Response Surface Methodology Optimization of Palm Rachis Biochar Content and Temperature Effects on Predicting Bio-Mortar Compressive Strength, Porosity and Thermal Conductivity

ABSTRACT

Since cement manufacturing contributes significantly to CO₂ pollution worldwide, biochar provides a novel opportunity to integrate it into the construction materials and eventually substitute a portion of cement usage. Consequently, this investigation aims to explore the response surface methodology (RSM) to predict compressive strength and identify optimal values for each parameter that affects the preparation of bio-mortars cement with biochar produced from Washingtonia filifera waste pyrolysis (WFWB). The status of the 7-days and 28-days samples compressive strength, porosity, as well as thermal conductivity of the bio-mortars produced by partially substituting cement at different rates (0%, 1%, 2%, 3%, 4%, and 5%) with pyrolyzed WFWB biochar at varying temperatures (300°C, 400°C, and 500°C) were examined experimentally and statistically. Moreover, the parameter effect on the experimental data performance was identified through analysis of variance (ANOVA). Results indicated an increase in the compressive strength at 28 days of almost 12%, 3%, and 2% at an optimum biochar content of 1% for the WFWB500, WFWB400 and WFWB300 samples respectively. In addition, the findings confer the feasibility of producing bio-mortars with a compressive strength of 63.81 MPa at 28 days with a 1% replacement rate of WFWB500 and coefficient of thermal conductivity of 0.52 W/m.K.

摘要

由于水泥制造在全球范围内对二氧化碳污染做出了重大贡献，生物炭提供了一个新的机会，将其整合到建筑材料中，并最终替代部分水泥使用. 因此，本研究旨在探索响应面方法（RSM），以预测抗压强度，并确定影响用来自华盛顿州丝状菌废弃物热解（WFWB）的生物炭制备生物砂浆水泥的每个参数的最佳值. 在不同温度（300°C、400°C和500°C）下，用热解WFWB生物炭以不同比例（0%、1%、2%、3%、4%和5%）部分替代水泥，对7天和28天样品的抗压强度、孔隙率以及生物砂浆的导热性进行了实验和统计检验. 此外，通过方差分析（ANOVA）确定了参数对实验数据性能的影响. 结果表明，WFWB500、WFWB400和WFWB300样品在最佳生物炭含量为1%时，28天抗压强度分别增加了12%、3%和2%. 此外，研究结果证明了生产28天抗压强度为63.81 MPa、WFWB500替代率为1%、导热系数为0.52 W/m.K的生物砂浆的可行性.

KEYWORDS:

• Cement mortar
• washingtonia filifera waste biochar
• compressive strength, thermal conductivity, optimization
• response surface methodology

关键词:

• 水泥砂浆
• 废料生物炭
• 抗压强度
• 热导率
• 优化
• 响应面方法

1. Introduction

To attenuate CO₂ emissions on the planet, the incorporation of waste into the construction materials is being globally encouraged. Various alternatives were mentioned in the literature, like the incorporation of biomass waste (Shi et al. 2019) and ash (Onorevoli et al. 2018), to replace cement in mortars and concretes to develop new materials. Considerable research has discussed the sustainability issues relating to cementitious materials due to its biomass degradation of alkaline nature (Boumaaza, Belaadi, and Bourchak 2022b). The introduction of biochar to building materials enables carbon sequestration and its enclosure inside the structure for decades. Indeed, biochar can mitigate more than 870 kg of CO₂ equivalent per ton of dry biomass greenhouse gases (Woolf et al. 2010). The biggest advantage of biochar over other bio-based waste products is its generation technique (pyrolysis). This eliminates the emissions from the combustion process, while contributing to waste elimination (Gupta, Kua, and Low 2018). Biochar emerged as a building material, and its utilization as a cement addition/substitute in building materials is currently under development (Maljaee et al. 2021).

However, since biochar has several different raw materials, the conditions and types of biomass preparation are the most significant factors that influence the performance of biochar/cement composites. Numerous investigations have indicated an increase in the compressive strength after the incorporation of biochar into cementitious mortars. Gupta et al. utilized biochar from wood waste and food residues such as rice as a carbon retention admixture in cementitious mortars and achieved the same mechanical strengths as the baseline mortar with 1–2 wt% addition of biochar (Gupta, Kua, and Koh 2018). They also noticed an improvement in compressive strength by more than 20%. (Akhtar and Sarmah 2018) explored the biochar influence on composite mechanical properties by replacing a fraction of the cement by 1% of its volume for various biochar types using rice husk, litter from poultry, and paper wastes. The compressive strength was found to be similar to the baseline material by substituting 0.1 wt% of total mixture with biochar from paper mill sludge. A study by (Ahmad et al. 2015) utilized pyrolyzed bamboo fibers as a reinforcement in cement mortars. It was observed that a minor contribution of 0.08 wt% bamboo biochar improved the compressive strength and mortar matrix toughness. Similarly, Zeidabadi et al. substituted a proportion of cement with rice husk and bagasse biochar (Zeidabadi et al. 2018). They found an improvement of more than 22% and 50% of compressive strength over the concrete baseline for the mix with 10% and 5% by weigth biochar replacement, respectively.

However, flexural strength, tensile strength, and compressive strength depend on input factors such as biochar type, biochar density, pyrolysis temperature, water-cement ratio, etc., which require several sample tests, resources, and time. RSM are highly recognized regression modeling approaches that are capable of providing better prediction of process quality due to their precision and varied use in the engineering field as described by (Boumaaza, Belaadi, and Bourchak 2021) and (Tayebi and Nematzadeh 2021). Lately, RSM had been widely used in the field of construction materials to predict their mechanical properties (Li, Lu, and Gao 2020; Sultana et al. 2020) with many studies being performed in the field of recycled concrete. RSM conceptions utilize a minimum experimental trial number, assess concrete characteristics with reasonable accuracy, and offer high performance when optimizing the input parameters as described in the results by (Benzannache et al. 2021) and (Belaadi et al. 2020). It has been noticed that there is a lack of work in the field of biochar application in WFWB cementitious mortars. Subsequently, the novelty and originality of this study lies in the prediction of bio-mortar properties in the form of porosity, water absorption, thermal conductivity, and compressive strength on the 7th and 28th day of a novel bio-mortar by approach RSM. This investigation will examine the influence of two main variables, the pyrolysis temperature of biochar and mass of substituted cement, in relation to the total volume of cement bio-mortars by partial cement substitution and their optimization, to overcome this knowledge gap. An experimental investigation was conducted to evaluate the bio-mortar properties to develop the predictive models and produce the ideal mix design that are still unknown among biochar-based cement mortars. The RSM models developed will be examined using several pertinent performance parameters such as the determination coefficient (R²), root mean square error (RMSE), mean absolute deviation (MAD) and mean absolute percentage error (MAPE).

2. Research significance

A large variety of waste materials is available and encourage in the construction industry. The utilization of biomass waste in the construction industry has the potential to provide a good alternative to naturally occurring aggregates in concrete and mortar. Many researchers studied the development of biochar applications resulting from biomass pyrolysis and its potential usage to minimize the carbon footprint of cement-based building materials. Therefore, this study is to examine the response surface methodology (RSM) to predict the compressive strength, porosity, and thermal conductivity of bio-mortars by substituting partially cement at various ratios (0%, 1%, 2%, 3%, 4%, and 5%) with biochar produced from the pyrolysis of Washingtonia filifera (WFWB) waste at different temperatures (300°C, 400°C, and 500°C). Thus, the importance of this paper is to determine the influence of biochar rate as well as its pyrolysis temperature on the compressive strength, porosity, as well as thermal conductivity of the produced bio-mortars in order to identify the optimal values for each parameter affecting the bio-mortars preparation. In addition, predictive empirical equations are generated to predict the compressive strength, porosity, and thermal conductivity of the bio-mortars for different biochar contents and temperatures.

3. Materials and methods

3.1. Cement, sand and biochar preparation

WF palm is now a real ornamental tree in rural and urban areas of Algeria. Due to its continued maintenance annual growth, it generates large volumes of agricultural residues valued between 10,000 and 12,000 tons per year, capable of producing great potential as an economic material in industrial applications as a renewable source (Figure 1a). The rachis wastes of WF locally collected in east Algeria in the region of Guelma, is obtained by removing the WF palm leaves (Figures 1b,c). This waste is then reduced to lengths of 30 to 50 cm and used as biomass for the production of biochar. They were then pyrolyzed in an oven for 30 min in the range of 300°C up to 500°C. The biochar was crushed in grinder to obtain finer particles and subsequently placed in a hermetic tank to be chilled to provide bio-mortar. The locally acquired CEM II/A-S 42.5N type cement from an Algerian factory and in accordance with ASTM C150 was utilized in all bio-mortars. For the mortar production, it was used with natural sand obtained from an Algerian company’s quarry, National Society of Aggregates, having a size of 4 mm maximum in accordance with ASTM C33. Biochar grains have a size lower as compared to sand to cement, which indicates these biochar particles provide bonding filler for larger ones.

Figure 1. (a) Washingtonia filifera tree (b) dead palm leafs rachis and (c) rachis waste.

3.2. Experimental conception according to RSM technique

RSM statistical analysis method is very efficient prediction for assessing independent variables influence on responses within limited number of tests as described in the results by (Kursuncu et al. 2022) and (Boumaaza, Belaadi, and Bourchak 2022a). This method is mainly applied if many input variables are influencing the output (response). An orthogonal experimental design using a central composite design (CCD) with two independent variables was chosen to treat the different data using RSM trials using Design Expert 13 software on bio-mortars where cement was replaced partially by WFWB biochar. The actual and coded variable levels are shown in Table 1. The variable levels considered were five levels of biochar content (0%, 1%, 2%, 3%, 4% and 5%) and three levels of pyrolysis temperature (0°C, 300°C to 500°C). After codes are identified and test plan obtained, the tests were conducted, and responses were registered to provide the relations of these variables with the obtained results. The CCD plan was composed of 4 axial (factorial) and 4 cubic points having 8 repetitions in the central locations, which establish an experiment number of 16 carried out based on the two adopted variables: biochar content and pyrolysis temperature with their level during the trials according to (Equation 1(1) $\mathit{N}=2^p+2\mathit{p}+\mathit{r}$(1) ).

Table 1. Configuration of selected parameters and levels for testing.

			Levels
Variable	Unit	Coded	Min (−1)	Medium (0)	Max (+1)
Temperature	°C	B	0	300	500
WFWB	%	A	0	3	5

(1) $\mathit{N}=2^p+2\mathit{p}+\mathit{r}$(1)

with p indicates the number of variables, 2^p denotes the factorial points, 2p represents the axial points, and r denotes remaining tests in the points center.

RSM objective was to perform models regression based on independent variables correlations and their levels predicting output responses as described by (Nematzadeh, Maghferat, and Herozi 2021) and (Dashti and Nematzadeh 2020). These regression models are predicated on the basis of second-order polynomial (Eq. 2).

(2) $\mathit{Y}=B_0+\sum B_i{X}_i+\sum B_{\mathit{ii}}{X}^2+\sum B_{\mathit{ij}}{X}_i{X}_j$(2)

where Y represents the response (the compressive strength or porosity), where B₀ is the constant parameter, and Bi, Bii, and Bij denote linear coefficients, quadratic factors and linear interaction, respectively (Hammoudi et al. 2019).

Table 1 indicates variables and levels specifically the temperature (B) and WFWB biochar wt% (A) utilized to develop experimental design. Variable levels involved in design of experiments (DOE) are denoted as (−1) and (+1) codes, i.e., the lowest and highest values attributed to the factors centered at a mean level (0). In order to perform this research, 16 experiments were conducted depending on variables levels of testing (Table 2).

Table 2. 7 and 28 days compressive strength, porosity, capillary water absorption and thermal conductivity of bio-mortars prepared with biochar at different temperatures.

		Input variables		Outputs
Runs	Code	A-WFRB (%)	B-T (°C)	σc7 (MPa)	σc28 (MPa)	Porosity	WA (%)	Thermal conductivity (W/m.K)
1	Control mortar	0	0	47.24 ± 2.21	56.35 ± 1.02	7.85 ± 0.05	5.03 ± 0.18	0.69 ± 0.05
2	WFRB500–1%	1	500	58.25 ± 1.12	63.81 ± 2.13	7.40 ± 0.02	4.23 ± 0.19	0.54 ± 0.03
3	WFRB500–2%	2	500	46.36 ± 2.36	55.81 ± 1.59	7.83 ± 0.06	4.68 ± 0.18	0.52 ± 0.08
4	WFRB500–3%	3	500	40.12 ± 1.26	49.82 ± 2.91	8.20 ± 0.09	5.30 ± 0.21	0.49 ± 0.01
5	WFRB500–4%	4	500	36.54 ± 1.78	45.82 ± 2.09	8.95 ± 0.08	6.35 ± 0.22	0.47 ± 0.02
6	WFRB500–5%	5	500	30.65 ± 0.98	39.87 ± 2.79	9.44 ± 0.09	6.79 ± 0.22	0.45 ± 0.07
7	WFRB400–1%	1	400	55.66 ± 1.46	58.03 ± 2.49	7.32 ± 0.09	4.12 ± 0.22	0.56 ± 0.05
8	WFRB400–2%	2	400	43.24 ± 2.01	49.4 ± 2.67	7.70 ± 0.08	4.57 ± 0.16	0.53 ± 0.04
9	WFRB400–3%	3	400	38.11 ± 1.06	45.33 ± 1.56	8.20 ± 0.06	5.21 ± 0.18	0.52 ± 0.03
10	WFRB400–4%	4	400	34.37 ± 2.16	42.16 ± 2.34	8.75 ± 0.06	6.25 ± 0.21	0.50 ± 0.05
11	WFRB400–5%	5	400	29.35 ± 1.96	35.43 ± 2.44	9.40 ± 0.04	6.73 ± 0.20	0.49 ± 0.09
12	WFRB300–1%	1	300	51.42 ± 2.46	57.26 ± 1.23	7.10 ± 0.06	4.04 ± 0.18	0.59 ± 0.05
13	WFRB300–2%	2	300	40.28 ± 1.16	46.87 ± 1.59	7.57 ± 0.07	4.50 ± 0.16	0.54 ± 0.04
14	WFRB300–3%	3	300	37.44 ± 1.24	44.96 ± 2.88	8.18 ± 0.08	5.16 ± 0.14	0.53 ± 0.02
15	WFRB300–4%	4	300	32.19 ± 1.66	40.01 ± 1.39	8.72 ± 0.08	6.18 ± 0.11	0.51 ± 0.05
16	WFRB300–5%	5	300	28.63 ± 1.06	36.1 ± 1.57	8.99 ± 0.09	6.68 ± 0.16	0.49 ± 0.08

Note: WFRBX°C-Y%: X°C (Temperature), Y% (% biochar).

3.3. Bio-mortars production

Bio-mortars composed of a mixture with sand and partly substituted cement with WFWB biochar being manufactured according to the experimental plan. A mechanical mixer meeting the recommendations of ASTM C305 was used to mix the mortar samples. A total of 16 series of experiments were performed. The bio-mortar mixes were placed in cylindrical molds with sizes of 50 by 50 mm to obtain samples for compressive strength testing. All samples cast, were subsequently removed from the mold after 24 h and conserved at ambient temperature (23 ± 2°C). Cement, sand and water proportions used for the bio-mortars mix were of 1:3:0.5.

3.4. Determination of biochar reinforced bio-mortar properties

3.4.1. The capillary water uptake measure

Cementitious mortar water uptake was determined at 28 days according to the capillary water uptake test, as defined in ASTM C1585. To determine the rate of water absorption in cement mortars, three specimens were studied with a 50 ± 3% humidity and 23 ± 1°C air temperature for each mortar type. The specimens were regularly taken out of the water to measure their water retention at different intervals. The specimens were desiccated at 90°C for 48 h and to cool at ambient conditions for 5 h before initial mass determination. The samples were subsequently weighed at 5 min, 10 min, 30 min, 1 h, 24 h, 48 h, 72 h, 96 h, 120 h, 144 h, 168 h and 192 h (Tan et al. 2020). The % water absorption in the reference mortar and the biochar containing mortars was measured at selected time periods up to completely saturated. Water uptake is calculated by the formula Eq 3. Where M_dry is the oven dry mass after 48 h (g); M_sat stands for mass saturated after specimen immersion (g).

(3) $\mathit{WA}\left(\mathrm{\%}\right)=100\frac{{\mathit{M}}_{\mathit{sat}}-M_{\mathit{dry}}}{M_{\mathit{dry}}}$(3)

3.4.2. Porosity measurement

Porosity is important for all granular mixes and for all applications involving granular materials. The hydrostatic balance was used to evaluate the water available (porosity), conforming to the NF AFNOR 2010. Porosity was determined using the hypothesis that the specimen pores would be completely saturated during the immersion period with water (Zhang et al. 2023). Thus, the mass loss caused by oven curing would be a measure of pore space filled with water. The porosity P was determined using the mass of the samples taken in water, M_water, in saturated air, M_air, and oven-dried at 90°C, M_dry, according to the following equation:

(4) $\mathit{P}\left(\mathrm{\%}\right)=100\frac{\left({\mathit{M}}_{\mathit{air}}-M_{\mathit{dry}}\right)}{\left(M_{\mathit{air}}-M_{\mathit{water}}\right)}$(4)

3.4.3. Thermal conductivity

The thermal conductivity represents a significant parameter indicating the capacity of a construction material to provide thermal conductivity. As the material is more thermally insulating, the factor λ will be lower. For this purpose, various samples of bio-mortar were tested for their thermal conductivity with a thermo-test apparatus using ASTM D5930 standard procedure. After curing for 28 days, the thermal conductivity λ (W/m.K) was measured for all three prismatic sizes (40 × 40 × 160) mm³ for each specimen performed. The thermal conductivity could be determined using the average value:

$\mathit{\lambda }=\frac{\mathit{Q}\mathrm{x}d}{2\mathrm{x}A\mathrm{x}\left(T_1-T_2\right)}$

Where Q (W) is the heating power of the heating unit; d (m) is the width of the specimen; A (m²) is the effective heat transfer area, T₁ and T₂ (K) are the temperatures of the heating unit and cooling unit, respectively.

3.4.4. Compressive test

Compression tests were conducted after a curing period of 7 and 28 days with a universal Servo Electric testing machine Zwick/Roell Z005 having a 5 kN load cell at 2 mm/min displacement speed according to ASTM C109. A computer enabling data transmission with test Xpert V10.11 software monitored the machine. The compressive strength at 7 and 28 day was determined for three samples investigated in each mixture.

4. Statistical and experimental analysis results

4.1. WFWB biochar effect on compressive strength

The test results of compressive strength at 7 and 28 days after substituting cement with WFWB300, WFWB400, and WFWB500 are shown in Table 2 and Figure 2a,b. As a result, all the findings showed adequate coherence. During the first days of curing, a typical variation in the compressive strength of the cement mortars incorporated with biochar was observed as the biochar content increased. Replacing cement partially with biochar caused a decrease in 7- and 28-day compressive strength, excluding the 1% by weight addition of biochar. Replacing cement with 2% WFWB500 resulted in a 2% and 1% decrease in 7-day and 28-day compressive strength, respectively. However, the compressive strength of 1% of added WFWB500 was found to be 58.25 MPa and 63.81 MPa, which is 23% and 13% greater than the baseline specimen with 47.24 and 56.35 MPa at the 7^th and 28^th days, respectively. On the other hand, the addition of 1% of WFWB400 and WFWB300 caused an increase in compressive strength of 18% and 9%, respectively, on the 7th day and 3% and 2%, respectively, on the 28th day, compared to bio-mortar without biochar. However, adding 3, 4, and 5% of WFWB500 led to a decrease in resistance of 1%, 11%, and 18%, respectively, at 28 days. In addition, an identical tendency is noticed where the addition of 2%, 3%, 4% and 5% of WFWB400 and WFWB300 decreased the compressive strength. When the percentage of WFWB is higher than 2%, the decrease in compressive strength of WFWB300 was found to be significantly greater, compared to WFWB400 and WFWB500, owing to the greater hydrophilicity and storage capacity of WFWB, which is produced at a pyrolysis temperature of 300°C. For proportions above 2%, WFWB particles in the bio-mortars attract water, which inhibits hydration and decreases the compressive strength of bio-mortars with WFWB. The results of this research corroborate with other investigations where the inclusion of biochar in smaller substitution levels resulted in increased compressive strength (Praneeth et al. 2021; Sirico et al. 2021). As such, Gupta et al. (Gupta, Kua, and Pang 2018), observed that 1 and 2 wt% addition of biochar pyrolyzed by 500°C and 300°C resulted in an improved compressive strength of (14%, 10%) and (7%, 3%), respectively, in comparison to the base mortar. In fact, the compressive strength increased up to 1% substitution of cement with biochar and decreased for the other percentages for all specimens. The compressive strength increased less for WFWB400 and WFWB300 than for WFWB500 and this for 1% of WFWB. An analogous result is reported by (Tan et al. 2020), 1% pyrolyzed biochar content at 500°C gave a compressive strength of about 52 MPa, which was 20% higher than the baseline mortar. Nevertheless, the mortar with higher biochar content (5% and 10% by weight) showed a reduced compressive strength. However in the study conducted by the authors recently on the prediction of bending properties of bio-mortar produced by partially substituting cement with the same WFRB (Boumaaza et al. 2022). It was also observed that a partial cement replacement of 1% WFRB pyrolysis at 500°C, exhibited improvements in flexural modulus, flexural strength, and displacement of 265%, 5%, and 20%, respectively, over the control mortar.

Figure 2. Experimental values of (a) 7 days, (b) 28 days compressive strength, (c) porosity, (d) capillary water absorption and (e) thermal conductivity of bio mortars versus wt % biochar pyrolyzed in the range of 300°C, 400°C and 500°C.

4.2. Biochar inclusion influence on porosity, capillary water absorption and thermal conductivity

Water accessible porosities results are reported in Table 2. Accordingly, the 1% and 2% cement substitutes with WFWB500, WFWB400, and WFWB300 biochar produced porosity values of (7.40%, 7.32% and 7.10%) and (7.83%, 7.70% and 7.57%), respectively, lower than the baseline bio-mortar porosity of 7.85%. Indeed, a very small decrease in porosity for 2% WFWB500 content. Increases of 5%, 14%, and 20% were obtained for bio-mortars formulated with 3%, 4%, and 5% substitution of cement with WFWB500 biochar, respectively (Figure 2c). The decrease in porosity with 1% and 2% of cement weight substitution by WFWB biochar is associated to the reduced water uptake capacity. In addition to the bio-mortar blend, the biochar soaked up and maintained some of the curing water, thus causing the quantity of loose water contained in the wet mixture to decrease. The increased porosity of bio-mortar with 3%, 4% and 5% biochar is due to a high proportion of porous biochar particles that impacts the consistency of mortar, thus leading to more voids in cured mortars (Achour, Ghomari, and Belayachi 2017). Analogous findings were reported by (Maljaee et al. 2021) where a partial cement substitute with 1–4 wt% biochar resulted in increased porosity of the cement mortars because of its pores present in its texture. In addition, Gupta et al. (Gupta, Kua, and Pang 2018) noticed lower fluidity in mixtures with high content 5–8 wt% biochar in the composition of mortars, impacted mortar compactness, leading also to higher porosity in the cured mortar. The reported findings corroborated with those observed by Gupta et al. (Gupta and Kua 2018), where the biochar produced at 500°C displayed more closely intersecting pores of uniform form over the biochar at 300°C, which ascribed to fuller liberation of volatiles and organics at an increased pyrolysis temperature. The compressive strength plotted against porosity was illustrated in Figure 3a where there is a clear reduction in the compressive strength as porosity increased.

Figure 3. (a) Compressive strength 28-days (b) capillary water absorption and (c) thermal conductivity according to porosity of the bio-mortars.

The experiment was performed over a period of 8 days for samples dated 28 days. The profile of capillary uptake of water in bio-mortars containing 1–5% WFWB prepared at 500°C (p-values are less than 0.05 at 95% confidence interval) is illustrated in Figure 2d. A linear regression of the slope of water uptake, which occurred for the initial 6-hours -period of testing ($\sqrt{\mathit{second}}=147$), can be used to obtain the primary level of uptake. The subsequent process of water uptake corresponds to the secondary level of water uptake, where water seals the minor voids in the specimen continuously to saturation (1 to 8 days). The findings revealed that the water uptake was reduced in the samples containing 1–2 wt% WFWB500 compared to the control mortar, while for 3%, the absorption was similar to the control. This decrease can be explained by the hydrophilicity of WFWB, which causes an increased friction with the capillary wall inside the mortar, thus leading to the decreased capillary water uptake rate. However, increasing the WFWB500% by 4% and 5% by weight increased the capillary water absorption by 26% and 35%, respectively. This result was in agreement with Tan et al. (Tan et al. 2020), who stated that higher water uptake with increased content of WFWB in the bio-mortar was likely caused by the increasing void ratio in the mortar. A similar tendency was observed in the capillary water uptake results for WFWB400 and WFWB300, which indicates that the capillary water uptake increased with an increase in the WFWB inclusion rates, but reduced in specimens with 1 wt% and 2 wt% WFWB. These findings correlated well with the porosity measurements of the mortar that contained 1–5% WFWB as shown in Figure 3b.

The variation of thermal conductivity with biochar content is shown in Figure 2e. The findings indicated a decrease in thermal conductivity as the biochar content increased. Nevertheless, the thermal conductivity of bio-mortars with 1–5% biochar pyrolyzed to 500°C, 400°C and 300°C reduced by 22–35%, 19–29% and 15–41%, respectively, compared to the reference mortar. This demonstrates the significant effect of biochar content on thermal conductivity. These results were obtained due to the increased porosity of cured bio-mortars caused by the elevated biochar water uptake ability, which results in a swell ability on contact with water, thus resulting in the reduced thermal conductivity of the bio-mortar. This results corroborated with literature reports (Tan et al. 2020). Figure 3c depicted the thermal conductivity data variation according to the porosity. A slight reduction in thermal conductivity was observed as the biochar pyrolysis temperature increased. Thermal conductivity of WFWB500-reinforced bio-mortars for 1% and 5% content was about 8% and 7% lower than that for the WFWB300 alternative, respectively. The results agreed with those observed in literature (Tan et al. 2020).

4.3. Conception of mathematical model

This research was conducted in accordance with CCD to obtain the influence of different parameters to predict the 7-day and 28-day compressive strength, porosity, and thermal conductivity of the bio-mortar mix for various factor values. The quadratic models satisfy the choice conditions identified before, as they show the highest coefficients in terms of correlation, predicted R² and adjusted R² (Table 3). Moreover, the linear and 2FI models were also inappropriate based on their considerably small correlation coefficients. On the other hand, the cubical model was dismissed due to the imprecision in adjusting the plots. To determine significance and relationship of the variables according to each individual response model, an analysis of variance (ANOVA) was performed (Table 3). For CCD design, the model fitting process is performed iteratively to obtain a precise model for the response. Initially, for estimating the variable-response dependence using experimental data, a quadratic model (Equation (5)(5) ${\sigma }_{\mathit{c}7}=47.2591-10.1759\ast \mathit{WFWB}+0.05220\ast \mathit{T}-0.0058\ast \mathit{WFWB}\ast \mathit{T}+1.0820\ast \mathit{WFW}{B}^2-\mathit{\hspace{0.17em}}0.000015\ast T^2$(5) to (8(8) $\mathrm{Thermal}\mathrm{conductivity}=0.6890-0.0357\ast \mathrm{WFWB}-0.0002\ast \mathrm{T}+0.0001\ast \mathrm{WFWB}\ast \mathrm{T}+\mathit{\hspace{0.17em}}0.0016\ast \mathrm{WFW}{\mathrm{B}}^2+1.5798\mathrm{e}-08\ast {\mathrm{T}}^2$(8) )) is adopted. It is then monitored by eliminating irrelevant terms in the model using statistical analysis. The results obtained from the ANOVA analysis indicated an adequate description in the equations of the relationship between the independent factors and the responses. Additionally, correlation coefficients and P-values of the acquired model were discussed.

Table 3. ANOVA of quadratic model for bio-mortar/biochar compressive strength at 7 and 28 days, porosity and thermal conductivity.

Source	DF	SS	MS	F-value	Prob.	Remarks
a) σc7 (MPa)
Model	5	1238.30	247.66	125.12	<0.0001	significant
A-WFWB	1	252.47	252.47	127.55	<0.0001
B-Temperature	1	37.71	37.71	19.05	<0.0014
AB	1	7.38	7.38	3.73	0.0224
A^2	1	49.89	49.89	25.20	0.0005
B^2	1	0.5197	0.5197	0.2626	0.6195
Residual	10	19.79	1.98
Cor Total	15	1258.09
SD = 1.41 Mean = 40.55 Coefficient of variation = 3.47			R^2 = 0.9843 R^2 adjusted = 0.9764		R^2 predicted = 0.9659 Adequate precision = 33.2224
b) σc28 (MPa)
Model	5	1027.00	205.40	166.35	<0.0001	Significant
A-WFWB	1	134.78	134.78	109.15	<0.0001
B-Temperature	1	5.71	5.71	4.62	0.0057
AB	1	10.51	10.51	8.51	0.0154
A^2	1	4.36	4.36	3.53	0.0297
B^2	1	15.37	15.37	12.45	0.0055
Residual	10	12.35	1.23
Cor Total	15	1039.34
SD = 1.11 Mean = 47.98 Coefficient of variation = 2.32			R^2 = 0.9881 R^2 adjusted = 0.9822		R^2 predicted = 0.9156 Adequate precision = 40.4181
c) Porosity (%)
Model	5	8.17	186.58	158.11	<0.0001	significant
A-WFWB	1	1.37	1.37	132.61	<0.0001
B-Temperature	1	0.0596	0.0596	5.76	<0.0373
AB	1	0.0156	0.0156	1.51	0.0498
A^2	1	0.0054	0.0054	0.5240	0.0697
B^2	1	0.1535	0.1535	14.85	0.0032
Residual	10	0.1033	0.0103
Cor Total	15	8.27
SD = 0.1016 Mean = 8.23 Coefficient of variation = 1.23			R^2 = 0.9875 R^2 adjusted = 0.9768		R^2 predicted = 0.9642 Adequate precision = 36.9806
d) Thermal conductivity (W/m.K)
Model	5	0.0472	0.0094	250.94	<0.0001	Significant
A-WFWB	1	0.0042	0.0042	110.61	<0.0001
B-Temperature	1	0.0019	0.0019	49.63	0.0001
AB	1	0.0002	0.0002	0.6333	0.4446
A^2	1	0.0001	0.0001	2.82	0.1237
B^2	1	0.0000	0.0000	0.0160	0.0142
Residual	10	0.0004	0.0000
Cor Total	15	0.0476
SD = 0.0061					R^2 = 0.9921
Mean = 0.5262 Coefficient of variation = 1.17					R^2 adjusted = 0.9881 R^2 predicted = 0.8677 Adequate precision = 62.0227

(5) ${\sigma }_{\mathit{c}7}=47.2591-10.1759\ast \mathit{WFWB}+0.05220\ast \mathit{T}-0.0058\ast \mathit{WFWB}\ast \mathit{T}+1.0820\ast \mathit{WFW}{B}^2-\mathit{\hspace{0.17em}}0.000015\ast T^2$(5)

(6) ${\sigma }_{\mathit{c}28}=56.4465-4.4095\ast \mathit{WFWB}-0.0108\ast \mathit{T}-0.0069\ast \mathit{WFWB}\ast \mathit{T}+0.3198\ast \mathit{WFW}{B}^2+\mathit{\hspace{0.17em}}0.0001\ast T^2$(6)

(7) $\mathit{Porosity}=7.8581+0.3349\ast \mathit{WFWB}-0.0058\ast \mathit{T}+0.0002\ast \mathit{WFWB}\ast \mathit{T}+0.0112\ast \mathit{WFW}{B}^2-7.9840\mathrm{e}-06\ast T^2$(7)

(8) $\mathrm{Thermal}\mathrm{conductivity}=0.6890-0.0357\ast \mathrm{WFWB}-0.0002\ast \mathrm{T}+0.0001\ast \mathrm{WFWB}\ast \mathrm{T}+\mathit{\hspace{0.17em}}0.0016\ast \mathrm{WFW}{\mathrm{B}}^2+1.5798\mathrm{e}-08\ast {\mathrm{T}}^2$(8)

The model F-values for 7-day and 28-day compressive strength, porosity and thermal conductivity models were 125.12, 166.35, 158.11 and 250.94 respectively, thus indicating the excellent significance of these models obtained by ANOVA analysis. Furthermore, the p values (<0.0001) were considerably less than 0.05 and validate the significance model terms. While the terms A, B, AB, and A² were considered significant for the compressive strength on the 7^th and 28^th day, the terms A, B, and B² were considered important for porosity and thermal conductivity in the current models. The discrepancy in the R² predicted and R² adjusted values was found to be less than 0.2 in all models and the accuracy values (good accuracy) that assess signal-to-noise values, which were 33.22, 40.42, 36.98, and 62.02 for the 7-day and 28-day compressive strength, porosity, and thermal conductivity models, respectively, were greater than 4. These values indicate an appropriate signal, and allow the utilization of these models to investigate the conceptual field. Additionally, it is important to validate the fitting and accuracy of the quadratic models of biochar-based bio-mortars using diagnostic graphs to the experimental values. Figure 4 shows the precision and pertinence of the models through plotting. The experimental data distribution was estimated with the normal probability approach which is commonly employed to evaluate the distribution of the data using a normal probability plot. All data was noticeably distributed approximately normally, as illustrated in Figures 4a–j because the data, which was visualized using the graph, was plotted and dispersed along a right straight. The comparison of the predicted and actual values reveals a right line distribution of the points to the diagonal, and thus indicates the perfect relevance of the model-predicted values (Figure 4b–k). The residuals plot showed a clustering of values aligned on a straight line, which indicated an error of normal distribution. In addition, in order to assess the precision of the predicted equations, residual analysis was investigated. The residual scattering, as suggested by (Aziminezhad, Mahdikhani, and Memarpour 2018), did not contain the undesired distribution modes, especially the important residuals. Following which, in a subsequent process, the accuracy of the model was evaluated through residual testing such as residual graphs and residual standard error, where the adequacy of the chosen model is graphically judged. The residual in the current model was small and evenly scattered over the entire data range, thus showing no errors in the data as observed in (Figures 4c–l).

Figure 4. Normal probability versus residuals, Actual versus predicted and Residuals versus predicted plots of (a-c) 7 days compressive strength, (d-f) 28 days compressive strength, (g-i) porosity and (j-l) thermal conductivity bio-mortars data.

4.4. Principal effects and response surface curves of bio-mortars

After the compressive strength, the porosity and thermal conductivity models were validated, the main effects and results of response surface curves were examined. Figure 5 illustrated the main effects of content WFWB and the pyrolysis temperature biochar on the compressive strength at 7 and 28 days, porosity and thermal conductivity of bio-mortars. Figure 5a and b showed that the compressive strength increases until the pyrolysis temperature reached 500°C and decreased when the percentage content WFWB increased. Furthermore, Figure 5c and d showed that increasing the pyrolysis temperature slightly decreased the porosity and thermal conductivity, however, the higher WFWB content, made the porosity increased, but the thermal conductivity decreased, confirming further the experimental results. Figures 6 and 7 show the responses surface and 3D curves for the interaction of the two factors pyrolysis temperature and WFWB on compressive strength at 7 and 28 days, porosity and thermal conductivity. It can be noticed that the compressive strength increased with increasing pyrolysis temperature and that increasing the WFWB content boosted the porosity and improved the thermal conductivity.

Figure 5. Principal effects plot (a) 7 day compressive strength data, (b) 28 day compressive strength data, (c) porosity and (d) thermal conductivity.

Figure 6. Surface contour tracings (a) 7 day compressive strength data, (b) 28 day compressive strength data, (c) porosity and (d) thermal conductivity.

Figure 7. 3D response plots RSM models: (a) 7 day compressive strength data, (b) 28 day compressive strength data, (c) porosity and (d) thermal conductivity.

After investigating the effect of experimental parameters on the 7-day and 28-day compressive strength, porosity, and thermal conductivity of bio-mortars, the ranges of these variables that result in the optimal values were identified. The desirability portion of the Design Expert software was utilized to optimize the models. This function provides information about the input and output (desired response) of the optimal parameters simultaneously based on optimal levels of the input parameters (Figure 8). The maximum values of the 28-day compressive strength, porosity, and thermal conductivity obtained from optimization using the software were 63.45 MPa, 7.37%, and 0.54 W/m.K, respectively. The associated values for the pyrolysis temperature and WFWB content were 500°C and 1%, respectively as shown in Table 4 and Figure 9.

Figure 8. Optimal values of compressive strength and porosity corresponding to optimum parameters of bio-mortars with a desirability = 0.816.

Figure 9. Optimal parameters for bio-mortars (a,b) 7 days compressive strength data, (c,d) 28 days compressive strength data, (e,f) porosity and (g,h) thermal conductivity.

Table 4. Best solutions of bio-mortar production parameters with corresponding responses.

Number	T°C	WFWB%	σc28	Porosity	Thermal conductivity	Desirability
1	500.000	1.000	63.455	7.397	0.540	0.988	Selected
2	500.000	1.151	63.348	7.405	0.536	0.983
3	500.000	1.000	63.203	7.393	0.548	0.979
4	485.000	1.000	62.298	7.154	0.558	0.962
5	482.649	1.000	62.124	7.157	0.564	0.958
6	465.000	1.000	60.877	7.181	0.565	0.930
7	456.205	1.000	60.296	7.193	0.568	0.917
8	411.325	1.000	57.760	7.253	0.569	0.857
9	408.885	1.000	57.642	7.257	0.570	0.855
10	385.000	1.000	56.602	7.288	0.572	0.828

5. Conclusion

This study aimed to contribute to environmental protection by partially substituting cement with biochar obtained by Washingtonia filifera pyrolysis waste for the manufacture of bio-materials. Substitution of biochar produced from Washingtonia filifera rachis waste for 1 and 2 wt% cement in bio-mortar mixes increased the compressive strength. However, at higher rates exceeding 2%, when biochar was incorporated as a cement substitute, the compressive strength decreased, which is attributed to low porosity by the addition of 1 and 2 wt% of WFWB, compared to that of an addition of 3, 4, and 5 wt%. In addition, the substitution of cement with WFWB500 biochar provided superior strength, compared to WFWB400 and WFWB300, in the developed bio-mortars. However, the porosity and capillary water absorption of bio-mortars showed increases in specimens with higher biochar content and a significant improvement in thermal conductivity, which favors their application as insulating materials. RSM models were found to be adequate and appropriate for predicting the compressive strength, porosity, and thermal conductivity. The local accessibility of Washingtonia filifera wastes makes their incorporation as a biochar substitute for cement very suitable for various purposes related to paving and unstructured building elements, road concrete, and joints mortar. It is important to consider that the use of 1% WFWB in the cementitious matrix provides a composite with improved thermal and mechanical properties.

Although many investigations were conducted of the properties of mortars incorporating natural fibers, limited research exists in the literature on the use of biochar from biomass pyrolysis in mortars. Furthermore, no research was performed on the substitution of cement with biochar from Washingtonia filifera fiber waste in cementitious mortars even after the mentioned references. The use of natural wastes in construction can provide a positive environmental substitute for natural aggregates in concrete and mortar. There are many researchers exploring the development of biochar applications in the cementitious mortars as well as the possible application of biochar produced by biomass pyrolysis in order to mitigate the carbon footprint of cement building materials. Due to the easy availability and low cost of environmentally wastes, their incorporation as a cement substitute as biochar is strongly suggested in several applications like pavement mortar, paving, joint mortar and non-structural concrete elements. For further work, the experimental program will induce other mixes with varying proportions of cement-sand and several ranges of water-to-binder ratio.

Highlights

• Compressive strength, porosity and thermal conductivity of the bio-mortar substitute cement with WFWB were measured

• Compressive strength decreases with increasing porosities in bio-mortars.

• An optimization process for bio-mortar mixture offering the highest CS.

• The RSM models of CS, porosity and thermal conductivity can be deployed to predict new bio-mortar mixtures.

Acknowledgment

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under grant no. (KEP-3-135-42). The authors, therefore, acknowledge with thanks DSR technical and financial support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors declare no funding information.