# Neutralization Treatment for Recycling Construction-Generated Soils
## 4 Equation Derivation  
Equation (1) shows the general relationship of normality in neutralization titration. \[n_{a}v_{a}=n_{b}v_{b} \tag{1}\]  
where \(n_{a}\) is the acid mole (mol) number, \(v_{a}\) is the acid valence, \(n_{b}\) is the base mole (mol) number, and \(v_{b}\) is the valence of the base. To derive the theoretical formula, the following assumptions were made. 1. All alkaline components in construction soil come from calcium hydroxide (\(v_{b}=2\)). Calcium carbonate (CaCO\({}_{3}\)) from cement is the only major compound found in construction-generated soil. Only a negligible presence of other chemicals exists, such  
Figure 3: Details of the cone penetrometer used to determine the cone index. that their influence can be ignored. When water is added to CaCO\({}_{3}\), it undergoes a hardening phase while ionizing into ions, which combine with the water to form calcium hydroxide [26]. Equation (2) describes the process of calcium hydroxide generation in cement. However, there are still many unresolved aspects of this process, since the assumed reactions are complicated by the fineness of the cement, the amount of water, and temperature, but their influence is assumed to be negligible in this study. \[\text{CaCO}_{3}+\text{H}_{2}\text{O}\rightarrow\text{Ca(OH)}_{2}+\text{CO}_{2}\] (2) The ionization degree of the neutralizer and the calcium hydroxide shall be 1, and all acids and bases shall be ionized. Under normal circumstances, acids and bases are ionized when dissolved in an aqueous solution, and their degree of ionization varies depending on several factors. To be precise, weak acids and weak bases ionize only partially in an aqueous solution, while strong acids and strong bases show an ionization degree of 1. However, as it is difficult to estimate the degree of ionization, it is assumed to be 1 in this study. (3) The neutralization reaction occurring in construction-generated soil with a neutralizer is assumed to be the same as that occurring in an aqueous solution, where the neutralization reaction occurs in all directions. In the case of a neutralization reaction in an aqueous solution, the reaction takes place in all directions because of the fluidity of the solution. However, in the case of neutralization reactions occurring in soil, fluidity is not ensured because the soil is granular and neutralization from all directions is impossible. Since there are no instruments that can easily measure the total amount of alkali present in construction soil, the amount of alkali material in construction soil is estimated from the pH of the construction soil. When calculating the amount of base substance in construction soil from the pH, water is added so that the mass ratio of water to furnace dry mass of the construction soil becomes 5. The Japanese Geotechnical Society prescribed this pH measurement method as \"JGS 0211-2000\". Firstly, the molar concentration of the base is calculated using Equation (3) [26; 27]:  
\[\left[\text{OH}^{-}\right]=10^{(pH-14)} \tag{3}\]  
where \(\left[\text{OH}^{-}\right]\) is the molar concentration of the base (mol/L) and \(pH\) is the pH value of the construction-generated soil. The volume of the aqueous solution is calculated using Equation (4). \[V_{aq}=\frac{5m_{s}\big{(}1-\frac{w}{100}\big{)}}{\rho_{w}} \tag{4}\]  
where \(V_{aq}\) is the volume of the aqueous solution (L), \(m_{s}\) is the wet mass of the construction soil (g), \(w\) is the water content ratio of the construction soil (%), and \(\rho_{w}\) is the density of water (=998 g/L). The amount of base material, shown in Equation (5), can be derived using Equations (3) and (4). \[n_{b}=\left[\text{OH}^{-}\right]\times V_{aq}=10^{(pH-14)}\times\frac{5m_{s} \big{(}1-\frac{w}{100}\big{)}}{\rho_{w}} \tag{5}\]  
The theoretical equation for the amount of neutralizer required for the neutralization titration reaction, shown in Equation (6), can be derived using Equations (1) and (5).