# Risk Assessment of Soil Contamination with Heavy Metals from Municipal Sewage Sludge
## 2 Materials and Methods
### Contamination Assessment Methodology  
Geoaccumulation index of heavy metal in soil (\(I_{gao}\))  
The \(I_{gao}\) is used in order to assess the degree of accumulation of heavy metals. At first, the \(I_{gao}\) was used for the ecological risk assessment of sediments [33]. It was also used for the assessment of the contamination of soil [34], sewage sludge [3], and sewage sludge ash [35]. The \(I_{gao}\) is described in the equation [36; 37]:  
\[Igeo\ =\ log_{2}\frac{Cn}{1.5\cdot Bn} \tag{1}\]  
where:  
_Ct_--content of a given element from the group of heavy metals contained in sewage sludge, mg\(\cdot\)kg\({}^{-1}\) d.m.; \(Bn\)--content of a given element from the group of heavy metals present in the soil, mg\(\cdot\)kg\({}^{-1}\) d.m. (Table 6). The constant value 1.5 is introduced for better analysis of the natural variability of the content of the chosen substance in the environment.  
The classification of the heavy metals \(I_{gao}\) is: \(<0\)--no pollution; 0--1--no pollution, moderate pollution; 1-2--moderate pollution; 2-3--moderate or high pollution; 3-4--high pollution; 4-5--high or very high pollution; \(>\)5--very high pollution [37].  
Potential environmental risk indicator (PERI)  
The PERI is a measure of the environmental risk of soil contamination with heavy metals and is described in the following formulas [36; 38]:  
\[C_{f}^{i}\ =\ \frac{C_{D}^{i}}{C_{R}^{i}} \tag{2}\]  
where:  
\(C_{f}^{i}\) --pollution factor; \(C_{D}^{i}\)--concentration of the \(i\)-th element from the group of heavy metals present in sewage sludge, mg\(\cdot\)kg\({}^{-1}\) d.m.; \(C_{R}^{i}\)--concentration of the \(i\)-th element from the group of heavy metals in the soil, mg\(\cdot\)kg\({}^{-1}\).  
\[E_{r}^{i}\ =\ T_{r}^{i}\cdot C_{f}^{i} \tag{3}\]  
where:  
\(E_{r}^{i}\)--indicator of the potential ecological risk of the \(i\)-th element from the group of heavy metals; \(T_{r}^{i}\)--toxicity factor of the \(i\)-th element from the group of heavy metals. Heavy metals differ in degree of toxicity, which takes into account the toxicity factor (\(T_{r}^{i}\)): lead--5; cadmium--30; chromium--2; copper--5; nickel--5; zinc--1 [37].  
The sum of indicators of potential ecological risk of the contamination with heavy metals (HMs) from sewage sludge (SS) in the ground is defined by the formula [37]:  
\[PERI=\ \sum_{i=1}^{n}E_{r}^{i} \tag{4}\]  
Table 7 shows the degree of the potential environmental risk in relation to the \(PERI\) value.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(B_{n}\) *, mg\(\cdot\)kg\({}^{-1}\) & **Cu** & **Cr** & **Cd** & **Ni** & **Pb** & **Zn** \\ \hline \(\text{B}_{\text{S1}}\) & 4.6 & 7.4 & 0.37 & 4.6 & 22.4 & 39.6 \\ \(\text{B}_{\text{S2}}=\text{B}_{\text{S3}}\) & 3.0 & 3.3 & 0.09 & 2.4 & 10.8 & 19.3 \\ \(T_{r}^{i}\) ** & 5 & 2 & 30 & 5 & 5 & 1 \\ \hline \hline \end{tabular}  
* \(Bn=C_{R}^{i}\)—values determined on the basis of the report on the realisation of stage III of the procurement [26]. Measurement points were located adequately in relation to the analysed wastewater treatment plants ** on the basis of [36].  
\end{table}
Table 6: \(Bn\) and \(T_{r}^{i}\) of heavy metals (HMs) from sewage sludge (SS).