2.2.1 EICP

The urease enzyme used in this study was purchased from Millipore Sigma, with a specific activity of 50 000–100 000 units/g solid. For EICP treatment, first, a cementation solution is prepared containing a 300 mM equimolar solution of urea and calcium chloride, followed by preparation of a second solution of 0.3 g/L of urease. The cementation solution and urease are pre-mixed immediately before the specimens are immersed in the solution to prevent premature chemical reactions. Fresh urease-cementation solution is then replaced every day for 3 days (Table 2).

2.2.2 SA for biopolymer-modified EICP (BP-EICP)

SA (NaC6H7O6) is a natural hydrophilic polysaccharide derived from the cell walls of marine brown algae (Maiti & Kumari, 2016; Santos, 2017). SA is composed of (1–4) linked β-d-mannuronic acid (M units) and α-l-guluronic acid (G units) (Arab et al., 2024; Maiti & Kumari, 2016; Santos, 2017). Studies have shown that the G-blocks of alginate form strong intermolecular crosslinking, also called an egg-box structure, with calcium ions (Figure 3; Maiti & Kumari, 2016; Santos, 2017). For example, when SA is mixed with CaCl2, the monovalent ions in SA (i.e., Na+) are exchanged for divalent ions in CaCl2 (i.e., Ca2+). This reaction transforms the solution from a low-viscosity solution to a gel structure, which consequently enhances the mechanical properties of alginate gels (Maiti & Kumari, 2016; Santos, 2017). The SA used in this work had a reported viscosity of 5–40 cP (1% solution, 25°C) and an estimated molecular weight range of 12 000–40 000 Da. The batch-specific guluronic/mannuronic (G/M) ratio of the SA was reported by the manufacturer (Millipore Sigma-aldrich) to be approximately 1.56. In this study, the SA (biopolymer) used was 1.2% of the average mass of the sandstone rock specimens (in this case, 2 g of SA). The SA is then mixed with the EICP solution before immersion of the rock mass.

4.2.1 Elastic mechanical response

To estimate Young's modulus of rocks, the International Society of Rock Mechanics (ISRM) suggests three methods (Bell & Lindsay, 1999; Małkowski et al., 2018): (a) tangent Young's modulus [Etan] (slope at a fixed percentage of the UCS), (b) average Young's modulus [Eavg] (slope of the straight-line part of the stress–strain curve), and (c) secant Young's modulus [Esec] (slope of the line from the origin to a fixed percentage of the UCS). Małkowski et al. (2018) suggested that the tangent modulus (when calculated within a 30%–70% range of peak stress) and the average modulus are the most reliable methods, while the secant modulus is a less reliable method, as it incorporates pore compaction and microcrack effects. Therefore, this work first examines both proposed methods (tangent and average modulus) to estimate Young's modulus of biocemented rocks and then evaluates which method is most suitable for biocemented rocks. To determine the best method for determining Young's modulus of rocks, the coefficient of determination (R2) between UCS and E can be utilized (Małkowski et al., 2018; Ocak, 2008), with a high R2 indicating a better method determination.

The estimated Young's modulus using the secant (Esec) and tangent methods (Etan) was further analyzed and compared with Young's modulus obtained from the average method (Eavg). Figure 9 shows the relationship between the average Young's modulus (Eavg) and UCS (Figure 8a), and the relationship between the tangent Young's modulus (Etan) and UCS (Figure 8b). The results show that Eavg and Etan have R² values of 0.94 and 0.97, respectively. Because the difference in R² between the two methods is insignificant (0.03), this study used Eavg for the analysis of the elastic properties of biocemented rocks. Since biocementation involves complex biogeochemical processes that are highly dependent on multiple factors that cannot be assumed or generalized, in the case of biocemented rocks, it is important to utilize a method that accounts for these variables by using the entire recorded stress–strain data. The tangent method, which assumes linearity at the 30%–70% range of peak stress without considering the entire data set, may lead to generalizations that do not fully capture the elastic response of biocemented rocks. In contrast, the average method incorporates the complete linear stress–strain record, which is necessary for accurate analysis of such complex biogeochemical interactions in rocks.

Using the Eavg method, it was found that the EICP-biocemented rocks cured at a lower temperature showed a 169% increase in stiffness (E), while those cured at 45°C showed a 165% increase (Figure 10a,b). Similarly, the BP-EICP-biocemented rocks cured at a lower temperature demonstrated a 192% increase in stiffness, whereas those cured at 45°C showed a 178% increase (Figure 10a,c). These results align with our initial hypothesis for this work, as previous studies had suggested that high-temperature curing limits crystal growth, which in turn restricts biocementation. Conversely, curing at lower temperatures promotes the formation of larger, well-defined crystals (Cashman, 1993; Marsh, 1981; Mullin, 2001; Myerson, 2002), which can enhance biocementation and improve stiffness in granular media. However, temperature differences had a greater impact on BP-EICP biocementation than on EICP biocementation. In EICP-biocemented rocks, the stiffness improvement at a lower temperature was only 4% greater than that at a higher temperature, suggesting that temperature may not have a significant influence on this change. However, in BP-EICP, low-temperature curing resulted in a 16% greater improvement in rock stiffness compared to high-temperature curing. This discrepancy suggests that low temperature alone is insufficient for large biocement crystal formation, and thus, factors such as urease activity (Chen et al., 2024; Myerson, 2002; Zhang et al., 2022) and in the case of our current study, the presence of biopolymer gel, increased the ability of rocks to resist deformation under compressional stress. This suggests that the biopolymer (calcium alginate gel) in BP-EICP contributed to stiffness retention under varying temperature conditions.

Young's modulus (E) and UCS are essential parameters that are typically applied independently in the analysis of underground stability (Aladejare et al., 2021; Kahraman et al., 2003; Lü et al., 2012). The ratio of UCS to E defines the MR, which is widely used in rock mass estimations and the derivation of rock mass deformation modulus when direct field testing is not feasible (Hoek & Diederichs, 2005; Ocak, 2008; Palchik, 2010). Studies have shown that ignoring the UCS–E correlation can undermine geotechnical reliability, leading to over- or underestimation of rock engineering assessments (Aladejare et al., 2021; Wang & Aladejare, 2016). Therefore, this study also examined the change in the modulus ratio due to biocementation. Previous research has emphasized that the use of the MR of rocks is project-specific (Aladejare et al., 2021) and that there is a positive correlation between UCS and E of rocks (Karakus et al., 2005; Palchik, 2010; Sonmez et al., 2004, 2005). Yet, there has been an overgeneralized use of MR of rocks with the assumption that increasing modulus ratio implies an increase in both E and UCS (Palchik, 2010), which ultimately suggests a more desired rock characteristic in rock engineering applications. However, biologically induced reactions introduce cementitious materials that increase rock strength (Gao et al., 2019; Kolawole et al., 2021; Ngoma & Kolawole, 2024; Ngoma, Kolawole, Lu, 2024; Ngoma, Kolawole, Olorode et al., 2024), relative to untreated rocks, and this can yield a lower value of stiffness to UCS ratio (MR) in such biocemented rocks. Therefore, the generalized application of MR is not applicable in the case of biocemented rocks, which do not obey simplistic MR assumptions. Additionally, even though rocks with high UCS are generally stiffer (higher E), exceptions occur due to mineral composition, porosity, and microfractures, which can weaken or strengthen this relationship.

Table 4 shows that the MR of biocemented rocks decreases after biocementation, with EICP-treated rocks showing the greatest reduction. For EICP-biocemented rocks, MR declined from 145 to 117 at a lower temperature (31°C) and to 114 at a higher temperature (45°C). Similarly, BP-EICP-biocemented rocks showed a decrease in MR from 145 to 125 at lower temperatures and 127 at higher temperatures (Table 4). These results indicate that curing temperature has minimal influence on MR, whereas the type of biocementation method (EICP vs. BP-EICP) has a more significant impact. Specifically, MR decreased by 20% in EICP-biocemented rocks, compared to a 13% reduction in BP-EICP-biocemented rocks, highlighting the greater effect of EICP in altering the relationship between stiffness and strength. Therefore, we can conclude that although biocementation enhances both the strength (UCS) and the stiffness (E) of rock masses (Figures 6 and 7), the relationship between them (MR = E/UCS) does not follow a fixed trend. This means that while both UCS and E increase, they may not do so at the same rate. As a result, the modulus ratio can either increase or decrease depending on how much each parameter changes relative to the other. This variability highlights the complex interaction between strength and stiffness in biocemented rocks, which is influenced again by critical factors, which are biocementation distribution, inherent porosity, and microstructural changes.

4.2.2 Inelastic mechanical response

Comparisons of the peak strength of sandstone rocks before and after bio-reinforcement indicate that the EICP-biocemented rocks cured at a lower temperature (31°C) showed a +213% increase in strength, whereas those cured at a higher temperature of 45°C showed a +220% increase in strength (Figure 11a,b). This contradicts our elastic response hypothesis, as crystallization dynamics and previous studies have suggested that rapid cooling at higher temperatures limits crystal growth and lower temperatures promote the precipitation of larger, more well-defined crystals (Cashman, 1993; Marsh, 1981; Mullin, 2001; Myerson, 2002). However, Myerson (2002) emphasizes that low temperature alone is insufficient for large crystal formation; slow cooling, urealytic activity, and the quantity of biocementation (Chen et al., 2024; Wang et al., 2024; Zhang et al., 2022) are also essential factors that control biocementation in rock masses. Unlike previous studies (Ngoma & Kolawole, 2024; Ngoma, Kolawole, Olorode et al., 2024), the current work utilized a lower urease concentration relative to previous EICP treatments (0.3 g/L vs. 2 g/L), which may explain why the rock masses cured at 31°C showed a marginally lower increase in strength (+213%) compared to the rocks cured with biocementation at 45°C (+220%), thus contradicting assumptions that lower temperature curing would yield more substantial improvement in biocemented rocks. Therefore, we can infer that in this case, temperature effects were negligible on the inelastic rock property changes due to biocementations. Nevertheless, despite using a relatively lower urease concentration in this study for biocementation in rocks, the results demonstrate that this quantity was still sufficient (up to +216% UCS and +170% E) to significantly enhance rock properties, even surpassing improvements reported in previous studies that utilized large urease amounts for EICP (Ngoma & Kolawole, 2024; Wang et al., 2024). This suggests that the higher pore volume of the rocks in this study provided more void space for effective biocementation. Consequently, other studies may have used more urease enzyme than necessary, especially given that our results indicate better reinforcement with a lower enzyme concentration. Therefore, urease enzyme dosage should be optimized based on the specific rock type and its inherent porosity to maximize efficiency in rock bio-mediated processes for biocementation.

It is also important to note that studies have often presented contradictory findings regarding the impact of temperature on geomaterials, with some suggesting that higher temperatures enhance urease activity, leading to improved biocementation (Park & Choi, 2021; Wang et al., 2022; Zhang et al., 2022), and others propose that lower temperatures (Xue et al., 2024) and urease inhibitors (Wang et al., 2023) are necessary to slow enzyme activity, which can reduce surface clogging and promote uniform precipitation within geomaterials, and lead to better biocementation overall. Additionally, these studies define high and low temperatures differently, with some considering values from 4 to 31°C as low temperatures, while others classify temperatures above 65°C as high. This shows the complex interplay between temperature and urease activity, suggesting that future work on biocementation in rocks should aim to identify an optimal balance (between temperature and urease activity) where precipitations can effectively penetrate the rock pores without prematurely clogging pores, ensuring better enhancement.

For the inelastic response of BP-EICP-biocemented rocks, the crystallization dynamics hypothesis holds, as rocks cured at a lower temperature (31°C) demonstrated a higher increase in strength (+219%) compared to those cured at 45°C (+199%) (Figure 11a,c). In this case, despite the lower urease concentration, the presence of SA biopolymer ensured more strength improvement in BP-EICP. The addition of biopolymer in the biocementation likely compensated for the limited urease, as its gelation process is temperature-dependent. At lower temperatures, calcium ion diffusion occurs gradually, forming a more structured and homogeneous gel, which enhances mechanical strength (Jeong et al., 2020). Conversely, at higher temperatures, gelation occurs more rapidly, leading to a less uniform, weaker gel. Additionally, higher temperatures reduce alginate viscosity, affecting crosslinking efficiency (Jeong et al., 2020). Therefore, unlike EICP-biocemented rocks, where the temperature effect is negligible, the BP-EICP-biocemented rocks were affected by temperature, and the presence of both urease enzyme and SA biopolymer played an important role in maintaining their peak strength.

The inelastic failure mode of rocks under compressive stress was also examined (Figure 12). These failure modes depend on the rock's internal structure and pre-existing weaknesses, due to the tendency of rocks to fail along the path of least resistance (weakest plane). Rocks under uniaxial compression typically fail through axial splitting or shear failure mode (Chakraborty et al., 2019; Fakhimi & Hemami, 2017; Fjær et al., 2021). Studies have shown that these failure modes are closely related to the strength (UCS) of the rock (Chakraborty et al., 2019; Hajiabdolmajid & Kaiser, 2003; Xie et al., 2024; Yagiz, 2008), because UCS determines a rock's ability to withstand axial stress before failure, and the failure mode describes how the material ultimately breaks under stress. Specifically, rocks with relatively higher UCS show minimal plastic deformation upon failure, typically failing through axial splitting due to their limited ability to accumulate large strain (Chakraborty et al., 2019; Xie et al., 2024). However, rocks with lower UCS often show shear failure, where material displacement occurs along the weakest planes (Chakraborty et al., 2019; Xie et al., 2024).

In this study, EICP-biocemented rocks cured at 31°C failed in the shear mode (Figure 12a), despite showing an increase in strength (UCS). This indicates that crystalline calcite reinforcement alone (without biopolymer gel) was insufficient to fully seal pre-existing microfractures. In contrast, BP-EICP-biocemented rocks cured at a lower temperature (31°C) recorded the highest increase in UCS (Figure 11a) and failed in the axial splitting mode (Figure 12c). This suggests that the combination of calcite precipitate and biopolymer gel provided stronger reinforcement, reducing the likelihood of shear deformation. We can therefore infer that with the addition of biopolymers (like in BP-EICP), additional urease enzyme, or extended biocementation treatment, the weakest zones (with discontinuities, cavities, and openings) in the rock masses can be more effectively biocemented, potentially shifting the failure mode from shearing to axial splitting. At higher curing temperature (45°C), both BP-EICP- and EICP-biocemented rocks showed a mix of shear and axial failure (Figure 12b,d), suggesting that calcite and calcium alginate gel precipitation do not always guarantee maximum biocementation of microfractures at this temperature. Moreover, it is important to note that since the specific sandstone rocks (Berea sandstone) analyzed in this work are heterogeneous, the presence of laminations and the distribution of microfractures in the rock may have varied among specimens, resulting in the observation of different failure patterns after biocementation. In some rocks, complete sealing of the pore network and microfractures may have occurred, while other rocks still retained fewer localized weak zones, leading to a mix of shear and axial failures after biocementation. A previous study (Wang et al., 2024) reported a complete shift from shear failure before biocementation to tensile failure after EICP treatment; however, our findings on enzymatic and biopolymer-modified biocemented rocks contradict this trend. A key distinction is that the results reported by Wang et al. (2024) may have been influenced by the artificially induced fractures during the rock specimen preparation in that study, which aligned parallel to the rock's longitudinal axis, thereby creating a pre-determined failure mode of axial splitting. However, our findings in this current work suggest that failure modes in biocemented rocks are more complex and can vary between axial and shear failure depending on the curing temperature, urease activity, rock heterogeneity, and biocementation type.

Although this work offers valuable first insights on the potential effect of biopolymer-modified EICP on the mechanical response of weak rock masses under varying curing regimes, there are a few limitations that should be addressed to further improve on this technique as follows: (i) the number of tested specimens could be increased and (ii) a wider temperature range could be considered for curing regime studies. Despite the constraints, the results show that EICP and BP-EICP can significantly influence rock behavior and improve the strength under controlled curing regimes. This knowledge provides a baseline understanding for future work to further explore the influence of biocementations on different rocks mass types under field-specific conditions. Additionally, the applicability of this work may be extended beyond the rock mass type used in this study, as previous studies (Ngoma, Kolawole, & Lu, 2024; Ngoma, Kolawole, Olorode et al., 2024) have shown that the effectiveness of biocementation also depends on the inherent porosity, mineralogy, and bedding orientation of rocks. These findings suggest that extending BP-EICP to other lithologies is feasible and will require careful consideration of mineralogical compatibility and pore structure.