# Recent Developments on Biomineralization for Erosion Control
## 3 Multi-Investigations of Biomineralization Erosion Control in Ocean Engineering
### Stability Evaluation of MICP-Reinforced Seabed  
In addition to erosion protection, MICP technology can also be used to reinforce the seabed and improve stability. Considering the high cost and control difficulty of the physical experiments, numerical simulation was first developed for analysis. To date, numerical studies on MICP reaction are mainly based on the convection-diffusion-reaction theory and seepage framework in porous media. [PERSON] et al. (2014) used the first-order kinetic equation to establish a reaction model of urea hydrolysis and calcium carbonate precipitation but ignored the effect of calcium carbonate precipitation on the evolutions of porosity and permeability ([PERSON] et al., 2012). [PERSON] and [PERSON] (2012) as well as [PERSON] and [PERSON] (2020) established a bio-chemo-hydro-mechanical model for MICP reaction and a bio-chemo-hydro model considering the concept of effective porosity, respectively ([PERSON] et al., 2013; [PERSON] et al., 2014). Recently, a bio-chemo-hydro-mechanical model of transport, strength, and deformation for bio-cementation applications was developed by [PERSON] et al. (2024) to design MICP treatments for specific geotechnical problems, such as bearing capacity ([PERSON] et al., 2014). Although the above models well reflect the temporal and spatial evolutions of biochemical substances and permeability in the MICP reaction, it is not applicable to the ocean environment because of the neglect of the ocean dynamic environment factors. [PERSON] developed an MICP reaction model for seabed reinforcement considering the wave actions under the framework of [PERSON]'s consolidation equation ([PERSON] et al., 2014; [PERSON] et al., 2020). According to the existence form of bacteria in the seabed, the total bacteria (\(C_{\text{total}}\)) are divided into suspended bacteria (\(C_{\text{bacl}}\)) and attached bacteria (\(C_{\text{bacs}}\)) on the sand particle surface, assuming that they satisfy the first-order kinetic equation:  
\[\frac{\partial C_{bacl}}{\partial t}=-k_{\text{d}}C_{bacl} \tag{3}\]  
\[\frac{\partial C_{bacs}}{\partial t}=k_{\text{att}}C_{bacl}-k_{\text{d}}C_{ bacs} \tag{4}\]  
\[\frac{\partial C_{bacl}}{\partial t}=-k_{\text{att}}C_{bacl}-k_{\text{d}}C_{ bacl} \tag{5}\]  
where \(k_{\text{d}}\) is a constant decay rate, and \(k_{\text{att}}\) is the constant attachment rate. Urea hydrolysis is described with the adoption of the Michaelis-Menten kinetic equation. \[k_{\text{rea}}=u_{\text{sp}}(C_{bacs}+C_{bacl})\cdot\frac{C_{\text{urea}}}{C _{\text{urea}}+k_{\text{m}}}\cdot\exp((T-25)/\frac{\ln 3.4}{10})\exp(-\frac{t}{t_{ \text{d}}}) \tag{6}\]where \(k_{\rm m}\), \(T\), \(u_{\rm sp}\), \(C_{\rm urea}\), \(t\), and \(t_{\rm d}\) denote the half-saturation constant at which the reaction rate drops by 50%, environmental temperature, maximum urease activity constant, urea concentration, reaction time, and time constant, respectively. The hydraulic field is described using [PERSON]'s law. \[q=-\frac{K}{\mu_{\rm I}}\cdot(\
abla p_{\rm I}+\rho_{\rm I}g) \tag{7}\]  
where \(q\) is the Darcy flow rate, \(K\) is the matrix permeability, and \(g\) stands for gravitational acceleration, while \(\mu\)L, \(p_{\rm I}\), and \(\rho_{\rm I}\) represent liquid viscosity, excess pore pressure, and liquid density, respectively. All liquid components--including urea, calcium, ammonium, and suspended bacteria--are assumed to be governed by convection-diffusion-reaction equations, as illustrated in Equations (8)-(11).