# Effect of Particle Size on Mechanical Property of Bio-Treated Sand Foundation
## 1 Introduction  
The traditional foundation treatment of mechanical preloading, cement, or chemical grouting has exposed their limitations in the current infrastructure construction [1; 2; 3]. Mechanical preloading can only strengthen surface soil, and the treatment methods of cement and chemical grouting are at a disadvantage for its short flow distance, long consumption time, and serious environmental pollution. Consequently, more and more attention has been paid to environmentally friendly and sustainable soil improvement techniques [4]. The advantages of cementing loose sand with microbially induced calcite precipitation (MICP) technology, such as lower permeability coefficient, more environmental protection, controllable reaction process, and long transmission distance, have been studied in depth [5; 6; 7; 8; 9]. MICP is a widely existing biological mineralization process in nature [10]. Microbial mineralization involves complex biochemical reactions. Hydrolysis of urea is catalyzed by urea-producing bacteria attached to the surface of sand particles to produce carbonate ions (CO3\({}^{2-}\)) and ammonium ions (NH4\({}^{+}\)), and then the CO3\({}^{2-}\) combines with the externally injected calcium ions (Ca2\({}^{+}\)) to form a cementitious calcium carbonate precipitation on the surface of the loose sand particles. Loose sand particles are solidified to form a building material with a certain mechanical strength [10], making it possible for soft sand foundation to be modified and solidified in situ by bio-treatment [11; 12; 13]. Moreover, it is a promisingly sustainable construction material [14]. In order to make the best of MICP technology in engineering practice, the most effective treatment method and process optimization are critical to guide the use of MICP technology under different geological conditions. [PERSON] et al. [9] explored the viability of the MICP technique for improving the engineering properties of a typical tropical residual soil, and the effectiveness of MICP was evaluated by optimizing the treatment conditions. [PERSON] [15] reported that the ideal size range was 50-400 \(\upmu\)m for bio-treatment. [PERSON] and [PERSON] [16] solidified the desert aeolian sand, primarily composed of sand grains with diameters of 100-250 \(\upmu\)m, the feasibility and effectiveness of use of this process was then evaluated based on the density, permeability, calcium carbonate content, unconfined compressive strength, and microstructure of the treated sand. [PERSON] [12] investigated that the biomineralization tests were manipulated on potentially liquefiable saturated riparian soil (The particle size range of 91-210 \(\upmu\)m) in the laboratory and field. The biomineralized soils showed properties that indicate calcite precipitation increased their resistance to seismic-induced liquefaction. [PERSON] [17] conducted a series of test using ureolytic bacteria to reinforce the organic clay (The particle size range of 12-99 \(\upmu\)m), with cementation reagent with different concentrations flowing to the soil under pressures. After treatment, the unconfined compression strength can increase by up to 370%, and the permeability coefficient can be reduced by about one order of magnitude. [PERSON] et al. [18] tested the bio-treated columns on a wide range of grain sizes comprised of sand, silty sand, and silt and concluded that the MICP treatment was equally robust for these soils. Additionally, the effect of particle size on the mechanical behavior of other building materials was also reported. [PERSON] et al. [19] evaluated the impact of aggregate gradation on asphalt mixture performance. They used two mixture types having nominal maximum aggregate sizes (NMAS) of 9.5 mm and 19.0 mm to evaluate the sensitivity of asphalt mixture performance to gradation changes. The effect of particle-size distribution on the one-dimensional compressive behaviour of granular soil materials was investigated using the discrete-element method (DEM) by [PERSON] et al. [20]. [PERSON] et al.