## 5 Calculations of Stability for the Planned Engineered Landfill  
### Model and Calculation Assumptions Based on Case 1 Results (Chemical Plant)  
The goal of the numerical studies was just to prove that the modified parameters of the resulting soil-cement composite guarantee safe conduct of the earthworks and further stability of the earth structure. That was not evident and all laboratory works had to be conducted prior to the extensive and expensive field operations. The numerical model is not very sophisticated; however, it is a cautious estimate of the real situation. The stability of the \"engineered landfill-ground\" system was analyzed using the finite element method, and calculations were made using the Z_Soil 2011 software [28; 29]. The calculations were made in a plain strain state. Due to the layered structure of the site, as per Section 2, a cross-section through the waste storage location was selected. The calculation analysis was divided into the following stages. First, a primary stress condition was generated in the ground. Secondly, the construction of subsequent layers of artificial fills was simulated. The next stage was to assume a load on the site crest to simulate the operation of heavy equipment (excavators, transport vehicles) in the form of \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mean** & **Standard** & **Characteristic Value** \\  & **Value** & **Deviation** & **Characteristic Value** \\ \hline Unit weight [kN/m\({}^{3}\)] & 14.00 & 1.28 & 14.64 \\ Angle of shearing resistance [\({}^{\circ}\)] & 35.79 & 7.62 & 31.98 \\ Cohesion [kPa] & 37.64 & 23.46 & 25.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tested physical and strength parameters of waste. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Time of Curing** & **Soil–Cement** & **Soil–Cement** \\  & **[Days]** & **Composite** & **Composite +** \\  & & **1.5\% Active Carbon** \\ \hline compressive strength & 7 & 2.547 & 2.729 \\
[MPa] & 28 & 3.749 & 4.129 \\  & increase [\%] & 32.1\% & 33.9\% \\ elastic modulus & 7 & 509.700 * & 374.780 \\
[MPa] & 28 & 473.550 & 540.260 \\  & increase [\%] & \(-\)7.6\% * & 30.6\% \\ unloading/reloading & & & \\ elastic modulus & 28 & 768.420 & 829.880 \\
[MPa] & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of mechanical parameters of the composite (strength and stiffness). an evenly spread load with a value of 10 kPa (Figure 10). The final stage of the calculations, which is key to this discussion, was stability analysis. An elastic-perfectly plastic material model with a Mohr-Coulomb plasticity surface and non-associated flow rule was assumed for the soil system. The system's behavior within the elastic work range is described by two parameters: elastic (Young's) modulus (E) and Poisson's ratio (\(\
u\)), while the plastic surface position depends on cohesion (c) and angle of shearing resistance (\(\phi\)). The benefit of using this model is the ability to identify its parameters based on standard tests, e.g., in a direct shearing test. The soil base and waste parameters were assumed on the basis of the geotechnical documentation, construction design, and the author's own research (Table 3). Standard geotechnical boundary conditions were applied--horizontal and vertical displacements were blocked at the bottom edge of the system, while horizontal displacements were blocked at the lateral vertical edges. The reduction in cohesion (c) and angle of shearing resistance tangent (tg\(\phi\)) method was used to calculate the safety factor using the numerical method [30]. For the two-parameter models used in the analysis in question, five stages can be identified in the stability calculation algorithm [28]:  
* Assumption of a safety factor (SF\({}_{\text{n}}\)) equal to an initial value defined by the user (SF\({}_{0}\))--most commonly a boundary problem of the system equilibrium state is solved,  
Figure 10: Numerical model (final state). The numbers given to soil layers correspond to the numbers in Table 3 below.