# Water Retention Curve of Biocemented Sands Using MIP Results
## 1 Introduction  
Biocementation is a soil treatment technique wherein bacteria living in soil pores promote the precipitation of calcium carbonate (biocement). This biocement bonds soil particles and therefore improves the overall mechanical behavior and reduces permeability (see Reference [1], for example). The improvement effect depends on the amount precipitated, soil density, and grading size distribution [2, 3]. The process depends on the hydrolysis of urea, CO(NH\({}_{2}\))\({}_{2}\), (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)). This soil treatment technique is mostly adopted to increase the load-bearing capacity of foundations [1, 4], provide resistance to erosion and against liquefaction [5, 6, 7], and decrease permeability in barriers [8]. Recently, it was used for reducing the collapse potential of soils [9, 10]. The soils most adequate for this treatment are sandy soils because of their relatively large pore size with consequent high permeability, which is necessary for the circulation of the treatment fluid and compatible with bacteria size [11]. When using this technique in real cases, it is important to predict the improvement achieved (amount of calcium carbonate, strength increment, and permeability reduction) and trust in its durability. To help with such a purpose, it is important to model infiltration, as it occurs during the treatment and in service conditions, especially by taking into consideration most of the applications of this treatment. For example, one of the most recent applications of thistreatment is to provide resistance against erosion of slopes by creating a resistant cover but still allowing infiltration in order to avoid water runoff. Therefore, it is fundamental to know the water retention curve of the treated material. The study of the unsaturated behavior of bioemented soils and, in particular, their water-retention properties, is relatively new, and no references were found in terms of water retention curves [12; 13], which are required for numerical modeling:  
\[\text{CO(NH}_{2})_{2}+2\;\text{H}_{2}\text{O}\rightarrow\text{CO}_{3}{}^{2-}+2 \;\text{NH}_{4}{}^{+} \tag{1}\]  
\[\text{Ca}^{2+}+\text{CO}_{3}{}^{2-}\rightarrow\text{CaCO}_{3} \tag{2}\]  
The water retention curves (WRCs) of sandy soils are characterized by having a very small air entry value, followed by an almost horizontal zone and then a sharp transition for the highest suctions at the residual water content [14; 15]. The air entry value is small because the pores sizes are very large, in proportion to the grains size. The sharp transition occurs when the water in the soil pores is no longer in the free form but is adsorbed into the grains. Because the particles are mainly silt instead of clay minerals, the amount of adsorbed water is very low so the water content when this transition occurs (named as residual water content) is also very low. Therefore, the water retention curve depends on pore size distribution, and this is the origin of the definition of the water retention curve, firstly defined as a tool to estimate soil permeability [16; 17]. Naturally that the changes of water-retention properties were then investigated as a function of the evolution of pore size distribution caused by grading size distribution, as well as stress and suction changes [18; 19; 20]. Further studies allowed us to better understand the coupled hydro-mechanical behavior of the soils occurring during wetting and drying, particularly when volume changes caused by water absorption and desorption were relevant (clayey soils), and how this behavior was affecting the measurement of the water retention curves (for example, see References [15; 21; 22; 23; 24]). Later, the WRCs were incorporated into constitutive models for unsaturated soils to reflect this coupled behavior (for example, see References [25; 26; 27]).