predicted response, and given the experimental findings regarding stress and Young's modulus in bending (see Fig. 6 a) and compression tests (see Fig. 6 b). The curves obtained evaluate the distribution of the predicted values on the ordinate ( Y ) compared to the experimental values on the abscissa ( X ) and show that the fits of the quadratic model are adequate for the responses studied with a normal distribution. 3.2 Analysis of 3D response surfaces Figure 7 shows the 3D mechanical responses, with the Z-axis representing the bending strength of the bio-mortars reinforced with sisal fibers, generated by the four elaboration factors combined two by two represented on the X and Y axes. For each response, the significant interaction combinations are highlighted, for which Fig. 7 a shows the interaction effect of the NaOH concentration as a function of the fiber length as well as its effect on the bending stress. The highest stress value of 5.39 MPa was obtained by incorporating 1% of sisal fiber having 5 mm length treated with 1% NaOH. Similarly, the maximization of the bending Young's modulus is shown in Fig. 7 b. For the 3D response surface graph, four more significant interaction combinations are obtained: the fiber % (A) with the NaOH concentration % (C), the fiber % (A) with the fiber length (B), the immersion time (D) with the NaOH concentration % (C), as well as the NaOH % (C) with the fiber length (B). The analysis of these four combinations led to the highest value of Young's modulus of 1.130 GPa, found between the interaction A and C, while the lowest was 0.766 GPa between the interaction of factors C and D. All the results obtained are summarized in Table 7 . For the same analysis carried out for compression tests, the 3D response surfaces obtained are shown in Fig. 8 . Regardless of the combinations, the maximum increase in stress is observed, when the factor A is maximum (5%), and the others are minimum, i.e. factors B, C and D are equal to 5 mm, 1% and 2h, respectively. Figure 9 shows three combinations of interactions obtained for Young's modulus under compression, whose maximum value of 48.91 GPa is obtained for l% sisal fibers and with an immersion time of14 h into1% alkaline solution (NaOH). 3.3 Optimization of manufacturing parameters of bio-mortars As reported above, the objective of this study is to maximize the bending and compressive mechanical properties of a bio-mortar by optimizing its production parameters. The approach adopted was to create a desirability function based on the RSM methodology to maximize the stress and Young's modulus of the bio-mortar. For this purpose, it is essential to select the values assigned to the optimized manufacturing factors, as well as to construct desirability indices, with those of a single objective being maximized in the two responses indicated previously. Desirability function values approaching 1 (or 100%) were identified as the most critical parameter values concerning the response factor. In this case, as shown in Table 8 , and confirmed by Fig. 10 , it can be observed that, following the BBD technique, RSM leads to the 10 best cases progressively among a multitude of solutions. From Table 8 , and for the two loading modes, it can be observed that the highest responses values are 5.393 MPa and 1.066 GPa for stress and Young's modulus in bending, respectively, and 37.524 MPa and 43.722 GPa for compression, respectively, and found for a bio-mortar containing 1.00% sisal with a length of 7.94 mm immerged for 14 h in 1.85% NaOH solution. Compared to the experimental values shown in Table 3 (run 12), they are 5.39 MPa and 1.13 GPa for the bending tests and 34.94 MPa and 48.91 GPa for the compression ones, respectively, and were found for a bio-mortar containing 1.00% sisal fiber with a length of 10.00 mm subject to a treatment with 1.0% NaOH for 8 h. Therefore, the results obtained by the desirability function and from the experimental tests are of the same order of magnitude for the bending response (5.39 MPa for the bending stress and 1.07–1.13 GPa for Young's modulus, but with the theoretical value within the dispersion range observed for the experimental values). However, for the compressive performance, they are very close and with an error of 7.4% for the compressive stress (37.524–34.94 MPa) and 10.5% for the compressive Young's modulus (43.722–48.91 GPa).Therefore, these results can be reproducible because they were obtained using the desirability function (range 1 in Table 8 ) and based on the optimization of the experimental parameters defined for the optimal values of fiber percentage, length, NaOH concentration, and immersion time, which are equal to 1%, 7.95 mm, 1.85% and 14 h, respectively, allowing the achievement of the best mechanical properties. The values of the mechanical characteristics obtained experimentally (best results in Table 3 ) are very close to those obtained by the function of desirability function. Figure 11 shows the surface graphs with contour lines that produce the interaction between the different varieties of bio-mortar formulation parameters and their influences regarding the responses, including stress and Young's modulus in bending and compression, according to the quadratic regression models presented previously by the equations(1), (2), (3) and (4).According to the analysis of the desirability function values, it was possible to determine six of the most significant binary interaction configurations that affect the mechanical characteristics of the bio-mortar, namely: A-B, A-C, A-D, B-C, B-D, and C-D to predict the maximum bending stress and Young's modulus of 5.39 MPa and 1.06 GPa, respectively, and in compression of 37.52 MPa and 43.72 GPa, respectively (see Fig. 11 ). 4 Conclusions In this study, cement bio-mortars reinforced with short sisal fibers randomly arranged were produced and tested under 3-point bending and compression loading, according to the RSM methodology following an experimental design of 29 tests (L29), with the following main conclusions: In comparison to the reference mortar, the bio-mortar exhibiting optimal mechanical properties was augmented with 1% fiber, measuring 10 mm in length, and subjected to 1% NaOH treatment for 8 hours, resulting in substantial enhancements of 66.3% in compressive strength and 82.8% in Young's modulus. This formulation permits increases of 34.8% in bending stress and 21.5% in modulus. On the other hand, the bio-mortar reinforced with 3% sisal fibers, measuring 10 mm in length and treated with 3% NaOH for 8 hours, has the lowest compressive strength, with a 40.8% decrease relative to the reference mortar; The fracture damage study indicated that the incorporation of sisal fibers modifies the damage mode, retards crack propagation, and enhances ductility in the bio-mortars; A quadratic model was developed by ANOVA analysis to identify the primary development variables affecting the mechanical properties of bio-mortar, utilizing the highest correlation values R2, Adjusted R 2 , and Predicted R 2 . This research demonstrated that the significance of the developmental variables was assessed independently or dependent on the two mechanical characteristics (stress and Young's modulus) and for the two conducted tests (bending and compression). All essential variables from the two replies acquired for each test type were subsequently utilized to derive the final expression of the most suitable mathematical models; The desirability function created by the RSM analysis allows the optimization of the predicted development parameters of the bio-mortars, as well as the responses assigned to them. This approach leads to the maximization of stress and Young's modulus in bending and compression, and the ten best solutions found have been discussed. Furthermore, the experimental values found are of the same magnitude or very close to those obtained by the desirability function. Declarations Acknowledgments The authors express gratitude to the DGRSDT and ATRST of the Ministry of Higher Education and Scientific Research of Algeria for their support of this research. This research was also sponsored by national funds through FCT – Fundação para a Ciência e a Tecnologia, under projects UID/00285 - Centre for Mechanical Engineering, Materials and Processes and LA/P/0112/2020. Funding No funding was received from any organization or individuals. Conflicts of interest/Competing interests The authors declare that they have no conflict or competing financial interests that could have appeared in this paper. CRediT author statement / Authors’ contributions H. Khelifa: Conceptualization, Methodology, Data Curation, Writing - Original Draft A. Bezazi: Conceptualization, Methodology, Validation, Writing - Review & Editing H. Boumediri: Methodology, Data Curation, Writing - Original Draft G.G. del Pino: Methodology, Investigation, Writing - Review & Editing S. Ellagoune: Validation, Writing - Review & Editing P.N.B. Reis: Conceptualization, Methodology, Validation, Writing - Review & Editing F. 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Journal of Materials Research and Technology 8, 2865-2879. https://doi.org/10.1016/j.jmrt.2019.02.019 Tables Tables 1 to 8 are available in the Supplementary Files section Supplementary Files Tables.docx Cite Share Download PDF Status: Published Journal Publication published 13 May, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Editorial decision: Accept as is for Publication 29 Apr, 2025 Reviewers agreed at journal 15 Apr, 2025 Reviewers invited by journal 15 Apr, 2025 Editor assigned by journal 15 Apr, 2025 First submitted to journal 11 Apr, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5844500","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":443322685,"identity":"b7bb6545-4c59-48da-9edc-9b2fdd77e4c3","order_by":0,"name":"Hocine Khelifa","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Hocine","middleName":"","lastName":"Khelifa","suffix":""},{"id":443322686,"identity":"d0278011-bf27-4d04-b797-9c8faf7c080f","order_by":1,"name":"Abderrezak Bezazi","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Abderrezak","middleName":"","lastName":"Bezazi","suffix":""},{"id":443322687,"identity":"cbc76c9f-45ba-4b58-b69f-2b31ea6cdc7d","order_by":2,"name":"Haithem Boumediri","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Haithem","middleName":"","lastName":"Boumediri","suffix":""},{"id":443322688,"identity":"12f9adb7-31cf-499f-9ed2-18c3f8fb5f89","order_by":3,"name":"Gilberto Garcia delPino","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Gilberto","middleName":"Garcia","lastName":"delPino","suffix":""},{"id":443322689,"identity":"e31af566-979a-4fb9-8f64-a85f08c9ff7b","order_by":4,"name":"Salah Ellagoune","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Salah","middleName":"","lastName":"Ellagoune","suffix":""},{"id":443322690,"identity":"938e4262-294f-4be3-8728-693bf3d956d4","order_by":5,"name":"Paulo Reis","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYHACxgMgko2B+YAE0XqgWtgSYFoYG4jSwsDAY0CcFnP2MwYHPjDck+PjP/PxxscchsT+Bt7jD/BpsezJMTg4g6HYmE0id7PlzG0MiTMO8CXitcXgQI7BYR6GhMQ2Cd5t0rxALRsYeAzxazn/Bqylvo3/zDPpv0RpuQGxJYGNIYdNmpEYLZYznhUcnGGQYNgmkWZs2btNwnjGYb7EGfi0mPMnb3zwoSJBXr7/8MMbP7fZyPa39wKDEJ/DkEgQAEYNMw8+DciKEYCAllEwCkbBKBhxAACWmUcOpSS3CQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-5203-3670","institution":"University of Coimbra: Universidade de Coimbra","correspondingAuthor":true,"prefix":"","firstName":"Paulo","middleName":"","lastName":"Reis","suffix":""},{"id":443322691,"identity":"10f9a951-d638-4b92-accc-a1f7ff76c3d9","order_by":6,"name":"Fabrizio Scarpa","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Fabrizio","middleName":"","lastName":"Scarpa","suffix":""}],"badges":[],"createdAt":"2025-01-16 20:28:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5844500/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5844500/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-025-15664-y","type":"published","date":"2025-05-13T15:57:24+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":80720181,"identity":"af65d712-055e-4d67-9f1e-b8a9908ac3d5","added_by":"auto","created_at":"2025-04-16 10:52:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":511175,"visible":true,"origin":"","legend":"\u003cp\u003eSisal fibers: a) In their raw state; b) SEM image showing their longitudinal aspect; c) SEM image showing their transversal aspect.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/fbceb9b2f94362dae455d564.png"},{"id":80721752,"identity":"17a84bc4-6531-4dd3-b743-e4d204e0c29a","added_by":"auto","created_at":"2025-04-16 11:08:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":434474,"visible":true,"origin":"","legend":"\u003cp\u003eBio-mortar samples showing: a) The configuration used in the bending tests; c) The configuration used in the compression tests.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/911718dd97729ef7747c16dd.png"},{"id":80720183,"identity":"a8395446-0b3a-4e42-aa43-3a6c74bedfef","added_by":"auto","created_at":"2025-04-16 10:52:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":87599,"visible":true,"origin":"","legend":"\u003cp\u003eStresses and Young's modulus for: a) Bending response; b) compression response\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/31abc505629419917ce2fbd2.png"},{"id":80721106,"identity":"a75806df-5204-4310-8fd6-e9b5a754fc6e","added_by":"auto","created_at":"2025-04-16 11:00:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1014379,"visible":true,"origin":"","legend":"\u003cp\u003eFailure damages for: a) reference mortar, b) bio-mortar having better response c) bio-mortar having the worst response for the 3-point bending test\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/80f06c62cd4d6691b1c009d0.png"},{"id":80721105,"identity":"32d87932-302c-40f7-8705-5717b66001d7","added_by":"auto","created_at":"2025-04-16 11:00:28","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":548345,"visible":true,"origin":"","legend":"\u003cp\u003eFailure damages for: a) reference mortar, b) bio-mortar having better response c) bio-mortar having poor response for the compression test\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/2e027162c68a282a031e57d5.png"},{"id":80721748,"identity":"9502b70a-6422-45cf-b581-6ee0e9de1b1e","added_by":"auto","created_at":"2025-04-16 11:08:28","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":251212,"visible":true,"origin":"","legend":"\u003cp\u003ea) Normal probability plot of residuals and b) plot of measured results vs predicted values\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/dee0215b2ab3f9d210c812e4.png"},{"id":80720191,"identity":"cac1188d-ed74-41c7-bdd5-2efca387b6ba","added_by":"auto","created_at":"2025-04-16 10:52:28","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":612947,"visible":true,"origin":"","legend":"\u003cp\u003eInteraction effect for: a) Bending strength; b) Bending modulus\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/5e51a739df9c2694ff2f16e7.png"},{"id":80720189,"identity":"ceedadc1-97f4-4900-bc9f-9ed18ab82cd2","added_by":"auto","created_at":"2025-04-16 10:52:28","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":399219,"visible":true,"origin":"","legend":"\u003cp\u003eInteraction effects on compressive strength\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/4430a786e48d1f9a78dcb322.png"},{"id":80721110,"identity":"21d9a9db-fdc0-4035-9e11-882730030fad","added_by":"auto","created_at":"2025-04-16 11:00:28","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":313804,"visible":true,"origin":"","legend":"\u003cp\u003eInteraction effects on compressive modulus.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/8d7c51f0b80b4801483e74db.png"},{"id":80720193,"identity":"e440c664-949b-4f5f-8ac2-ac01be411d7d","added_by":"auto","created_at":"2025-04-16 10:52:28","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":116924,"visible":true,"origin":"","legend":"\u003cp\u003eOptimal factors identified for the bio-mortar production parameters together with their respective responses in bending and compression performance\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/50a5c0879dd9608e96c60616.png"},{"id":80720194,"identity":"2b4375c0-ee53-494f-9003-32eb8932d4c1","added_by":"auto","created_at":"2025-04-16 10:52:28","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":623207,"visible":true,"origin":"","legend":"\u003cp\u003ea) Contour plot for desirability, b) Perturbation graph of bending strength, bending modulus, compressive strength, compressive modulus, and desirability.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/1b866b261bce74f06fe3da5a.png"},{"id":83067791,"identity":"46162aa7-f80d-485f-a565-7c946d9fb57b","added_by":"auto","created_at":"2025-05-19 16:06:12","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6164428,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/c1666f0e-6213-470f-b810-092fa86ff314.pdf"},{"id":80721104,"identity":"128151ed-ce88-4513-9a43-57172ca2e7e2","added_by":"auto","created_at":"2025-04-16 11:00:28","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":65814,"visible":true,"origin":"","legend":"","description":"","filename":"Tables.docx","url":"https://assets-eu.researchsquare.com/files/rs-5844500/v1/569257acfac5e3c3e8e79bd2.docx"}],"financialInterests":"","formattedTitle":"Mechanical properties optimization using response surface methodology (RSM) of a bio-mortar manufactured based on sisal fibers","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe effectiveness of composite materials that use cementitious matrices, such as mortars and concrete, lies in their high compressive strength and acceptable flexural strength, associated with good structural durability. In the case of reinforced concrete, and depending on its applications, it may be necessary to add metallic reinforcements to increase tensile and flexural strength [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. However, although the mechanical properties of these metallic constituents can be improved by using precisely controlled temperature, heating, and cooling rates [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], these procedures must be carried out before they are combined with the matrices, because any increase in temperature provides greater evaporation of the mixing water and its hardening is much faster, leading to the occurrence of cracks and other adverse effects on mechanical performance [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].For the same reasons, the effect of the increase in ambient temperature that has been affecting the Earth should not be excluded. Therefore, it is crucial to develop more ecological, economical and efficient infrastructures to achieve a balance between environmental sustainability and the durability of construction materials.\u003c/p\u003e \u003cp\u003eFor this purpose, several researchers have proposed the insertion of cellulose-based natural fibers as a reinforcing element in cement-based construction materials to improve their strength, durability as well as thermal insulation and/or phonic [\u003cspan additionalcitationids=\"CR6 CR7\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Furthermore, the advantages attributed to the use of natural fibers to reinforce cementitious composites, known as fiber-cement [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], include biodegradability, relatively low cost, the availability of raw materials from renewable sources, low density, and thermal conductivity, resulting in minimal environmental impact [\u003cspan additionalcitationids=\"CR10 CR11 CR12 CR13 CR14\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].As a consequence of all these benefits, the incorporation of natural fibers in the building sector has increased by around 13% in the last decade [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] and, given the wide variety of existing natural fibers, it is not surprising that the literature reports several studies focused on their applications and optimization of the mechanical properties [\u003cspan additionalcitationids=\"CR17 CR18\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Many of them analyze the incorporation of lignocellulosic fibers into earth bricks, coatings for buildings walls when associated with a mineral matrix or even in transformed materials (steel/vegetable fiber, Portland cement) [\u003cspan additionalcitationids=\"CR21\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. In the latter case, for example, the use of concrete/mortar coupled with various fibers stands out [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAkhzeroun \u003cem\u003eet al\u003c/em\u003e [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] proposed novel low-cost compressed earth blocks (CEB) reinforced with date palm stems (DPS) capable of satisfying the masonry requirements of green earthen constructions. The results showed that for CEB reinforced with 2% DPS raw with 0.5 mm of length treated by immersion and those treated by autoclaving led to increases in bending strength by 25.71% and 20.00%, respectively, and compressive strength by 12.82% and 22.71%, respectively, compared to unreinforced blocks. Amziane and Arnaud [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] even suggested a construction process using agricultural raw materials (Canosmose procedure) to build houses entirely out of hemp. Currently, sisal fibers are the most widely used in the construction sector because they are widely cultivated and relatively cheap, providing a very economical material for reinforcement. This interest arose due to the fact that they present mechanical properties very similar to those of polypropylene fibers [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], and there is a growing desire to materialize them as a reinforcement element in construction composites with a cementitious matrix [\u003cspan additionalcitationids=\"CR28 CR29\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. After six months of hardening, for example, cementitious composites reinforced with short sisal fibers present 83.3% of their initial strength and a slight reduction in toughness [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. However, compared to unreinforced cement mortars, the compressive strength of those reinforced with sisal fibers having lengths of 25 and 45 mm showed reductions of around 11% and 22%, respectively [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Wei and Meyer [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] investigated the impact of incorporating rice husk ash into sisal fiber-reinforced cement composites and found that the flexural strength of these composites decreased by 25%, 68%, and 87% after undergoing 5, 15, and 30 wetting and drying cycles, respectively, compared to the initial value (control group). According to the author, this can be explained by the aging of sisal fiber and the deterioration of the interfacial bonding strength between the fiber and the cement matrix, while the addition of rice ash improved the flexural properties by around 18%and the durability to exposure to wetting and drying cycles. Izquierdo \u003cem\u003eet al\u003c/em\u003e [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] performed experimental compression tests and numerical studies to evaluate the mechanical response of brickwork reinforced with 1 wt.% sisal fibers, finding that both the compressive strength and modulus decreased by about 25% and 61%, respectively. Klerk \u003cem\u003eet al\u003c/em\u003e [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] studied the flexural strength of a cementitious matrix reinforced with sisal fibers, and in particular the effect of its treatment with NaOH using different concentrations (2%, 6%, 10%, 20%, and 30%), having observed only slight increases of 8.8% and 9.2%, compared to the reference mortar, when they were treated with 2% and 6%NaOH, respectively.\u003c/p\u003e \u003cp\u003eHowever, the studies reported in the literature are essentially limited to the analysis of one or two parameters used to develop bio-mortars reinforced with sisal fibers and the respective maximization of the mechanical properties in both compression and bending. Most of them report reductions of up to 25% and 61% in terms of strength and modulus, respectively, or slight increases with a maximum value of 9%.In this context, this work aims to optimize different parameters in order to maximize the mechanical properties of Portland cement-based mortars reinforced with sisal fibers to values higher than those reported in the literature. For this purpose, four criteria will be considered, i.e., the percentage of fiber incorporated, fiber length, the percentage of alkali (NaOH) used in the chemical treatment, and the immersion time of the fibers in the chemical solution. The mechanical properties evaluated will be strength and modulus in both bend and compression, to obtain environmentally friendly, resistant and good quality mortars for application in the construction sector. The response surface method (RSM) will be used, combining the four parameters mentioned above, each with three levels, which leads to an experimental design of 29 types of bio-mortar tests. Therefore, it is possible to optimize the production conditions, reduce the number of samples and the test time of this study without losing its efficiency. In fact, RSM is a method used by several researchers in various fields, including the bio-composites [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], construction materials [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], and optimization of experimental conditions [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"2 Experimental methodologies","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Fiber preparation\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eFor this study, sisal fibers were chosen due to their availability, good mechanical, thermal and acoustic properties, reasons that explain the huge interest from the construction sector. The fibers have a beige hue and possess an average diameter of around 200 \u0026micro;m in their raw state (see Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), which were obtained commercially by the Laboratory of Mechanics of New Materials (LMNM) of the University 8 May 1945 from Guelma. Sisal fibers were used in their raw state and chemically treated with sodium hydroxide (NaOH) at different concentrations (1%, 3% and 5%) and for different immersion times (2h, 8h, 14h) to increase fiber/matrix interfacial adhesion and provide better fiber resistance to moisture by reducing the surface energy. Subsequently, after being extracted from the chemical solution, they were immersed in sulfuric acid for 5 min, washed with tap water and, finally, submerged in distilled water for 15 minutes to equilibrate the pH. The fibers were dried, cut into pieces of 5, 10, and 15 mm long, and stored in airtight bags for later use.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Experimental design and statistical analysis\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eThe different bio-mortar types produced were optimized by Response Surface Methodology (RSM) to examine the influence of individual development factors and their combinations on mechanical performance in compression and bending modes. The four development parameters are symbolized by: the percentage of fiber reinforcement (A), fiber length (B), percentage of alkaline element (C), and immersion time (D). Therefore, the experimental plan was designed using Design Expert 12 software, employing the Box-Behnken design (BBD) with three levels for each parameter to establish the Design of Experiments (DOE) based on the L29 orthogonal array (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e).The use of the BBD design assumes that all design parameters are continuous, quantifiable, and experimentally controllable with minimal errors [\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e], comprising the central point (0) and the extreme points (+\u0026thinsp;1 and \u0026minus;\u0026thinsp;1), as shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e delineates the experimental plan for the various parameters for the bio-mortar developed according to the Box-Behnken design L29.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Production of the bio-mortar samples\u003c/h2\u003e\n \u003cp\u003eThe bio-mortars samples involving cementitious matrix reinforced with sisal fibers were developed from the BBD L29 experimental plan (see Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), according to European Standard NF-EN 196-1[\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e]. To properly reinforce the mortar, the mass quantities of sisal fibers were added gradually from the beginning of the sand, cement, and water mixture. The binder consists of Portland cement, the sand was dried at 105\u0026deg;C for 24 hours and sieved before usage, and the water utilized is tap water. The mortar was dozed according to the following protocol: four parts sand, one part cement, and half a part water. In this case, to produce four specimens with a volume of 125 cm\u003csup\u003e3\u003c/sup\u003e each, the following contents were used: 1172\u0026thinsp;\u0026plusmn;\u0026thinsp;5 g of sand, 293\u0026thinsp;\u0026plusmn;\u0026thinsp;2 g of cement, and 146.5\u0026thinsp;\u0026plusmn;\u0026thinsp;1 g of water. All of them were mixed with different amounts of sisal fibers randomly distributed. Stainless steel molds were used to produce the specimens, and their dimensions for the bending and compression tests followed the recommendations of the ASTM C293.2010 [\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e] and ASTM C 109/C 109M\u0026ndash;02 [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e] standards, respectively. Following a 24-hour drying period, all specimens were extracted from the mold and subjected to curing at ambient temperature for 28 days before being tested (see Figs. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4 Mechanical test methods\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eThis study evaluates the mechanical performance of bio-mortars reinforced with sisal fibers by analyzing stress and Young\u0026apos;s modulus under both loading regimes (bending and compression). For this purpose, three-point bending (3PB) and compression tests were carried out at room temperature using a Walter \u0026amp; Bai universal test machine, with a displacement rate of 2 mm/min and a span of 100 mm for the 3PB tests.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3 Results and discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003cp\u003e\u003cstrong\u003e3.1 Mechanical characteristics using ANOVA approach\u003c/strong\u003e\u003c/p\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eFrom the bending and compression tests, the mechanical responses were analyzed in terms of stress and Young\u0026apos;s modulus, whose experimental values are shown in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e. It is possible to observe that the incorporation of sisal fibers in the mortars both improves and decreases the mechanical performance in relation to control specimens. In fact, finding a compromise between the different factors to maximize mechanical properties is a complex operation, but to highlight the influence of each factor it is enough to establish comparisons between the formulations shown in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, keeping three factors constant and one variable. In this case, the following four comparisons can be made for bending: (a) The comparison between formulations 24 and 11, with fiber contents of 1% and 5%, respectively, leads to bending stresses of 4.5 MPa and 2.1 MPa, i.e., the increase in fiber content promotes a stress reduction of 53.33%; (b) Considering formulations 4 and 24, whose fiber lengths are 5 mm and 15 mm, respectively, the bending stress is 4.98 MPa and 4.5 MPa, which means that increasing the fiber length leads to a reduction of 9.64%; (c) Formulations 12 and 23, which compare the responses of fiber-reinforced mortars treated with 1% and 5% NaOH, respectively, led to bending stresses of 5.39 MPa and 4.27 MPa, representing a reduction of around 20.78%; (d) Finally, formulations 3 and 7 compare treatment times of 2 hours and 14 hours, respectively, promoting bending stresses of 1.97 MPa and 2.11 MPa, i.e., a slight increase of 7.11%.Therefore, it is possible to conclude that the fiber content is the parameter that has the highest influence on the bending stress(which can lead to gains of 53.33%), followed by the NaOH concentration(with gains of up to 20.78%), while the fiber length and immersion time provided marginal benefits (around 9.64% and 7.11%, respectively).\u003c/p\u003e\n \u003cp\u003eRegarding the compression performance, and based on the same comparative analysis established previously, it is observed that between formulations 24 and 11 there is now an increase in compression strength of around 19.73% (from 23.57 MPa to 28.22 MPa), while formulations 4 and 24 lead to a decrease of 30.16% (from 33.75 MPa to 23.57 MPa). Finally, comparing formulations 12 and 23, a decrease of around 34.95% is observed (from 34.94 MPa to 22.73 MPa), as well as for formulations 3 and 7 of about 43.53% (from 29.52 MPa to 16.67 MPa). In this case, it is clear that the parameters affect the mechanical properties of the mortars differently, whose response to compression is positively affected in decreasing order by the immersion time (with gains of up to 43.53%), NaOH concentration (up to 34.95%), fiber length (up to 30.16%) and fiber content (up to 19.73%).\u003c/p\u003e\n \u003cp\u003eIt should also be noted that, for example, the bio-mortar with the lowest compressive strength (14.92 MPa) was obtained with parameters of 3% fiber fraction, 10 mm length, 3% NaOH and 8 hours of immersion. These values compared with the previous ones show that there may be a neutral/critical zone, where none of the parameters are optimized to maximize the mechanical properties. On the other hand, when comparing these parameters with those that led to the production of the mortar with the highest compressive strength (line 12 of Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e), it is noted that both the fibers fraction and the alkali content decreased (in both cases from 3\u0026ndash;1%). Therefore, it is possible to conclude that the values of the parameters involved in the manufacture of mortars should not be considered in isolation to maximize the mechanical properties but rather analyzed to establish an interdependent balance between them.\u003c/p\u003e\n \u003cp\u003eTherefore, the effect of short sisal fibers randomly incorporated into mortars can be summarized in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e for clarity. From Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea, it can be observed that, compared to the control mortar, the configuration that showed the best bending results (1% fiber fraction, 10 mm length, 1% NaOH and 8 hours of immersion) presented improvements of 34.8% in stiffness and 21.5% in strength, while one of the worst configurations (5% fiber fraction, 10 mm length, 3% NaOH and 14 hours of immersion) promoted decreases of around 47.3% and 86.9%, respectively. The same comparison for the compression properties based on Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb shows that the best mortar (1% fiber fraction, 10 mm length, 1% NaOH and 8 hours of immersion) has compressive strength and stiffness about 66.3% and 82.8% higher than the control, while one of the worst configurations(3% fiber fraction, 10 mm length, 3% NaOH and 8 hours of immersion) led to reductions of 29% in terms of stress and an increase of 11.6% in terms of stiffness, respectively. This ambiguity of benefits related to the parameters involved in the manufacturing processes is in line with the literature. For example, Ars\u0026egrave;ne et al. [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e] studied the bending response of a mortar reinforced with banana trunk fibers and sugarcane residues with different contents (1%, 2%, and 5%) and treatments (sulfuric acid and calcium hydroxide) at a concentration of 5% for one hour. The authors found that untreated banana fibers led to an increase in bending strength of 33.6%, 25.8%, and 6.5% for contents of 1%, 2%, and 5%, respectively, but when the fibers were treated with sulfuric acid and calcium hydroxide led to a decrease of 22.6% and 25.8%, respectively.\u003c/p\u003e\n \u003cp\u003eFurthermore, as described/observed above, the different parameters involved in the mortar manufacturing process affected their response to bending and compression differently, due to the damage mechanisms intrinsic to each loading mode. To substantiate this evidence, the damage mechanisms for the different bio-mortars analyzed are shown in Figs.\u0026nbsp;4 and 5 for the bending and compression modes, respectively. In the first case, the control specimens (see Fig.\u0026nbsp;4a) evidence the initiation of a crack, approximately halfway between the supports and in the lower region subject to tensile stresses, which propagates very fast towards the point of load\u0026rsquo;s application, causing a sudden rupture typically associated with a brittle fracture. On the other hand, this brittle fracture changes to ductile behavior when the bio-mortar is reinforced with sisal fibers, reaching its maximum value at 5% of reinforcement (see Fig.\u0026nbsp;4c). In this case, not only does the crack propagate more slowly, but also the distance between the two cracks faces is much smaller and, in some cases, almost unnoticeable (see Figs.\u0026nbsp;4a and 4c). As can be seen in the SEM images, when sisal fibers are incorporated, they act as reinforcement, absorbing and distributing stress more effectively. When a crack forms, the fibers can bridge the gap, preventing the crack from spreading rapidly. In addition, the fibers can help to stop the crack at their interfaces, forcing it to change direction or become more diffuse. In this context, the sisal fibers absorb part of the energy and reduce the rapid propagation of cracks, resulting in ductile behavior. In terms of length, longer fibers are generally more effective in delaying crack propagation, because they provide better crack-bridging, crack deflection, and toughness, contributing to improved durability and performance of the bio-mortars under stress. However, effectiveness depends on their alignment, which is quite difficult to guarantee during the manufacturing process adopted, and on the fiber-mortar bonding. In the latter case, the fiber content is crucial, because its increase leads to the appearance of defects and, consequently, stress concentration points, or promotes voids/air pockets in the mortars due to insufficient filling of the spaces between the fibers. Moreover, although the strain at maximum load was the highest, the bending stress and Young\u0026rsquo;s modulus were the lowest due to the higher porosity rate. Nevertheless, as porosity decreases, it is expected that these values may be slightly higher.\u003c/p\u003e\n \u003cp\u003eRegarding the failure damage observed in compression (see Fig.\u0026nbsp;5), the control specimen exhibit brittle behavior with a single dominant vertical crack along the entire length of the specimen (from top to bottom as shown in Fig.\u0026nbsp;5a). This behavior is similar to that observed in bending and which was described in detail above. However, the introduction and corresponding increase in fiber reinforcement leads to a reduction in dominant cracks and an increase in micro- and macro-cracks due to the increase in mortar/fiber interfaces, which are characterized by their weak interfacial strength. For example, for the mortar reinforced with 1% of sisal fibers, characterized by the highest values of stress and Young\u0026apos;s modulus in compression, it was possible to observe multiple micro- and macro-cracks, but when the reinforcement was 5%, they increased much more due to the compaction evidenced by the increase in the modulus.\u003c/p\u003e\n \u003cp\u003eSubsequently, the experimental results were analyzed using the ANOVA analysis to determine the primary determinants affecting the mechanical characteristics of the manufactured bio-mortars (see Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Polynomial regression analysis models were used for each response, namely: the linear model, two-factor interaction (2FI) model, quadratic model, and cubic model (see Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eHowever, only one regression model should be selected from the four proposed. For this purpose, the selection criteria are duly reported by several authors [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e], where the significance of each model derives from the existence of the highest correlation coefficients R\u003csup\u003e2\u003c/sup\u003e, Adjusted R\u003csup\u003e2\u003c/sup\u003e and Predicted R\u003csup\u003e2\u003c/sup\u003e. In this study, the two quadratic and cubic regression models established for the two responses and each test is highly significant compared to the Linear and 2FI models. On the other hand, according to the response surface approach, the cubic model should be aliased its configuration, because evaluating all its aspects independently necessitates multiple elevated design points, thus resulting in erroneous and disturbed images [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e].This suggests the use of the quadratic model, selected to develop the response surface in a later optimization procedure. Consequently, to assess the precision of the chosen quadratic regression model, ANOVA was employed once more to analyze the ultimate stress and Young\u0026apos;s modulus for the bending and compression tests, as presented in Tables \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, respectively. The development factor codes A, B, C and D are considered, as well as their combinations.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003eThree indices for assessing the reliability and accuracy of the quadratic polynomial model for the significance of the bio-mortar development factors are quantified, namely: F-value, R\u003csup\u003e2\u003c/sup\u003e, and the probabilistic parameter P-value. The postulated hypothesis considers that if the P-values are less than 0.05, the factors used to develop bio-mortars are considered significant. This means that, for the two mechanical responses (bending stress and Young\u0026apos;s modulus), the independent parameters A, B, and C are significant, while the parameter D is considered insignificant. On the other hand, the AC and BC combinations for the bending stress, as well as the AC, AB, BC, and CD combinations for the bending modulus are considered significant. This hypothesis is also applied to identify the significance of the development parameters for the compression tests. All independent terms A, B, C, and D with the combinations AB, AC, AD, BD, and CD are significant for the compressive stresses, while for Young\u0026apos;s modulus, the independent terms A, C, and D with the AD, BC, and CD combinations are also significant.\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eAll significant parameters of the two responses obtained for each test were employed to derive the ultimate formulation of the most suitable mathematical model, and the Design-Expert 12 software was applied to fit a multi-parameter quadratic polynomial that brings together all the significant factors (independent or combined). Therefore, based on Tables \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, the following mathematical equations are obtained, which allow the mechanical properties under study to be optimized/maximized:\u003c/p\u003e\n \u003cp\u003eY\u003csub\u003e1\u003c/sub\u003e(\u0026sigma;\u003csub\u003ef\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;2.926\u0026ndash;1.3155\u0026times;A \u0026minus;\u0026thinsp;0.20725\u0026times;B \u0026minus;\u0026thinsp;0.441583\u0026times;C\u0026thinsp;+\u0026thinsp;0.0318333\u0026times;D\u0026thinsp;+\u0026thinsp;0.118\u0026times;AB\u0026thinsp;+\u0026thinsp;0.3195\u0026times;AC\u0026thinsp;+\u0026thinsp;0.2\u0026times;AD\u0026thinsp;+\u0026thinsp;0.9365\u0026times;BC \u0026minus;\u0026thinsp;0.08575\u0026times;BD\u0026thinsp;+\u0026thinsp;0.17675\u0026times;CD\u0026thinsp;+\u0026thinsp;0.21425\u0026times;A2\u0026thinsp;+\u0026thinsp;0.349125\u0026times;B2\u0026thinsp;+\u0026thinsp;0.329625\u0026times;C2\u0026thinsp;+\u0026thinsp;0.2095\u0026times;D2 (1)\u003c/p\u003e\n \u003cp\u003eY\u003csub\u003e2\u003c/sub\u003e(E\u003csub\u003ef\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;0.591\u0026ndash;0.394417\u0026times;A \u0026minus;\u0026thinsp;0.0825833\u0026times;B \u0026minus;\u0026thinsp;0.0939167\u0026times;C \u0026minus;\u0026thinsp;0.0175833\u0026times;D\u0026thinsp;+\u0026thinsp;0.07375\u0026times;AB\u0026thinsp;+\u0026thinsp;0.082\u0026times;AC \u0026minus;\u0026thinsp;0.0335\u0026times;AD\u0026thinsp;+\u0026thinsp;0.15775\u0026times;BC\u0026thinsp;+\u0026thinsp;0.03075\u0026times;BD\u0026thinsp;+\u0026thinsp;0.1145\u0026times;CD \u0026minus;\u0026thinsp;0.00358333\u0026times;A2 -0.0690833\u0026times;B2\u0026ndash;0.0213333\u0026times;C2\u0026ndash;0.0375833\u0026times;D2 (2)\u003c/p\u003e\n \u003cp\u003eY\u003csub\u003e3\u003c/sub\u003e(\u0026sigma;\u003csub\u003ec\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;14.927\u0026ndash;2.55658\u0026times;A \u0026minus;\u0026thinsp;1.14142\u0026times;B \u0026minus;\u0026thinsp;2.96275\u0026times;C \u0026minus;\u0026thinsp;2.40892\u0026times;D\u0026thinsp;+\u0026thinsp;3.99875\u0026times;AB\u0026thinsp;+\u0026thinsp;2.526\u0026times;AC -4.0325\u0026times;AD \u0026minus;\u0026thinsp;0.2355\u0026times;BC- 2.748\u0026times;BD\u0026thinsp;+\u0026thinsp;2.37475\u0026times;CD\u0026thinsp;+\u0026thinsp;7.44621\u0026times;A2\u0026thinsp;+\u0026thinsp;4.66496\u0026times;B2\u0026thinsp;+\u0026thinsp;3.57496\u0026times;C2\u0026thinsp;+\u0026thinsp;4.01171\u0026times;D2 (3)\u003c/p\u003e\n \u003cp\u003eY\u003csub\u003e4\u003c/sub\u003e(E\u003csub\u003ec\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;29.836\u0026ndash;10.6943\u0026times;A\u0026thinsp;+\u0026thinsp;0.524333\u0026times;B\u0026thinsp;+\u0026thinsp;2.59942\u0026times;C\u0026thinsp;+\u0026thinsp;7.31358\u0026times;D\u0026thinsp;+\u0026thinsp;0.15475\u0026times;AB\u0026thinsp;+\u0026thinsp;1.2725\u0026times;AC \u0026minus;\u0026thinsp;4.40425\u0026times;AD\u0026thinsp;+\u0026thinsp;2.582\u0026times;BC \u0026minus;\u0026thinsp;1.93925\u0026times;BD \u0026minus;\u0026thinsp;3.24675\u0026times;CD \u0026minus;\u0026thinsp;2.27425\u0026times;A2\u0026ndash;14.209\u0026times;B2\u0026ndash;8.00887\u0026times;C2\u0026ndash;3.54987\u0026times;D2 (4)\u003c/p\u003e\n \u003cp\u003eThe quadratic regression models established by equations (1) to (4) concern the bending stress Y\u003csub\u003e1\u003c/sub\u003e(\u0026sigma;\u003csub\u003ef\u003c/sub\u003e), bending modulus Y\u003csub\u003e2\u003c/sub\u003e(E\u003csub\u003ef\u003c/sub\u003e), compressive stress Y\u003csub\u003e3\u003c/sub\u003e(\u0026sigma;\u003csub\u003ec\u003c/sub\u003e), and compressive modulus Y\u003csub\u003e4\u003c/sub\u003e(E\u003csub\u003ec\u003c/sub\u003e). Figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows the graphical representation of the efficiency obtained for each model based on the ANOVA hypothesis. Essentially, the relationship between the normal probability distribution and the internal residuals is established, as well as the relationship between the predicted response, and given the experimental findings regarding stress and Young\u0026apos;s modulus in bending (see Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea) and compression tests (see Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003eb). The curves obtained evaluate the distribution of the predicted values on the ordinate (\u003cem\u003eY\u003c/em\u003e) compared to the experimental values on the abscissa (\u003cem\u003eX\u003c/em\u003e) and show that the fits of the quadratic model are adequate for the responses studied with a normal distribution.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Analysis of 3D response surfaces\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e shows the 3D mechanical responses, with the Z-axis representing the bending strength of the bio-mortars reinforced with sisal fibers, generated by the four elaboration factors combined two by two represented on the X and Y axes. For each response, the significant interaction combinations are highlighted, for which Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003ea shows the interaction effect of the NaOH concentration as a function of the fiber length as well as its effect on the bending stress. The highest stress value of 5.39 MPa was obtained by incorporating 1% of sisal fiber having 5 mm length treated with 1% NaOH. Similarly, the maximization of the bending Young\u0026apos;s modulus is shown in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003eb. For the 3D response surface graph, four more significant interaction combinations are obtained: the fiber % (A) with the NaOH concentration % (C), the fiber % (A) with the fiber length (B), the immersion time (D) with the NaOH concentration % (C), as well as the NaOH % (C) with the fiber length (B). The analysis of these four combinations led to the highest value of Young\u0026apos;s modulus of 1.130 GPa, found between the interaction A and C, while the lowest was 0.766 GPa between the interaction of factors C and D. All the results obtained are summarized in Table \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003eFor the same analysis carried out for compression tests, the 3D response surfaces obtained are shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e. Regardless of the combinations, the maximum increase in stress is observed, when the factor A is maximum (5%), and the others are minimum, i.e. factors B, C and D are equal to 5 mm, 1% and 2h, respectively.\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e shows three combinations of interactions obtained for Young\u0026apos;s modulus under compression, whose maximum value of 48.91 GPa is obtained for l% sisal fibers and with an immersion time of14 h into1% alkaline solution (NaOH).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3 Optimization of manufacturing parameters of bio-mortars\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eAs reported above, the objective of this study is to maximize the bending and compressive mechanical properties of a bio-mortar by optimizing its production parameters. The approach adopted was to create a desirability function based on the RSM methodology to maximize the stress and Young\u0026apos;s modulus of the bio-mortar. For this purpose, it is essential to select the values assigned to the optimized manufacturing factors, as well as to construct desirability indices, with those of a single objective being maximized in the two responses indicated previously. Desirability function values approaching 1 (or 100%) were identified as the most critical parameter values concerning the response factor. In this case, as shown in Table \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, and confirmed by Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e, it can be observed that, following the BBD technique, RSM leads to the 10 best cases progressively among a multitude of solutions.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003eFrom Table \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, and for the two loading modes, it can be observed that the highest responses values are 5.393 MPa and 1.066 GPa for stress and Young\u0026apos;s modulus in bending, respectively, and 37.524 MPa and 43.722 GPa for compression, respectively, and found for a bio-mortar containing 1.00% sisal with a length of 7.94 mm immerged for 14 h in 1.85% NaOH solution. Compared to the experimental values shown in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e (run 12), they are 5.39 MPa and 1.13 GPa for the bending tests and 34.94 MPa and 48.91 GPa for the compression ones, respectively, and were found for a bio-mortar containing 1.00% sisal fiber with a length of 10.00 mm subject to a treatment with 1.0% NaOH for 8 h. Therefore, the results obtained by the desirability function and from the experimental tests are of the same order of magnitude for the bending response (5.39 MPa for the bending stress and 1.07\u0026ndash;1.13 GPa for Young\u0026apos;s modulus, but with the theoretical value within the dispersion range observed for the experimental values). However, for the compressive performance, they are very close and with an error of 7.4% for the compressive stress (37.524\u0026ndash;34.94 MPa) and 10.5% for the compressive Young\u0026apos;s modulus (43.722\u0026ndash;48.91 GPa).Therefore, these results can be reproducible because they were obtained using the desirability function (range 1 in Table \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e) and based on the optimization of the experimental parameters defined for the optimal values of fiber percentage, length, NaOH concentration, and immersion time, which are equal to 1%, 7.95 mm, 1.85% and 14 h, respectively, allowing the achievement of the best mechanical properties. The values of the mechanical characteristics obtained experimentally (best results in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e) are very close to those obtained by the function of desirability function.\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e shows the surface graphs with contour lines that produce the interaction between the different varieties of bio-mortar formulation parameters and their influences regarding the responses, including stress and Young\u0026apos;s modulus in bending and compression, according to the quadratic regression models presented previously by the equations(1), (2), (3) and (4).According to the analysis of the desirability function values, it was possible to determine six of the most significant binary interaction configurations that affect the mechanical characteristics of the bio-mortar, namely: A-B, A-C, A-D, B-C, B-D, and C-D to predict the maximum bending stress and Young\u0026apos;s modulus of 5.39 MPa and 1.06 GPa, respectively, and in compression of 37.52 MPa and 43.72 GPa, respectively (see Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e).\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eIn this study, cement bio-mortars reinforced with short sisal fibers randomly arranged were produced and tested under 3-point bending and compression loading, according to the RSM methodology following an experimental design of 29 tests (L29), with the following main conclusions:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eIn comparison to the reference mortar, the bio-mortar exhibiting optimal mechanical properties was augmented with 1% fiber, measuring 10 mm in length, and subjected to 1% NaOH treatment for 8 hours, resulting in substantial enhancements of 66.3% in compressive strength and 82.8% in Young's modulus. This formulation permits increases of 34.8% in bending stress and 21.5% in modulus. On the other hand, the bio-mortar reinforced with 3% sisal fibers, measuring 10 mm in length and treated with 3% NaOH for 8 hours, has the lowest compressive strength, with a 40.8% decrease relative to the reference mortar;\u003c/li\u003e\n \u003cli\u003eThe fracture damage study indicated that the incorporation of sisal fibers modifies the damage mode, retards crack propagation, and enhances ductility in the bio-mortars;\u003c/li\u003e\n \u003cli\u003eA quadratic model was developed by ANOVA analysis to identify the primary development variables affecting the mechanical properties of bio-mortar, utilizing the highest correlation values R2, Adjusted \u003cem\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e, and Predicted \u003cem\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e. This research demonstrated that the significance of the developmental variables was assessed independently or dependent on the two mechanical characteristics (stress and Young's modulus) and for the two conducted tests (bending and compression). All essential variables from the two replies acquired for each test type were subsequently utilized to derive the final expression of the most suitable mathematical models;\u003c/li\u003e\n \u003cli\u003eThe desirability function created by the RSM analysis allows the optimization of the predicted development parameters of the bio-mortars, as well as the responses assigned to them. This approach leads to the maximization of stress and Young's modulus in bending and compression, and the ten best solutions found have been discussed. Furthermore, the experimental values found are of the same magnitude or very close to those obtained by the desirability function.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors express gratitude to the DGRSDT and ATRST of the Ministry of Higher Education and Scientific Research of Algeria for their support of this research. This research was also sponsored by national funds through FCT – Fundação para a Ciência e a Tecnologia, under projects UID/00285 - Centre for Mechanical Engineering, Materials and Processes and LA/P/0112/2020.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo funding was received from any organization or individuals.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflict or competing financial interests that could have appeared in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT author statement / Authors’ contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eH. Khelifa:\u003c/strong\u003e Conceptualization, Methodology, Data Curation, Writing - Original Draft\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eA. Bezazi:\u0026nbsp;\u003c/strong\u003eConceptualization, Methodology, Validation, Writing - Review \u0026amp; Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eH. Boumediri:\u003c/strong\u003e Methodology, Data Curation, Writing - Original Draft\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eG.G. del Pino:\u0026nbsp;\u003c/strong\u003eMethodology, Investigation, Writing - Review \u0026amp; Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eS. Ellagoune:\u0026nbsp;\u003c/strong\u003eValidation, Writing - Review \u0026amp; Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eP.N.B. Reis:\u003c/strong\u003e Conceptualization, Methodology, Validation, Writing - Review \u0026amp; Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eF. Scarpa:\u0026nbsp;\u003c/strong\u003eMethodology, Validation, Writing - Review \u0026amp; Editing\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eDe Azevedo ARG, Marvila MT, Tayeh BA, Cecchin D, Pereira AC, Monteiro SN (2020) Technological performance of a\u0026ccedil;a\u0026iacute;natural fibrer reinforced cement-based mortars. Journal of Building Engineering33, 101675.https://doi.org/10.1016/j.jobe.2020.101675\u003c/li\u003e\n \u003cli\u003eMishra S, Mohanty AK, Drzal LT, Misra M, Hinrichsen G (2004) A Review on Pineapple Leaf Fibers, Sisal Fibers and Their Biocomposites. Macromolecular Materials and Engineering. 289, 955\u0026ndash;974. https://doi.org/10.1002/mame.200400132\u003c/li\u003e\n \u003cli\u003eTseng ML, Aslam MI,. Ismail E AA, Awwad FA, Gorji NE (2024) CT scan, EBSD and nanoindentation analysis of 3D-printed parts with post-process heat-treatment. Metallurgical Research and Technology. 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Measurement 111, 284\u0026ndash;294. https://doi.org/10.1016/j.measurement.2017.07.054\u003c/li\u003e\n \u003cli\u003eLi M, Pu Y, Thomas VM, Yoo CG., Ozcan S, Deng Y, Nelson K., Ragauskas AJ (2020) Recent advancements of plant-based natural fiber\u0026ndash;reinforced composites and their applications. Composites Part B: Engineering 200, 108254. https://doi.org/10.1016/j.compositesb.2020.108254\u003c/li\u003e\n \u003cli\u003eKorjenic A, Zach J, Hroudov\u0026aacute; J (2015) The use of insulating materials based on natural fibers in combination with plant facades in building constructions. Energy and Buildings Volume 116,45-58.https://doi.org/10.1016/j.enbuild.2015.12.037\u003c/li\u003e\n \u003cli\u003eNdong Engone JG, Vanhove Y, Djelal C, Kada H (2018) Optimizing mortar extrusion using poplar wood sawdust for masonry building block. Int J Adv Manuf Technol 95, 3769\u0026ndash;3780 https://doi.org/10.1007/s00170-017-1323-9\u003c/li\u003e\n \u003cli\u003eKhelifa H, Bezazi A, Boumediri H, Del Pino GG, Reis PNB, Scarpa F, Dufresne A (2021) Mechanical characterization of mortar reinforced by date palm mesh fibers: Experimental and statistical analysis. Construction and Building Materials 300,124067. https://doi.org/10.1016/j. conbuildmat. 2021.124067\u003c/li\u003e\n \u003cli\u003eAkhzeroun A, Semcha A, Bezazi A, Boumediri H, Del Pino G G, Scarpa F (2023) Development and characterization of a new sustainable composite reinforced with date palm stems for rehabilitation and reconstruction of earthen built heritage. Composite Structures 316, 117015 https://doi.org/10.1016/j.compstruct.2023.117015\u003c/li\u003e\n \u003cli\u003eAmziane S, Arnaud L (2007) Bio-aggregate-based Building Materials Applications to Hemp Concretes. Series Editor No\u0026euml;l Challamel. 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(Using 2-in. or [50-mm] Cube Specimens)\u003c/li\u003e\n \u003cli\u003eArs\u0026egrave;ne MA, Okwo A, Bilba K, Soboyejo ABO, Soboyejo WO (2007) Chemically and Thermally Treated Vegetable Fibers for Reinforcement of Cement-Based Composites. Materials and Manufacturing Processes, 22: 214\u0026ndash;227, 2007. DOI: 10.1080/10426910601063386\u003c/li\u003e\n \u003cli\u003eMori Y, Suzuki T(2018) Generalized ridge estimator and model selection criteria in multivariate linear regression. Journal of Multivariate Analysis Volume 165, 243-261. https://doi.org/10.1016/j.jmva.2017.12.006\u003c/li\u003e\n \u003cli\u003eNoryani M, Sapuan SM, Mastura MT, Zuhri MYM, Zainudin ES (2019) Material selection of natural fibre using a stepwise regression model with error analysis. Journal of Materials Research and Technology 8, 2865-2879. https://doi.org/10.1016/j.jmrt.2019.02.019\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTables 1 to 8 are available in the Supplementary Files section\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Sisal fiber, Bio-mortar, RSM methodology, Bending and Compression, Mechanical properties, Desirability function","lastPublishedDoi":"10.21203/rs.3.rs-5844500/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5844500/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe application of lignocellulosic fibers to reinforce mortars with cementitious matrices was investigated for possible use in non-structural applications. A Box-Behnken design L29 (BBDL29) experimental design, using the response surface method (RSM), was used to obtain the combination that maximizes the bending stress and modulus. Four input parameters were evaluated for this purpose: fiber content percentage in the mortar, fiber length, NaOH concentration percentage, and immersion duration. Subsequently, different bio-mortars were produced and tested after 28 days of drying in compression and 3-point bending mode. The results showed that the reinforcement of mortars with sisal fibers allows reductions or increases in mechanical properties, while in literature it generally decreases. In comparison to the reference mortar, the optimal combination exhibited a substantial enhancement of 66.3% and 82.8% in compressive stress and modulus, respectively, while in bending, the increases were 34.8% and 21.5%. The RSM analysis of the mechanical outcomes facilitated the development of a quadratic regression model exhibiting a high correlation coefficients (𝑅2) value. Furthermore, the desirability function was employed in multi-objective optimization to generate ten ideal combinations, yielding results that closely aligned with those obtained experimentally for compressive and bending stresses.\u003c/p\u003e","manuscriptTitle":"Mechanical properties optimization using response surface methodology (RSM) of a bio-mortar manufactured based on sisal fibers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-16 10:52:23","doi":"10.21203/rs.3.rs-5844500/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accept as is for Publication","date":"2025-04-29T15:27:58+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-04-15T14:00:02+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-15T13:59:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-15T07:21:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2025-04-11T12:26:47+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"286b212f-c066-460f-8a06-4f226dc32180","owner":[],"postedDate":"April 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-05-19T16:00:16+00:00","versionOfRecord":{"articleIdentity":"rs-5844500","link":"https://doi.org/10.1007/s00170-025-15664-y","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2025-05-13 15:57:24","publishedOnDateReadable":"May 13th, 2025"},"versionCreatedAt":"2025-04-16 10:52:23","video":"","vorDoi":"10.1007/s00170-025-15664-y","vorDoiUrl":"https://doi.org/10.1007/s00170-025-15664-y","workflowStages":[]},"version":"v1","identity":"rs-5844500","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5844500","identity":"rs-5844500","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}