Numerical Simulation of Forming MICP Horizontal Seepage Reducing Body in Confined Aquifer for Deep Excavation

Abstract

The drawdown outside of a deep foundation pit has to be controlled during excavation. However, the vertical curtain cannot cutoff a deep and thick confined aquifer during deep excavation. In this study, a microbial-induced carbonate precipitation (MICP) horizontal seepage reducing body (HSRB) was proposed to control drawdown combined with a partially penetrating curtain. MICP HSRB is formed by using the seepage field generated by the recharge wells to drive the migration of a Sporosarcina pasteurii solution, stationary solution, and cementation solution into the deep confined aquifer. The migration of each solution was numerically simulated to study the HSRB formation process. The influence of different factors on solute migration was studied. The results show that the solutes in the fixed fluid and cementation fluid can reach the area under the driving of the seepage field, which proves that MICP HSRB can be formed. The calcium ions and urea in the cementation solution are more likely to migrate to the designated area than the bacterial solution. Increasing the injection rate of bacterial solution and adding recharge wells both made the bacterial solution migrate more quickly to the designated area. In the case of multiple grouting, the solute migration in the later stage will be hindered by the plugging of pores caused by calcium carbonate generated in the earlier stage. Therefore, different grouting methods need to be designed to drive the seepage field so that the solute injected in the later stage can continue to migrate. The MICP HSRB grouting technology can be used in foundation pit dewatering, providing reference for similar engineering.

1. Introduction

A vertical curtain is often used to cut off confined aquifers to control drawdown during deep excavation. However, the vertical curtain cannot cut off deep and thick confined aquifers. When a partially penetrating waterproof curtain cannot control the drawdown inside and outside of the pit, recharging and horizontal curtains are often possible measures. Normally, forming a waterproof horizontal curtain is too expensive. In the current study, a microbial induced carbonate precipitation (MICP) horizontal seepage reducing body (HSRB) was developed to solve the problem.

MICP belongs to a class of new, environmentally friendly engineering technologies used in rock and soil reinforcement, concrete crack repair, ancient building reinforcement, and contaminated soil treatment [1,2,3,4,5]. This bioreinforcement method has simple response, a controllable process, is green, is environmentally protective, and has broad application. MICP technology is widely used in various types of bad soils [6,7,8,9]. The MICP technology utilizes some bacterial strains in nature to precipitate calcium carbonate, which can fill and repair cracks in stone and concrete materials, strengthen soil, improve soil strength, prevent building leakage, avoid sand liquefaction, and prevent slope damage and other disasters [10,11,12,13,14]. In addition, MICP technology can also reduce soil permeability [15]. Compared with traditional chemical grouting, the bacterial and cementing solutions used in this method have lower viscosity and can easily penetrate into geotechnical materials [16,17,18], which make it suitable for handling deeper and thicker geological materials [19]. Therefore, it is feasible to utilize MICP technology to form a horizontal seepage reducing body (HSRB) in a deep confined aquifer. 3D simulation of solute migration in porous media has been widely used [20]. A solute is different from an ordinary solute when it is transformed into living organisms, such as microorganisms. Living substances move themselves and react with the surrounding environment when they migrate in underground water. At present, most mathematical models of microbial migration are based on the convection dispersion equation. Powelson and Pang et al. proposed colloidal filtration theory on the basis of the convection dispersion equation [21,22]. However, a large number of soil column tests have shown that filtration and desorption, especially filtration, have an important effect on microbial migration and retention [23,24]. Desorption, death, and inactivation of microorganisms have a definite effect on migration [25,26]. Therefore, Bhattacharjee established a microbial migration model based on the convection dispersion equation and comprehensively and accurately described the migration process of microorganisms [26]. The previous research results of pollutants and microbial migration provide theoretical support for the numerical simulation of microbial and cementation fluid used in MICP technology. Seepage blockage problem-solving methods are also developed based on numerical analysis [27,28,29,30,31,32], analytical solutions [33,34], experimental work, field investigations [35,36,37,38,39], and experimental investigation [40].

In this study, the foundation pit of the No. 4 working shaft of the Guanyuan project in the Pudong New Area of Shanghai was taken as the engineering background. The MICP HSRB formation method was developed and verified through numerical simulation. On the basis of laboratory experiments regarding the formation mechanism of MICP HSRB [41], S. pasteurii and cementation solutions were selected as the MICP injecting into the fine sand of layer ⑨ with a recharging well. The solute migration of each solution was numerically simulated to study the formatio n process of MICP HSRB. The optimal scheme using MICP grouting technology to form HSRB was established through the analysis of the main influencing factors of solute migration, which can provide guidance for MICP HSRB application.

2. Overview of the Engineering

The foundation pit of the No. 4 working shaft of the Guanyuan project in the Pudong New Area of Shanghai was selected as the background. The foundation pit is located at Jihui Road, 97.1 m away from the West 220 kV high voltage tower, 12 m away from the east substation, and 8.5 m away from the pump house (Figure 1a). The size of the foundation pit is 55 m × 50 m, the ground elevation is 4.5 m, the excavation depth is 39.6 m. The foundation pit bottom is located in the silty clay of layer ⑤. The retaining system includes a diaphragm wall and a trench-cutting remixing deep wall, together with internal support. Dewatering, drainage, and water proof measures are adopted to control ground water. The surrounding environment of the foundation pit is complex and the dewatering subsidence has to be strictly controlled. The soil layer within 150 m depth of the site is composed of Quaternary Holocene to middle Pleistocene sedimentary strata. The strata are divided into 13 main engineering geological layers (Figure 1b):layers ①–②, layer ③, layer ④, layer ⑤₁, layer ⑤₂ (clayey silt with silty clay), layer ⑤₃ (silty clay), layer ⑤₄ (silty clay), layer ⑦₁ (sandy silt), layer ⑦₂ (silt), layer ⑧₂₁ (interlayer of silty clay and silt), layer ⑧₂₂ (silty sand with silty clay), layer ⑨ (silt), and layer (11) (silt). The aquifers consist of a phreatic aquifer (shallow soil layers), a slightly confined aquifer (layer ⑤,) confined aquifer I (layer ⑦), confined aquifer II (layer ⑨), and confined aquifer III (layer (11)). The stratum distribution and groundwater situation are shown in Figure 1b, and the corresponding parameters are shown in Figure 2. The water level of confined aquifer layer ⑦ is −1.40 to −2.64 m; the water level of confined aquifer layer ⑨ is −1.00 m; the water level of confined aquifer layer (11) is −2.15 m. The anti-gushing calculation of confined water and safe drawdown of layers ⑦, ⑧₂₁, ⑨, and (11), according to the above water level, is shown in

Table 1. Checking calculation of anti-gushing stability of each confined aquifer of the No. 4 Foundation Pit (safety factor is 1.05).

Layer No.	Pit Depth (m)	Borehole	Aquifer top Elevation (m)	Initial Water Level (m)	Confined Water Pressure (kPa)	Overburden Pressure (kPa)	Drawdown (m)	Critical Excavation Depth (m)	Note
⑦	39.437 (−34.937)	BXZ21	−36.95	−1.40	373.3	38.8	31.86	20.76	Layers ⑦ and ⑧21 were summarized as a confined aquifer
⑧21		BXZ27	−56.19	−1.40	575.3	403.7	16.34	29.85
⑧22		BXZ22	−71.29	−1.00	738.0	686.8	4.88	36.57	Layers ⑧22 and ⑨ were summarized as a confined aquifer
⑨		BXZ21	−74.75	−1.00	774.4	749.7	2.35	38.05

Notes: The design elevation of the foundation pit ground is + 4.50 m. The selected borehole is the most unfavorable for the shaft foundation pit.

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The normal depth of a traditional horizontal waterproof curtain is approximately 50 m to 70 m, although the maximum depth of the diaphragm wall has reached 150 m, forming a horizontal curtain in the aquifer when the depth exceeded 70 m in Shanghai. The materials used in a traditional horizontal waterproof curtain-forming method are mainly cement and lime cementitious materials, which may cause adverse effects on the ecological environment of groundwater. Traditional grouting materials cannot enter the deep sand layer with small pores without destroying the soil structure.

3. Materials and Methods

3.1. MICP HSRB Formation Method

The MICP technology based on urea hydrolysis is the most commonly used method for producing calcium carbonate crystals. S. pasteurii is one of the most commonly used bacteria in the application of MICP technology in geotechnical engineering, which is a natural underground non-pathogenic bacterium [42,43]. S. pasteurii has high urease activity because it can produce a lot of urease, can survive in a high alkaline environment, and has high calcium ion concentration [44,45]. In this study, S. pasteurii was selected as the strain of HSRB to be formed by MICP technology. The solutions designed to be injected into the confined aquifer by MICP grouting technology included a bacterial solution (S. pasteurii) and cementation solution (urea and CaCl₂ solution). When the bacterial solution and cementing solution were injected into the soil, the urea in the cementing solution was hydrolyzed rapidly to NH₄⁺ and CO₃^2- under the catalysis of urease produced by S. pasteurii, as shown in chemical Equations (1)–(4). As the extracellular polymer of the metabolites of S. pasteurii was a negative ion group, the negative charge on its surface would continuously absorb the Ca²⁺ provided by the surrounding CaCl₂ solution, aggregate on the external surface of bacterial cells, and combine with the CO₃^2- continuously decomposed under the action of urease, thus forming calcium carbonate crystals with bacterial cells as crystal nuclei (see chemical Equations (5) and (6)).

$$\mathrm{CO}{\left({\mathrm{NH}}_2\right)}_2+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{H}}_2\mathrm{COOH}+2{\mathrm{NH}}_3,$$

(1)

$${\mathrm{H}}_2\mathrm{COOH}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{NH}}_3+{\mathrm{H}}_2{\mathrm{CO}}_3,$$

(2)

$$2{\mathrm{NH}}_3+{\mathrm{H}}_2\mathrm{O}\leftrightarrow 2{\mathrm{NH}}_4^{+}+2{\mathrm{OH}}^{-},$$

(3)

$$2{\mathrm{NH}}_3+{\mathrm{H}}_2{\mathrm{CO}}_3\leftrightarrow {\mathrm{CO}}_3^{2-}+2{\mathrm{H}}_2\mathrm{O},$$

(4)

$${\mathrm{Ca}}^{2+}+\mathrm{Cell}\to \mathrm{Cell}-{\mathrm{Ca}}^{2+},$$

(5)

$$\mathrm{Cell}-{\mathrm{Ca}}^{2+}+{\mathrm{CO}}_3^{2-}\to \mathrm{Cell}-{\mathrm{CaCO}}_3,$$

(6)

MICP HSRB was introduced where the slurries included S. pasteurii solution, CaCl₂ solution, and urea solution. The particle size of the solute was small and could be seeped into the fine sand layer without damaging the aquifer structure. The recharging well was used to form a stable seepage field to drive the slurry to the designated position. Sporosarcina pasteurii (ATCC 11859) purchased from the Shanghai Bioresource Collection Center (SHBCC) was used in this study. Laboratory experiments on the formation of MICP HSRB using the ATCC 11859 in a confined aquifer had been performed by the authors for deep excavation. In accordance with the solute migration parameters preiously determined by the authors [41], the solute had small adsorption and a weak retardation effect in the silty fine sand layer. Using the seepage field formed by the recharge wells, the solute was driven to migrate to the silty fine sand layer and cover the bottom of the foundation pit.

When water was injected into the aquifer through the recharge well, the groundwater level around the recharge well continued to rise. The water level formed a water head difference with the surrounding groundwater level. The seepage field formed by the recharging well was used to drive the solution used in MICP to form HSRB.

The site injection steps were as follows:

(1) The foundation pit was divided into several concentric ring areas and the recharging wells were installed along the separating lines, as shown in Figure 3a.

(2) Booster pumps were used to form a stable seepage field, as shown in Figure 3b.

(3) Bacteria and cement were injected into the outer area. The inner recharge wells were used to prevent the accumulation of calcium carbonate in the pipe mouth from blocking. The seepage field formed by the inner recharging wells was used to continuously drive the bacteria and cement fluid injected from outer recharge well to prevent the bacteria and cement fluid from stopping, as shown in Figure 3c.

(4) The recharge well was washed back intermittently after recharging for a certain time to eliminate the plugging of the reinjection well.

(5) The above steps were conducted step by step after the outer layer was covered by bacteria and cement until HSRB had been formed in the entire pit.

(6) The remaining center part was directly injected into the bacteria and cement from the central recharge well, and the final HSRB was finally filled.

The solutions were controlled within the vertical curtain when the S. pasteurii, CaCl₂, and urea solutions were injected into the deep aquifer.

3.2. Numerical Model

The equation of convection dispersion, adsorption, and migration of solute in the second confined aquifer of Shanghai by S. pasteurii and cementation solution used in MICP technology is as follows:

$$\frac{\partial \left(\theta C\right)}{\partial t}=\frac{\partial }{\partial x_i}\left(\theta D_{ij}\frac{\partial c}{\partial x_j}\right)-\frac{\partial }{\partial x_i}\left(\theta v_{i}C\right)+q_s{C}_s+{\displaystyle \sum R_n},$$

(7)

where θ is porosity, dimensionless; $C$ is solute concentration (M·L⁻³); $t$ is time (T); $x_i$, $x_j$ is distance of solute along X and Y coordinate axis (L); $D_{ij}$ is hydrodynamic diffusion tensor (L²·T⁻¹); $v_i$ is average actual velocity of pore water (L·T−1); $q_s$ is volume discharge of source and sink per unit volume of aquifer (L³·T⁻¹); $C_s$ is concentration of components in source and sink water (M·L⁻³); ${\displaystyle \sum R_n}$ is chemical reaction term (M·L⁻³T⁻¹).

MT3DMS was used to simulate the S. pasteurii and cementation solution used in MICP technology. The solute migration of each solution was numerically simulated to study the formation process of HSRB. The simulation of solute migration was based on groundwater seepage. In order to simplify the analysis, the adsorption and reaction behavior of solute was not considered. The migration of urea affecting the urea hydrolysis and the relationship of solute migration and reaction will be further studied in the next study.

With the shaft foundation pit as the center, a modeling range of 2000 m × 2000 m and 150 m deep was selected. The range was generalized into a 3D heterogeneous, horizontally isotropic, and unstable groundwater seepage system. The model was divided into 10 layers according to soil layer distribution. The model divided the plane into 50 × 50 grids, and then each row and column of the grid within 3 times the width of the foundation pit were further refined into 40 copies (Figure 4). The ground elevation was +4.5 m. The outer boundary was defined as a constant water head boundary, and the bottom was set as an impermeable boundary. The model hierarchy and its parameters are shown in

Table 2. Hydraulic conductivity of the soil layers.

Layer	Soil	Experimental Value (cm/s)		Recommended Value	${\mathit{S}}_{\mathit{s}}$ (1/m)
		${\mathit{K}}_{\mathit{v}}$	${\mathit{K}}_{\mathit{h}}$	(cm/s)
/	Shallow clay layer	2.21 × 10−7	3.69 × 10−7	5.0 × 10−5	8.0 × 10−4
⑤2	Clayey silt with silty clay	1.25 × 10−4	1.97 × 10−4	3.0 × 10−4	4.5 × 10−4
⑤3	Silty clay	7.07 × 10−5	8.97 × 10−5	8.0 × 10−5	8.0 × 10−3
⑤4	Silty clay	3.46 × 10−7	4.17 × 10−7	4.0 × 10−5	8.0 × 10−3
⑦1	Sandy silt	1.04 × 10−7	1.70 × 10−7	1.48 × 10−3	4.5 × 10−4
⑦2	Silt	4.21 × 10−4	5.84 × 10−4	1.40 × 10−3	5.0 × 10−4
⑧21	Interlayer of silty clay and Silt	4.6 × 10−5	5.8 × 10−4	6.0 × 10−5	4.5 × 10−4
⑧22	Silty sand with silty clay	1.0 × 10−3	6.4 × 10−3	6.4 × 10−3	5.0 × 10−4
⑨	Silt	1.0 × 10−2	9.0 × 10−2	5.0 × 10−2	2.0 × 10−5
(11)	Silt	5.0 × 10−3	4.9 × 10−2	1.0 × 10−2	3.0 × 10−5

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3.3. Parameter Selection

The HSRB depth was set to 82 m and the HSRB thickness was 4 m. The depth of the filter pipe of the recharging well ranged from 82 m to 86 m. The location and number of the recharge wells were constantly adjusted and determined in accordance with the numerical simulation results. The structure of recharge well is shown in

Table 3. Structure information of injection well.

Aperture(mm)	Pipe Diameter (mm)	Wall Thickness (mm)	Top Buried Depth of Filter Pipe (m)	Buried Depth of Filter Pipe Bottom (m)	Length of Filter Tube (m)
850	400	8	82	86	4

. In accordance with the results of the solute migration analysis and laboratory test performed before, the parameters involved in the process of solute migration were determined [41], as shown in

Table 4. Solute transport parameters.

Solute	S. pasteurii	Cementation Solution		Stationary Solution (CaCl2 Solution)
	${\mathit{K}}_{\mathit{d}}\left(\mathbf{L}/\mathbf{mg}\right)$	${\mathit{K}}_{\mathit{l}}\left(\mathbf{L}/\mathbf{mg}\right)$	$\overline{\mathit{S}}\left(\mathbf{mg}/\mathbf{Kg}\right)$	${\mathit{K}}_{\mathit{l}}\left(\mathbf{L}/\mathbf{mg}\right)$	$\overline{\mathit{S}}\left(\mathbf{mg}/\mathbf{kg}\right)$
Adsorption parameters	1.5 × 10–7	2.98 × 10–5	2404.8	2.98 × 10–5	2404.8
Concentration	OD600 = 0.9	1.5 mol/L		0.05 mol/L
Dispersion	11.5 cm

$K_d$ is partition coefficient; $K_l$ is Langmuir constant; $\overline{S}$ is the maximum adsorption concentration, which represents the maximum mass of solute that can be absorbed by porous media per unit mass. In the case of low solute concentration, Langmuir isotherms are approximately linear isotherms, $K_d=K_l\overline{S}$.

. The solute migration characteristics of the entire cementation solution were directly expressed in terms of the adsorption characteristic parameters of Ca²⁺ due to the extremely low adsorption capacity of the urea in the fine sand.

The results show that the dispersity measured by the sand column test was less than that measured by the field test because the density of the soil column in the indoor dispersity sand column test was larger than that in the actual test and the soil was more uniform. However, the field dispersity test was conducted in situ, which did not damage the structure and composition of the water bearing layer, and the obtained dispersion parameters are close to the actual.

Neuman et al. conducted numerous statistical analyses on the data of flow path exceeding 100 m and obtained the empirical formula of field longitudinal dispersion and flow distance, as follows [46]:

$$a_l=0.0169L_s^{1.53}$$

(8)

The flow path could not be expressed by this formula when it exceeded 100 m, and other formulas were needed to determine the longitudinal dispersion [46]. To overcome this problem, Xu and Eckstein classified the field data reliability of different scale flow paths into three categories: high, medium, and low [47]. The empirical formula of longitudinal dispersion was obtained through regression analysis of field data, which was not limited by the size of the flow path.

$$a_l=0.83{\left(\log L_s\right)}^{2.414}$$

(9)

In the range of the No. 4 well foundation pit, the solute flow path did not exceed 20 m, and the longitudinal dispersion was calculated as 1.56 and 1.38 m by using empirical Equations (8) and (9) considering the scale effect. In the aspect of the indoor scale test, the results of the vertical dispersion of the sand column test by some scholars were approximately 0.2–1.0 cm. In accordance with the results of the sand column test conducted by the author, the dispersion of fine sand in the layer of Shanghai was 11.5 cm. Therefore, the longitudinal dispersion of MICP bacteria and cementation fluid in the layer of silty fine sand ranged from 0.2 cm to 1000 cm.

The solute migrated with the flow of water, and its migration speed mainly depended on the flow velocity. When the bacteria solution was driven by the seepage field formed by the recharging well, the water flow velocity in the seepage field formed by the recharging well was large due to the large amount of water injected by the reinjection well. The influence of convection was greater than that of other effects. At this time, only convection occurred in the sand, and the proportion of dispersion was extremely small. Therefore, determining the influence of longitudinal dispersion in the range of 0.2–1000 cm on solute migration under field conditions was necessary. Thus, numerical simulations were performed for the sensitivity analysis of longitudinal dispersion.

Set longitudinal dispersion $a_l$ was 0.2 cm, 12 cm, 50 cm, 100 cm, 200 cm, and 1000 cm. The solute migration of the six different longitudinal dispersions was numerically simulated. The initial injection rate of inner ring 4 diameter was 1000 m³/d. The outer ring well was injected with S. pasteurii at a recharge rate of 200 m³/d to simulate the solute migration of S. pasteurii in different time periods after the recharge reached equilibrium.

Regarding the migration of S. pasteurii on the 4th day when a_l = 0.2 and a_l = 1000. Under the condition of seepage field velocity formed by the designed recharge rate, the influence of dispersion on migration range was extremely small, although the dispersion difference was 5000 times. Taking time as abscissa and migration distance as ordinate, the migration distances of S. pasteurii in different time periods under different longitudinal dispersion conditions were obtained, as shown in Figure 5.

When the dispersion ranged from 0.2 cm to 1000 cm, the dispersion had minimal effect on the solute migration in the field. Therefore, in the numerical simulation of forming horizontal curtain in the confined aquifer II of Shanghai by using MICP grouting technology, the influence of dispersion value on solute migration was ignored when the dispersion value ranged from 0.2 cm to 10.0 m. Combined with the empirical formula of field dispersion, the longitudinal dispersion was 1.5 m. The selection of numerical simulation dispersion parameters are shown in

Table 5. Dispersion parameter table.

Parameter	Longitudinal Dispersion ${\mathit{a}}_{\mathit{l}}$ (m)	Lateral Dispersion ${\mathit{a}}_{\mathit{t}}$ (m)	Vertical Dispersion ${\mathit{a}}_{\mathit{v}}$ (m)
Value	1.5	$0.3a_l$	0.3$a_l$

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3.4. Simulation Condition Design

The main influencing factors forming HSRB by using the recharge well to inject S. pasteurii and the cementation solutions used in MICP technology into the silty fine sand of layer ⑨ included the reinjection rate of the inner reinjection well forming seepage field, the reinjection rate of bacteria and the cementation solution, and the location of the reinjection well. S. pasteurii solution and cementation solution were injected by using a three-step grouting method: (1) S. pasteurii bacteria solution was injected, (2) CaCl₂ stationary solution (0.5 mol/L) was injected, and (3) cementation solution (1.5 mol/L) was injected. The simulation condition is shown in

Table 6. Working condition of HSRB formed using MICP Technology.

Working Condition	Reinjection Rate of Inner Circle Reinjection Well (m3/d)	Outer Circle Bacterial Solution Infusion Rate (m3/d)	Layout Interval of Reinjection Wells (m)
1	1000	100	Horizontal: 10; Vertical: 11
2	2000	100	Horizontal: 10; Vertical: 11
3	1000	200	Horizontal: 10; Vertical: 11
4	1000	300	Horizontal: 10; Vertical: 11
5	1000	400	Horizontal: 10; Vertical: 11
6	1000	2000	Horizontal: 5; Vertical: 5.5

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4. Results

4.1. Influence of the Irrigation Rate of Inner Circle Recharge Well on Migration

The design of condition 1 was conducted and used as a benchmark for comparative analysis with the subsequent conditions. In accordance with the field pumping test design, four dewatering wells were arranged. The dewatering wells on the horizontal plane are shown in Figure 6.

The recharge wells in the inner circle were first recharged at a recharge rate of 1000 m³/d. The water level of the second confined aquifer did not change after 4 days of recharging (Figure 7), and a stable seepage field was formed by the recharge wells.

The outer circle recharge well was filled with 5000 mg/L (OD600 = 1.0) of S. pasteurii at a reinjection rate of 100 m³/d after the formation of stable seepage field. With the continuous injection of S. pasteurii solution, the bacteria were constantly migrating and expanding the coverage, as shown in Figure 8 and Figure 9. The plane shape of the whole migration was roughly spindle because the seepage field formed by the reinjection of the inner circle reinjection well was flowing to the outside of the pit. In the vertical direction, the high concentration of S. pasteurii, which obviously affected MICP, was concentrated around the broken filter pipe of the reinjection well, and the concentration of the bacteria, which migrated deep down, was extremely low.

As shown in Figure 8c,d and Figure 9c,d, the bacterial solution no longer had the significance of reducing the permeability when the bacterial solution concentration of 3000 mg/L was taken as the limit and when the concentration was lower than the limit. The plane range of bacterial solution migration from a single reinjection well was generalized as an ellipse, and the coverage range of the effective bacterial solution concentration was calculated, as shown in Figure 10. The coverage area of the bacteria after migration increased with the increase of continuous injection time. However, the poured bacteria bypassed the vertical curtain and flowed into the underground water outside the foundation pit if the injection time was extremely long, thereby affecting the environment outside the pit.

As shown in Figure 8 and Figure 9, S. pasteurii cannot cover the designed area through migration under the condition 1. Thus, the designed scheme needed to be improved. In order to study the effect of the recharge rate of the inner circle reinjection wells on the migration of S. pasteurii, working condition 2 was designed, which was based on working condition 1, the recharging rate of the inner circle recharging wells was increased to 2000 m³/d, and other conditions remained unchanged. Recalculating the time when the seepage field reaches stability is necessary after increasing the recharging rate of the inner circle reinjection wells, as shown in Figure 11. The seepage field reached stability after 5 days. At this time, the outer circle reinjection well began to inject bacterial solution, and the bacterial migration was obtained.

Figure 12 shows the migration of S. pasteurii after four days. Compared with working condition 1, increasing the recharging rate of the inner circle reinjection wells did not increase the migration coverage area of effective high concentration bacterial solution but did accelerate the bacterial solution leakage and reduced the effective concentration coverage area. Therefore, increasing the reinjection rate of the inner recharging well, which formed the seepage field, was inadvisable. It is necessary to further study the effect of the fluid injection rate on migration.

4.2. Influence of Bacterial Solution Injection Rate on Migration

In order to study the influence of the injection rate of bacterial solution in the outer ring recharge wells on the migration of S. pasteurii, working conditions 3, 4, and 5 were designed. Based on working condition 1, the injection rate of bacterial solution in the outer ring recharge wells was increased to 200, 300, and 400 m³/d, respectively. In working conditions 3, 4, and 5, other conditions remained unchanged. The bacterial migrations were obtained as shown in Figure 13, Figure 14 and Figure 15.

By comparing the bacterial migration in conditions 1, 3, 4, and 5, it can be found that the coverage area of 3000 mg/L effective bacterial solution concentration was obviously increased by increasing the bacterial solution injection rate of the outer ring reinjection wells. Therefore, increasing the bacterial coverage area by increasing the injection rate of the bacterial solution is preferred. The plane coverage area of the bacterial solution migration in a single reinjection well was generalized as an ellipse to quantitatively evaluate the relationship between the bacterial solution injection amount and the coverage area. The bacterial coverage areas in different time periods of working conditions 1, 3, 4, and 5 were calculated, as shown in Figure 16 and Figure 17.

As shown in Figure 16, the coverage area of bacteria increased with the increase of continuous infusion time under the same condition of S. pasteurii solution infusion rate. However, the slope of the curve decreased with the increase of time, and the coverage area growth rate decreased. Specifically, the effect of continuous infusion gradually decreased with the increase of infusion time. The growth of the effective coverage area corresponding to each irrigation rate was extremely low after 3 days. From the perspective of bacterial activity, the activity of the bacterial solution in the earlier period gradually decreased with the increase of time.

As shown in Figure 17, the higher the bacterial infusion rate, the larger the area covered by bacterial migration under the condition of the same continuous infusion time. No phenomenon occurred where the effect of increasing the coverage area decreased with an increase of time. The bacterial solution should be poured in as short of a time as possible to achieve the designed bacterial coverage area. The effect of 400 m³/d bacteria solution for 1 day was better than that of 200 m³/d bacteria solution for 2 days. Therefore, increasing the daily rate of bacterial solution was better than increasing the continuous time of bacterial solution when the total amount of bacterial solution is constant.

4.3. Influence of Reinjection Wells Layout on Migration

As shown in the calculation results of condition 5 (Figure 15), the entire area coverage cannot be achieved after 4 days of bacterial solution injection at 400 m³/d when the low concentration connection part is between the reinjection wells.

In order to cover the low concentration coverage part between the reinjection wells, one reinjection well was added between the original designed outer reinjection wells in design condition 6. A total of 12 reinjection wells were added. In accordance with the analysis results of the total amount and time, the bacterial solution injection rate of 400 m³/d was divided into two wells, and the injection rate of each well is 200 m³/d. No increase was observed compared with the total injection amount of condition 5.

As shown in Figure 18 and Figure 19, increasing the number of reinjection wells with bacterial solution in the outer ring can effectively increase the coverage area of bacterial fluid and fill the blank area that cannot be covered by condition 5. When the bacteria solution was continuously injected for 2 days, the increased coverage area was no longer obvious. On the third day, all the areas required by the design were covered. The bacteria solution with a high concentration of 3000 mg/L began to seep out of the vertical curtain. Therefore, the duration of bacteria solution injection should not exceed 3 days. Therefore, the injection amount of one reinjection well can be divided into two wells for injection under the condition that the total amount of injection remains unchanged, which can achieve better results.

If the time of continuous infusion was extremely long, then the activity of the bacterial solution injected in the early stage was reduced. The infusion should be completed in the shortest time to ensure the activity of the bacterial solution. In accordance with the analysis results of condition 6, each well could not meet the requirements of covering the design area in 1 day when it was injected with 200 m³/d of bacterial solution. Thus, increasing the bacterial solution injection rate is necessary. After trial calculation, the bacterial solution filling rate was increased to 400 m³/d under design condition 7 (Figure 20).

From Figure 20, it can be found that the foundation pit can be covered, except for the four corners of the vertical curtain after one day pouring at the pouring rate of 400 m³/d. Setting working condition 8, a pumping well was set up in the vertical curtain to solve the problem of blank corner coverage, and the pumping rate of 1000 m³/d was used to pull the bacteria migration to the corner position.

As shown in Figure 21, the addition of pumping wells in the four corners can play a traction role in the migration of bacteria and make the bacteria reach the corner where erecting the curtain is difficult. The amount of bacterial solution flowing out of the vertical curtain was reduced because of the traction effect of the pumping well.

In order to avoid the accumulation of bacteria solution at the wellhead of the recharge well and the later MICP reaction to generate calcium carbonate blocking the recharge wellhead, the flushing of the recharge well with bacteria solution can be adopted, or the injection of water into the recharge well in the inner circle can be used to drive the migration of bacteria solution at the recharge wellhead after stopping injection of the bacteria solution. Figure 22 shows that if the inner ring recharge well continues to irrigate for 0.5 days after the stop of bacterial fluid perfusion, the injected bacterial solution will leave the recharge well driven by the seepage field, so as to avoid the blockage of the recharge well by the calcium carbonate generated by the MICP reaction.

4.4. Stationary Solution Migration

The CaCl₂ solution (0.05 mol/L) was injected to pretreat the sand sample, and then the cementation solution was injected. This process was performed to improve the uniformity of calcium carbonate generated in the sand after the bacteria were injected into the sand and attached to the surface of the soil particles This method can avoid the problem of grouting mouth blocking, to a certain extent, to improve the permeability.

In accordance with the analysis results of bacterial migration and referring to the injection scheme of bacterial solution, 0.05 mol/L CaCl₂ solution stationary solution with the irrigation rate of 400 m³/d was injected into the inner recharge well after the stable seepage field was formed by the inner circle reinjection well with an irrigation rate of 1000 m³/d. As shown in Figure 23, the stationary solution can easily reach the required area under the drive of the seepage field because the adsorption of Ca²⁺ on the silty fine sand of the layer in Shanghai is weaker than that on S. pasteurii. Therefore, the fixed solution can fully meet the design requirements after adjusting the scheme of the bacteria injection.

4.5. Cementation Fluid Migration

The bacterial solution was replaced with 1.5 mol/L of cementation solution on the basis of this scheme after determining the injection scheme of the S. pasteurii solution. The cementation solution was composed of CaCl₂ solution and urea solution. In accordance with the test results of the migration parameters, the adsorption capacity of urea in the fine sand of the layer was extremely low and could easily migrate in a large area. The migration range of Ca²⁺ can be reached by urea. The MICP reaction only occurred when S. pasteurii, urea solution, and CaCl₂ solution were mixed together. The urea solution and CaCl₂ solution were added together as a cementation solution. Therefore, the numerical simulation directly used the migration simulation of Ca²⁺ in the CaCl₂ solution to replace the solute migration simulation of the entire cementation solution.

In accordance with the analysis results of bacterial migration and referring to the injection scheme of bacterial solution, 1.5 mol/L of cementation solution was injected at an irrigation rate of 400 m³/d after the stable seepage field was formed by the inner circle reinjection well with an irrigation rate of 1000 m³/d. As shown in Figure 24, the solute Ca²⁺ and urea in the cementation solution can completely migrate to the designated area because the adsorption of the Shanghai layer fine sand to the cementation solution was smaller than that of the S. pasteurii solution.

5. Discussion

The feasibility of migrating bacterial and cementing solutions to a confined aquifer via a recharge well had been preliminatively proved by simulation. The uneven distribution of the generated calcium carbonate was a problem that affected the integrability of MICP curing [13]. The reason was that bacterial cells had negative charges on their surfaces. Electrostatic forces between the cells repelled each other, but this negative charge attracted Ca²⁺ from the solution, which neutralized the charges and clumps together. The aggregated aggregates blocked the pores of the sand particles, which was not conducive to subsequent liquid transport, resulting in uneven calcium carbonate production throughout the sand column. Most MICP curing laboratory tests had noted the uneven distribution of carbonate deposition, mainly due to the plugging of perfusion points [48]. Through different grouting methods, the uniformity and distribution of calcium carbonate precipitation after MICP treatment could be changed, so as to change the strength and permeability of the soil after MICP treatment. The simplest grouting method was to inject the mixture of bacterial and cementation solution into the soil. However, this method easily caused the clogging of precipitated calcium carbonate crystals around the injection point and their non-uniform distributions over time, which blocked the channel, preventing the subsequent slurry from being injected into the soil. Thus, the spatial distribution of soil strength after MICP treatment was also highly non-uniform [49]. Whiffin et al. proposed a step-based grouting method [50]. After injecting a bacterial solution into the soil, it stood for a period of time so that bacteria could be absorbed on the surface of the soil particles before injecting the cementing solution. Compared with the mixed perfusion method, the sand porosity was obviously reduced, so as to improve the effect of improving permeability. On this basis, Harkes et al. improved the two-step grouting method [51]. After instillating a bacteria solution into soil for a period of time, a stationary solution (0.05mol/L, CaCl₂ solution) was injected at a low speed to pretreat sand samples. On the basis of the two-step grouting method, a three-step grouting method was proposed. The stationary solution injection was added after bacterial solution injection and before cementation solution injection, which played a role in the uniform distribution of bacteria. This method increased the cementing length and significantly improved the plugging situation at the grouting mouth. However, when the MICP grouting technology was used to form the HSRB, the permeability of the sand layer under the action of MICP was gradually reduced, with the pores between the sand particles gradually filled by calcium carbonate precipitation. The sand layer needed to be injected several times over several days to achieve the designed hydraulic conductivity. With the MICP reaction of each solution in the previous MICP technology, calcium carbonate precipitation was generated, and the pores were filled gradually. Subsequently, the injection of bacteria solution, stationary solution, and cementation solution was hindered. In this simulation, the permeability and porosity of the model were changed to simulate the hindrance of solute migration in the later filling solution. In accordance with the test results of MICP reducing the permeability of sand, the hydraulic conductivity of the involved area was reduced in a corresponding proportion in the model, as shown in

Table 7. Hydraulic parameters of different time models.

Time	Laboratory Test K(cm/s)	Numerical Model K(cm/s)
0	2.1 × 10−3	5.0 × 10−2
1	1.96 × 10−3	4.67 × 10−2
2	1.67 × 10−3	3.98 × 10−2
3	1.35 × 10−3	3.21 × 10−2
4	8.9 × 10−4	2.12 × 10−2
5	5.5 × 10−4	1.31 × 10−2
6	3.2 × 10−4	7.62 × 10−3
7	1.9 × 10−4	4.52 × 10−3

.

In accordance with the laboratory test results, MICP technology to reduce the permeability of sand was effective after 7 days, that is, the hydraulic conductivity of sand was reduced to the lowest after 7 days of grouting, and the pores between sand particles were filled with calcium carbonate to the maximum. At this time, the solute migration of each solution used by MICP technology was hindered the most. Therefore, the solute of each solution can migrate before 7 days if the hydraulic conductivity and porosity of the area covered by MICP solute migration were set to the value after 7 days of perfusion and if the solute of each solution can still migrate to the designed area through the seepage field formed by the reinjection well after 7 days. This condition proved that forming a horizontal curtain by using MICP technology is feasible.

(1) Bacterial migration

According to the analysis results of bacterial migration before, refer to the infusion plan of bacterial solution, bacteria solution (5000 mg/L, OD600 = 1) was injected at an irrigation rate of 400 m³/d after the stable seepage field was formed with an irrigation rate of 1000 m³/d in the recharging well. From the calculation results, as shown in Figure 25a, it was more difficult for the solution to migrate to the outer ring than to the inner ring after filling the pores with the calcium carbonate produced by the MICP reaction in the early stage. In order to solve this problem, and to minimize the re-addition of bacteria solution, the method of stopping the injection of bacteria solution into the outer ring and continuing the injection of water into the inner ring recharge wells at an irrigation rate of 1000 m³/d was adopted to promote the migration of existing bacteria solution outward. The calculation result is shown in Figure 25b. After the slurry injection is stopped, the seepage field formed by the inner ring recharge well continues to promote the migration of bacteria solution to the outside, enabling bacteria to break through the blocking effect caused by the carbonate generated in the earlier stage. However, this method will cause some bacteria solution to leak out, and it is necessary to replenish the bacteria solution.

(2) Migration of stationary solution

Stationary solution (0.05 mol/L, Ca²⁺ concentration 2000 mg/L) was injected at an irrigation rate of 400 m³/d after the stable seepage field was formed at an irrigation rate of 1000 m³/d in the recharging well. As shown in Figure 26a, the migration of the stationary solution injected in the later stage was hindered by the calcium carbonate generated between the pores of the sand particles in the early stage. The cost increased slightly by increasing the injection amount of the fixation solution because the concentration of CaCl₂ solution used was low. Therefore, the method of increasing the injection amount was changed to the fixation solution, with an injection rate of 800 m³/d. The results are shown in Figure 26b; Ca²⁺ migrated to the designated area under the condition of being hindered by increasing the irrigation rate.

(3) Migration of cementation solution

The cementation solution (1.5 mol/L, Ca²⁺ concentration 60,000 mg/L) was injected at an irrigation rate of 400 m³/d after the steady seepage field was formed in the recharging well at an irrigation rate of 1000 m³/d. As shown in Figure 27a, the migration of the cementation solution poured in the later period was hindered by the calcium carbonate generated in the pores of the sand particles in the earlier period. However, the migration distance of the cementation solution was farther than that of the bacteria, and the coverage area was wider than that of S. pasteurii because the adsorption of Ca²⁺ in the fine sand of the layer in Shanghai was smaller than that of S. pasteurii. Using the same method as injecting bacteria, the cementing fluid was stopped in the outer ring, and the inner ring reinjection well continued to recharge at an irrigation rate of 1000 m³/d to promote the existing cementing outward migration. As shown in Figure 27b, driven by the seepage field, the existing cementation solution began to break through the obstruction and migrate outward. However, some cementation solution leaked out, and the concentration of some covered areas was low. Thus, supplementing the cementation solution is necessary.

6. Conclusions

An innovative MICP HSRB formation method was developed. S. pasteurii and cementation solution were used in MICP HSRB. Reinjection wells were used to form a stable seepage filled from pit center to outside. MICP HSRB was formed using the seepage field generated by the recharge wells to drive the migration of bacteria solution, stationary solution, and cementation solution into the confined aquifer. The effects of the recharge rate of the inner circle recharge wells, injection rate of bacterial and cementing solution, and the layout of the recharge wells on migration were studied. The conclusions are as follows:

(1) Under the condition of the same S. pasteurii solution injection rate, the coverage area of bacteria increased with the increase of continuous infusion time. However, the growth rate of coverage area decreased with the increase of time. The effect of continuous infusion gradually decreased with the increase of infusion time. Therefore, when the upper limit of the bacterial covered area is reached, the infusion of bacterial solution can be stopped.

(2) The main factors affecting the coverage area of bacteria migration were the injection rate of the inner circle reinjection well and the recharge rate of the outer circle bacteria solution. However, increasing the recharge rate of the inner circle recharge well did not increase the migration coverage area of the effective high concentration bacterial solution, but did accelerate the bacterial solution leakage and reduced the effective concentration coverage area. On the contrary, the coverage area of the effective bacterial solution concentration obviously increased by increasing the bacterial solution recharge rate in the outer recharging well. The time spent injecting the bacterial solution should be minimized.

(3) Increasing the number of reinjection wells with bacterial fluid in the outer ring can effectively increase the coverage area of the bacterial fluid. The condition of constant total amount of reinjection can achieve a better effect to split the amount of one reinjection well into two wells.

(4) The migration process of solute in the later filling solution was blocked by calcium carbonate generated in the earlier filling slurry of MICP technology. In accordance with a different solution, different methods were adopted to re-drive the seepage field to break through the plugging effect and make the solute migrate to the designated area.