Assessing the biocementation of lateritic soil using hydraulic conductivity and bioinspired optimization approach

Abstract

The effectiveness of microbially induced calcite precipitation (MICP) in reducing the hydraulic conductivity (HC) of soils has been evaluated in several geotechnical engineering applications. However, optimizing MICP parameters to achieve minimal hydraulic conductivity for waste containment liners remains underexplored. This study presents a comprehensive laboratory analysis investigating the influence of bacterial suspension density and compaction energy on compacted lateritic soil, prepared under varying moisture conditions. Bacillus megaterium (B. megaterium) was introduced at different suspension densities, followed by compaction. Results revealed that increased bacterial density and compaction energy significantly reduced hydraulic conductivity due to calcite formation, confirmed through XRD, SEM, XRF, and FTIR analyses. To optimize the hydraulic conductivity, bio-inspired algorithms including particle swarm optimization (PSO), smell agent optimization (SAO), and bacterial foraging optimization (BFO) were deployed. Successive iterations demonstrated that PSO achieved the lowest hydraulic conductivity (k = 2.27 × 10⁻¹¹ m/s), followed by SAO (k = 2.85 × 10⁻¹¹ m/s) and BFO (k = 2.66 × 10⁻⁹ m/s). These findings highlight the critical role of compaction effort, moisture content, and bacterial density in designing compacted lateritic soil liners for geotechnical applications. Optimization results underscore PSO’s superior performance in achieving design criteria for liners.

Introduction

The growing global concern regarding waste management has emphasised the need for effective waste containment systems that minimize environmental risks. In particular, the management of hazardous and non-hazardous waste in landfills requires advanced engineering solutions to prevent leachate migration and soil contamination. Soil stabilization techniques have become increasingly important in this regard, with microbial-induced calcite precipitation (MICP) emerging as a promising approach. This eco-friendly method utilizes naturally occurring microorganisms to precipitate calcium carbonate, thereby enhancing soil strength and reducing hydraulic conductivity^1,2,3,4,5. It can be particularly beneficial for weak or loose soils, such as sandy or silty soils, and can help in improve their load-bearing capacity⁶.

MICP has been used in a variety of applications, including; soil stabilization for construction projects, erosion control⁷ and the remediation of contaminated soils^8,9 restoration of calcareous stone materials¹⁰ bioremediation¹¹ reinforcement of concrete¹² contaminants immobilization^13,14 erosion mitigation and water infiltration control¹⁵ lessening of hydraulic conductivity and enhanced soil strength^1,16,17 reduction in the saturation as well as liquefaction prospective of soil¹⁸ reduce desiccation induced shrinkage in soils^19,20,21 improve plasticity of clay soil^22,23. MICP compatibility investigations involving lateritic soil relationship with leachate have also been reported by Osinube et al.,²⁴.

Lateritic soils, which have abundance of iron as well as aluminium oxides, possess unique properties that make them suitable for use in waste containment applications. These soils are abundant in tropical regions and have been recognized for their engineering characteristics, such as good load-bearing capacity and resistance to erosion^25,26. However, their inherent variability in hydraulic conductivity poses challenges when considered as liners in waste containment structures. Understanding how to optimize these soils through bio-cementation techniques is crucial for improving their performance in real-world applications²⁷ .

Despite the potential benefits of using bio-cemented lateritic soils in waste containment application, significant challenges still exist and need to address. Existing researches done predominantly focused on sandy and coarse-grained soils with limited studies on tropical lateritic soils. Consequently, there is limited understanding of how various factors-such as compaction energy, moisture content, and microbial concentration-interact to affect the hydraulic conductivity of bio-cemented lateritic soils^28,29. The current literatures lacks systematic investigations that assess the joint effects of compaction energy and moisture content on the hydraulic properties of bio-cemented lateritic soils. Furthermore, the existing research has not adequately explored the optimization of these parameters using algorithms that can effectively model and predict soil performance under varying conditions. As a result, the application of bio-cementation in waste containment systems remains underexplored and lacks clear practical guidelines. Optimization of MICP processes using advanced techniques such as PSO, SAO and Bacteria Foraging Optimization (BFO) remains underexplored. These optimization methods have demonstrated efficacy in various domains but are yet to be comprehensively employed to enhance MICP efficiency and precision.

The objective of this study is to optimize bio-cemented lateritic soil through a comprehensive laboratory analysis as well as bio-inspired optimization approach. This study is projected to make substantial assistances to the fields of soil bio-stabilization and waste management engineering. The study aims to establish evidence-based protocols for enhancing soil stabilization techniques. The findings could serve as a panacea to engineers and environmental scientists on how to optimize soil properties for effective waste containment solutions, thereby improving the sustainability and safety of landfill operations³⁰. Additionally, the study will contribute to the growing body of knowledge surrounding MICP, by bridging the gap between laboratory research and practical application. The application of optimization algorithms helps in facilitate the translation of experimental results into practical guidelines, enabling the efficient design of bio-cemented soil liners that meet regulatory requirements, and environmental standards³¹.

Materials and methods

Materials

Soil

Samples of disturbed reddish-brown soil were gathered from a gully erosion site located in Njikoka (6°10′00′′ N and 7°0′0′′ E), Anambra state, Nigeria. The location map of the study area is shown in (Fig. 1). The initial step involved clearing debris of organic materials from the surface within the soil sampling area. This was done to prevent soil contamination with the insitu organic deposits which can affect the soil’s response to MICP and distribution of calcite. Soil samples were obtained at a depth of 1 m to 1.5 m. Ensuring preservation, these samples were carefully stored in waterproof bags and subsequently transported to the Soil Mechanics Research Laboratory at Ahmadu Bello University (ABU). Under natural laboratory conditions, the samples were air-dried, and dried lumps were further broken down into finer particles and sieve through 4.75 mm sieve. It is noteworthy that lateritic soils are not confined to the study location, as residual deposits extend throughout the southern geographical region of Nigeria. Chemical characterization of the samples carried out include X-ray fluorescence (XRF) analysis using the NitonTM XL3t XRF analyzer, X-ray diffraction (XRD), and infrared analysis (IR). The XRF analysis was done at Centre for Minerals Research & Development (CMRD) laboratory at Kaduna Polytechnic, Nigeria. XRD analysis was conducted at National Geo-Science Research Laboratories in Kaduna state, Nigeria. Additionally, IR spectroscopy was carried out in the multipurpose user laboratory ABU Zaria Nigeria.

Fig. 1

map of location study.

Constitution of cementation solution and bacterial suspension density

The cementation solution was used to enhance calcite precipitation while at the same time, the presence of calcium chloride in the mixture increases the rate of calcium carbonate precipitated. The weight of individual reagents by composition that make up to 0.5 M concentration are: CO(NH₂)₂ (30.03 g), NaHCO₃ (2.12 g), NH₄Cl (10 g), CaCl₂ (55.49 g) Nutrient broth (3 g) dissolved in 1 L of water. The preference of 0.5 M of cementing solution applied in this research is the optimal concentration obtained in the earlier part of this study⁴. Therefore, this section of study is an extension of investigations not covered in the initial report by same authors. The cementing solution was prepared under non-sterile condition as the cementing solution was arranged using tap water and was not subjected to autoclaving in order to mimic the actual occurrence in the field. This approach was used because it will be problematic to conduct autoclaving in large-scale field implementation.

The bacteria used for this study was isolated from the soil through a sequence of biochemical confirmatory test. The bacteria colonies were stored in nutrient agar solution at 4^oc. The nutrient agar solution is a composition of agar C₁₄H₁₈0₁₁ that solidifies the nutrient agar solution and allow bacteria to attach to the surface and form colonies. Peptone C₃₀H₄₅0₂₃N₇ rich in substance provides nitrogen, carbon, and other essential nutrients for bacterial growth. In addition, nutrient broth added to the bacterial solution provides appropriate minerals, amino acids in addition to providing vitamins. It also provides a caring environment for inherent soil bacteria culture for bacterial growth. A nutrient broth enrichment solution is considered useful for increasing the culturing of the gram-positive bacteria and consequently, provide a favourable ecosystem for bacterial growth. The nutrient broth was added individually to cementing and enrichment solutions.

Methods

Bacteria inoculation and determination of bacteria cell concentration

The bacteria culture solutions were prepared and placed in a gentle shaker incubator for 24 h at 37 °C to guarantee good aeration and nutrient availability. After incubation, the solutions under observation became turbid. The turbidity expressed the bacteria (B. megaterium) growth in solution (see Fig. 2a). The turbidity was measured using the McFarland turbidity standard for 0.5, 2, 4, 6, and 8 McFarland which are correlated to bacterial suspension densities of 1.5 × 10⁸, 6 × 10⁸, 1.2 × 10⁹, 1.8 × 10⁹, and 2.4 × 10⁹ cells/ml respectively³² .

Treatment, sample preparation and testing

The experimental processes for the various stages involved bacterial isolation, bio-treatment of sample, compaction into mould, bio-cementation inducement by gravity percolation, setting up bio-cemented sample for hydraulic conductivity and calcite content determination as shown in Fig. 2. Prepared soil sample was mixed with one-third pore volume of bacteria solution and then compacted to the required dry density. Bioactivity for urease enzyme was then activated using 0.5 M cementation solution dispensed in three cycles. Two-third 0.5 M cementation solution was dispensed and allowed to diffuse gradually into the sample under gravity in three cycles at interval of 6, 12, and 24 h for 1st, 2nd and 3rd cycles, respectively (see Figs. 2b and c). This account for different degrees of saturation^33,34. This method allows bacteria to saturate and circulate efficiently, Also the cementation solutions percolate autonomously by gravity which is cost effective. Cost, time and processes involve in using a specialized pressure or injection equipment for injecting, spraying, or dispensing bacterial suspensions, cementation solutions, or other reagents used in MICP are eliminated. Nonetheless, a key similarity across all methods is that the treated samples ultimately become solidified as a result of calcite precipitation. However, the various methods exist in terms of time required to achieve MICP, with each technique exhibiting its own rate of calcite formation³⁵. The cycle of cementing solution application was considered up to the third cycle because beyond the third cycle from preliminary experimental observation, the level of saturation with cementation solution slowed down due to aggravated precipitate of calcium carbonates formed at the upper top surface of the specimen, thereby clogging the soil pores and fluid pathway and thus inhibit the free flow and immediate saturation of specimen. The amount by volume of bacteria and cementation solutions used by weight of soil were determined using Eqs. (1)−(3).

$$\:{\text{T}}_{\text{P}\text{V}}=\:\frac{{\text{o}\text{m}\text{c}}_{\text{n}}}{100}\times\:\:\text{s}\text{o}\text{i}\text{l}\:\text{w}\text{e}\text{i}\text{g}\text{h}\text{t}$$

(1)

$$\:{\text{V}\text{b}\text{s}\text{d}}_{\left(\frac{1}{3}\right)}=\frac{1}{3}\:{\text{T}}_{\text{P}\text{V}}$$

(2)

$$\:{\text{V}\text{c}\text{s}}_{\left(\frac{2}{3}\right)}=\frac{2}{3}\:{\text{T}}_{\text{P}\text{V}}$$

(3)

where omc_n = optimum moisture content of natural soil; T_PV = total pore volume; Vbsd = volume of bacteria suspension density; Vcs = volume of cementation solution.

The pore volume is defined as the numerical difference between the initial degree of saturation before soaking in water and the final degree of saturation after full saturation of the soil sample in water²⁴. This approach considers the soil’s three-phase composition namely; solid particles, water, and air with the understanding of much of the air is expelled during compaction allowing for a more accurate estimation of the pore volume. Accordingly, the optimum moisture content for natural soil (OMC_n) was determined for each level of compactive effort. These values were then used to estimate the required volumes of bacterial suspension and cementation solution for a 3000 g soil sample. Precisely, one-third of the pore volume was allocated for the bacterial suspension and two-thirds for the 0.5 M cementation solution. Table 1 presents the volumes of bacterial suspension and cementation solution used in this study for each of the four compactive efforts.

Table 1 Volume of bacteria suspension density and 0.5 M cementation solution.

On completion of the MICP preparation and treatment processes, the specimen were saturated in tap water for 24–48 h, allowed to drain before setting up for hydraulic conductivity test, by falling head method for fine grained soil (see Fig. 2d). Tap water was permeated intermittently until steady head difference was measured with time after 24 h interval and the coefficient, k of hydraulic conductivity was computed, for the various microbial density (cells/ml). Side wall leakage was ignored as recommended by Daniel³⁶. The permeability coefficient is known as saturated hydraulic conductivity k, which was determined as outlined in Daniel³⁶ and Osinubi et al.³⁷. After the termination of permeability test, sample were removed from mould and sliced into five layers for determination of calcite content (see Fig. 2e). The calcite content test was determined at five different layers to measure the spread of calcite with depth. Qualitative microanalysis using scanning electron microscopy (SEM), x-ray diffraction (XRD), x-ray florescence (XRF) and fourier transformed infrared (FTIR) were analysed to validate the correlations of calcite content.

Fig. 2

(Source: Etim et al.⁴) (d) falling head hydraulic conductivity test set up of bio-treated samples and (e) sliced layers of bio-treated lateritic fine grain soil after termination of test for determination of calcite distribution. Keys: 1-Soil, 2-Extracting, isolation and purifying process of bacteria from soil, 3-Isolated bacteria cultured in nutrient agar petri dish, 4-Bacteria inoculated into enrichment solution (bacteria suspension density), 5-Infusion/reinjection of bacteria enrichment solution back into the initial soil, 6-Mixing process after bacteria infusion, 7-Mixed soil-bacteria enrichment solution confined for 12-hours for uniform wetness and bacteria circulation, 8-Sample transferred into mould for compaction, 9-Compacted soil, 10 − 0.5 M Cementation solution, 11-Cementation solution injected in cycles into compacted soil for MICP process, 12- treated zone that shows cementation solution freely percolating/saturating under gravity for continuous bio-cementation, 13-Mould, 14-Filter paper, 15-Circular perforated base plate and 16-Support base of set-up.

(a) Enrichment bacteria suspension density: 1.5 × 10⁸, 6 × 10⁸, 1.2 × 10⁹, 1.8 × 10⁹, and 2.4 × 10⁹ cells/ml equivalent to 0.5, 2, 4, 6 and 8 McFarland standard (MP), respectively (b) introduction of cementation solution (c) overall experimental process.

Calcite content determination

Following the completion of the permeability test, during which a steady flow rate was achieved to establish saturated permeability, the experimental process was terminated. The apparatus was disassembled, and the mould, containing the specimen from the standard proctor test, was removed from water. Subsequently, it was placed on a workbench for a duration of 24–48 h to allow for the complete drainage of moisture. The specimen was meticulously extruded from the mold, and the upper surface was first cleared off. Calcite content for this cleared portion was then evaluated with the understanding that this portion corresponds to the ground surface and/or zero depth of the profile. The remaining block sample was divided into five equal portions; A1, A2, A3, A4, and A5 with each one-fifth layer representing an approximate depth of 20, 40, 60, 80, and 100 mm, respectively. Each section was then spread onto porcelain plates and left to dry under room temperature. After drying, the specimen was crushed into a powder state and sieved through a 75 μm mesh before the determination of calcite content using the acid washing method³⁸. The CaCO₃ was liquefied by mixing a 5 g sample with 20 ml of 1 M hydrochloric acid. The consequential mixture was washed using distilled H₂O and sieved with filter paper. The residue was then conveyed to an oven for drying at 60 °C for 24 h. The carbonate content (%) was computed by the application of Eq. (4)

$$\:{\text{C}}_{\text{c}\text{o}\text{n}\text{t}.}\:\left(\text{\%}\right)=\frac{{\text{m}}_{\left(\text{c}\text{a}\text{l}\text{c}\text{i}\text{u}\text{m}\:\text{c}\text{a}\text{r}\text{b}\text{o}\text{n}\text{a}\text{t}\text{e}\right)}}{{\text{m}}_{\text{a}\text{f}\text{t}\text{e}\text{r}\:\text{d}\text{r}\text{y}}}\times\:100=\frac{{\text{m}}_{\text{p}\text{d}}-{\text{m}}_{\text{a}\text{d}}}{{\text{m}}_{\text{a}\text{d}}}$$

(4)

where C_{cont. =} calculated calcite content (%); m_{(calcium carbonate)} = calculated mass of carbonate (CaCO₃); m_pd = 5 g measured soil prior acid washing; m_ad = mass of acid washed soil after oven dried (oven dry mass of residue).

Optimization process

Optimization process used in this study was done using MATLAB 2022 software. Three algorithms were used to determine the least hydraulic conductivity value among several outputs. Bacterial Foraging optimization(BFO), Particle Swarm Optimization (PSO) and Smell Agent Optimization(SAO) algorithm programmes were used to define the least hydraulic conductivity, based on the outcome of a combination laboratory measured variables, which include Bacillus megaterium (B. megaterium), void ratio (e), dry density (ρ_d), water content relative to optimum (WCRO), compactive effort (CE), pH, degree of saturation (S_r), plasticity index (PI), liquid limit (LL) and viscosity (Vs)) that produced the minimum lab hydraulic conductivity value.

The fitness function used in optimising the hydraulic conductivity is given in Eq. (5). The equation was developed using GeneXproTools 5.0^39,40.

$$\begin{aligned} y & = \tan ^{{ - 1}} \left[ {\left( {\frac{{\left( {x_{{10}} + 10.83} \right)}}{{x_{9} \cos x_{1} }} + x_{4} ^{4} } \right)^{6} } \right] + \tan \left( { - 196.06} \right) - \frac{{x_{5} }}{{\log x_{{10}} }} + x_{3} x_{6} \\ & + \tan ^{{ - 1}} \left[ {\frac{{\left( {e^{{x_{4} }} } \right)^{2} }}{{x_{8} }} - \left( {e^{{x_{2} }} + 2x_{4} } \right)} \right] + \tan \left[ {\cos \left( {\frac{{2x_{4} - x_{7} }}{{ - 0.61x_{8} \cos - 6.06}}} \right)} \right] \\ \end{aligned}$$

(5)

Where: $\:{x}_{1}$ =B. megaterium suspension density (B.meg), $\:{x}_{2}$= void ratio (e), $\:{x}_{3}$= dry density (ρ_d), $\:{x}_{4}$= water content relative to optimum (WCRO), $\:{x}_{5}$= compactive effort (CE), $\:{x}_{6}$= pH, $\:{x}_{7}$= degree of saturation (Sr), $\:{x}_{8}$= plasticity index (PI), $\:{x}_{9}$= liquid limit (LL), $\:{x}_{10}$= viscosity (Vs), Y = ln(k)=hydraulic conductivity.

The constraints on the other hand states the margins as well as limits at which the structure is being studied define as follows;

$\:1.33\text{E}-10\le\:\text{y}\le\:4.05\text{E}-06$ Hydraulic conductivity

$\:0\le\:{x}_{1}\le\:2.4\text{E}-09$ B.megaterium suspension density

$\:-1\le\:{x}_{5}\le\:2$ Compactive effort; RBSL=-1, BSL=0, WAS=1, BSH=2

$\:7.8\le\:{x}_{4}\le\:17.6$ Moulding water content covering dry to wet within the four CE considered

Results and discussion

Material characterization

The summary of the properties of the natural lateritic soil used is given in (Table 2). The soil has a natural moisture content of 11.6%. 35.4% of its particles passed the sieve No. 200 (75 μm opening). The soil is classified as A-4(3), AASHTO⁴¹, and SC, ASTM⁴². Soil samples were compacted with four levels of energies including Reduced British Standard light (RBSL), British Standard light (BSL), West African Standard (WAS) and British Standard heavy (BSH). The gradation distribution of the lateritic soil is shown in (Fig. 3).

Table 2 Properties of natural lateritic soil.

Fig. 3

Particle gradation curve of the natural lateritic soil.

Figure 4 shows the XRD results for the lateritic soil, revealing the predominant non-clay minerals (Quartz, SiO₂, and Haematite, Fe₂O₃) alongside the clay mineral (Kaolinite, Al₄Si₄O₁₀ (OH)₈). The spectrum intensity indicates varying concentrations of these minerals. The fundamental component of kaolinite is the structural relative ratio of alumina and silica arranged in repeated sheets and bonded together, as expressed in its chemical formula. The reddish-brown coloration of the soil is attributed to the presence of haematite. Overall, the soil is identified as lateritic, characterized by fine particles with predominantly crystalline constituents, particularly the kaolinitic clay mineral.

Fig. 4

x-ray diffraction of lateritic soil.

Figure 5 shows the FTIR spectra of the natural lateritic soil, a key source of kaolin confirmed by XRD. The results align with XRF and XRD, emphasizing kaolinite dominance. Intensity variations in the spectrum correspond to essential kaolinite functional groups. Notably, bands at 3693.8 and 3652.8 cm⁻¹ indicate in-phase OH stretching of inner-surface hydroxyl groups specific to kaolinite. A 1636.3 cm^− 1 band suggests H-O-H bending or water deformation influenced by minor minerals like smectite. The finger print regions showing relative sharp bands of 1032.5, 1036.2, and 913.2 cm^− 1 relate to Si-O stretching and OH deformation⁴³. The 779 cm-1 band is likely linked to OH associated with Al³⁺. Bands from 685.8 to 752.9 cm^− 1 pertain to non-clay minerals like quart, while unassigned bands at 2885, 2791, and 2050 cm⁻¹ may be due to trace amounts of minor minerals or structural interference.

Fig. 5

Fourier transformed infra-red (FTIR) spectra of the natural lateritic soil.

Couple effect of bacterial cell concentration and compaction energy on hydraulic conductivity

The hydraulic conductivity (HC) assessment focuses on specimens bio-cemented with a 0.5 M cementation solution concentration, identified as the optimal concentration yielding effective cementation calcite. The results are systematically analyzed to serve as key indicators of Microbially Induced Calcite Precipitation (MICP), compactivity (specifically, compactive effort), and the diverse bacterial cell units. In Fig. 6, the hydraulic conductivity (HC) of bio-cemented lateritic soil is depicted in relation to varying concentrations of B. megaterium cells/ml. The dashed lines represent the criterion limit of hydraulic conductivity for design of waste containment system. Intriguingly, as the amount of bacterial suspension density increased, reaching up to 2.4 × 10⁹ cells/ml, the HC exhibited a consistent decrease across different compactive efforts. For specimens prepared at -2% OMC, the HC values decreased from 4.00 × 10^− 6, 4.38 × 10^− 7, 2.28 × 10^− 7, and 4.84 × 10^− 8 m/s at 0 cell/ml (representing the natural specimen) to low values of 5.72 × 10^− 9, 8.13 × 10^− 9, 3.22 × 10^− 9, and 7.21 × 10^− 10 m/s when bio-treated with up to 2.4 × 10⁹ cells/ml of B. megaterium suspension density for RBSL, BSL, WAS, and BSH, respectively. This translates to a substantial reduction in HC, with percentages of 99.9%, 98.1%, 98.8%, and 98.3%, underscoring the impactful bio-cementation process. Similar declining trends were also evident for specimens prepared at OMC, + 2, and + 4 OMC (see Figs. 6b-c). The decline in HC is triggered by the hydrolysis of urea, leading to a pH shift that fosters the growth of calcite, partially obstructing soil pores and fabric. The mechanism of calcite formation and bio-cementation is influenced by the size of microorganisms relative to the magnitude of soil pores and throats^18,44,45. Furthermore, the observed decrease in HC with increased compaction energy is ascribed to the deformation and destruction of clay peds in the soil fabric, eliminating macro pores^44,46. Generally treated soil with a minimal 1.2 × 10⁹ cells/ml compacted with BSL.WAS and BSH met the minimum governing hydraulic conduction value of 1.0 × 10^− 7 cm/s for waste containment applications. Further investigation using XRD, SEM and FTIR evaluations was targeted at providing insight that would showed the presence of imprinted calcite which further confirms the MICP effectiveness in deposition of inorganic calcite.

Fig. 6

Plot of HC of soil with B. megaterium suspension density for specimens prepared at: (a) −2% OMC (b) OMC (c) + 2% OMC (d) + 4% OMC.

Relationship between moulding water content relative to optimum and hydraulic conductivity

The HC of densified soil is significantly influenced by its MWC⁴⁷. The relationship between HC and MWC for natural and bio-treated lateritic soil is displayed in (Fig. 7). Experimental results show that HC initially reduced with MWC from − 2% OMC to OMC and afterwards increased with higher MWC (+ 2% and + 4%). It was observed that the lowest values of HC were obtained for bio-treated specimen prepared at OMC for the four compaction energies considered. Similar findings depicting this trend were also reported by Yohanna et al.⁸. The trend of the results obtained here are like those recorded at 6.0 × 10⁸ cells/ml, 12.0 × 10⁸ cells/ml, 18.0 × 10⁸ cells/ml and 24.0 × 10⁸ cells/ml.

Fig. 7

Plot of HC of soil with MWC for varying B. megaterium suspension density: (a) 0 cells/ml (b) 1.5 × 10⁸ cells/ml (c) 6 × 10⁸ cells/ml (d) 1.2 × 10⁹ cells/ml (e) 1.8 × 10⁹ cells/ml and (f) 2.4 × 10⁹ cells/ml.

Influence of degree of saturation on hydraulic conductivity of bio-cemented lateritic soil

The relationship derived from the HC of bio-cemented lateritic soil and degree of saturation (DOS) for varying B. megaterium suspension density and compacted using four energy levels is shown in (Fig. 8). The unpredictability in the degree of saturation could probably be due to the uneven or spatial spreading and distribution of the precipitated product (CaCO₃) within the soil pores. This may have probably translated to partially filled pore spaces within the soil grains hence permitting fluid passage^34,48. The minimum and maximum degrees of saturation that fell within the requisite HC values ≤ 1 × 10^− 9 m/s are 82.0% and 99.9% for specimens treated with B. megaterium suspension density up to 24.0 × 10⁸ cells/ml.

Fig. 8

Plot of HC of soil with degree of saturation for varying Bacillus megaterium suspension density: (a) 0 cells/ml (i.e., Natural soil) (b) 1.5 × 10⁸ cells/ml (c) 6 × 10⁸ cells/ml (d) 12 × 10⁸ cells/ml (e) 18 × 10⁸ cells/ml and (f) 24 × 10⁸ cells/ml B.megaterium suspension density bio-cemented soil.

Profiles of calcite (CaCO₃) with depth/height of specimen with corresponding pH

The calcite content and corresponding pH was assessed to understand its distribution with depth (see Fig. 9). The distribution of calcite content with depth exhibited non-uniform variations, generally decreasing from the top portion to the bottom accordingly. Calcite distribution ranged from 1.1 to 1.7%, 2.8 to 3.3%, 3.2 to 4.2%, 3.5 to 5.4%, 4 to 5.7%, and 5.2 to 5.9% for natural conditions and 1.5, 6, 12, 18, 24 (×10⁸ cells/ml), respectively (see Fig. 9a). This non-uniform distribution of calcite may be linked to the non-continuous access/entrant of the cementation solution to nucleation sites of bacteria cells, un-even percolation of cementation solution due to blockade of micro-pores by calcite formed during the initial biocementation cycle, and fabric/particle size orientation^34,49. The non-uniformity and indeed high calcite presence within the upper first layer of one-fifth (1/5th ) layer specimen could probably be as a result of high bacterial aggregation or concentration^5,50,51. However, it is possible that the initial bacterial concentration may have likely increased due to or aided by active multiplicity of bacteria caused by breathability of bacteria as observed or caused by adequate exposure and or aeration of topmost layer⁵². It could be that that oxygen, vital for the metabolic processes of calcite-precipitating bacteria, becomes less available with increasing soil depth, thereby diminishing bacterial activity and subsequently reducing calcite precipitation⁵³. Moreover, the dominance of a clay mineral with a relatively high specific surface area (SSA) at the top surface may contribute to limiting the saturation rate of the cementation solution. This limitation, coupled with variations in pH levels at different depths (see Fig. 9b), affects microbial activity, potentially diminishing the effectiveness of calcite precipitation. The decrease in pH could be attributed to the metabolic process of some unidentified indigenous bacteria in the soil that are not part of the MICP protocol. It is possible that as these bacteria consume nutrients, they release metabolic by-products that may include acidic metabolites or acidic waste products, which contribute to the decrease in pH. The pH except for few cases were in most part alkaline all within the various bacteria concentration and depth that favours the condition for MICP. The decline in pH at greater depths could account for the observed decrease in calcite concentration. The compaction process itself introduces variations in soil structure and density, influencing microbial activity and, consequently, the distribution of calcite. The soil’s pore structure and connectivity further impact the movement of fluid, including enrichment and cementation solutions, as microorganisms influence the transport of calcium ions and microbial cells, thereby shaping calcite distribution. Additionally, substrate availability, exemplified by urease enzyme presence, and the intricate biogeochemical interactions within the soil undergo changes with depth. These factors collectively emphasize the significance of predicting and optimizing microbially induced calcite precipitation (MICP) processes at different depths in fine-grained soils. While this study primarily emanates from laboratory conditions, the challenges encountered underscore potential variations and challenges upon upscaling.

Fig. 9

Calcite content and pH variation of bio-treated lateritic soil: (a) concentration profile of calcite with depth, and (b) corresponding pH at various depth.

Chemical composition and microanalysis of bio-cemented lateritic soil

The percentage distribution of oxide composition in the natural soil sample, which underwent analysis by XRF after passing over a 0.075 mm sieve, is presented in (Table 3). The ratio of SiO₂ to the combined Al₂O₃ and Fe₂O₃, denoted as the silica-sesquioxides ratio [(SiO₂)/(Al₂O₃ + Fe₂O₃)], is calculated to be 1.77. This falls within the recommended or classified range of 1.33–2.0 for lateritic soil, as stipulated by Bell⁵⁴ ensuring the authenticity of the soil classification. The comparison of chemical composition of natural lateritic soil and bio-treated soil using the XRF analysis shows variation in composition. Each specimen for the respective bio-treated specimen were representative specimen collected from each of the five slice, that make up the depth and mixed before testing. The results confirms formation of binding inorganic precipitate of calcite as seen in increased calcium oxide (CaO) content in contrast to the natural soil having lower percent. Also, other major compound in the soil were represented in the bio-treated specimen. The increase in CaO of bio-treated with bacterial cell specimen is due to the higher formation of calcite triggered by hydrolysis reaction of bacteria urease enzyme.

Table 3 Chemical composition of soil and bio-augmented.

XRD of Bio-treated specimen

The X-ray diffraction (XRD) analysis of lateritic soil subjected to bio-augmentation with enrichment solution - B. megaterium inoculum of 10⁸ cells/ml was conducted at increasing suspension densities of 1.5, 6, 12, 18, and 24, using an optimal 0.5 M cementation solution. The results confirm the precipitation of calcite, as evidenced by distinct diffraction peaks at various 2theta angles (Fig. 10). Notably, alongside inorganic quartz and hematite minerals, strong diffraction peaks of inorganic calcite, interspersed with intrinsic quartz and hematite, were observed. This observation aligns with findings reported by Oliveira and Neves⁵⁵ supporting the identification of calcite at specific 2theta values (i.e. 2θ = 27.316, 29.497, and 33.229). It is essential to note that the intensity of diffraction peaks for a mineral is contingent on its relative abundance in the analyzed specimen, as established in studies by Chipera and Bish⁵⁶ and Sharma et al.,⁵¹. The prevalence of calcite, manifested at varying 2theta angles, exhibited an increasing trend corresponding to the rise in bacterial cells/ml but cannot be quantified numerically using XRD. Previous research has shown presence of calcite as prevalent crystal in bio-cementation processes^57,58. Precipitation potential of calcite due to influence of biogeochemical interactions in MICP techniques tends to increase with an increase in enzyme content and or bacterial suspension densities^45,57.

Fig. 10

X-ray diffraction spectra of: bio-cemented lateritic soil specimens.

The natural, untreated lateritic soil image shows the soil’s original fine grain structure, characterized by cohesive to loosely packed particles oriented partly as interfacial dispersed/flocculated structure and cohesive structure. It is obvious that marginal dispersed calcite can be seen clearly as shown in the natural/control lateritic sample. This could probably be due activation of unidentified variants of indigenous bacteria inherit in soil and or principally from the cementation composition source.

The alteration in morphology induced by the formation of inorganic binding calcite as identified in XRD spectroscopy can be conveniently viewed from the image displayed by Phenomworld scan electron microspcope SEM. Photomicrographs from the SEM investigation established numerous fabric features probably associated with the pH level and or bacteria concentration, cementation saturation during bio-treatment biocementation action, interaction/MICP protocol, calcite distribution, pore size orientation and distribution relative to interstitial particle contact and cohesion with calcite and probably degree of saturation by both permeant (tap water) and cementation solution. SEM Image of natural soil specimen show a relatively dispersed grain fabric morphology (Fig. 11a). The bio-cemented specimen (Fig. 11b–f) present a relatively aggregated and thick lumps distributed unevenly⁵⁹. The general features of both closed and disaggregated structure, suggest possible changes induced by that connectivity and associations between the soil particles translated into an active bonding caused by the products of calcite. The after effect is the aggravated crystal that covers and filled the soil grains but the filling of inter-particle pores and bio-cementing inter-particles grains was more obvious as shown by the cloudy and floppy/ fluffy calcite coverage of photomicrograph of 2.4 × 10⁹ cells/ml sample (Fig. 11f). These activity could be accountable for the low permeability⁵². This observation corroborate the low hydraulic conductivity value recorded at higher B. megaterium density.

Fig. 11

SEM Image for the (a) natural lateritic soil specimens and lateritic soil bio-cemented with (b) 1.5 × 10⁸ cells/ml (c) 6 × 10⁸ cells/ml (d) 1.2 × 10⁹ cells/ml (e) 1.8 × 10⁹ cells/ml and (f) 2.4 × 10⁹ cells/ml.

Furthermore, the success of the biotreatment as well as the chemical bonds, mineralogy, and microstructure of lateritic soil was studied again using FTIR. The FTIR analysis was done by means of transparent KBr disks, and the outcomes were evaluated with the aid of an adsorption bands measured at characteristic wave numbers between 700 and 4000 cm − 1. The FTIR spectra of biotreated lateritic soil are shown in (Fig. 12). The band at 3697, 3523, and 3452 cm^− 1 point to an octahedral OH stretching vibrations^38,60. In the fingerprint region, the sharp bands at 1006.98, indicates the Si-O stretching. The existence of vaterite and calcite correlates to the absorption bands at 745.36. Comparable absorption bands of vaterite (747 and 1085/1084 cm⁻¹) and calcite (708/712 cm⁻¹) were also described in the works of Ferral-Pérez et al.⁶¹. Moreover, 1636.3 was gotten based on the H-O-H bending/deformation of water possibly as a results of smectite interference. The deficiency in satisfactory vibrational bands for calcite may be linked to; (1) dissolution of calcite under lengthy permeation and (2) interloping created with other inorganic compounds bearing in mind that the FTIR analysis was not performed on a pure synthesized carbonate.

Fig. 12

Fourier transformed infra-red (FTIR) spectra of treated lateritic soil.

Optimization approach

The optimizations approach involved the selection of a best possible option or choice from a number of available options using a robust mathematical computer program and approach. The best choice option also known as optimal value is usually a value relative to extreme minimum and maximum in an array of outcomes. A wide range of many engineering specializations have successfully used different optimization techniques^{40,62,63,64,65,66}.

The various output used in measuring the performance of the developed model and its corresponding validation results are contained in (Table 4). Evaluation the performance of BFO, PSO and SAO algorithms involves comparing their outputs using predefined metrics on the fitness/objective function. A comparative evaluation of the results revealed that PSO and SAO optimization approaches recorded good results and met the minimum hydraulic conductivity value of 1E-09 m/s for use as liner material, at all iterations considered, while BFO underperformed and did not meet the minimum requirement of 1E-09 m/s for use as liner material, for all iterations considered. For instance, a comparative study of the three optimizations approaches at 500 alterations each recorded predicted minimum hydraulic conductivity value of 2.7E-09 m/s with 2.4E-09cells/ml B. megaterium, WAS compaction energy, for BFO. A minimum hydraulic conductivity value of 2.27E-011 m/s at 1.2E-09cells/ml B. megaterium, WAS compaction energy, for PSO. In the case of SAO, a minimum hydraulic conductivity value of 4.45E-011 m/s at 2.4E-09cells/ml B. megaterium compacted at WAS compaction energy was recorded. The best recorded result of the least hydraulic conductivity is in the order of PSO > SAO > BFO. Several studies recorded similar findings of impressive results of using PSO in numerous engineering optimization^{62,63,64,65,66}.

Table 4 Variables generated by genexprotools 5.0 for training (model) and validation data.

The association between predicted HC values against the measured laboratory values is shown in (Figs. 13 and 14). The result showed a resilient association between the predicted and the measured values with documented coefficient of determination R = 0.936. This designate that the independent variables used to generate the regression equation has substential effect on the HC values of soil/B. megaterium mixtures and should thus be prudently considered in the process of design and construction of a landfill system.

Fig. 13

Scatter plot obtained from GenXprool model.

Fig. 14

Plot of observed value against observation from GenXprool model.

The fitness function developed for HC within the basic constraints and self- determining factors is fitted into a BFO, PSO and SAO algorithm programmes which were iterated over a wide number range to obtain minimum hydraulic conductivity. The various hydraulic conductivity values obtained and plotted against iterations number using BFO, PSO and SAO algorithm are shown in Figs. 15, 16 and 17 respectively. The detail rundown and summaries of the optimization results using these algorithms under selected varied iterations number of 10–500, 10–700 and 10 -2000 for BFO, PSO and SAO algorithm, are presented in Tables 5, 6 and 7 respectively.

Fig. 15

Plots of HC versus changes in iteration numbers using BFO algorithm for; (a) 10 (b) 100 (c) 200 (d) 300 (e) 400 and (f) 500 iterations.

Fig. 16

Plots of HC against changing iteration numbers using PSO algorithm for; (a) 10 (b) 100 (c) 200 and (d) 400 iterations.

Fig. 17

Plots of HC against changing iteration numbers using SAO algorithm for (a) 10 (b) 100 (c) 1000 and (d) 2000 iterations.

The basic constraints of compactive effort, moisture content and B. megaterium suspension density should be mainly taken to consideration amongst other factors at both design and construction of bio-treated compacted clay liner for field implementation. These considerations will meet the acceptable designed hydraulic conductivity without compromising other basic engineering parameters, both during the useful life or post active period of the facility or for any associated geotechnical engineering applications.

Table 5 Bacteria foraging optimization results.

Table 6 Particle swarm optimization results.

Table 7 Smell agent optimization algorithm results.

Conclusion

The following conclusion are derived from this study:

• (1) The hydraulic conductivity decreased with increased bacteria suspension density ranging from 1.33 × 10^–10 to 4.05 × 10^− 8 m/s within 7.8 to 17.6% moulding water content regardless the compactive effort.

• (2) SEM and XRD analysis confirmed carbonates precipitation in bio-treated lateritic soil; treated with B. megaterium inoculum density range from 1.5 × 10^− 9 cells/ml to 24 × 10^− 9 cells/ml. The strengthening of diffraction peaks, particularly at 2θ angles corresponding to calcite, demonstrates a clear correlation between higher bacterial densities and increased calcite formation, reinforcing the effectiveness of bio-mediation in enhancing bio-cementation processes.

• (3) The FTIR analysis confirmed the presence of vaterite and calcite in biotreated lateritic soil, highlighting key chemical and mineralogical changes. However, the absence of clear calcite bands suggests possible calcite dissolution or interference from other compounds, indicating complexities in characterizing the treated soil.

• (4) Based on the results and data obtained from the statistical analysis and optimization techniques, the three optimization algorithms are ranked in the order of suitability or best performance based on the least hydraulic conductivity (k) which satisfies the regulatory values for liners as follows: PSO ( k: 2.27E-11 m/s) > SAO (k: 2.85E-11 m/s) > BFO (k: 2.66E-09 m/s).

• (5) Particle swarm optimization (PSO) and smell agent optimization (SAO) algorithms can be conveniently use to predict the hydraulic conductivity of a typical barrier material made from lateritic soil bio-mediated with Bacillus megaterium species in nutrient media solution of up to 24 × 10⁸ cells/ml.