Characterizing the Deformation Evolution with Stress and Time of Biocemented Sands

Two types of pure silica sands were used in this study: fine-grained Itterbeck sand (Smals SA, Cuijk, Netherlands) and medium-grained sand (Bernasconi, Bern, Switzerland). Both have been reported in the literature as the base geomaterials of previous MICP studies (Esnault-Filet et al. 2012; Terzis and Laloui 2019b). They were characterized using sieve analysis tests according to ASTM D422 (ASTM 2007), and their respective particle size distribution curves are shown in Fig. 1. Per the Unified Soil Classification System (USCS), both sands are labeled poorly graded SP according to ASTM D2487 (ASTM 2018). A summary of their properties is presented in Table 1.

MICP treatment was achieved through a two-solution approach, namely a bacterial solution and a urea-calcium chloride solution, referred to as the cementation solution. The composition of the solutions and their concentrations are summarized in Table 2. The biological preparation process was similar to that presented in Terzis and Laloui (2019b), where Sporosarcina pasteurii (strain designation ATCC 11859) was used as the urease-bearing bacterium. A freeze-dried state, instead of a vegetative state, was adopted as a more representative inoculum for real applications. The previously prepared bacterial powder was brought back to room temperature (25°C) and rehydrated under aerobic conditions and constant stirring in a nutrient-rich solution consisting of urea and peptone. The bacterial solution had an optical density (${\mathrm{OD}}_{600}$) of 0.7 and an activity of $0.32\mathrm{mM}/\min$. Distilled water was used in the preparation of all solutions. Monitoring the increase in electric conductivity (EC) allowed us to follow the hydrolysis of the added urea per Eq. (1), with an average $\mathrm{\Delta }\mathrm{EC}=2.3\mathrm{mS}/\mathrm{cm}$ in 2 h.

Soil samples were prepared in plastic recipients of 60-mm diameter and 120-mm height by dry pluviation and manual tamping. MICP treatment was administered by batch injections. The volume of each injection was 140 mL, or 1.2 times the pore volume, and was circulated using a peristaltic pump (MasterFlex $\mathrm{L}/\mathrm{S}$, Model 7518-10, Bruchsal, Germany) at $5\mathrm{mL}/\min$ while alternating the injection-extraction inlets. An initial inoculation solution introduced the suspended bacteria into the soil, where they were allowed to attach to the sand grains for 12 h. Cementation solution batches were followed with a 6-h retention time, with pH and conductivity measurements carried out systematically before and after each injection. Once treatment was completed, samples were flushed with distilled water at a volume equal to approximately 10 times the initial pore space and then oven-dried.

The degree of cementation was determined by gravimetric acid washing. After testing, samples were oven-dried and weighed, washed with 1-M hydrochloric acid (HCl), rinsed with distilled water, oven-dried, and reweighed. The calcium carbonate content percentage ($C$) was then expressed as the ratio of mass change to the mass of pure soil after digestion.

The volume of calcite ($V_c$) following treatment, prior to any loading, can be computed from the mass of calcite ($m_c$) and by assuming a calcium carbonate density (${\rho }_c$) of ${2.71\mathrm{g}/\mathrm{cm}}^3$ (smallest value within the proposed range for ${\mathrm{CaCO}}_3$ between 2.7 and ${2.95\mathrm{g}/\mathrm{cm}}^3$ considering the lighter aspects of biogenic compared with geologic calcite, as later covered in the discussion section). The mass of calcite $m_c$ is given as per Eq. (3), where $m_d$ is the total dry mass of the sample and $C$ is the gravimetric content. As such, $V_c$ is obtained as per Eq. (4). The volumetric content percentage ($C_{iv}$) can then be expressed as the ratio of calcite volume to sample volume, while the porosity-to-cement ratio is expressed using the initial porosity before initial loading

The void ratio and axial strain versus vertical effective stress are shown in Figs. 2 and 3. The results suggest that both sands in their untreated condition yield a similar response, with slight variations, due to their varying initial characteristics. Similar findings on the comparison of these same materials in the untreated state were reported in Terzis and Laloui (2019b). At similar densities, MICP treatment enhanced the overall deformability response by reducing the accumulated strains with increasing stress level. For instance, for medium-grained sand at a similar testing void ratio ($e_0=0.74$), ${\epsilon }_a$ at 1,000 kPa was reduced from 2.5% for ILS-M-0-2 (untreated) to 1% and 1.5% for ILS-M-4 and ILS-M-5 (calcium carbonate contents of 4% and 5%), respectively, despite having larger $e_i$ values (initial looser state). Similarly, for fine sand, a 4% calcium carbonate content (ILS-F-4) reduced ${\epsilon }_a$ from 2.1% for the untreated sand (ILS-F-0-1) to 1.6% (both at $e_0=0.56$). This improvement could be explained by the coupled effects of densification and bonding induced by treating the sand fabric.

At lower stresses, the predominant mechanism governing the response was bonding, as the observed enhancement improved with increasing bond content, with little to no effect of the initial void ratio of the samples. As stresses increased, the results progressively diverged, where eventually, at 1,000 kPa, the total accumulated axial strains could not be explained solely by calcium carbonate content without considering initial densities. A gradual loss of soil structure was inferred with increasing stresses, during which bonds broke while the sample accumulated more deformation until the behavior converged back to that of the uncemented state of the granular assembly, predominantly governed by compacity. Note that pure calcite and silica grains exhibit different bulk moduli and similar shear moduli. More precisely, their shear moduli are comparable at approximately 44 and 32 GPa for quartz and calcite, respectively, while their bulk moduli differed by a factor of 2 at 37 and 73 GPa, respectively (Belkofsi et al. 2018; Schmitt 2015; Wang et al. 2015). However, calcite bonds resulting from MICP should not be considered pure geologic calcite due to the complex nucleation and growth processes that have been reported to yield bonds with nano- to microscale impurities and dislocations (De Yoreo et al. 2015). For the medium sand, ILS-M-0-2 (untreated) and ILS-M-3-1 (3% ${\mathrm{CaCO}}_3$) converged progressively toward the same total accumulated axial strain at 1,000 kPa, while ILS-M-3-4 (3% ${\mathrm{CaCO}}_3$) eventually reached a larger ${\epsilon }_a$ compared with ILS-M-0-2 since it corresponded initially to a looser state ($e_i$ of 0.78 and 0.74, respectively). With progressive damage caused by increasing stress, the bond contribution to the overall response was gradually taken over by compacity, as both samples had the same initial void ratio before the MICP treatment, with $e_i=0.74$. The same was observed for the fine sand, with ILS-F-0-1 (untreated) and ILS-F-7-2 (7% ${\mathrm{CaCO}}_3$) having the same $e_i=0.56$. The divergence observed between samples at the final loading step was thus dependent on the initial compactness ($e_i$), treatment level (% ${\mathrm{CaCO}}_3$), and accumulated damage, itself a function of the treatment efficiency (number of induced active bonds) and applied stress. Overall, the results agreed with the values and trends identified in other works dealing with MICP-treated sands (Feng and Montoya 2014; Lin et al. 2016).

Most cemented samples with low or high calcium carbonate contents exhibited a continuous accumulation of deformations in their response to increasing load without immediate collapse, which has sometimes been reported in works dealing with artificially cemented soils using portland cement (Yun and Santamarina 2005) or soil cementation in general (Länsivaara 2020). The immediate collapse behavior was shown to depend primarily on the state of compactness (loose) of the base material. This was notably the case for two loose fine sand samples, ILS-F-5 ($D_r=62\%$) and ILS-F-4 ($D_r=50\%$), which exhibited large settlements at initial loading and at unloading-reloading at 500 kPa, respectively. Overall, the behavior of the MICP-treated and artificially cemented sands (Yun and Santamarina 2005) remained in the same range at similar compactness and (bio)cement contents.

The variation in ${\epsilon }_a$ with the porosity to cement ratio $\eta /C_{iv}$ is shown in Fig. 4 at different stress levels. A power law ($Y=k{X}^{\alpha }$) was used to fit the measured strains with the $\eta /C_{iv}$ ratio, as proposed in other studies (Consoli et al. 2012, 2013, 2019). For medium sand at low stresses, satisfactory relationships were established ($R^2>0.9$); however, these relationships were not maintained at higher stresses, where degradation of bonding led to rapid deformation and the development of compaction bands. Eventually, at the maximum stress of 1,000 kPa, the calcite bond content in the matrix, quantified either in gravimetric terms ($C$) or in volumetric terms ($C_{iv}$), was no longer a suitable parameter to capture the mechanical response due to the irreversible loss of active bonds in the soil skeleton. This degradation front was captured when comparing successive increasing stress levels. Shear-wave velocity measurements (Montoya et al. 2019) also validated the degradation front phenomenon in similar setups and for loading-unloading cycles. Fine sand had a poor correlation with the $\eta /C_{iv}$ ratio, especially considering the narrow margin of $\eta /C_{iv}$ values. Note that the ratio was originally conceived for artificially cemented soils, essentially using portland cement and thus assumed the contribution of most of the cementing agent in the mechanical response. Multiple studies, however, have reported a lower efficiency for MICP treatment in fine soils (Tang et al. 2020; Terzis and Laloui 2018). As such, a high percentage of ${\mathrm{CaCO}}_3$ content was recorded for fine sand, but fewer active bonds actually contributed to the stiffening of the soil. This variation in the proportion of active/passive precipitated ${\mathrm{CaCO}}_3$ was also at the root of the discrepancy between replicate samples, which were extruded from different recipients yet had similar initial void ratios and treatment levels, eventually resulting in different accumulated strains upon loading. In those cases, such as for ILS-M-3-1 and ILS-M-3-2 for the medium sand and ILS-F-7-1 and ILS-F-7-2 for the fine sand, despite similar compacity and treatment levels, a divergence in the efficiency of the treatment was noted with regard to the mechanical improvement, potentially due to the formation of shear bands and inner fabric collapse.

The compression index ($C_c$), recompression index ($C_r$), and preconsolidation stress ($p_c^{\prime }$) values are summarized in Table 4, as determined for the range of applied vertical stress (up to 1,000 kPa). Values of $C_c$ typically varied between 0.010 and 0.056, falling within the established range for loose to dense quartz sands (Mesri and Vardhanabhuti 2009). MICP treatment was not observed to largely alter $C_c$ values, as Lee et al. (2013) noted, suggesting that the ${\mathrm{CaCO}}_3$ minerals lost their function under a high applied stress. The values of $C_r$ ranged 0.004–0.007 for the natural sands and decreased to 0.001–0.003 following MICP treatment. The unloading step from 500 to 60 kPa highlighted the sensitivity of the response to loading history, where even at the previously experienced stress level of 500 kPa, additional destructuration was observed, similar to that reported in Mendoza-Ulloa et al. (2020). Values of $p_c^{\prime }$ depended on both the initial void ratio and the cementation level, with a linear decrease with increasing $\eta /C_{iv}$ for medium sand ($R^2=0.96$) but poorer correlation for fine sand, consistent with that previously established.

The oedometric modulus ($E_{oed}$) for each step is shown in Fig. 5. When first comparing the untreated states, as expected, denser packing increased stiffness. For fine sand, the early compaction of the loose natural state under increasing stresses rendered its $E_{oed}$ practically similar to the dense state. In contrast, MICP-treated samples showed an increased stiffness compared with their representative loose state before treatment. Similar findings were reported by Feng and Montoya (2016). For some cases, distinctively higher $E_{oed}$ values were noted in at approximately 450 MPa for ILS-M-5 (5% ${\mathrm{CaCO}}_3$) and 700 MPa for ILS-F-7-1 (7% ${\mathrm{CaCO}}_3$) for medium- and fine-grained sands, respectively. Such values were more comparable with those of natural sandstone samples than with those of artificially cemented sands (Lashin et al. 2021; Wichtmann et al. 2017), embodying the intermediate state of biocemented geomaterials between soils and soft rock. Unlike the untreated state, little improvement was noted for treated samples with increasing stresses since the rearrangement of grains into a denser packed state was blocked by the active bonds. In contrast, notable drops in $E_{oed}$ were eventually observed for the same samples, ILS-M-5 and ILS-F-7-1. Only the mild improvement effect due to densification was permanently retained.

A typical result is shown in Fig. 6, where a sample of both treated states (ILS-M-3-1 and ILS-F-4) and untreated states (ILS-M-0-2 and ILS-F-0-2) are compared at low (60 kPa) and high (1,000 kPa) stresses. For both sands, the major contributor to the total recorded settlement was immediate settlement, with more than 90% of the total ${\epsilon }_a$ attained just after the load was applied. At 60 kPa, MICP did not greatly alter overall behavior, as a large portion of ${\epsilon }_a$ was still quasi-instantaneous for the biocemented cases. It is postulated that this was the result of asperity closures, as not all grain-to-grain contacts were expected to be biocemented. However, at higher stress (1,000 kPa), the share of immediate settlement was reduced to only 45% of the step’s total axial strain. Noticeably, the proportion of secondary, or delayed, deformation was higher for biocemented samples and for higher stresses.

A quantification of the secondary deformation of each loading step is provided using the coefficient of secondary compression ($C_{\alpha }$). All values of $C_{\alpha }$ for both sands are summarized in Fig. 7. Loose natural sands had consistently higher values than the denser state at each stress level. $C_{\alpha }$ values also slightly increased with increasing stresses. In comparison, biocemented samples followed an overall similar trend, albeit with a different magnitude. Overall, at low stresses the $C_{\alpha }$ values for MICP-treated cases were similar to those of natural sands. However, as the applied stress increased, so did the $C_{\alpha }$ values, which progressively exceeded those of the untreated states. In some instances, such as for ILS-M-3-2 (medium) and ILS-F-4 (fine), $C_{\alpha }$ at 1,000 kPa exceeded the loose untreated state by a factor of 3. Since $C_{\alpha }$ decreases with increasing density and increases with increasing stress, a plateau was observed, for instance between 15 and 500 kPa, for each natural sand due to compensation between the latter effects. No similar situation was observed for the treated cases, as they did not benefit from large compaction, consistent with what was observed for $E_{oed}$.

The results of the sustained loading series are shown in Fig. 8. In accordance with previous results, most recorded deformation okto place at the end of primary consolidation in less than 5 s. Despite some additional deformation sustained over the three-month loading duration, no major collapse in void ratio was noted. For natural sand, the sustained load over 75 days yielded similar results to those for a regular incremental load step, validating the low time-dependent deformability of quartz sand, for which a quasi-negligible $C_{\alpha }$ was recorded independently of the loading duration. Most biocemented samples had $C_{\alpha }$ values within the established range, as captured via the ILS campaign. As such, the imposed stress remained the main determinant of the contribution of secondary compressibility for MICP-treated sands. A few samples, however, such as SLS-3-40 and SLS-4-400, exhibited a larger $C_{\alpha }$ relative to the sustained stress level, exceeding the expected range suggested by the ILS data. For such cases, the time factor was also key in determining the contribution of secondary compressibility to the overall response.

To better isolate the evolution of delayed deformation with elapsed time, Fig. 9 presents the axial strains normalized to the initial value recorded after immediate loading. Five treated samples, at both 40 and 400 kPa, showed continuous strain accumulation following initial deformation at a decreasing rate that eventually stabilized to form a plateau, beyond which there was no major strain accumulation, also referred to as fading creep (Mitchell and Solymar 1987). The same behavior was exhibited by the control natural sand sample (SLS-0-400). In contrast, four marked samples in Fig. 9 reveal a yield point at which the stabilization process was instead reversed to accelerate strain rate accumulation before stagnating again. For these samples, a sustained load over time triggered delayed destructuration in the form of punctual events similar to stress increase events, albeit of a lower magnitude.

To compare the behavior of all tests, it is possible to normalize the preconsolidation pressure of a test ($p_c^{\prime }$) to the effective vertical stress (${\sigma }_v^{\prime }$) at each loading step. For all samples, for both the medium and fine sands, the variation in $C_{\alpha }$ rapidly increased when ${\sigma }_v^{\prime }$ exceeded the recorded $p_c^{\prime }$ for each test, as shown in Fig. 10. Additionally, when examining the loading curves for all the steps of the conducted tests, such as the example shown in Fig. 6, the deformation of biocemented sands appeared to repeatably stabilize under the sustained load before eventually yielding with an additional deformation increment. Such a progressive deformation that mobilized in stages highlights an overstressed matrix typical of perceived apparent ductility conveyed to a system by crushable components, continuously shifting the inner fabric to a temporary equilibrium before breaking with each deformation increment (Ciantia et al. 2017). This dependence between the theoretical onset of damage in a sample ($p_c^{\prime }$) and an accelerating creep response highlights the interdependence between stress- and time-related phenomena, as the latter could not be dissociated from structural damage in the fabric, itself conveyed to a sample by MICP treatment. A study of the damage to artificially cemented soils using mercury intrusion porosimetry found slow damage evolution in the quasi-elastic stage, which then evolved more rapidly with increasing stress (Huie et al. 2018). Such concepts have been proposed in recent studies, where, for instance, the initiation of bond breakage has been attributed to the bilinear feature of the void ratio versus the logarithm of vertical stress plots, marking the transition between different stages of the compression response (Xiao et al. 2020).