# Water Retention Curve of Biocemented Sands Using MIP Results

^{1}

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^{3}

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## Abstract

**:**

## Featured Application

**WRC, MIP, biocementation, and sands.**

## Abstract

## 1. Introduction

_{2})

_{2}, (Equation (1)) releasing carbonate ions CO

_{3}

^{2−}. Calcium carbonate, CaCO

_{3}, precipitates in the presence of a feeding solution containing calcium ions, Ca

^{2+}(Equation (2)).

_{2})

_{2}+ 2 H

_{2}O → CO

_{3}

^{2−}+ 2 NH

_{4}

^{+}

^{2+}+ CO

_{3}

^{2−}→ CaCO

_{3}

## 2. Model Proposed

_{Hg}, using the Laplace equation (Equation (3)):

_{w}and T

_{Hg}are the surface tensions of water and mercury, respectively (T

_{w}= 0.073 N/m and T

_{Hg}= 0.489 N/m); and θ

_{w}and θ

_{Hg}are the contact angles of water and mercury, respectively (θ

_{w}= 0° and θ

_{Hg}= 120°).

_{rm}is the degree of saturation computed by considering the volume of mercury intruded until that step in relation to the maximum volume of intruded mercury (Equation (6)), and w

_{res}represents the voids that cannot be filled with mercury (Equation (7)). Both parameters are determined by knowing the e

_{MIP}, the void ratio filled with mercury until the current stage (volume of mercury intruded divided by the volume of solids of the sample), and e

_{MIP,max}, the maximum void ratio that was filled in the intrusion phase (maximum volume of mercury intruded divided by the volume of solids of the sample). Finally, w

_{sat}is the water content of the soil when fully saturated. The void ratio, e, at preparation is determined as usual (Equation (8), where G

_{s}is the density of the solid particles):

_{res}in the model proposed here is updated during the intrusion process to consider changes in the void ratio, Δe (Equation (9)), of the soil when compressed inside the intrusion penetrometer. These changes are assumed to be isotropic and elastic during intrusion, and therefore the elastic compressibility index, κ, is adopted to compute the reduction in void ratio during compression caused by increasing mercury pressure (Equation (10)). From a physical point of view, it must be ensured that the void ratio computed while considering volume changes must be larger than e

_{MIP,max}:

## 3. Materials and Methods

#### 3.1. Soil and Soil Samples

_{50}= 0.65 mm and 1.2% of particles with a diameter of D < 0.075 mm. The volumetric weight of the solid particles is 26.1 kN/m

^{3}.

^{3}and water content of 5% to reproduce in situ conditions (initial void ratio is e = 0.58). This amount of water was enough to prepare a fluid sandy material that was homogeneous. They were mounted in oedometric stainless steel rings to perform oedometer and permeability tests and have samples to extract pieces for other tests. The material was premixed with distilled water before being placed by tamping in the rings (7 cm diameter and 2 cm height). Previous studies have shown that the soil has a moderate collapse potential [37] because the collapse index is 7.9%, as determined by using ASTM D5333-03 [38] (collapse deformation measured when the soil is fully saturated under the vertical stress of 200 kPa), which corresponds to a soil classified as having moderately severe collapse potential.

#### 3.2. Bacteria and Feeding Solution

_{600}). This corresponds to approximately 10

^{8}cells/mL. The composition of the feeding solution is of 0.5 M urea (30.03 g/L) and 0.5 M (55.40 g/L) of calcium chloride (calcium source), 1:10 diluted growth medium, 2.12 g/L of sodium bicarbonate, and 10 g/L of ammonium chloride.

#### 3.3. Biocementation Treatment

_{V}, was added each day; one-third of this volume (1/3V

_{V}) consisted of bacteria solution, and the other two-thirds of void volume (2/3V

_{V}) consisted of feeding solution. Then the samples were submerged in the feeding solution for the last three days. It can be assumed that all the samples were fully saturated during and after the treatment.

#### 3.4. Tests Performed

#### 3.4.1. Oedometer Tests

#### 3.4.2. Saturated Permeability

#### 3.4.3. Tests to Confirm the Presence of Biocement

_{3}, is given by Equation (11):

_{dry soil before}is the initial weight of the soil after being oven-dried at 105 °C for 24 h, and m

_{dry soil after}is the weight of the soil after being washed by the acid until no more gas bubbles were liberated and then dried in an oven at 105 °C for 24 h. The soil was washed with distilled water before this test to remove dry precipitates from the feeding solution.

#### 3.4.4. Mercury Intrusion Porosimetry Tests

^{3}) after being air-dried in the laboratory environment for 48 h. These tests were performed to find the pore size distributions of the untreated soil (with the water content at preparation) and after the biocementation treatment. The equipment used was AutoPore IV 9500. The low pressures applied were from approximately 3.6 to 155 kPa, and the high pressures were from approximately 0.17 to 227 MPa, with 78 s intrusion time. The contact angle adopted for the mercury was 140°.

#### 3.4.5. Water Retention Curve

## 4. Results and Discussion

#### 4.1. Oedometer Tests

_{y}(see Table 1).

#### 4.2. Saturated Permeability

^{−5}m/s, and the one measured for the treated samples was 4.1 × 10

^{−5}m/s. Permeability decreased slightly after the treatment. This is expected because the amount of biocement precipitated should have had some clogging effect of the soil pores [2].

#### 4.3. Presence of Biocement

#### 4.4. Mercury Intrusion Porosimetry Tests and Water Retention Curve

_{MIP,max}= 0.308, e = 0.582; water MIP—untreated soil: κ = 0.033, e

_{MIP,max}= 0.314, e = 0.588). It can be seen that there is a good adjustment of the curve to the measured points.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**SEM images of the soil: (

**a**) before treatment; (

**b**) after treatment, showing calcite crystals.

**Figure 5.**Pore size distributions of the samples tested (bacteria—biocemented soil; water—untreated soil in natural state).

**Figure 6.**Water retention curve and its adjustment from using the equations proposed in this paper in which the material behaves elastically under isotropic compression. (Bacteria—biocemented soil; water—untreated soil in natural state).

**Figure 7.**Adjustment water-retention data, using the equation proposed by Van Genuchten [17] (Equation (12)) to fit (

**a**) the experimental points and (

**b**) the curve computed by using pore size distribution. (Bacteria—biocemented soil; water—untreated soil in natural state).

Sample | δε_{vol} (%) | Cc | Cs | κ | λ(s) | σ′_{y} (kPa) | |
---|---|---|---|---|---|---|---|

Untreated soil—water (initial suction s = 67.5 MPa) | Saturated | -- | 0.137 | 0.014 | 0.034 | 0.316 | 80 |

Unsaturated | 3.0 | 0.034 | 0.015 | 0.035 | 0.114 | 100 | |

Biocemented soil—bacteria (initial suction s = 62.7 MPa) | Saturated | -- | 0.162 | 0.013 | 0.031 | 0.372 | 100 |

Unsaturated | 0.2 | 0.109 | 0.016 | 0.037 | 0.285 | 120 |

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**MDPI and ACS Style**

Cardoso, R.; Vieira, J.; Borges, I.
Water Retention Curve of Biocemented Sands Using MIP Results. *Appl. Sci.* **2022**, *12*, 10447.
https://doi.org/10.3390/app122010447

**AMA Style**

Cardoso R, Vieira J, Borges I.
Water Retention Curve of Biocemented Sands Using MIP Results. *Applied Sciences*. 2022; 12(20):10447.
https://doi.org/10.3390/app122010447

**Chicago/Turabian Style**

Cardoso, Rafaela, Joana Vieira, and Inês Borges.
2022. "Water Retention Curve of Biocemented Sands Using MIP Results" *Applied Sciences* 12, no. 20: 10447.
https://doi.org/10.3390/app122010447